Running head: MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

EFFECTIVE MATH INTERVENTIONS IN THE ELEMENTARY PSSA GRADES

A Doctoral Capstone Project
Submitted to the School of Graduate Studies and Research
Department of Secondary Education and Administrative Leadership

In Partial Fulfillment of the
Requirements for the Degree of
Doctor of Education

Kristopher Michael Vancas
California University of Pennsylvania
July 2020

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

© Copyright by
Kristopher Michael Vancas
All Rights Reserved
July 2020

ii

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Acknowledgements
I would like to thank Dr. David Foley and Dr. Michelle Saylor for their guidance
and support through this Capstone journey. I would also like to thank my classmate and
colleague, Duffy Besch, for his suggestions and ideas as we collaborated on our Capstone
Projects over the past two years. Thank you to the teachers in the Bellefonte Area School
District who participated in the study and provided valuable information and data.
Finally, the biggest thank you must go to my wife, Tina and my children, Alexis and
Peyton for their support and patience over the past two years.

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Table of Contents
Acknowledgements
List of Tables

iv
viii

Abstract

x

Chapter I. Introduction

1

Chapter II. Review of the Literature

5

Introduction

5

PSSA State Wide Trends

8

Factors Contributing to Low/No Growth

9

High Achieving Schools Best Practices

16

Interventions

22

Technology Based Interventions

27

Everyday Math

31

Departmentalized Math Classes

33

Professional Learning

34

Conclusion

35

Chapter III. Methodology

37

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Purpose

37

Setting and Participants

38

Research Plan

43

Data Collection

49

Validity

51

Closing

52

Chapter IV. Data Analysis and Results

53

Introduction

53

Data Analysis

53

Results

54

Discussion

79

Summary

81

Chapter V. Conclusions and Recommendations

82

Introduction

82

Conclusions

82

Concerns

84

Recommendations

85

Future Directions for Research

89

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Summary

91

References

92

Appendix A. IRB Approval

99

Appendix B. Letter of Participation

101

Appendix C. Questionnaire

103

Appendix D. Questionnaire Responses

107

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List of Tables
Table 1. Bellefonte Area School District Demographic Data

7

Table 2. PSSA Statewide Results

8

Table 3. PSSA Bellefonte Area School District Results

8

Table 4. Number of Students and Math Teachers

40

Table 5. School Demographics A

40

Table 6. School Demographics B

41

Table 7. PSSA 3-Year Average

55

Table 8. Benchmark Assessment End-of-Year Average

56

Table 9. Classroom Diagnostic Test 3-Year Average

57

Table 10. PVAAS Teacher Specific Rating

58

Table 11. Average Ranking of Effectiveness

58

Table 12. Top Ranked Teachers

60

Table 13. Grade 3 Teacher Responses

60

Table 14. Grade 4 Teacher Responses

65

Table 15. Grade 5 Teacher Responses

70

Table 16. Effects of Departmentalization Questionnaire Responses

75

Table 17. PSSA Math Proficiency Rates

76

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Table 18. PVAAS 3 Year Growth Measures-PVAAS Value Added Reports

77

Table 19. Professional Learning Questionnaire Responses

77

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Abstract
This mixed-methods study was conducted to determine the math interventions and
strategies that are showing a positive increase in student achievement and growth in
grades three, four, and five across the Bellefonte Area School District. Effective math
teachers were first identified by looking at multiple academic data sets and then
questionnaire responses were compared to determine similarities in their instructional
practices. The similar interventions and strategies will be shared with teachers through
professional learning sessions and ultimately used with students in classrooms. The
strategies and interventions that were identified to be showing success were guided/small
group math instruction, extra and focused work on open-ended math questions, the use of
online math programs like Reflex Math, and data use. The effectiveness of
departmentalization was also analyzed. The qualitative data supports departmentalization
while the quantitative data does not. This area will require additional analysis in the
future. Finally, the professional learning needs of staff were identified and will help guide
the district’s professional learning plan and its Comprehensive Plan. Some of these areas
that will be focal points are guided math, the integration of technology, and data use.

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

CHAPTER I
Introduction
As the principal of Benner Elementary School in the Bellefonte Area School
District, I closely monitor the scores of my school as well as the scores of the other three
elementary schools in my district on the Pennsylvania System of School Assessment
(PSSA). This high stakes assessment measures progress for grade three through grade
five students in elementary schools across the state of Pennsylvania. The assessment
measures Math and English Language Arts for students in grades three through five, and
also Science for students in grade four.
Math is the content area that I continue to revisit and analyze. My school district
has experienced stagnant, or declining, student math scores over the past five or more
years at the elementary level. We have also identified a lack of consistency in math
curriculum implementation and low scores in our student growth indicators. These
struggles can be traced back to possible issues in curriculum gaps, student data use,
implementation of the Everyday Math program, and how teachers implement
instructional strategies and interventions. We currently have an inconsistent mix of
interventions being implemented across the district. We have canned programs like IXL
and Reflex Math along with other website-based programs. We also have small group or
1-1 teacher lead intervention lessons and activities like Guided Math. The goal of this
study is to determine what interventions are showing a positive increase in student
achievement and growth and provide this information to our teachers through
professional learning opportunities.

1

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The Bellefonte Area School District has four elementary schools serving students
from kindergarten through fifth grade. Each of the buildings has a principal who is
responsible for the managerial and instructional leadership of their buildings. Part of the
instructional leadership portion of the position is to monitor the academic progress of
students and make informed decisions and changes to the academic setting when
necessary. Low and stagnant math scores have led me to this research project in hopes of
finding out why and to find ways to help my teachers and students make improvements.
This research study will be completed during 2019-2020 school year. Data will be
collected and analyzed from the 2016-17, 2017-18, and 2018-19 school years through a
mixed methods research process. Quantitative math data will be collected and analyzed
from the students in grades three through five. Data that will be collected will include
PSSA data, Classroom Diagnostic Testing scores, end of year district benchmark
assessment scores, and teacher specific PVAAS data. Qualitative data will be collected
from teachers through the use of a survey. Open ended and closed ended questions will
be used. The survey will focus on teachers’ impressions of the Everyday Math Program.
This is the core program being used in our district. The survey will also target the
instructional strategies and interventions teachers are using to increase student
achievement in math.
The data and findings from this study will allow me to work closely with our
district’s math coach to develop and implement professional learning for teachers focused
on interventions and strategies designed to improve student achievement.
There will be very little upfront expense involved in collecting and analyzing the
data for this project. The expense will come from the recommendations generated from

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the project. I plan to utilize my district’s Math Instructional Coach to help lead the
professional learning activities that center around the data analysis review, data protocols,
and effective math interventions. These tasks will fit into the coach’s daily assigned
duties and will not be an additional expense. The biggest expense will come from paying
substitutes for the teacher professional learning days. I can also envision the findings
from this study could encourage the district to purchase a specific math intervention
program for all intermediate math teachers.
An improvement in student math achievement and overall growth is the ultimate
objective of this project. This will happen by improving math instruction, selection and
intervention use, and data analysis in my district as teachers will be utilizing data to
determine effective intervention strategies for students. This study will affect the focus of
the professional learning that will be held with staff members during the 2020-21 school
year.
The questions that will be answered in this study are ones that educators in my
district have thought about for years, but have not been able to definitively answer.
Hopefully, this study will provide us with the answers and will positively impact students
in the intermediate grades and beyond.
I will focus my research on the following questions:
What instructional strategies are teachers using across the district to increase the
growth in student math skills?
How has departmentalization in the elementary schools aided the students in their
math growth or hindered their progress?

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What professional learning opportunities does the district need to provide teachers
to insure more consistent use of data protocols, as well as appropriate intervention
strategies?

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CHAPTER II
Review of the Literature
Introduction

The growing importance of standardized testing across elementary schools in
Pennsylvania has put student test scores at the forefront of many educational
conversations. State-wide assessments have led to debates about school effectiveness,
teacher effectiveness, and program effectiveness. While many schools continue to show
growth and positive academic achievement on the yearly Pennsylvania System of School
Assessments, many other schools are not experiencing growth or success. Even more
important than growth on standardized tests is the overall growth and achievement of our
students in the Bellefonte Area School District. Educators are realizing that their students
are not reaching the level of academic growth and achievement for success in applying
math skills to real-world math scenarios, nor are they exhibiting the skills to be able to
take the advanced math classes that will make them college and career ready once they
graduate.
Elementary schools are recognizing math deficiencies and are implementing
interventions across all grade levels in hopes of closing the achievement and growth gap.
Some interventions have proven to be effective while others have not shown as much
promise. The effects of math interventions used by educators are informing classroom
practice while also providing professional learning opportunities for classroom teachers
that address student challenges. Along with interventions, identifying and implementing
effective instructional techniques is crucial to remedying this problem.

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This study will analyze the PSSA math trends in the state over the past several
years. Factors contributing to little or no growth will be described, as well as best
practices found in the Bellefonte Area School District’s most successful classrooms in
grades three, four, and five. The study will also research various math interventions being
used in the school district’s elementary schools to determine their effectiveness. The
information will help administrators in the district plan professional learning for teachers
so that interventions and strategies can be successfully implemented in classrooms across
the district.
Various technology-based interventions are becoming popular with schools and
students today. The effectiveness of these programs will also be analyzed along with how
they make differentiation in math classes more manageable. At the conclusion of this
study, the effectiveness of interventions and teaching practices will be identified.
Teacher professional learning sessions will be planned and implemented based on these
findings in hopes of them directly impacting student achievement and growth.
In order to further understand the setting and results of this study, the
demographics of the Bellefonte Area School District must be described. There are four
elementary schools servicing grades K-5 in the district. The demographic data is
summarized in the table below. Pleasant Gap Elementary and Bellefonte Elementary are
both Title I schools. The socioeconomic status is spread throughout the district, but the
diversity is minimal with approximately 94% of students being white. Special education
student needs in grades three, four, and five are typically serviced within the regular
education classroom with push-in services from the learning support teacher or the
learning support aide. There are also a growing number of students in each classroom

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with math deficiencies who are not receiving special education services but require
intensive interventions. In addition to these students, there is an increasing number of
students in the testing grade levels who receive counseling or behavioral intervention
support to help address social and emotional deficits. These deficits or challenges detract
from the potential learning and success of the students.
Table 1
Bellefonte Area School District Demographic Data
(Data was taken from the Pennsylvania Future Ready Index website.)

School

Total
Enrollment

RaceWhite

Economically

EL
Students

Special
Education

Gifted

Bellefonte 371
Elementary

91.6%

50.9%

0.8%

18.3%

0.8%

Benner
231
Elementary

93.9%

22.1%

1.3%

13.9%

2.6%

Marion371
Walker
Elementary

96%

16.4%

1.3%

14.8%

0.5%

Pleasant
222
Gap
Elementary

93.7%

36.9%

6.8%

18.5%

0.4%

Disadvantaged

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PSSA Statewide Trends
Data from 2015 through 2019, taken from the Pennsylvania Department of
Education website, illustrate student achievement scores have fluctuated within the upper
50 percentile range to the lower 40 percentile range. Grade 3 students have performed
stronger than grade 4 and 5 students. Grade 5 students have been consistently the lowest
of the three grade levels statewide.
Table 2
PSSA Statewide Results

Grade

2019 %
Adv/Prof

2018 %
2017 %
2016 %
2015 %
Adv/Prof Adv/Prof Adv/Prof Adv/Prof

3

56

54

55

54

49

4

46

44

47

47

44

5

43

45

44

44

43

Table 3
PSSA Bellefonte Area School District Results

Grade

2019 %
Adv/Prof

2018 %
2017 %
2016 %
2015 %
Adv/Prof Adv/Prof Adv/Prof Adv/Prof

3

67

71

66

63

62

4

62

65

59

77

60

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

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Grade

2019 %
Adv/Prof

2018 %
2017 %
2016 %
2015 %
Adv/Prof Adv/Prof Adv/Prof Adv/Prof

5

54

56

58

64

56

The scores for Bellefonte Area School District students trend similarly to the
statewide scores except that the advanced/proficiency rates are higher. These scores are
higher than the average scores across the state, but the scores have remained stagnant,
and seem to have plateaued. The bigger concern is the scores of the fifth-grade students
as they have not only flatlined but have been consistently much lower than our scores in
grades three and four.
The goal of this study is to determine what intervention strategies and math
instructional practices teachers within the Bellefonte Area School District are most
successful with assisting students in reaching the proficiency threshold on the
mathematics PSSA. This literature review will investigate the factors contributing to little
or no growth in math for students, math teaching best practices, math interventions, and
professional learning for teachers.
Factors Contributing to Low/No Growth
Children enter the schoolhouse doors with varied levels of readiness for learning.
About 6% of children have major obstacles in learning math (Chan and Wong, 2019).
Many more students suffer from other math difficulties that slow math growth and
achievement. Some students have been fortunate enough to have been involved in
formalized educational preschool programs. Many come from educationally rich and

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vibrant home settings. Of course, some students have not had these early learning
benefits. How schools instruct students who begin their formalized schooling behind
grade-level expectations can become a problem for the schools and the students. How
schools structure their learning settings can also be a problem. It is very easy to place
higher-level learners in more challenging classes with supportive teachers and lowerlevel learners in remedial classes with teachers who may become frustrated and less
supportive due to the high needs of the students (Crosnoe et al., 2010). Assigning and
instructing students as Crosnoe (2010) describes can become a problem and lead to lower
levels of achievement for the neediest students. In typical classrooms, lower achieving
students receive lower levels of instruction due to the expectations of the students by the
teachers. Basic or low levels of inferential instruction are related to lower test scores for
low performing students. Crosnoe (2010) reports that this is the approach that most
schools are taking which then causes many students to stay behind their higher peers and
make little to no growth.
Friesen and Poscente (2014) discuss the age-old math lesson consisting of
remember, recall, and regurgitate facts. Teachers demonstrate a procedure and students
practice it repeatedly with similar questions. Friesen and Poscente (2014) refer to this as
the North American teaching script, and it has proven to be ineffective. These researchers
assert, the inability to change this mindset of teachers continues to stunt the growth of
math development of our students.
There are many other factors that can contribute to low math achievement or
growth. Chan and Wong (2019) identified several types of math difficulties. They
identify number sense deficit, numerosity coding deficit, symbolic deficit, and working

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memory deficit. Students who are struggling may show deficits in a number of these
areas. Chan and Wong (2019) recommend that students should be assessed
comprehensively to determine their weak areas in math so that the correct interventions
are put in place. Chan and Wong (2019) also state that these students should be
reassessed over time, as their areas of difficulty can change. Early intervention and
correctly matched interventions have been found to have positive effects on the
acquisition of math concepts later in students’ education. The success in matching the
intervention to the child points to the reason why a comprehensive assessment to
determine the exact gaps that children have in their math learning is important. Research
done by Karakonstantaki et al. (2018) finds that a deficit in number sense, the ability to
represent and manipulate number quantities on a number line or as an array of objects, is
commonly found in students with math impairments. Number sense deficiency leads to a
diminished understanding of numbers and their relations with each other. Even more
prevalent, according to Karakonstantaki et al. (2018) is poor math achievement caused by
the inability to understand the numerical meaning of numbers through symbols.
There is also a correlation between the amount of teacher and student conflict in a
classroom and how much a student gains from classroom instruction. The better the
relationship with the teacher, the better the student learns and achieves (Crosnoe, 2010).
Along with this relationship, is the attitude of the student toward math. Most students
begin their schooling with positive attitudes toward math, and based on their experiences
in the first few years in school that attitude could remain the same or change. A positive
attitude improves a student’s desire to learn while a negative one can result in the
opposite. Haciomeroglu (2017) states that there is a positive relationship between a

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positive attitude and math achievement. This relationship is stronger in the lower grades
(1-4) than in the higher elementary grades (4-6). Negative attitudes lead to poor
engagement and low performance.
Another contribution to poor math achievement found in the literature is the issue
of a student and even a teacher having math anxiety. Math anxiety is defined as an
intense fear, nervousness, and dread related to math that leads to the avoidance of math
activities and the hindering of mathematical learning (Ruff & Boes, 2014). Math anxiety
can begin as early as kindergarten, which can result in students missing out on the
building blocks of the skills necessary for later success in math. Anxious math students
may even be discouraged from science and math-related career paths later in their lives
due to their inabilities to overcome math anxiety.
The causes of math anxiety can vary but fall mostly into three categories: social
factors, cognitive factors, and academic factors. Data from research studies indicate that
some students are affected by social factors such as race and gender stigmas or the lack of
parental support, especially in economically disadvantaged families. Studies have shown
that girls are more likely to have higher math anxiety and less math success than boys
(Ruff & Boes, 2014). When stereotyped as low-achievers, ethnic minority students can
lose interest and motivation in math, which continues to snowball into less success and
more anxiety (Ruff & Boes, 2014). Students from economically disadvantaged families
typically have parents who were not successful in math as students. They therefore may
also have anxiety and are not as encouraging to their children or comfortable enough with
math to provide them support at home.

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Cognitive factors also can work in tandem with the math anxiety that some
students exhibit. These factors include a weak working memory and Dyscalculia.
Dyscalculia is defined as a difficulty in making mathematical calculations as a result of a
brain disorder. When students are stressed, the emotional feelings of that stress can
impede their working memory, which is critical to success in math.
Academic factors contributing to math anxiety include the traditional math
curricula used in schools, ineffective teaching styles, and students being taught by
anxious teachers. Classroom work that focuses on basic skills, teacher lecture, seatwork,
and whole-class instruction is more likely to have students exhibiting math anxiety than
classes that focus on real- life problems and application. Explaining the why of math
instead of focusing on facts and operations leads to less anxiety in math classrooms.
Math anxiety also affects teachers. Anxious teachers may spend more time
avoiding math in class, or when they do teach they may rely on the textbook rather than
planning ways to teach math creatively. Ruff and Boes (2014), suggest the areas of
teacher math anxiety need to be studied more extensively. They recommend that school
counselors be more invested in assisting anxious students and even teachers. Teachers
could be taught how to identify students suffering from math anxiety and also be
provided with interventions for their classroom lessons that can reduce stress and anxiety
for anxious students. School counselors are encouraged to raise an awareness of the
psychological aspect of math learning with parents, teachers, and administrators.
Systemic school-wide changes were also mentioned by Ruff and Boes, (2014). Ruff and
Boes (2014) recommend changing the method of math instruction and teaching styles
along with working with teachers to acknowledge and work on the math anxiety they

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may possess were areas that could be changed. The idea of providing parent education in
ways to help their students and talk to their students about math was also offered as a way
to assist highly anxious students (Ruff & Boes, 2014).
The math anxiety cycle is a topic that is also explained in a study by Leung and
Cohen (2004). Leung and Cohen (2004) focus their work on teacher anxiety and how
that anxiety translates back to the students. The authors explain that the cycle begins
when teachers are in elementary school and have negative math experiences and results.
The poor experiences result in knowledge gaps in their foundational learning which
makes picking up new math concepts difficult. The difficult early math experiences leads
to a lack of confidence in math and ultimately an avoidance of math. As the students
grow older they avoid higher math classes and math or science career opportunities.
Elementary teachers cannot avoid math. Elementary teachers can avoid higher
level math but must still be proficient and comfortable with math to effectively teach
their students. Therefore, the cycle continues as students taught by anxious teachers
become elementary teachers themselves and transfer the same math anxiety to a new
batch of students.
The anxiety problem for math teachers continues or intensifies as new math
curriculum or methods of teaching math are implemented by school districts. When
teachers are required to move from traditional forms of teaching math to more modern
styles of teaching, more anxiety for the teacher can be the result. Students may sense the
anxiety and absorb that same uncomfortableness about math. Lueng and Cohen (2004)
suggest that this cycle can be broken. Lueng and Cohen (2014) discuss mastery goals.
With students, teachers set mastery goals for students to acquire the knowledge and

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understanding necessary to demonstrate competency in math performance. Teachers can
do this as well by adopting a mastery goal to become a more proficient math teacher.
Adopting a mastery goal can happen by recognizing the math experiences they had as
young students and to provide more positive experiences for their current students. When
searching for mastery they also become more aware of their teaching and its effect on
their students.
Another factor contributing to student difficulties in math would be a student’s
lack of computational fluency (Burns, Nelson, Ysseldyke, and & Kanive, 2014).
Computational fluency is the efficient and accurate completion of math calculations.
(National Council of Teachers of Mathematics, 2000). Computational fluency is the
ability to store basic math facts in your head and pull them from memory easily and
quickly. Students with strong computational fluency skills are better able to solve a
variety of complex problems and think deeper about mathematical concepts (Burns et, al,
2014). When students have strong computational fluency, time and energy can be
devoted to the actual problem and solution rather than on the basic math computations of
the problem. Earlier success with basic math skills predicts later success in higher order
thinking math skills (Burns et, al, 2014).
The inability and difficulty of solving long, complicated, multi-step word
problems continues to be a skill area that is weak with many students and one that
educators are struggling to address effectively in their math instruction (Hord and Xin,
2013). Students who exhibit struggles with word problems typically have limited
strategies to pull from and the strategies the students have are not typically transferable
from one problem to the next problem. Another weakness the students exhibit is the

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ability to accurately represent the problem in their minds or on paper. Middle to high
achieving students rely on schematic representations of problems while low achieving
students rely on pictorial representations like drawing pictures or objects.
Another contributing factor of weak problem-solving skills is a low working
memory capacity combined with difficulties processing information. This affects students
by making it difficult for them to retain information from the first part of a word problem,
process the rest of the problem, and then combine both pieces of information to solve the
problem.
Basic reading and comprehension skills are important areas that affect the math
abilities of some students. The ability to read accurately, fluently, and being able to
comprehend the problem are areas that must be recognized and addressed by teachers so
that the focus can be on math thinking and reasoning. The thinking and reasoning
required to navigate a problem is an area that is not focused on as much by teachers. Too
often, teachers believe that teaching how to solve the problem by looking for keywords is
more important than spending time on the thinking and reasoning behind a problem.
Time spent on the conceptual understanding behind a problem is a more effective
strategy than teaching the steps to problem solving (Hord and Xin, 2013).
High Achieving Schools Best Practices
Specific instructional strategies have been shown to increase student success in
math according to (Ysseldyke, Spicuzza, Kosciolek, and Boys 2003). Ysseldyke,
Spicuzza, Kosciolek, and Boys (2003), identified matching the level of instruction to the
level of the learner along with the appropriate amount and kind of practice. Matching the

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levels of the learner with the instruction provided is known as differentiating instruction.
Differentiated instruction is a teaching method used to meet the diverse needs of learners.
Differentiated instruction targets all learners from high performers to low performers.
Just as reading teachers match instruction to student reading levels, math teachers should
do the same (Burns et, al, 2014). Differentiated Classrooms have several common
structures in place and they include: an ample amount of student responsibility,
opportunities for student choice, peer tutoring, flexible grouping, and modified
instruction. These classroom structures can allow students to find success and to see
themselves as successful math learners. Motivation in math, engagement in the learning
process, and a positive attitude can be the result of differentiation when implemented
correctly. Both high and lower performing students show an increase in academic
achievement and overall attitude towards math when instructed in classrooms where
differentiated strategies are in place. Students’ desire to work on math, to improve in
math, as well as confidence in their abilities increase.
Pre-assessment tools, formal or informal are an effective way to assess a student’s
understanding of a topic which can then lead to effective differentiation. (Grimes &
Stevens, 2009). The use of direct and frequent monitoring of student progress along with
the use of corrective, motivational feedback is a common practice found in successful
classrooms (Ysseldyke et al., 2003).
These authors also state that time engaged in an appropriately leveled task is a
strong predictor of academic achievement. Zank (2015) emphasizes a variety of strategies
that appeal to all learning styles creates intrinsic motivation as students experience
success. Removing barriers to learning such as frustration or avoidance leads to students

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focusing on personal growth. Zank’s work follows many of the same differentiation
recommendations already mentioned, but also emphasizes the simple importance of
identifying students’ deficiencies in conceptual understanding, basic computation, fact
fluency, problem solving and planning direct instruction in those weak areas.
A strong school-wide intervention framework or RtI is stressed in Zank’s
research. Zank (2015) states that creating and using an Instructional Strategy Checklist
that monitors the frequency and use of instructional strategies is an effective resource for
teachers. This checklist should have examples of each strategy and an explanation for
implementing the strategies. This resource is helpful in guiding and supporting the
teacher through the intervention process with a student or group of students. Another best
practice is the use of explicit and systematic instructional strategies targeting problem
solving that encourages students to think conceptually. Examples of these types of
approaches include memory devices to remember strategies, math talk and think alouds
that encourage reasoning and explanations, and problem-solving strategies. Zank’s final
recommendation is the creation and use of quality assessment tools that track progress as
well as common assessments for each grade level.
Ulichnie (2011) emphasizes small group instruction to help students’ master
learning. What students should be assisted are identified through targeted preassessments. Sound assessment practices are another quality of highly effective schools
emphasized in Ulichnie’s research. Pre-assessments measure whether the students have
the prerequisite skills and knowledge for success. The pre-assessment data allows
teachers to plan instruction to meet their students’ needs. Formative assessments help
identify what a child knows, understands, and is able to do (Ulichnie, 2011).

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Parent involvement in the home and in the school is an area that can be used as a
tool to strengthen a school's environment and academic scores (Park, Stone, & Holloway,
2017). Park et al., (2017) focused on school-based parent involvement like belonging to
PTA groups, volunteering in classrooms, and fundraising. The research showed positive
indications of school-level student achievement in math and a more stimulating
environment in schools where the parents were involved in school activities and had
formed school related peer networks with other parents and school staff. Involvement by
the parents allowed them to take some of the responsibility of their child’s learning from
the teachers. Park et al., (2017) also concluded that a child’s overall academic
achievement is not only affected by the involvement of that student’s parents, but even
more so by the involvement of the average level of parental involvement in the entire
school. In other words, students with little to no parental involvement in the school still
benefit from other parents being involved to create a better educational environment.
Involved parents lead to schools reporting a higher percentage of students meeting or
exceeding the national standard for math and reading skills (Park et al., 2017).
Another promising best practice is described by Crosnoe et al., (2010). In this
study, the researchers state that in order to grow low achieving students, the students
must be challenged by higher order mathematical concepts and thinking skills. Low
achieving students must be in the same higher-level math classes as the other students.
Equity must exist in their math instruction and experiences. Equitable experiences in
classrooms goes against conventional thinking as educators typically believe that lower
students should be segregated from the higher achieving students and taught basic
remedial math skills in order to build the foundation for future higher-level math

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learning. Simply challenging lower students with an equitable curriculum is not enough
unless the lower achieving students also have a supportive teacher guiding the students
through the inevitable difficulties and frustrations associated with challenging
expectations. Without support, challenging students with lower math abilities in higher
level math content and classes could be unsuccessful and counterproductive for the
students. Therefore, providing all students a common higher-level curriculum allows
lower achieving math students the opportunity to close the achievement gap (Crosnoe et
al., 2010). Higher order instruction combined with a positive, supportive teacher
promotes more achievement than a rote basic skills approach (Crosnoe et al., 2010).
In the practice guide from the Institute of Education Sciences from 2009 entitled
Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for
Elementary and Middle Schools, eight recommendations are listed for schools as best
practices and are summarized briefly below (Gersten, R., Beckmann, S., Clarke, B.,
Foegen, A., Marsh, L., Star, J.R., & Witzel, B. 2009).
1.

Screen all students to identify those at risk and provide interventions to identified
at-risk students. The report emphasizes that no one screening measure is perfect
and that schools should closely monitor those students who scored slightly above
or below the cut-off score for intervention.

2. Instructional materials should focus on whole numbers in kindergarten through
grade five and rational numbers in grades four through eight. These materials
should be selected by a committee. They also argue that the focus and in-depth
coverage provided to proficient students should also be allotted to the students

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with mathematical difficulties. Connections should be made between the concepts
in the intervention and the current grade level material being taught.
3. Instruction during the intervention should be explicit and systematic. The
instruction should provide models for problem solving, verbalizing thought
processes, guided practice, corrective feedback, and frequent cumulative reviews
of the material.
4. Interventions should provide instruction with solving word problems. An
example of this is instruction with problems associated with addition and then
with the inverse operation of subtraction.
5. The materials should allow opportunities for students to work with visual
representations of mathematical ideas in order to translate symbols and numbers
into meaningful understandings.The interventionists should be proficient in the
use of visual representations.
6. Interventions at all grade levels should devote about ten minutes in each session
on basic fact fluency practice. This can be done with technology or with flashcard
type activities.
7. Monitor students receiving interventions and others who are at risk. Use
curriculum-based assessments to determine how well the student has learned the
day or week’s lesson. Also, continue to progress monitor in order to see how the
intervention and overall math program is affecting the student.
8. Include motivational strategies within the intervention program. Active
engagement and students accomplishments should be encouraged and recognized.

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Interventions
According to the National Council of Teachers of Mathematics Principles and
Standards for School Mathematics (2000), mathematics should be taught equitably to all
children. Students must all have opportunities to be active participants in their learning.
There are two types of math intervention programs, ones that focus on procedural
skills with explicit instructions and programs that rely on a conceptual framework of
teaching. Procedural skills-based programs such as Connecting Math Concepts, Cover,
Copy, and Compare, Flash Math and Reflex Math are systematic approaches that teach
math procedures step-by-step in order to perform operations and solve problems.
Conceptual based approaches look to improve the understanding of the math principles
being used and the “why” behind these principles. Conceptual based approaches focus on
building concepts gradually from the concrete to the more abstract. Examples include
Mathematics Recovery, The Numeracy Recovery Program, ST Math, and Number
Worlds (Karakonstantaki et al., 2018). An issue identified by Karakonstantaki (2018) is
that most interventions for elementary math students are designed for students in grades
kindergarten through third and that these programs focus on helping students catch up
with grade level peers, while not addressing the underlying factors of these students'
problems in math. Karakonstantaki (2018) also finds that a focus on conceptual
understanding combined with procedural teaching benefitted students the most.
Leali, Byrd, and Tungmala (2012) found that all students need access to important
mathematics and that children who need interventions should be provided the support
necessary to reach proficiency. Ulichnie (2011) questioned the impact of an intensive
math intervention on student math achievement and suggested that students need an equal

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amount of support in math compared to what a struggling student would get in reading.
Teachers must be aware that often vocabulary and language barriers can create an issue
for math learners (Leali, Byrd, and Tungmala, 2012). Leali, Byrd, and Tungmala (2012)
found that English Language Learners must be given frequent and direct instruction to
move them from simply learning about math vocabulary and symbols to a deeper
understanding of math concepts and properties (Leali, et al., 2012). Their research on
English Language Learners seems relevant when thinking about all students in need of
interventions. As Leali, et al. (2012) explain, math teachers must find different ways of
talking about mathematical objects and mathematical situations to bring the concepts into
daily conversation and factors other than mathematical skills contribute to success in
conversations about solving word problems. Vocabulary understanding and verbal skills
are some factors that assist with solving word problems. The setting of the word problem
may not be familiar to students and should be discussed. Students may get distracted
trying to understand the story rather than focusing their time and energy on pulling the
important math information out of the problem. Sufficient background knowledge must
be provided to the student and problems can be reworded to fit their prior knowledge if
necessary. Graphic organizers and visual representations should be provided to the
students along with modeling troublesome vocabulary words or idioms can also be a
helpful strategy. Allowing students to verbalize and work on word problems together,
with support when needed, can also be a powerful strategy (Leali, et al., 2012).
Mong and Mong (2010) report that both Mastery to Mastery and the Cover, Copy,
Compare intervention programs show promise in increasing math fluency in children as
measured by digits correct per minute. Computational fluency is a necessary skill for

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math success and repeated practice of basic facts is a key component to help develop
mastery (Burns et, al, 2014). Extensive practice of basic facts is not found in many math
curriculums today, therefore schools should find ways to supplement basic facts
instruction in the classroom. Cover, Copy, Compare and Reflex Math are both programs
designed to improve the accuracy and fluency of student responses to basic fact
problems. Factors that contribute to both program’s success include the brief time needed
to complete learning trials which allows students to complete many learning trials and
keeps motivation high. The other key component is the self-evaluation component which
prevents students from practicing incorrect responses.
Math to Mastery relies on the preview of problems, repeated practice, immediate
feedback, summative and formative feedback, and self-monitoring of progress. Students
working with the Math to Mastery intervention also benefit from the modeling that is part
of the program. Modeling shows the correct way to solve the math problems and the
appropriate rate at which problems should be solved.
IXL is another technology-based program that differentiates instruction and
provides immediate feedback to students. IXL explains incorrect responses when students
get a problem wrong. Repeated practice, immediate corrective feedback, goal setting,
progress monitoring and self-charting have been shown to increase academic
performance.
Both programs, Math to Mastery and IXL, contain many of the same key
components. The Math to Mastery program relies on an interventionist to model and
provide feedback to the student rather than a worksheet approach as found in the Cover,
Copy, Compare program. The social feedback is a valuable component of the Math to

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Mastery program. Math to Mastery and Cover, Copy, Compare were both shown to
increase student math fact fluency and proficiency, but Math to Mastery showed higher
scores with the students which support the need for repeated practice interventions to
build fact automaticity in students (Mong & Mong, 2010).
Florez and Wilkins (2016) studied the use of manipulatives by students in math
classes. Florez and Wilkins (2016) summarized that student learning is most effective
through engaging learning lessons which involve multiple representations of the
mathematical content. Math manipulatives are tools used to provide a better
understanding of math concepts. Florez and Wilkins (2016) focused on manipulative use
over time from grades K-5, and wanted to see if manipulatives affected student learning
or growth. Manipulatives are defined as objects that can be touched, moved, rearranged,
or stacked. Examples include base-10 blocks, counters, geometric shapes, and pattern
blocks. Virtual manipulatives, that students are finding on computer based interactive
programs, are being utilized increasingly more in schools. Florez and Wilkins (2016)
found a positive relationship between manipulative use and math learning over time, and
that the frequency of manipulative use positively affects math learning. The continued
use of manipulatives with students in the upper elementary grades is also beneficial to
student learning (Florez and Wilkins, 2016). Interestingly enough, their research shows
that manipulative use decreases as students progress through the grade levels. The use of
manipulatives in the intermediate grades would be an area that would warrant additional
professional learning for teachers to become more familiar with manipulatives and how
to implement them in their classrooms.

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The research regarding manipulative use has been mixed over the years, but more
studies point to the benefits than the negatives (Liggett, 2017). Liggett (2017) emphasizes
that math instruction should be real for the students and using manipulatives can help
make this happen. Liggett (2017) cautions that manipulatives must be used appropriately
or they could cause frustration and disrupt student motivation and learning. Liggett
(2017) finds that manipulatives will help teachers differentiate their instruction and
provide multiple pathways for students learn the new content. Again, manipulatives are
not only effective with primary grade students, but also with intermediate students and
are especially helpful with students who need remedial help. Liggett (2017) focused on
manipulative use for second grade students and the results showed that students who used
manipulatives performed better on a post-test than students who did not use
manipulatives. Liggett (2017) believes that manipulative use not only increases the
overall test score, but also gives students additional methods or strategies for solving
problems and being more successful math students. This math understanding and success
will transfer later in life to additional success in their schooling and open up varied career
opportunities.
Strategies for working with students who struggle with word problems is the
focus of the work by Hord and Xin (2013). Metacognition instruction is a skill that can
help students organize their thinking and representation of the problem. Teaching
students to use schematic representations rather than pictorial representations is another
useful strategy to teach students. This decreases the difficulties in storing, organizing, and
processing the information needed for the problem. The final point made by Hord and
Xin (2013) is to teach the student how to transfer the skills and knowledge from one

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problem or situation to similar ones in the future. The lessons and strategies students
learn from solving a word problem should be transferable and connected to past and
future word problems. Teachers need to help students make these connections.
Technology Based Interventions
Almost every upper level elementary student owns and uses some type of mobile
device, iPad, cellphone, etc. Educators are using this technology to improve student
engagement, peer interaction, and collaboration. Technology, like mobile devices, can
also be used to provide more equitable and personalized instruction, expose students to
the technology that are prevalent in the world and workplaces, and improve test scores
(Hollands & Pan, 2018). They are also using forms of technology to collect classroom
feedback, improve communication, reduce technology costs, and extend the time and
place of learning (Karakonstantaki et al.,2010). Elementary teachers are beginning to use
technology to improve learning by supplementing teacher led instruction or at times
replacing teacher led instruction (Hollands and Pan, 2018).
The most popular mobile learning initiative is the one-to-one laptop, but the
inconsistent use and high costs lessen the effectiveness of the initiative at times. Using
mobile devices for educational gaming is becoming popular in schools now. Mobile
gaming allows students to select their own learning paths based on prior knowledge and
learning progress. Students are typically highly engaged in the mobile-based
interventions. An interesting find noted by Karakonstantaki et al., (2010) is that the use
of computers for math instruction did not significantly enhance student performance, but
it did positively affect the performance of those students with math disabilities.

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In a study done by Kiger, Herro, and Prunty (2012), second and third grade
classrooms utilized the Everyday Math program resources along with mobile learning
apps on an iPad to increase skill level on multiplication facts. Students practiced 10
minutes a day. Other students utilized the Everyday Math program along with traditional
flashcard methods to practice multiplication facts. Students using mobile learning
interventions answered more items correctly on the final assessment. The same students
also answered more of the difficult items correctly. This study by Kiger, Herro, and
Prunty (2012), suggests combining a traditional curriculum with a mobile device may be
an effective way to improve student achievement. Keys to effective mobile learning
implementation include: administrative and school commitment, trained teachers,
instructional technology integration, classroom management and facilitation with the use
of the mobile device. Schools may also need an onsite resource person to support
teachers and the technology (Kiger et al., 2012).
Accelerated Math is an example of a technology-based intervention. Its primary
focus is to enhance a math curriculum so that teachers can use the program to give
students a boost of individualized practice on basic math skills which are necessary for
students to have in order to build application and problem-solving skills. Used to
complement Everyday Math in a Minnesota school, it has been shown to increase
students’ academic achievement in math as shown on standardized tests (Kiger et al.,
2012). Its use has enabled teachers with the ability to provide more individualized
instruction to the students either in the form of individual assignments or one-on-one
work with the teacher. Whole group instruction only amounted to 42% of classroom time
during math lessons when a supplemental online based math program is used. Utilization

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of a core curriculum program alone results in whole group instruction over 81% of the
time (Ysseldyke et al., 2003).
In the Ulchnie (2011) study, students utilized IXL for 30 minutes every day as an
intervention. IXL is an online program that supports the practice and reinforcement of
skills learned in the classroom (Holland & Pan, 2018). The activities in IXL are tied to
the Common Core State Standards. At the conclusion of the Ulchnie study all of the
students in the focus group made gains in overall math growth. Holland and Pan (2018),
referenced other studies that did not show that IXL use with students showed clear,
measurable growth. Holland and Pan (2018), also studied the effects of IXL and could
not claim causality between IXL and math achievement as measured by the Star Math
Assessment. Teachers of the students in this study cited the level of rigor as a concern
and stated that the level of rigor in the IXL questions was less than the level of difficulty
found on the Star Math Assessment. The same teachers also reported that IXL is useful
for practicing and reinforcing skills, but not as helpful in applying concepts to difficult
multi-step problems.
Reflex Math is another popular computer-based intervention program being used
daily with many students across the country. Reflex Math works on student recall of
basic addition, subtraction, multiplication, and division facts with the use of online games
for students. The program tracks fluency, measures response speed, and adjusts
instruction to meet students at their fact recall development level, while also providing
reports for teachers to track performance and usage (Sarrell, 2014). Reflex introduces
students to small sets of facts, allows them time to become proficient with the new facts,
has a timed component, regulates the difficulty of the facts, and ends each session with

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game-based practice (Sarrell, 2014). Sarrell (2014) concluded that at-risk middle school
students who participate in the Reflex Math program see higher improvements in math
facts than those students using only traditional methods.
Sarrell (2104), further analyzed the data to determine if the program affected
males and females differently. Both males and females using the program scored higher
on basic fact recall tests than other male and female students not using the program.
Females benefitted more than the males from the exposure to Reflex Math.
Spatial Temporal Math or ST Math is another online program. ST Math uses
images to help students develop spatial-temporal skills that can improve student
understanding of fractions, proportions, and other mathematical skills (Tran et al., 2011).
ST Math provides game-based challenges that utilizes visual puzzles. Interactive visuals
provide students with immediate feedback on their solutions (Wendt, Rice & Nakamoto,
2019). ST Math has been shown to have positive effects on student achievement after the
first year of implementation (Tran et al., 2011). Wendt et al., (2019) also studied the
effects of ST Math by comparing grade levels of students receiving ST Math against
same grade level students not receiving ST Math. Wendt et al., (2019) compared both
groups based on their average scores on state standardized tests and the percentage of
students reaching proficiency on these tests. The students in grades three, four, and five
who used ST Math had overall higher proficiency percentages on the same state
assessment than the same grade levels of students without the exposure to ST Math
(Wendt et al., 2019). Students in grades four and five performed better when comparing
the average achievement scores of these students. This was not the case with grade three
students as the results were not statistically significant (Wendt et al., 2019). Tran (2011)

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also reported the additional benefit of positive changes in teacher efficacy and
instructional practices after utilizing this program with their students.
Everyday Math
Everyday Math was a federally funded research project out of the University of
Chicago. Its philosophy was to build symbolic understanding of math through the use of
manipulatives, and student discussions with each other and the teacher. The program
focuses on basic fundamental math exercises in grades K-3. In grades 4-6 the focus shifts
to problem solving with information from the different curriculum areas as it builds on
the math experiences that students have already gained. The program is now in its 4th
edition and is the curriculum used in the Bellefonte Area School District.
Bell and Isaacs (2010), describe the program as being organized into nine strands
and six themes. The strands include Numeration and Order Relations; Operations and
Number Systems; Measures, Numbers in Reference Frames; Algorithms and Procedures;
Data and Chance; Geometry and Spatial Sense, Patterns, Rules, and Functions; and
Algebra. The themes that the authors feel students need to develop are estimation and
number sense, algorithmic and procedural thinking, mental arithmetic skills and reflexes,
problem solving and mathematical modeling, multiple representations and methods, and
links of mathematics to the everyday world.
According to McGraw-Hill Education, Everyday Math is a comprehensive k-6
math program that provides multiple pathways to learning to help teachers meet the
varied needs of the learners in their classrooms. The program contains assessment tools
as well as an online evaluation and reporting system. The key feature that Everyday Math

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has that most programs do not have is its spiraling feature. This means that lessons and
practice of each standard are spread across multiple lessons and units throughout the year.
The program offers interactive games for students to practice skills from classroom
lessons (mheonline.com/everydaymath4). A drawback of the program is the lack of
practice of basic facts (Ysseldyke et al., 2003). This approach to math and this program is
quite different than what most teachers are used to utilizing (Bell & Isaacs, 2010). Major
changes in how teachers think about math and instruct math needs to be taught to
teachers who utilize the Everyday Math curriculum.
Everyday Math has shown to be successful in promoting the growth and
achievement of students. In a study completed with a large group of third, fourth, and
fifth grade students from Texas, Waite (2000) found those students being instructed with
the Everyday Math curriculum had higher scores on the Texas Assessment of Academic
Skills and showed greater achievement gains than similar math students using a different
curriculum. The students using the Everyday Math curriculum scored 3.9 points higher
on the assessment and 81.4 percent of students passed the assessment compared to 72.3
percent. Waite (2000), also looked at all student demographic categories and each
category performed better with the exception of Hispanic students. African-American and
low-socio-economic students showed greater gains than some of the other groups. The
reason suggested for the Hispanic students not showing the same level of achievement
was their language barriers that many of them face. Language barriers and math success
is a connection that cannot be overlooked.

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Departmentalized Math Classes
Elementary teachers over the years have had to be curriculum and content experts
in all subject areas in order to meet the needs of their students in the traditional classroom
set-up. This structure has been made even more demanding with the pressures on teachers
caused by standardized testing (Nelson, 2014). This has made schools rethink their
elementary classrooms and some have transitioned to the departmentalized classroom
model. Departmentalized classrooms can be defined as a teacher being responsible for the
instruction of students in one academic area, or it can be thought of as students moving
from one classroom to another classroom for math, science, language arts, and their other
classes. Teacher in departmentalized settings can become content experts in their
teaching area and can devote their time and energy to plan for only one or two content
areas. Instead of having their planning and research for lessons spread out over four or
five subject areas, they can focus on one or two subject areas (Nelson, 2014).
A mainstay in elementary education over the years has been the emphasis of
relationships with each child and this can be difficult to cultivate in a departmentalized
setting. A research study completed by McGrath and Rust (1996) showed that fifth grade
self-contained classrooms score significantly higher on group achievement tests when
compared to departmentalized peers. In this study, self-contained students gained more
than departmentalized students in Total Battery, Language, and Science in fifth and sixth
grades, but no differences were found in Reading, Math, or Social Studies. Transition
time was more efficient in the self-contained classes. The average transition time was
3.27 minutes for self-contained classes and 4.55 minutes for departmentalized classes. No
significant differences were found in actual instruction time. Nelson (2014) wanted to

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compare the math performance of fifth grade students in departmentalized settings with
those in traditional settings. Nelson (2014) found that students educated in
departmentalized classrooms showed a significant statistical difference in achievement
compared to students in traditional classrooms. Educating fifth grade students in
departmentalized math classes, according to Nelson’s research could help students gain a
better understanding of mathematical concepts and prepare them for the higher-level
learning that awaits them in middle school. Nelson (2014) also believes that the
achievement gap is not so much about race or socio-economics, but may be more about
the educational setting and level of instruction in these classrooms. She states that
departmentalized classrooms provide all students with high levels of instruction and
equity in their education.
Professional Learning
Professional learning should be personalized for each teacher just as learning is
personalized for students (Hollands & Pan, 2018). The learning for teachers should be
job-embedded within their classrooms while learning alongside other teachers under the
guidance of math education experts (Friesen & Francis-Poscente, 2014). Friesen &
Francis-Poscente (2014) stress the need for teachers to have a combination of lesson
study, mentorship, and participation in Math Fair. Friesen & Francis-Poscente (2014)
define Math Fair as a collaboration with other math teachers on deep, higher level
thinking math problems that opens their eyes to how math can be taught differently.
Teacher learning must be differentiated based on their needs as math teachers.
Math teachers must have direct training on planning, implementing, evaluating, and
assessing student work. Friesen and Francis-Poscente (2014) stated teachers don’t need

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additional training on math concepts and procedures for teaching math, but more on
identifying the cause of student misconceptions and moving the student’s thinking
beyond those misconceptions.
Bell and Isaacs (2010), reported that teachers need to think about and teach math
differently now than they did in the past. Bell and Isaacs (2010) listed several areas for
teacher development in order for them to be successful, and stated that teachers need to
understand that mathematics is more than just arithmetic. Effective instruction is also the
linking of mathematics to its everyday uses. Strengthening students’ use of mathematical
vocabulary is another change as well as becoming more comfortable and being able to
facilitate partner and group work. The last area of improvement for teacher professional
learning is to become familiar with the many strategies that students can use to solve a
problem and to encourage students to use multiple strategies and be able to talk about
those strategies.
Conclusion
There are many interventions and strategies being implemented in elementary
school math classrooms across the United States and throughout the world. There is an
abundance of research explaining what works and what is not effective for students
exhibiting low math achievement. This study hopes to find out what is successful in my
district and what can be added to our math classrooms to fill the gaps. A key learning in
the literature review is the concept of high expectations and equity of educational
experiences. Lower achieving students must be challenged and provided with the same
level of rigor as higher achieving students. The difference is that lower achieving students
require more academic and emotional support from the teacher.

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Student and teacher anxiety in math is another area that is prevalent in the
literature. Math anxiety can halt a student’s determination and progress in math class.
Math anxiety also has long term effects as students affected with math anxiety typically
will avoid higher level math classes and career fields involving math or science.
It is no surprise that differentiation and identifying student strengths and
weaknesses through sound assessment practices are effective practices in high achieving
schools. Many schools are now taking advantage of students’ inclination for technology
as they are meeting the needs of students by implementing technology-based programs or
applications. There are many programs out there and the research is inconclusive about
many of them, but Reflex Math, ST Math, IXL are programs that are of great interest to
me since students in my district are exposed to these programs on a daily basis. The
research is finding that a combination of direct instruction with a traditional teacher led
curriculum and online program can be very effective in elementary math classrooms.
Ultimately, in order to have a positive effect on students and their learning,
teachers’ skill sets must be enhanced. Teachers should develop the skills to show students
how to think deeply about math concepts and to understand the concepts in ways that can
be transferred to other problems. Teachers must use strategies that were not prevalent or
used with them when they were in math classes as students.
The data that will be collected from this study will inform the research of the
strengths and weaknesses found in my district’s third, fourth, and fifth grade classrooms.
These identified areas will provide educators with strategies that can be enhanced through
professional learning opportunities so that what is learned by teachers can be transferred
to students to positively affect student growth and development in math.

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CHAPTER III
Methodology
Purpose
The purpose of this study is to determine the math interventions and instructional
strategies that are proving to be successful in third, fourth, and fifth grade classrooms
across the Bellefonte Area School District. Math scores on PSSA standardized
assessments vary from classroom to classroom and building to building across the
district. Student scores on the PSSA’s over the past five years are not seeing much
growth. This study will determine the classrooms that are finding success and the
commonalities between them. Additionally, this study will identify any trends in
classrooms that are not showing success. Instructional strategies and interventions that
are increasing growth will be identified. As a result of this research, successful areas of
math instruction and promising interventions will be shared with math teachers across the
Bellefonte Area School District. This will help improve the overall math achievement of
the students. The effect of departmentalization on math scores in the district will be
assessed during this study. Finally, the professional learning needs that will benefit math
educators and students will be identified.
In quantitative research studies, the collection and analysis of numerical data are
used to describe or explain the subject of the study. The quantitative data in this study
will focus on student achievement and growth data. This data will help identify the
classrooms that are demonstrating the most success as well as the classrooms that are not
as successful. By focusing on and analyzing only the numerical data, objectivity in the
findings is a strength of the quantitative research portion of this study.

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The purpose of qualitative research is to study the quality of a subject. This phase
of the research studies the quality of math instructional practices, strategies, and
interventions that are being used in classrooms. The qualitative data consists of a teacher
questionnaire that identifies the interventions and strategies that are being used in their
classrooms. Comparing the strategies used in the classrooms with the classrooms that are
showing the most positive results will provide valuable information to all math educators
in the Bellefonte Area School District.
Therefore, a mixed-methods approach to research is utilized to answer the
research questions. Mixed-methods research is defined as a study that includes both
quantitative and qualitative research (Mertler, 2019). Mixed-methods research allows for
the mixing of the collection of quantitative data, student archived academic data, with
qualitative data, the teacher survey data. Using both types of data prevents the researcher
from being limited by only considering one type of data. Mixed-methods research allows
for multiple perspectives to be included in the study. Both sets of data are stronger and
more informative when combined with each other since neither set of data can answer the
research questions alone. A mixed-methods approach to the research will provide depth
and breadth to a study (Mertler, 2019).
Setting and Participants
“Inspiring and Preparing Today’s Learners to Prepare for Tomorrow’s
Challenges” is the mission statement of the Bellefonte Area School District. Math
achievement is a major curricular area for students to master in order to meet the mission
of the school district. Math scores have been a constant area of interest in the district over
the years.

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The school district is located in the town of Bellefonte, Pennsylvania. Students
reside in Bellefonte and in several small neighboring communities. Bellefonte is located
approximately 8 miles east of the Pennsylvania State University and approximately 25
miles west of Lock Haven University. The district benefits from being in close proximity
to both of these higher institutes of learning. Many quality teachers from the district are
graduates from these universities. The district’s teachers also benefit from the
collaboration and professional learning opportunities that are available through these
universities. Many teachers within the district host student teachers from these schools.
Being this close to both of the universities produces a community that values education
and has high expectations for its students and schools. Parental support is a tremendous
resource for the school district.
The school district has a total enrollment of 2,636 students in grades kindergarten
through twelfth grade. The district has four elementary schools, one middle school for
students in grades six through eight, and a high school for grades nine through twelve.
This study is focusing on the students and math teachers across the four elementary
buildings in grades three, four, and five for the past three years.
Marion-Walker Elementary and Bellefonte Elementary are both similar in size but
opposite in demographics. Both of these schools are the larger elementary schools in the
district, but the number of economically disadvantaged students in Bellefonte Elementary
are much higher. The two similarly smaller sized schools in the district are Benner
Elementary and Pleasant Gap Elementary. Pleasant Gap Elementary has a much higher
economically disadvantaged student population than Benner Elementary. Both Pleasant
Gap and Bellefonte Elementary Schools are designated Title I Schools. Table 4, on the

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

40

next page, shows student population and teacher numbers in grades three, four, and five
for the past three years.
Table 4
Number of Students and Math Teachers
School

Year

Third
Grade

Fourth
Grade

Fifth
Grade

Total
Students

Benner

2018-19
2017-18
2016-17
2018-19
2017-18
2016-17
2018-19
2017-18
2016-17
2018-19
2017-18
2016-17

33
42
43
26
35
38
77
55
45
53
59
56

40
47
43
34
37
42
54
43
68
58
51
68

41
42
43
41
42
36
46
64
49
49
63
64

114
131
129
101
114
116
177
162
162
160
173
188

Pleasant
Gap
MarionWalker
Bellefonte

Number of
Math
Teachers
4

4

7

5

In order to more accurately describe each of the elementary schools, the
demographics of the schools are shown in percentages on the next page for the 2018-19
School Year.
Table 5
School Demographics A
School

Males/Females

White

Black

Hispanic

Asian

Native
American/Alaskan
Native

Native
Hawaiian/Pacific
Islander

2 or
More
races

Benner

56.4/43.6

96

0.9

0.4

1.3

0

0

1.3

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES
School

Males/Females

White

Pleasant

53.3/46.7

Black

41

Hispanic

Asian

Native
American/Alaskan
Native

Native
Hawaiian/Pacific
Islander

2 or
More
races

93.3 0.5

1.9

0

1.0

0

3.3

96.4 0

1.7

0

0.6

0

1.4

88.6 2.4

6.3

0

0

0

2.7

Gap
Marion48.9/51.1
Walker
Bellefonte 48.5/51.5

Table 6
School Demographics B
School

Economically
Disadvantaged

English Language
Learner

Special Education

Gifted
Students

Benner

20.7

4

11.5

0.9

Pleasant Gap

38.6

5.2

18.6

0

Marion-Walker

15.6

0.6

14

0.6

Bellefonte

47.9

1.8

21

1.2

The teachers in the study are selected naturally and purposefully. These teachers
are currently or recently teaching math in grades three, four, or five over the past three
years. The teachers range in years of experience from as little as two years of experience
to as much as 25 or more years of experience dating back to the 2016-17 school year.
They all have extended their education beyond a Bachelor’s Degree and many of them
have Master’s Degrees. They all have achieved tenure as of the 2019-20 school year.
The elementary schools departmentalize instruction in grades four and five.
Students in these grades switch classes for math, science, social studies, and language

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

42

arts. One teacher is responsible for math, science, and social studies instruction in each of
those grade levels while another teacher is responsible for language arts instruction. The
exact structure of the departmentalization in each building may look a little different
depending on the number of sections in each grade level.
Previous grade level teachers create classroom rosters. The rosters are finalized by
the building principal and many factors are considered when the rosters are created.
Equality between the classes across all categories is a priority in the heterogeneously
grouped classrooms. The categories considered as class rosters are created include the
number of males and females, special education students, English Learner students,
behavior concerns, academic abilities of the students, and the overall teacher-student fit.
The classroom rosters are created to be as equitable as possible within each school and
across the school district.
The district has a Math Intervention Specialist that services Marion-Walker
Elementary and Bellefonte Elementary, and a Math Instructional Coach who collaborates
and provides professional learning to all elementary teachers. Each of the schools is also
led by a building principal whose primary responsibility is managing and overseeing the
overall success of their school.
The math classrooms across the Bellefonte Area School District share a common
curriculum and have approximately 75 minutes of math instruction per day. Everyday
Math is the curriculum that is used in each classroom. Components of the program that
are utilized include the student reference book, the math journal, the games and activities,
and the online component. Classrooms also supplement with Reflex Math which is an
online program that targets basic facts acquisition for students. Reflex Math has been

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

43

used in Bellefonte Elementary for the past three years. The 2019-2020 year is the first
year that the three outlying buildings are using the program. The classrooms also
supplement instruction and provide interventions with various other programs of the
teacher’s choice.
Typical math lessons include the following components: mental math activity and
math message to begin the lesson, direct teaching, independent practice, differentiation,
games to reinforce, and a short daily formative assessment. Some teachers differentiate
their instruction more effectively by implementing the guided math strategy to their daily
instruction. Teachers are transitioning from whole group lessons for the majority of the
math class to shorter mini-lessons, math stations that are completed independently by the
students, and small group direct instruction based on students’ needs.
Technology use is extensive across the district. Every student has been assigned a
Chromebook. This 1:1 initiative allows for easy access to the resources and activities that
are technology based. All teachers across the district in grades three, four and five utilize
some form of technology within their instruction on a daily basis. Promethean Boards are
also utilized by each teacher to take advantage of the online resources that are used in the
classrooms. Students and staff are adept at utilizing technology resources to support and
enhance learning.
Research Plan
This research study follows a Mixed-Methods Research approach. Both
quantitative and qualitative research methods and data are utilized. The variables in the
study are not manipulated in any way. The variables are measured as they naturally occur
within each classroom and with each teacher and student. The variables in question are

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

44

the teacher practices used in the math classes and the math data supporting the results of
these strategies in how they affect student achievement and growth. The study explores
the reasons why some math teachers and classes perform better than other classes and
teachers. The researcher is seeking to evaluate causes of any differences within
classrooms by looking at archival math data and teacher questionnaire data. In this study,
the researcher’s goal is to describe and interpret the achievement and growth of the math
students in grades three, four, and five along with the teachers’ strategies and
interventions that are implemented within each classroom and grade level.
An explanatory sequential design method of collecting and analyzing the data is
used. In the first phase of the study, quantitative data is collected and analyzed. The
teacher’s classroom math data is the crux of the research study and is given priority by
the researcher. The second phase of the study includes the collection of qualitative data.
This data is the teacher questionnaire data. The qualitative data provides more clarity to
the quantitative data. The analysis of the quantitative data helps drive the type of
qualitative data the researcher needs to answer the research questions. It is the
researcher’s intent that the thoughts, beliefs, and perceptions of the teachers found in the
qualitative data will further enhance and explain the quantitative data.
The level of interaction between the quantitative and qualitative data is
interactive. The two strands of data are combined during the data collection and analysis
process as opposed to occurring only at the end of the study. Both sets of data receive
equal prioritization in addressing the goals of the study. The data is collected
sequentially, with the quantitative data collected first and then analyzed to help guide the
collection of the of qualitative survey data. The point of interface for the data will be

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

45

during the data analysis phase of the study. At this point both sets of the data are
combined to analyze and answer the research questions.
The research process involves collecting assessment data for the past three years.
The data is then organized and analyzed to allow for the ranking of teachers and their
classes. The teachers are ranked from highest to lowest in terms of student achievement.
Then survey data from math teachers over the past three years are collected. At this point,
the researcher begins to look at the assessment data and compares it to the teacher survey
data. Trends in teacher practice in higher performing classes and lower performing
classes will be identified. It is important to note that all student and teacher data is
confidential and neither teacher nor student is identified in the study. Teachers will be
identified by a number through a random selection process to protect their privacy.
The first step in the study is to identify the topic of interest or concern. In this
study, math achievement and growth are determined to be a concern and learning why
some teachers’ classes are more successful over the years than other classes is the
purpose of the study.
After identifying the topic and research questions, the next step is to identify the
teachers and students who are the natural participants in the study. As discussed earlier,
this is done by selecting the math teachers in grades three, and four, and five across the
entire district. The identification and selection process each require working with the
other building principals and the district’s Human Resources Department to determine
who the teachers of record were for the math classes during the three-year span that is
being studied.

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46

The data is identified and collected after the participants are selected. The
researcher determines the quantitative data sets that are consistent and can show the most
effective classrooms and teachers in grades three, four, and five. The data selected for the
study is PSSA math data, end of year final grade percentage for the students which is
based on common curriculum-based measures, and Classroom Diagnostic Tests scores at
either the end of the year or the middle of year depending on the final time the tests were
completed in each grade level. Classroom Diagnostic Test administration varies by grade
level and by year, but were consistent from grade level to grade level and teacher to
teacher each year. The final piece of quantitative data to collect is the teacher specific
PVAAS score for teachers in grades four and five. This shows the average amount of
growth on a three-point scale for teachers in grades four and five over a three-year
window.
Pennsylvania System of School Assessment (PSSA) data results are gathered for
the 2016-17, 2017-18, and the 2018-19 school years for all students in third, fourth, and
fifth grade during those years. The purpose of the assessment is to provide data for
teachers and administrators to improve academic performance in reading, math, and
science, and for students and parents to understand the student’s basic achievement in
those academic content areas. The scores are also used as part of the teacher evaluation
system and are a major component in each building’s School Performance Profile score.
For these same students, Classroom Diagnostic Testing (CDT’s) data are collected.
CDT’s are administered in the fall, winter and/or spring. These are assessments that
provide diagnostic information to guide instruction and support intervention and
enrichment in math, language arts, and science. The other piece of data used is the end of

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

47

year final math grades for students. This is the overall percentage earned by the student
on the local curriculum-based assessments. Teacher PVAAS data is also collected for
those that had it available in grades four and five.
The qualitative data was gathered through the use of Survey Research. The
process for creating the survey was to first identify the topic and the purpose for the
survey. Next, the target population was identified and since the number of potential
participants was limited, it was decided that all teachers would receive the survey. A
web-based Google Form was used as the survey tool. This worked well as the researcher
and the teachers are familiar with the Google platform since this is the primary online
platform utilized in the district. The cover letter and consent forms were developed,
followed by the draft of the survey questions. The survey questions were piloted with a
teacher and an administrative colleague for feedback. Feedback was received on the
amount of time need to take the survey, the clarity of the directions, and questions that
needed clarified or reworded. Once the revisions were made, the survey was emailed to
the math teachers along with the consent form.
The questionnaire contained both closed and open-ended questions. The purpose
of the survey was to gather teacher perceptions, opinions, and experiences on how they
feel about the current math program being used in the district. The survey also asked the
teachers about the interventions and strategies they use in the classroom and their
perceived effectiveness. The survey had 18 questions and a total of 14 teachers
participated.
Follow up letters and requests were sent to those teachers who did not complete
the survey to increase the participation rate. These responses were automatically tallied in

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

48

a Google Spreadsheet for easy manipulation and analysis. This process for collecting
survey data was fast, effective, and efficient. Advantages of this type of survey are that it
is low cost and the data can be collected quickly. The disadvantage that this researcher
found was that it was challenging to encourage the recipients to take the time to complete
the survey therefore making the response rate lower than expected.
Once the data is collected it must be organized to allow for analysis of the math
classrooms. The researcher averages and summarizes the quantitative data into a table.
The teachers are randomly assigned a number name in order to protect their identities and
keep the teacher and student data confidential. The point of this study is not to identify
weak or strong teachers, but instead to identify the common strategies used by each type
of teacher. The high performing and low performing classes and their teachers are
identified by the researcher in order to look more closely at questionnaire responses.
Fiscal implications at this stage of the project are nonexistent or minimal at best.
The quantitative data occur naturally within the school year and are already accumulated
into the grade level’s math spreadsheet. The teachers who decide to complete the survey
do so voluntarily. In the future, the results of the study may determine the level and type
of professional learning provided to the intermediate math teachers. The type of
professional learning and amount of time will determine the cost of substitutes for
teachers and materials for the learning sessions. The positive aspect of this approach is
that there are already days and materials budgeted into the yearly math expense accounts
for professional learning days. Additional expenses are dependent upon the results of the
study and whether a program or specific intervention is identified as one that the entire
district should utilize in the math grades studied.

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

49

Data Collection
The qualitative and the quantitative data is collected sequentially during the
second semester of the school year. The quantitative data is collected first with the help
of the district’s math coach. This district-wide archival data is primarily housed and
maintained by the math coach. The data is used to help her and other administrators plan
professional development and grade level meetings for the teachers throughout the
district.
The first step in collecting the data is to identify the teachers who taught math in
grades three, four, and five from 2016-2018 school years. These teachers are then
assigned a random letter by the researcher to protect their identity. The researcher uses
purposeful sampling to identify the participants. Due to the small number of teachers who
fit this qualifying category, the selection of participants was intentional. Every teacher
who taught or is teaching math in grades three, four, or five during the 2016-2019 school
years was selected. The total number of teachers included in the study is twenty. This
manageable number of participants allows the researcher the time to devote to each
participant in order to more fully understand and describe the results of the data.
The data collected from this sample of teachers may not provide findings that are
transferrable to other settings, but it will provide findings that are specific and meaningful
to the Bellefonte Area School District. Consistency in staffing was noted at Benner
Elementary and Pleasant Gap Elementary as there was less staff turnover, which resulted
in fewer teachers to analyze and more consistent results since these teachers were present
for all three years of the study. Whereas at Marion-Walker Elementary and Bellefonte
Elementary, since they are larger buildings, had more teachers and more teacher turnover.

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50

This led to more teachers to analyze with some not having three years’ worth of data to
study.
Next, the district-wide math data spreadsheets are shared with the researcher by
the math coach. These spreadsheets contain a cohort of students’ summative math data
from kindergarten through the present grade. In order to analyze three years’ worth of
teacher data, three separate cohorts of students needed to be analyzed for each teacher.
These spreadsheets provided student PSSA scores, Classroom Diagnostic Test scores,
and the end of year final percentages on district wide curriculum-based assessments. This
data was extrapolated for each teacher in the study and an overall average was calculated
for their students PSSA proficiency rate, Classroom Diagnostic Test average score, and
the end of year average grade by students on local curriculum-based assessments for each
of the three years. An additional piece of data was collected for teachers in grades four
and five. Their PVAAS three year rolling averages were collected to determine which
teachers had the biggest impact on student growth. All of this information was collected
and organized in numerous tables that are included in the next chapter.
As stated earlier, no teachers or students are identified in the data. All teachers are
given a random number as an identifier. Great care is given to ensure the confidentiality
of the data and other information is not identifiable or included.
Qualitative data is collected in the form of a survey or questionnaire. The purpose
of the questionnaire is to get a descriptive picture of what teaching strategies and
interventions were occurring in each classroom. The survey is completed using Google
Forms and consisted of eighteen questions that are designed to get teacher input about
their classroom math practices. The questions are demographic, attitudinal, and

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

51

behavioral types. There are closed-ended as well as open -ended questions. The data
collected is narrative in nature and does not lend to any type of statistical analysis. The
responses are analyzed for patterns in terminology of strategies and interventions. The
questionnaires are sent to twenty teachers and fourteen submitted survey results.
Questionnaire prompts and responses are found in Appendix A.
Validity
Precautions and checks have been put in place to ensure the validity of the study.
The data samples for the quantitative portion of the study are consistent for each teacher
and class. Each data point is used to determine the successful math classes. They show a
form of overall math achievement for each class. Using three years’ worth of data helps
minimize outlier classes or unforeseen circumstances that invalidate the data. The
qualitative questionnaire data and interviews support each other and are used to clarify
and strengthen the quantitative data.
In assessing the validity of qualitative data, the researcher ensures the
trustworthiness of the data and findings. In order to accomplish reliability, several
methods and sources of data are considered. Triangulation of the data supports the
validity of the researcher’s findings. Four types of quantitative data are used to determine
the achievement or growth of the classrooms and teachers rather than relying on one or
two types of data. This helps ensure the validity of the identification of the achievement
levels in each of the classrooms.
The researcher’s extensive familiarity with the area of study and of the
participants also allow for an accurate analysis of the findings which strengthens the
validity of the study.

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52

The quantitative and qualitative data are equally relevant in supporting the study
and answering the research questions. Both sets of data weigh equally in drawing
conclusions at the end of the study. The qualitative data and interview statements support
the quantitative results.
The final way to assess the validity of the study is through the use of peer
debriefing. Neither of the peers reviewing the study are invested personally in the study.
Their review focuses on looking for any inconsistencies or issues with the researcher’s
interpretation of the data. Interpretations of the data and discussions from the researcher’s
perspective are vital for this part of this process. The peer de-briefers identify any
alternative interpretations and possible bias from the researcher. The de-briefers did not
cite any bias or misinterpretations of the data and results.

Closing
This section describes the methodology that is used in the study, including the
setting and participants, research plan, data collection, validity, and closing. This study
determines the interventions and strategies that math teachers in the Bellefonte Area
School District are increasing student achievement and growth with in grades three, four,
and five.

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

53

CHAPTER IV
Data Analysis and Results
Introduction
In this chapter, the analysis and results of the data collected will be described and
summarized in order to answer the research questions. The questions that will be
answered are: What instructional strategies or interventions are teachers using in the
Bellefonte Area School District to increase growth in student math skills? How has
departmentalization in elementary schools aided students in their math growth or
hindered their progress? What professional learning opportunities does the district need
to provide teachers to ensure more consistent use of intervention strategies as well as data
protocols?
Data Analysis
To answer the research question about effective math interventions and strategies
being used by teachers in grades three, four, and five in the Bellefonte Area School
District, the efficacy of the participating teachers must first be analyzed. In this study,
effective teachers are identified by comparing their three-year average scores on three to
four sets of data depending on their grade level. Third grade teachers are ranked and
analyzed by looking at PSSA scores, end-of-year Math Benchmark average scores, and
Spring Classroom Diagnostic scores. The same data is used for fourth and fifth grade
teachers along with PVAAS teacher specific data. After collecting and organizing this
data, the data set rankings for each teacher were averaged to determine the final overall
ranking of each in the study. The questionnaire responses from the top two teachers from

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

54

each grade level were then compared and analyzed to determine if any trends existed
within their classroom structures or instructional approaches. These trends would be
identified as the effective math interventions or strategies used by district teachers.
The process used for answering the research question concerning the effectiveness
or lack of effectiveness of departmentalization was to analyze three sets of data. PSSA
and PVAAS data prior to and after departmentalization as well as teacher responses from
the questionnaire were the data sets used for this question. Fourth and fifth grade PSSA
math proficiency rates were compared over a four-year window prior to and after
departmentalization. PVAAS three-year Growth Measures were collected to analyze the
growth of students prior to and after departmentalization. Teacher perceptions were also
considered and compared to the academic data that was collected.
The final question concerning teacher professional learning utilizes the
questionnaire responses from the teachers and the findings from the first research
question. Commonalities were identified in the questionnaire responses, and the strategies
used by the most effective teachers helped in formulating the professional learning needs
of the district.
Results
For the first research question, teachers were ranked from highest to lowest on
each of the data sets available for the teacher and grade level. Teacher rankings were
based strictly on student achievement and growth scores. Their ranking average is shown
in the final table. These rankings enabled the researcher to identify the top-tier math

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

55

teachers in each grade level so that their habits and pedagogy could be more closely
studied to see what makes them more successful than other math teachers.
Looking at only the PSSA proficiency percentages in Table 7, five out of the top
seven teachers are third grade teachers. The other two teachers are fourth grade teachers.
The remainder of the fourth and fifth grade teachers can be found in the middle and
toward the lower end of the scores. Three out of the top five teachers in this data set are
from the same school.
Table 7
PSSA 3 Year Average
Ranking
1.
2.
3.
3.
3.
4.
5.
6.
6.
7.
7.
7.
8.
9.
10.
11.
12.
13.
14.
15.

Teacher-Grade
5-3
20-3
14-4
19-3
11-3
7-3
4-4
16-3, 5
8-3
17-3
12-3
1-5
9-5
3-5
10-4
6-3
2-3
15-3
13-4
18-5

PSSA 16-17
70
78
73
67
N/A
68
67
3-76
68
N/A
N/A
55
61
76
59
63
50
39
39
40

PSSA 17-18
90
77
80
82
71
67
70
60
62
N/A
N/A
75
N/A
54
58
63
53
67
53
40

PSSA 18-19
81
83
65
71
74
79
72
59
N/A
63
63
59
N/A
51
61
44
44
38
50
45

3-Year Avg.
80
79
73
73
73
71
70
65
65
63
63
63
61
60
59
57
49
48
47
42

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

56

Looking at the end-of-year Benchmark Assessment Data, a similar trend is
evident as with the PSSA data. Third grade teachers dominate the top four spots with
seven teachers, while a fourth grade and a fifth-grade teacher share the fifth spot.
The Classroom Diagnostic Test scores are interesting, as the scores show an
inverse in the rankings compared to the PSSA and the EOY Benchmarks. Fourth and fifth
grade teachers have scores much higher than the third-grade teachers. One explanation
may be that third grade is the first year that students take the CDT and other online
assessments, whereas the older students have had one or two additional years of
experience with these types of assessments. The assessment rankings are indicated in
Tables 8 and 9.
Table 8
Benchmark Assessment End-of-Year Avg.
Rank
1.
1.
1.
2.
3.
4.
4.
5.
5.
5.
6.
6.
6.
6.
6.
7.
7.
7.
8.

Teacher
5-3
20-3
7-3
11-3
19-3
17-3
15-3
14-4
18-5
9-5
1-5
3-5
10-4
16-3, 5
12-3
4-4
13-4
2-3
6-3

EOY Avg. 16-17
86
91
88
N/A
82
N/A
83
82
77
83.7
81
83
79
83-3
N/A
80
79
78
81

EOY Avg. 17-18
90
87
86
84
87
N/A
87
81
85
N/A
84
78
83
81-5
N/A
79
81
80
78

EOY Avg. 18-19
87
87
89
89
89
84
81
87
86
N/A
81
86
83
83
82
80
80
83
74

3-Year-Avg.
88
88
88
87
86
84
84
83
83
83
82
82
82
82
82
80
80
80
78

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES
Rank
9.

Teacher
8-3

EOY Avg. 16-17
73

57
EOY Avg. 17-18
72

EOY Avg. 18-19
N/A

3-Year-Avg.
73

Table 9
Classroom Diagnostic Test 3-Year Avg.
Rank

Teacher

CDT 16-17

CDT 17-18

CDT 18-19

1.
2.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.

14-4
9-5
4-4
1-5
3-5
18-5
10-4
20-3
16-3, 5
13-4
5-3
11-3
12-3
19-3
7-3
6-3
8-3
17-3
15-3
2-3

1024
1003
1015
984
1023
964
945
917
860-3
908
880
N/A
N/A
845
869
887
871
N/A
802
804

1,082
N/A
1001
1008
939
952
984
1000
997-5
951
955
885
N/A
886
877
855
842
N/A
857
808

991
N/A
993
979
960
962
946
932
974-5
903
907
938
897
930
897
863
N/A
829
776
821

CDT 3Year
Avg.
1,032
1,003
1,003
990
974
959
958
950
944
921
914
912
897
887
881
868
857
829
812
811

The final set of data to analyze is the PVAAS Teacher Specific Rating. This data
is available for only fourth or fifth grade teachers with at least three years of PSSA data
prior to the rating being calculated. The scores are represented in Table 10.

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

58

Table 10
PVAAS Teacher Specific Rating*
Rank

Teacher

PVAAS 16-17

PVAAS 17-18

PVAAS 18-19

PVAAS
3-Year
Avg.
1.
14-4
3.0
3.0
3.0
3.0
2.
4-4
3.0
2.3
3.0
2.8
3.
18-5
2.0
2.3
2.3
2.2
4.
10-4
1.9
2.15
2.3
2.12
5.
3-5
1.8
1.65
.47
1.31
6.
13-4
.43
.45
3.0
1.29
7.
1-5
1.5
1.0
.41
.97
*Grade 3 teachers do not receive a PVAAS Teacher Specific Rating. Grade 4 and 5 teachers must
have three years worth of data before a PVAAS rating is given.

In order to summarize Tables 7-10 and use all the data to determine the effective
teachers for each grade level, teacher rankings in the data categories were averaged to
come up with a final ranking. Table 11 shows the most effective math teachers in the
Bellefonte School District based on the data collected and analyzed in this study.
Table 11
Average Ranking of Effectiveness
Overall
Rank

Average

Teacher/Grade
Level

PSSA
Rank

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.

2.5
3.3
4.0
4.0
5.0
5.3
5.8
6.0
6.3
6.3
6.5

14-4
20-3
5-3
4-4
9-5
11-3
1-5
3-5
19-3
7-3
10-4

3
2
1
5
8
3
7
9
3
4
10

Benchmark
EOY
Rank
5
1
1
7
5
2
6
6
3
1
6

CDT
Rank

PVAAS
Rank

1
7
10
2
2
11
3
4
13
14
6

1

2

7
5

4

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES
Overall
Rank

Average

Teacher/Grade
Level

PSSA
Rank

12.
13.
14.
15.
16.
17.
18.
19.
20.

6.7
7.0
8.3
9.0
9.3
10.3
11.3
11.7
12.7

16-3, 5
18-5
12-3
13-4
17-3
8-3
6-3
15-3
2-3

6
15
7
14
7
6
11
13
12

Benchmark
EOY
Rank
6
5
6
7
4
9
8
4
7

59
CDT
Rank
8
5
12
9
17
16
15
18
19

PVAAS
Rank

3
6

As can be seen from the Table 11, teacher 14 had the overall highest average
ranking from the data analyzed. Unfortunately, this teacher is no longer teaching in the
district, and questionnaire data was not able to be collected. The same is true for the
teacher ranked in the fifth spot, teacher 9. Therefore, the remainder of the data analysis
for this research question will focus on the teachers who are still in the district and have
submitted questionnaire responses.
Fourteen out of twenty teachers submitted questionnaire responses. This
researcher will focus on the responses from the top two teachers in each grade level in
order to identify the strategies and interventions being used in their classrooms that are
helping their students be successful. The remaining survey teacher questionnaire results
will be found in Appendix B. The teachers and their schools are listed in the Table 12.
Responses from the teachers were compared by grade level and then all together with the
other grade levels to identify commonalities and differences.

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

60

Table 12
Top Ranked Teachers
Grade

Teacher

School

3

20

A

3

5

D

4

4

B

4

10

A

5

1

D

5

3

A

Triangulation was accomplished by comparing three or four sets of academic data
to determine the most effective teachers in each grade level. Also, six teacher
questionnaire responses were used to identify commonalties and consistencies in the
responses.
Table 13
Grade 3 Teacher Responses
Survey Question
What data are you utilizing
to inform your instruction?

Grade 3 Teacher 5
Daily exit tickets (RSAs)

Grade 3 Teacher 20
Observation of whiteboard
work during the lesson. I
check the independent
practice page in the students'
math journals. After every
few lessons I give an

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

61

How many times a week
do you review data to
inform your instruction?

3-4

assessment. Also, the end of
unit assessment.
Each day

How effective do you feel
your data analysis process
is in informing your
instruction.

4

4

How many times a week
do you meet in small
groups or with individual
students during math
class?

4-5

4-5

How do you feel about the
effectiveness of your
differentiated instruction
for math?

3

4

What components of the
Everyday Math program
are you using daily in your
instruction?

I used the first two
components as a modified
whole group lesson, and I
used the journal pages as
the backbone of the
guided practice.
EDM laid out a scope and
sequence that created a
good structure for student
learning. I also thought
the structure of the
lessons were okay with
modification. I also
thought the RSAs, again
with modification,
created valuable data that
could then be used to
guide instruction. I
thought the homework
component was very
weak. Students fell into
one of two groups; the
first could get it done in
less than 5 minutes and

I use the Math Journal pages.
Depending on the lesson, I
will use the manual to teach
it. Other times, I just take the
skill and teach it my own
way.
A weakness is the spiral.
Since third grade did not
group their lessons together,
students will often forget a
skill by the time we come
back to another lesson of it. I
think there are better ways to
incorporate reviews and
spirals than the way EDM
does. I also think there needs
to be more math word
problems. If students have a
good number sense, EDM
does a nice job teaching
various strategies, but it also
can confuse students who do
not have good number sense.

What are your impressions
on the strengths and
weaknesses of EDM?

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

What instructional
strategies are you using
with ALL students that are
outside of the of the
Everyday Math program?
Please indicate how often
you utilize the strategy.

What math interventions
are you using with your
students that you have
found to be successful in
promoting student growth?

What math basic fact
automaticity interventions
are you using with your
students that you have

got it done walking out to
the bus on the way home.
The second didn't
understand it at all, and
the homework just caused
frustration. Another
weakness was the lack of
transfer built into the
program on how to
answer an open-ended
question or attack a
multiple-choice math
question.
Almost every day IXL –
this was very important.
It allowed for
independent practice
assigned to the skill
taught in the whole group
lesson. I also used Math
Fact Pro almost every day
to practice math facts. I
also brought in practice
strategies on a weekly
basis that exposed
students to the format of
the PSSA test and
responding to open-ended
questions.
Intervention is hard in
math because of the way
math builds on each
component as building
blocks of understanding.
Once a student misses too
many of those building
blocks, they fall behind to
the point where what the
standard is doesn't make
sense to them even with
interventions.
Math Fact Pro worked the
best. It was a 5-minute
session (what the research
shows is best) that could
be done every day. The

62

Not following the EDM
lesson as is and teaching it in
small group each day. Fact
practice daily using Reflex
Math. I also have the
students complete study
guides to review prior to end
of unit assessments. The
students also play a mix of
EDM games and other
games I purchased on
Teachers Pay Teachers to
review skills (this is one of
their math stations).

Daily small group
instruction and reteaching
lessons as needed. Reflex
Math is helping with the fact
mastery.

Reflex Math

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

found to be successful in
promoting student growth?

What are your feelings
about the effectiveness of
departmentalization for
math instruction in grades
4 and 5?

What professional learning
opportunities do you feel
would be beneficial to you
and the other staff
members of the Bellefonte
School District?
How do you deliver your
math lessons?

Do you assign math
homework? If so, how
often?
What technology programs
do you find helpful and
how often do students use
these programs?

program automatically
took away facts students
mastered and slowly
added new facts for
students to learn.
From what I read, the
research shows there isn't
much of a difference in
student achievement.
However, teacher
satisfaction is better, and
teachers are more
confident in teaching the
subject matter. So, I think
it does help with teacher
morale and allows the
teacher to be a better
"expert."
All answers were based
on my previous
experience in third grade
math.

63

I think it is a great idea, and
I wish 3rd grade would
departmentalize!!!!!!!!!!!!!

More about small group
math.

5-10-minute review using
a Collins Writing
approach, 10-15 whole
group, then guided
practice where the
amount of help
corresponds to student
need
No homework given

math workshop model

IXL!!!, Math Fact Pro,
Google Classroom and
SeeSaw or Google docs –
students would take
pictures of their work and
explain their thinking.

Reflex Math daily. Early
finishes also play Prodigy.

Everyday

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

64

Looking at both of the teachers’ responses in Table 7 provides anecdotal data that
supports the achievement of their students. Both teachers state that they utilize student
data during each lesson to inform their instruction, and both consider their data analysis
process effective. Meeting in small groups is a common strategy in each of their
classrooms, as this occurs 4-5 times a week. When comparing their responses on the
EDM components they utilize, the math journal is used by both, but teacher 20 states that
sometimes, “I just take the skill and teach it my own way.” When discussing programs or
strategies that are utilized outside of the EDM program, teacher 3 listed IXL for
independent practice, Math Fact Pro to reinforce basic facts, and teaching strategies that
focus on open-ended tasks and the format of the PSSA test. Teacher 20 stated again that
not always following the EDM lesson format and focusing more on small group
instruction is helpful. Basic fact practice with the Reflex Math program, study guides,
and other math games during centers are additional strategies mentioned by teacher 20.
When asked to share successful interventions they use with students, teacher 3 did not
feel that interventions were effective for students in math because once their skill deficit
becomes too severe, it is difficult to provide them with an intervention that makes sense
to them. Teacher 20 emphasized daily small group instruction and reteaching lessons
along with Reflex Math. Both stated they use an intervention or program to assist with
the acquisition of basic facts. Teacher 3 uses Math Fact Pro and teacher 20 uses Reflex
Math. Other technology programs used include Google Classroom or SeeSaw for
students to practice explaining their thinking. Each teachers’ approach to teaching the
lessons are not traditional either as teacher 3 utilizes John Collins’ writing strategies,
whole group lesson, and then guided practice. Teacher 20 uses a math workshop model

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

65

where students meet with the teacher in small groups and visit centers when not with the
teacher. One interesting main difference in their classrooms is that teacher 3 does not
give math homework, while teacher 20 assigns math homework every day.
Table 14
Grade 4 Teacher Responses
Survey Question
What data are you
utilizing to inform your
instruction?

Grade 4 Teacher 4
Student performance on
homework, ACI checks,
performance on
assessments, CDT
information
2-3

Grade 4 Teacher 10
MasteryConnect, eSpark,
Wowzers, District Common
Assessment, daily quizzes,
observations

How effective do you
feel your data analysis
process is in informing
your instruction.

4

5

How many times a week
do you meet in small
groups or with
individual students
during math class?

4-5

4-5

How do you feel about
the effectiveness of your
differentiated instruction
for math?

4

4

What components of the
Everyday Math program
are you using daily in
your instruction?

Homelinks, online Daily
lessons

Everyday Math is nearly a
resource – not our
curriculum. Where it is used
as a resource in our
curriculum – I use it. I do not
utilize the online component,
as I use other resources that I

How many times a week
do you review data to
inform your instruction?

Each day

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

What are your
impressions on the
strengths and
weaknesses of EDM?

What instructional
strategies are you using
with ALL students that
are outside of the of the
Everyday Math
program? Please
indicate how often you
utilize the strategies.

EMP, I believe, does a
wonderful job of providing
the foundations for math
exploration. The rationale
is always indicated, and the
actual algorithms take a
back seat to ensuring
students grasp the
mathematical concepts that
provide guidance as they
progress through the
different math disciplines.
EMP provides for the
opportunities to have rich
discussions about ways in
which to solve problems.
A consistent knock on
EMP is the lack of
opportunity for practice
with basic facts, and I do
supplement, especially with
multiplication fact
acquisition. However, this
idea that we need to
revamp our math
curriculum is not held by
me, especially when we're
sliding back into more of a
traditional math class.
I do like "Reflex Math" for
purposeful fact practice.
All kids seemingly have
benefitted from the use of
the program. Occasionally,
I will use aspects of Khan
Academy to assist with a
strategy or algorithm
assistance.

66

feel are much more
beneficial.
Spiraling is a strength and
how they help students to
conceptualize the content
using manipulatives and
various strategies.
Weaknesses include "too
many strategies" presented
that students never do one
really well. Also, they
sometimes touch on a concept
briefly and then move on.
Some students need
consecutive days and
repetition to grasp a concept.
Also, EDM does not fully
align to the PA Math
Standards.

We are utilizing "guided
math" with math centers.
Students meet with me for a
small group lesson of 4-6
students. We cover the main
math concept in the
curriculum using a EDM or
Engage NY lesson... or a
lesson that is appropriate to
cover the eligible content
standard. Students finish the
lesson with a Google Forms
quiz to check their
understanding. When
students are not with me, they

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

What math interventions
are you using with your
students that you have
found to be successful in
promoting student
growth?

Reflex Math and simply
adhering to the tenants of
EM. I don't believe I'm
knowledgeable enough to
deviate from EM, as I do
not hold a degree in
mathematics instruction.
But I believe strongly that
students can progress quite
well when we maintain the
consistency of EMP and

67

rotate through other centers.
One of these is the
technology center, where
students do Reflex math to
work on their math fact
fluency. After doing Reflex
in this center, they move onto
eSpark. eSpark is a program
that assesses each student and
puts each of them into a
learning path appropriate for
their math understanding.
This program does a great job
at differentiating. The other
center is student teacher led.
Students engage in a
Constructed Response Task
or a Quick Check on a
specific standard. One day
students do a constructed
response task and then the
next quick check... rotating
back and forth between the
two. The student teacher
provides on-demand
interventions and instructions
if needed. The last center is
the game center. Students
engage in partner games to
practice various math skills,
standards, and concepts.
Throughout the course of the
math class – students can get
four or more math skills,
concepts, or standards.
eSpark – it differentiates for
each individual student. It
provides pre and posttests
AND provides students with
instruction and practice in a
child-friendly format.

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

What math basic fact
automaticity
interventions are you
using with your students
that you have found to
be successful in
promoting student
growth?
What are your feelings
about the effectiveness
of departmentalization
for math instruction in
grades 4 and 5?

What professional
learning opportunities
do you feel would be
beneficial to you and the
other staff members of
the Bellefonte School
District?

not pick and choose as so
many seemingly are doing.
Reflex Math and practice
sheets focusing on fact
acquisition in
multiplication.

I think it has enabled me to
focus on specific courses of
study, but I believe it
comes at a cost as well.
Having taught for many
years, I always considered
myself a 4th grade teacher,
not a math or science
teacher. I do not know the
strengths and weaknesses
of my students like I did
when I taught one group of
students all day. However,
I'm not sure that this is
possible with the
expectations placed on
everyone with all the
programs we're expected to
know and know well.
I'd love to see more
professional opportunities
for all math teachers,
especially newer ones
learning the philosophy and
practices of the EMP.
However, I think that ship
has sailed, and we'll simply
have more fragmentation of
the math program as
individuals make decisions
as to the order of
instruction and the
elimination of certain
lessons and units.

68

Reflex Math

I am a better math teacher
due to departmentalization. I
put more time and effort into
my one subject area being
taught rather than having to
spread myself thin over
several subjects. I am also
able to delve into data for my
one subject and specifically
target it. I'm not stealing time
from another subject to make
time up for one in which a
lesson went longer. All my
time is strictly devoted to
math.

With using MasteryConnect making common
interventions that teachers
could implement and pull
from would be extremely
helpful. Within
MasteryConnect you can see
easily where your students
need additional instruction
and interventions and it
would be nice to have a PL to
address next steps.

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

69

How do you deliver
your math lessons?

primarily whole group
instruction

math workshop model

Do you assign math
homework? If so, how
often?

3-4 days a week

Everyday

What technology
programs do you find
helpful and how often
do students use these
programs?

Reflex Math and students
engage in it about 3 times
per week in the classroom.

eSpark and Reflex math - we
use them daily

Looking at the 4th grade teacher responses from Table 8 show that both teachers
utilize data at least 2-3 times a week to inform instruction. Both use assessment
information and daily checks to inform instruction. Teacher 10 does this every day. Small
group instruction is a key component of both of their classrooms as they stated they meet
4-5 times a week with small groups. They did differ a bit on their use of the EDM
resources. Teacher 4 uses EDM online components, whereas teacher 10 uses the online
components as they best fit the student needs for that lesson or will supplement with
other resources. Guided Math was listed as an additional instructional strategy used by
teacher 10. Within the guided math lesson are additional centers or stations that students
rotate through each day. One noteworthy center is a constructed response center. Both
teachers express that Reflex Math is effective for reviewing and practicing basic math
facts. Teacher 4 also stated that Khan Academy can be helpful for some concepts.
Teacher 10 utilizes eSpark with the students. Reflex Math and eSpark were also
mentioned as interventions being used to promote student growth and these are
predominantly the only technology-based programs used by these teachers. They both
also differed in their delivery of math lessons as Teacher 4 uses traditional whole group

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

70

instruction, but teacher 10 uses a math workshop/Guided Math model. Homework
appears to be a key piece of promoting student growth in both classrooms as they assign
homework three or more times a week. One interesting statement made by teacher 4 was
that this teacher does not believe in deviating from the EDM lesson plans and follows the
scope and sequence closely.
Table 15
Grade 5 Teacher Responses
Survey Question
What data are you utilizing
to inform your instruction?

Grade 5 Teacher 1
A combination of student
observation, check-ins,
journal work, morning
work, Mastery Connect
CDT's, and PSSA's.
How many times a week do 2-3
you review data to inform
your instruction?

Grade 5 Teacher 3
Math assessments; daily
observations; review the
homework.

How effective do you feel
your data analysis process
is in informing your
instruction.

4

4

Each day

How many times a week do 3-4
you meet in small groups
or with individual students
during math class?

2-3

How do you feel about the
effectiveness of your
differentiated instruction
for math?

4

4

What components of the
Everyday Math program
are you using daily in your
instruction?

I use parts of the EDM
lessons in the manual and
the student journals.

Mostly the daily lesson,
whole group, small group,
independent work.

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

What are your impressions
on the strengths and
weaknesses of EDM?

71

Most of the lessons are
standards-based, but I have
found myself doublechecking because I don't
want to waste time
teaching non-standardsbased concepts. EDM does
not "spiral" effectively, so I
revisit the more difficult
skills during guided math
lessons. The open-response
tasks are not "rich" enough,
so I use outside resources
to fill the gap.
I think any instructional
strategy I use is in the
EDM program.

Strengths are they give the
students multiple strategies
and some flexibility in the
way they solve the
problems. Weaknesses –
sometime they put too
much into one lesson and
it can be overwhelming to
some students.

What math interventions
are you using with your
students that you have
found to be successful in
promoting student growth?

Small-group instruction,
eSpark, Reflex, IXL.

Mostly small group and
adapted homework sheets.

What math basic fact
automaticity interventions
are you using with your
students that you have
found to be successful in
promoting student growth?

Reflex is a great program
to promote automaticity.

Online programs and
activities such as Math 24.

What are your feelings
about the effectiveness of
departmentalization for
math instruction in grades
4 and 5?

I really like
departmentalization
because it has allowed me
to really focus on two
subject areas at a time
(math and science or math
and social studies
depending on the time of
year) instead of several.
When I am more focused, I
deliver better instruction

It is good in a sense that all
the students are getting the
same instruction from the
same teacher. It allows us
as the teacher to focus on
the specific strategies and
we're able to work with the
struggling kids. One
negative would be the time
constraints at times.

What instructional
strategies are you using
with ALL students that are
outside of the of the
Everyday Math program?
Please indicate how often
you utilize the strategy.

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

What professional learning
opportunities do you feel
would be beneficial to you
and the other staff
members of the Bellefonte
School District?

How do you deliver your
math lessons?

for the students, leading to
better understanding and
learning. I feel it's very
effective and hope it stays!
It would be great to
collaborate with 4th and
5th grade math teachers to
see how they use existing
resources and learn what
other effective resources
they use. Also, I would like
to see how they use Google
Classroom (or other techrelated programs) for math.
A combination of the two
approaches.

72

Grade level and
department meeting.

A combination of the two
approaches.

Do you assign math
homework? If so, how
often?

3-4 days

Everyday

What technology programs
do you find helpful and
how often do students use
these programs?

eSpark (average 3 times a
week), Reflex (average 3
times a week), IXL (almost
every day when teaching a
unit)

In the past I have used
Zearn and
MathGames.com.

The grade 5 responses from Table 9 show that both teachers utilize daily
observation of students to inform instruction along with reviewing student work like
homework and journal work. Data is utilized by teacher 1 two or three times a week and
teacher 3 uses data each day. They both utilize small group instruction at least two to
three days a week. They also stated that they use the EDM resources as the basis of their
instruction with little deviation. Teacher 1 stated in the question about strengths and
weaknesses of the program that the spiraling component does not provide enough review
for the students on certain topics which requires additional review during guided math
lessons. The open-response tasks are also not rich enough in this teacher’s opinion and

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

73

require modifications or additional resources. Both teachers stated that small-group
instruction is an intervention that has promoted student growth. Teacher 3 also stated that
adapted homework sheets are helpful, while teacher 1 mentioned eSpark, IXL, and
Reflex Math. Reflex Math was again mentioned as a basic fact intervention that has been
successful with students and teacher 3 stated online programs and Math 24 have been
helpful. Both teachers utilize a combination of whole group and a math workshop model
to deliver lessons and homework is assigned three or more days a week by both teachers.
After determining the most effective math teachers in each grade level and
comparing their responses on the questionnaire, the following can be summarized about
effective math interventions and strategies. Small group instruction is present in some
form in all six classrooms. Some teachers refer to it as Guided Math, others call it a math
workshop approach. Regardless of the terminology a form of differentiated small group
instruction is taking place in the classrooms. In conjunction with this is the use of
learning centers or stations to reinforce other math skills. These skills could include basic
fact practice, open-ended response activities, review of previously taught content, other
on-line math programs.
Another commonality found between the successful teachers is the use of
technology. Each of teachers mentioned multiple ways that technology is being used in
their classrooms to support and enhance student growth. The most popular program being
used is Reflex Math. This is a program that was purchased by the district this past year to
improve students’ basic fact retention. Teachers are finding success with it and students
are also liking the program. Teachers also mentioned programs like IXL, eSpark, as well
as others that they are finding to be helpful. Google Classroom was also mentioned as a

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way for students to explain, show, and share their work on open-ended tasks with their
teacher or other students.
The emphasis on mastering basic facts to improve students’ computational
fluency is also a common strategy seen in the responses. Through the use of on-line
programs like Reflex Math, these teachers are providing students the opportunity to
improve their basic recall math facts.
Extra practice on constructed response or open-ended tasks is another area that
these top tier teachers devote extra time to with their students. One described this as
creating additional activities and opportunities for students to practice their skills as
opposed to relying on the EDM open ended response activities. This teacher described
the tasks in the EDM program as not “rich enough” for the students.
Finally, an emphasis on data is seen in their daily instruction. Each of the teachers
uses data to inform their instruction at least 2-3 times a week. They each feel strongly
about their data analysis skills as they all rated themselves at a 4 or 5 which equates to
effective to very effective. Knowing their students’ strengths and weaknesses through the
use of data and planning instructional activities is a key to their students’ success.
The next research question to be answered is concerning departmentalization and
how it has or has not assisted with student growth in math. For this question the
researcher looked at three pieces of data to triangulate the findings. The data included
teacher’s questionnaire responses in Table 10, grade level PSSA math proficiency data
and PVAAS Value-Added Reports shown in Tables 11 and 12.

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Table 16
Effects of Departmentalization Questionnaire Responses
What are your feelings about the effectiveness of departmentalization for math
instruction in grades 4 and 5?
It is good in a sense that all the students are getting the same instruction from the same
teacher. It allows us as the teacher to focus on the specific strategies and we're able to
work with the struggling kids. One negative would be the time constraints at times.
From what I read the research shows there isn't much of a difference in student
achievement. However, teacher satisfaction is better and teachers are more confident in
teaching the subject matter. So, I think it does help with teacher morale and allows the
teacher to be a better "expert".
I think it has helped me to become a better math teacher because it has allowed me to
focus more on math and has given me more time to develop different activities to help
engage students.
I love it! I feel I spend more time focusing on the specific needs of my students and it
allows me the freedom to plan intensively for just math. I have become a better teacher
being able to just focus on math instruction.
I think it is a great idea and I wish 3rd grade would departmentalize!
I really like departmentalization because it has allowed me to really focus on two
subject areas at a time (math and science or math and social studies depending on the
time of year) instead of several. When I am more focused, I deliver better instruction
for the students, leading to better understanding and learning. I feel it's very effective
and hope it stays!
I think it has been very effective. I am a more knowledgeable teacher and all of my
professional learning opportunities are used to make me a more effective teacher.
I am a better math teacher due to departmentalization. I put more time and effort into
my one subject area being taught rather than having to spread myself thin over several
subjects. I am also able to delve into data for my one subject and specifically target it.
I'm not stealing time from another subject to make time up for one in which a lesson
went longer. All my time is strictly devoted to math.
I think it has enabled me to focus on specific courses of study, but I believe it comes at
a cost as well. Having taught for many years, I always considered myself a 4th grade
teacher, not a math or science teacher. I do not know the strengths and weaknesses of
my students like I did when I taught one group of students all day. However, I'm not
sure that this is possible with the expectations placed on everyone with all the
programs we're expected to know and know well.
I feel it is very effective. This was my first-year teaching in a departmentalized grade
and I thought it was beneficial to focus on teaching just math and science.

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Teachers are obviously proponents of departmentalization based on the comments
from the questionnaire. They reported being more comfortable and confident in teaching
the subject matter. They feel they are better prepared and are content experts. They also
benefit from their professional learning being more differentiated and pertinent to their
daily work with students. But, the academic data shown in the tables below does not
support the teacher’s views and opinions as far as it making a positive difference in
student performance.
Table 17
PSSA Math Proficiency Rates
Year

4th Grade

2011-12 through
77%
2014-15-Prior to
Departmentalization
2015-16 through
66%
2018-19Departmentalized

5th Grade

Overall

73%

75%

58%

62%

PSSA math proficiency rates decreased significantly in both departmentalized
grade levels over the four years of core content instruction being departmentalized.
The three-year window prior to departmentalization for the fourth and fifth grade
students across the district shows significant evidence of meeting the standard for
Pennsylvania Academic Growth. The opposite is true for the 2017-2019 three-window
within the departmentalized setting. There is moderate evidence of students not meeting
the standard for academic growth.

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Table 18
PVAAS Math 3 Year Growth Measure-PVAAS Value Added Reports
Years

4th Grade

5th Grade

Overall

2013-2015

2.3

2.6

2.5

2017-2019

2.2

-3.2

-0.5

Even though the teachers feel that departmentalization benefits students in the
Bellefonte Area School District the academic data is not supporting their feeling. Growth
and proficiency rates have dropped dramatically. There may be other reasons for this
drop, but this data is not supporting departmentalization in math at this time.
The final research question to be answered centers around the professional
learning needs of the teachers as they relate to consistent data protocols and effective
strategies or interventions to assist students. Table 13 shows teacher responses to the
questionnaire regarding this topic. Triangulation of this data was not achieved as the only
pieces of data used were the teacher questionnaire responses.
Table 19
Professional Learning Questionnaire Responses
What professional learning opportunities do you feel would be beneficial to you
and the other staff members of the Bellefonte School District?
I feel that we have a strong foundation when teaching math to our students. I think
professional learning opportunities could be more with how to teach the EDM lessons
using a math workshop model and how to use Mastery Connect to differentiate
More on teaching kids through a math workshop approach and using a flipped
classroom approach to teaching.
A math workshop approach.

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What professional learning opportunities do you feel would be beneficial to you
and the other staff members of the Bellefonte School District?
I'd love to see more professional opportunities for all math teachers, especially newer
ones learning the philosophy and practices of the EMP. However, I think that ship has
sailed, and we'll simply have more fragmentation of the math program as individuals
make decisions as to the order of instruction and the elimination of certain lessons and
units.
With using MasteryConnect - making common interventions that teachers could
implement and pull from would be extremely helpful. Within MasteryConnect you can
see easily where your students need additional instruction and interventions and it
would be nice to have a PL to address next steps.
It would be great to collaborate with 4th and 5th grade math teachers to see how they
use existing resources and learn what other effective resources they use. Also, I would
like to see how they use Google Classroom (or other tech-related programs) for math.
More about small group math.
I would love to have some time dedicated to guided math. To discuss and learn
strategies that work well and to learn how to implement it better. It is a fantastic
structure for math and I would love to see others move in this direction. It is easier for
me since math is all I plan for. I imagine as a 3rd grade teacher it would seem
overwhelming trying to create lessons in all the different subject areas, but having time
in a professional learning session to create the structures and the materials would be
helpful.
Integrating technology in a meaningful and useful way into math instruction.
Sometimes I do not feel like I get the most out of a 1:1 setting. I think this could be a
very powerful differentiation tool that I do not think I use to the fullest potential.
Grade level and department meeting.

Professional learning centering around small group instruction or guided math
was mentioned multiple times in the responses. This fits well with what the top tier
teachers in the district are currently doing with their students. The district has recently
adopted MasteryConnect to help with collecting and analyzing data. Some teachers
responded that professional learning in using MasteryConnect is necessary. Other
common themes in their responses was collaboration and common planning time with
their grade level teachers across the district, integrating technology in meaningful ways,
and time to learn or refresh their learning about the philosophy and practices of the EDM
program.

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Discussion
The focal point of this research project was to determine strategies used in the
classroom to increase the success of Bellefonte Area School District math students and
teachers. The questions that were answered identified the effective practices and
interventions that are found in the most successful classrooms, the effect of
departmentalization on math achievement, and determined the professional learning
needs of math teachers.
It was very interesting in determining the most successful math teachers in the
district. The researcher used the most appropriate data available and found that the
teachers who many thinks are strong teachers were confirmed to be strong teachers, but
some of the previously thought of weaker teachers were determined to be just as strong or
stronger based on the data used in this study.
The findings for the research questions did not surprise the researcher. This study
solidified what many educators know in the Bellefonte Area School District is best
practice and what needs improved. Differentiated, small group instruction or as some are
calling Guided Math was a strategy for many of the successful teachers. More
clarification and professional learning on what this look like in the classroom are
needed. Reflex Math is an online program that teachers in the district should continue to
use to enhance students’ basic fact acquisition as it was identified as beneficial to
students in the successful classrooms. This was good information as the district
purchased this program last year for all students in grades 2-5. Knowing that it is being
used and that teachers are seeing it make a positive difference in student growth justifies
the expense in the upcoming year. Consistent use of on-line programs or resources may

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be another area for the district look into as many teachers are utilizing a variety of
programs based on their interests or likes. Using programs that match what students need
and that provide accurate progress monitoring would be beneficial. Data is another area
that teachers say they are doing and that they feel they are doing effectively, but again the
consistency of data collected as well as its use could be improved on. Teachers also
emphasized areas that they enhance with other activities or resources like basic facts
practice or open -ended response questions. Gaining consistency across the district with
the areas that are being enhanced would be helpful to students and teachers.
The data collected about departmentalization confirms some of the research found
in the review of literature. Teachers confirm in their questionnaire responses that they
feel like they are becoming content area experts. This is documented in previous studies
about departmentalization. The inconsistency of student academic gains is also
documented. This study shows that the Bellefonte Area School District may want to take
another look at departmentalization or at least dive deeper into the struggles teachers and
students are having achieving high levels of math success within this structure. Even
though departmentalization is not necessarily an intervention, it is a strategy that is used
to increase student academic gains. This is not happening in this district’s classrooms.
Teachers do not feel as overwhelmed and their morale may be improved, but is it at the
expense of student growth and possibly even relationships with students. Much more
research needs to be completed in this area.
The research mentions that professional learning should be tailored to the needs of
math teachers and collaboration with other teachers is beneficial. The Bellefonte Area
School District math teachers who participated in this study also listed collaboration as

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grade level time to meet, discuss, and plan with their colleagues as important. This is an
area that can be implemented during math professional learning days. Also, another
important area to focus on is the strategy of guided math. Teachers have been using
guided reading techniques in the district for over ten years. This same idea needs to
transcend into math classes in order to provide the differentiation that students require to
be successful learners.
Summary
This chapter identified the strategies effective math teachers in third, fourth, and
fifth grade are using with their students in the Bellefonte Area School District. Guided
Math or a math workshop approach, technology use with programs like Reflex Math,
practice on open-ended responses along with more writing and explaining, an emphasis
on mastering basic facts, and data use were areas highlighted by the teachers in this
study. Departmentalization, even though loved by the teachers, is not showing the
academic growth in students as was expected. Further research must be completed to
determine whether the departmentalization is directly impacting student success or are
there other reasons derailing departmentalization. For students and teachers to be smore
successful, professional learning for teachers should be centered around collaboration
with grade level colleagues, Guided Math, use of technology, and consistent data
identification and use.
The final chapter will focus on the findings and how they can be applied to the
Bellefonte Area School District. The fiscal implications of applying the findings will be
identified and described. Additional research topics or questions will be discussed.

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CHAPTER V
Conclusions and Recommendations
Introduction
This study focused on three research questions. The questions sought answers
about effective math interventions and strategies used in the district’s third, fourth, and
fifth grade classrooms, the effects of departmentalization, and the professional learning
needs of upper elementary math teachers.
Academic data was analyzed, effective teachers were identified, and questionnaire
responses were summarized for patterns found in each teacher’s classroom. The
questionnaire responses also provided information about departmentalization and the
professional learning needs of teachers. These findings will be used to improve the
instruction of students and the professional learning of upper-level elementary math
teachers.
Conclusions
The results from this study will be helpful as the district moves forward with the
goal of improving student math achievement and growth. The interventions and strategies
identified by the effective teachers can be targeted in professional learning sessions or at
grade-level math meetings. The identified interventions and strategies are guided math,
concentrated work on open-ended responses, the use of the Reflex Math program for
basic fact mastery as well as other online learning programs, and the use of data to inform
instruction. The findings in this area were not as extensive as the researcher hoped to
uncover more specific ways that the effective teachers were making their students more

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successful. One promising area that was uncovered was the use of and interest in small
group math strategies like Guided Math. Also, the extra practice and work being done by
some teachers on open-ended/constructed response questions is interesting. Is this work
on open-ended/constructed response questions simply making students better test-takers
or is the extra practice on problem solving and explaining their reasoning making them
stronger math students?
The practice of departmentalization in grades three, four, and five was examined.
The questionnaire responses show that teachers are in favor of this organizational
structure. The academic data shows that student achievement and growth have both
declined sharply since the inception of departmentalization in the district’s math
classrooms. The data does not clearly support the use of departmentalization, nor does it
make a strong enough case to eliminate departmentalization. It is helpful to know what
the teachers’ feelings are about departmentalization and how it impacts them
professionally. Teacher views were very consistent across the district.
The information gleaned about effective strategies and interventions, along with
the teacher questionnaire responses will be used to help formulate a professional learning
plan for the district’s elementary math teachers. Areas included in this plan are guided
math training, the effective and consistent use of online math programs, data use and
protocols, and grade-level collaboration. Others areas to investigate would be effective
strategies to teach and practice problem solving skills through open-ended/constructed
response problems.

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Concerns
As stated earlier in the chapter, the results of this study were not as
groundbreaking as hoped for when the study began. The number of strategies identified
was not extensive, but they were conclusive after analyzing the questionnaire responses.
A variety of more specific interventions and strategies were expected to be identified by
the teachers. One reason for these general findings may be that the district has
emphasized complete fidelity in the implementation of the math curriculum and use of
the Everyday Math program for many years. This expectation of fidelity does not leave
much room to explore or incorporate different ideas and resources. Teacher’s feeling the
need to stay rigid with the programming is starting to lessen a little, but many of the
teachers in the study are still uncomfortable deviating away from what they are
accustomed to doing and the prior mandates.
Another concern was the availability and quality of the data used to determine the
effective teachers. Consistent sets of data for each of the grade three, four, and five math
teachers was difficult to find. This simple data issue points to a bigger problem within the
district. Formative as well as summative data sets need to be identified and used
consistently throughout the district. Teachers collect an abundance of data, but the
consistency and quality of data across the district and even within grade levels can be
questioned.
One piece of data the researcher was forced to use was Classroom Diagnostic
Testing data. It was used because the assessment was given across the grade levels
throughout the district. This data must be looked at closely, as the data does not show
achievement or growth; rather, it is more formative for the teacher to plan instruction and

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guide students’ future learning experiences. This data did allow for comparisons between
classes and teachers, but understanding that the data are not providing a summative score
is important to keep in mind. The other data sets such as PSSA proficiency rates, PVAAS
Teacher Specific data, and the students’ end of year averages on the common benchmark
assessments were more definitive and informative for the researcher. Through this
available data, the most effective teachers were identified, but the question still remains
whether different academic data would provide the same results. Regardless, based on the
data available and the teachers identified, common interventions or strategies were
identified.
The questionnaire responses used to identify perceptions about
departmentalization and professional learning needs were adequate, and the results will
be helpful as the future of the district is discussed. These findings will be beneficial as
the district is beginning work on its Comprehensive Plan. Math is an area of need across
the district and in each of the elementary buildings. The findings about interventions and
strategies will be helpful to include in the plan and will partner well with some of the
other evidence-based strategies that will be included in the plan.
Recommendations
All of the findings from this study will be shared with the district’s math coach
and math interventionist to be included in the work they do with teachers and students.
The math coach schedules grade-level math meetings three to four times a year. All of the
interventions and strategies identified will be part of the teachers’ discussions. Guided
Math is an area that is new to many teachers. Even if teachers feel strongly about their
skills in this area, there is a still a need for professional learning. Differentiation is not

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new for the teachers of the district, but deliberate, planned differentiation in math may be
new to some teachers. Becoming proficient at differentiating math instruction will take
some time and professional learning by the teachers to make it an effective strategy.
Utilizing some of our teachers who are comfortable with guided math to lead the
professional learning sessions will be a key to the success of the initiative.
Additional practice with Reflex Math for students will be recommended to
teachers based on the results of this study. As stated earlier, this program has been
purchased by the district with the purpose of providing a supplement to EDM for basic
facts practice. Students have continued to struggle with the acquisition of basic facts, and
teachers have been utilizing various methods and online programs to attack this issue.
Having one common approach and program will be an asset to the district.
Other technology programs will continue to be analyzed in hopes of settling on
one or two to use with students as an intervention. Currently, teachers are using a variety
of programs. Zearn, IXL, and eSpark are just some of the programs. Another
recommendation from this study would be to identify one or two programs that would be
best to use with students that also have comprehensive data reports that can be analyzed
to track student progress. These programs would be purchased and available for teachers
to use as interventions with students.
The practice of teachers developing special lessons and providing opportunities
for students to work specifically on open-ended math problems requiring an explanation
of their thinking was identified as an area to share with teachers. Like the work done with
text dependent analysis questions in English Language Arts classes, similar work must be
done in math classes. An emphasis on the strategy and thinking behind problem solving

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must be practiced along with showing the work and thinking on paper in an organized
way. This is another area that must be addressed by the district’s math coach through
grade-level meetings or professional learning sessions.
The last area common among the district’s most effective math teachers that must
be addressed involves the use of data. This is a two-fold area of improvement. Data and
data protocols should be analyzed and improved at the district and school level. Then
data analysis and the use of the data must be improved at the classroom and individual
teacher level to make a difference in student growth and achievement. Much of this can
be achieved by consistently utilizing the same assessments throughout the district at
regularly scheduled intervals. Aimsweb Plus is an assessment that is available to teachers
in the district, but in math the program has been used inconsistently in the upper
elementary grades. Classroom Diagnostic Tests should be reviewed to decide if these
data are meeting the needs of the district, especially in comparison to the time involved to
administer the test. Training for teachers should also be included in this plan so that all
teachers understand the assessments and data and are using the same terminology. This
will be very helpful as the district continues to move toward the MTSS model of support
for students.
Departmentalization is another major area that will need to be discussed and
further analyzed. The questionnaire responses show that teachers are in favor of this type
of organizational structure. The math data show that student achievement and growth
have both declined sharply since the inception of departmentalization in the district’s
math classrooms. Data in English Language Arts and Science will also need to be
analyzed to determine if departmentalization has any impact in these areas. Any type of

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deviation from departmentalization will not be popular with teachers and will be another
huge change for parents. This is the best time and the worst time to make a change as
drastic as abandoning departmentalization. With all of the safety concerns about returning
to school under COVID 19 conditions, keeping students together in one classroom with
one teacher makes sense. Schools must also think about major unnecessary changes to
begin a school year that will have an opening day of school like no other opening day in
history. So, this may not be the time to make any changes in the way grades four and five
are departmentalized, but if scores continue to falter it will be an area to look at in the
future.
The Bellefonte Area School District has an amazing professional learning
program that benefits all staff members. The professional learning topics gleaned from
the questionnaire results as well as from the identified strategies and interventions will be
shared with the committee that plans the professional learning days. The math coach,
interventionist, and expert teachers will lead sessions in guided math, open-ended
response strategies, data analysis, and effective use of online programs such as Reflex
Math. This training will be delayed this year as much of our beginning of the year
professional learning time will be focused on opening schools safely and preparing for
the possibility of virtual learning and teaching. Professional learning in math will
become a priority again once the uncertainty of this school year becomes clearer.
The fiscal implications for implementing the results of this study are minimal.
Reflex Math is already purchased by the district for each of the teachers in grades two
through five. There is a professional learning committee in place that will plan and
facilitate sessions throughout the school year. One additional expense may be incurred by

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seeking an outside expert to train staff on guided math if the internal expertise is not
available in this area. This may also need to occur since the district recently transferred a
math coach back to the classroom and will operate with one coach for the entire district.
This coach has been the secondary math coach and does not have experience at the
elementary level. The necessity to purchase an additional online resource may be another
expense as the district continues to look at its data needs as well as its intervention needs.
Overall, the majority of the findings from this study are not costly and can be
implemented with little to no additional expense.
Future Directions for Research
As stated earlier, the effectiveness of departmentalization in the school district
could be researched further to measure its effects on the academic success of students.
Research in departmentalized classes across the curriculum would be needed to see if the
data in English Language Arts or science is similar to the math data. The math data
declined so sharply that a potential change warrants another look. There are positives and
negatives for teachers and students within this structure so the academic data as well as
student and teacher perceptions should be considered.
While analyzing the academic data to determine the effective teachers in each
grade level it was observed that the end of year benchmark exam scores for all of the
teachers in the study were similar. The scores ranged from 73% to 88%, but most of the
scores were clumped closely together in the middle of that range. It would then be
expected that the PSSA scores would also follow a similar pattern, but they did not. One
school’s teachers had the lowest PSSA scores even though their end of year benchmark
scores were similar to the other teachers throughout the district. How are their benchmark

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scores similar, but their PSSA scores drastically lower? Is there a problem with the
fidelity of implementation of the benchmark assessments? There needs to be accurate
data gleaned from the benchmark assessments in order to plan instruction. This may be
an area of improvement for the district.
Does the grade level or building that a teacher is assigned to have more of an
effect on that students’ test scores than the teacher’s skills and pedagogy? Are some of
the best teachers in the district teaching in the toughest buildings or teaching in grades
that are historically low scoring across the district? Could this be affecting their overall
ranking in this study? How can the Bellefonte Area School District support these
teachers and students in the lower performing buildings is another area that should be
investigated?
Another area to further question and research is the effectiveness of the plethora
of online math resources that are available to schools. During these COVID19 times even
more programs have been developed and marketed for schools. Sifting through the
programs to match district needs with the strengths of each programs in order to
determine if any programs would be useful could benefit the district. Having consistent
intervention programs available to teachers and students is important as the district moves
toward an MTSS model of support for students.
Finally, anxiety was a topic that was discussed heavily in the literature review.
Math anxiety did not show up in this study, but it is something to consider as student
performance and even teacher performance is evaluated. Are some students and teachers
suffering from math anxiety? What can be done to alleviate anxiety caused by math
class? These findings could potentially be transferred to other content areas.

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Summary
In order for this study to impact the education of students in the Bellefonte Area
School District, further professional learning for teachers must occur in the areas of
guided math, data analysis, open-ended response questions, Reflex Math, and other
online programs. These areas are identified as strengths in practice by the successful
upper elementary math teachers in the district. Furthermore, if these strategies continue to
show promise they must become common practices utilized in each of the third, fourth,
and fifth grade math classrooms.

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References
Bell, M., & Isaacs, A. (n.d.). The case of everyday mathematics (pp. 9–15). National
Council of Teachers of Mathematics, Inc.
Bellefonte Area School District Future Ready PA Index, Future Ready PA Index
https://futurereadypa.org/District/FastFacts?id=124070145198054143208076158
070133190053167108129
Burns, M. K., Ysseldyke, J., Nelson, P. M., & Kanive, R. (2015). Number of repetitions
required to retain single-digit multiplication math facts for elementary students.
School Psychology Quarterly, 30(3), 398–405. doi: 10.1037/spq0000097
Chan, W. W. L., & Wong, T. T.-Y. (2019). Subtypes of mathematical difficulties and
their stability. Journal of Educational Psychology, 11, 1-18. doi:
10.1037/edu0000383
Crosnoe, R., Morrison, F., Burchinal, M., Pianta, R., Keating, D., Friedman, S. L., &
Clarke-Stewart, K. A. (2010). Instruction, teacher–student relations, and math
achievement trajectories in elementary school. Journal of Educational
Psychology, 102(2), 407–417. doi: 10.1037/a0017762

Mertler, C. A. (2019). Mixed-Methods Research. In Introduction to educational research
(pp. 120-121). Los Angeles, CA: SAGE.

McGraw-Hill. Everyday Mathematics 4 © 2016. (n.d.). Retrieved from
https://www.mheducation.com/prek-12/program/everyday-mathematics-420162016/MKTSP-TRA15M0.html

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

93

Friesen, S., & Francis-Poscente, K. (2014). Teaching and learning mathematics with
math fair, lesson study and classroom mentorship. The Mathematics Enthusiast,
11(1), 61–82. Retrieved from https://scholarworks.umt.edu/tme/
Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J.R., & Witzel, B.
(2009). Assisting students struggling with mathematics: response to intervention
(RtI) for elementary and middle schools (NCEE 2009-4060). Washington, DC:
National Center for Education Evaluation and Regional Assistance, Institute of
Education Sciences, U.S. Department of Education. Retrieved from
http://ies.ed.gov/ncee/wwc/publications/practiceguides/.
Grimes, K. J., & Stevens, D. D. (2009). Glass, bug, mud. Phi Delta Kappan, 90(9), 677–
680. Retrieved from https://doi.org/10.1177/003172170909000914
Haciomeroglu, G. (2017). Reciprocal relationships between mathematics anxiety and
attitude towards mathematics in elementary students. Acta Didactica
Napocensia, 10(3), 59–68. doi: 10.24193/adn.10.3.6
Hollands, F. M., & Pan, Y. (2018). Evaluating digital math tools in the field. Middle
Grades Review, 4(1) Art.8. Retrieved from
https://scholarworks.uvm.edu/mgreview/vol4/iss1/8
Hord, C., & Xin, Y. P. (2013). Intervention research for helping elementary school
students with math learning difficulties understand and solve word problems.
Learning Disabilities: A Multidisciplinary Journal, 19(1), 3–17. doi:
10.18666/ldmj-2013-v19-i1-4789

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

94

Karakonstantaki, E. S., Simos, P. G., Michalis, V., & Micheloyannis, S. (2018).
Assessment and conceptual remediation of basic calculation skills in elementary
school students. British Journal of Developmental Psychology, 36(1), 78–97.
doi: 10.1111/bjdp.12214
Kiger, D., Herro, D., & Prunty, D. (2012). Examining the influence of a mobile learning
intervention on third grade math achievement. Journal of Research on
Technology in Education, 45(1), 61-82. Retrieved from
https://www.scimagojr.com/journalsearch.php?q=21100301445&tip=sid
Leali, S., Bird, D. R., & Tungmala, M. (2012). Instructional strategies and word
problems of english language learners. Journal of the International Society for
Teacher Education, 16(2), 98–109.
Leung, P., & Cohen, R. (2004). Acquisition, development, and propagation of math
anxiety in elementary school. Roanoke, VA: Psychology of Mathematics &
Education of North America. Retrieved from http://www.pmena.org/
Liggett, R. S. (2017). The impact of use of manipulatives on the math scores of grade 2
students. Brock Education Journal, 26(2), 87–101. doi:
10.26522/brocked.v26i2.607
McGrath, C. J., & Rust, J. O. (2002). Academic achievement and between-class
transition time for self contained and departmental upper-elementary classes.
Journal of Instructional Psychology, 29(1), 40–43.

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

95

Mong, M. D., & Mong, K. W. (2010). Efficacy of two mathematics interventions for
enhancing fluency with elementary students. Journal of Behavioral Education,
19(4), 273–288. doi: 10.1007/s10864-010-9114-5
Nelson, K. A., (2014). A study comparing fifth grade student achievement in
mathematics in departmentalized and non-departmentalized settings. (doctoral
dissertation). Retrieved from https://www.semanticscholar.org/paper/A-StudyComparing-Fifth-Grade-Student-AchievementNelson/323f162d7fb8ab517919af589b90168797773c16
Park, S., Stone, S. I., & Holloway, S. D. (2017). School-based parental involvement as a
predictor of achievement and school learning environment: An elementary
school-level analysis. Children and Youth Services Review, 82, 195–206. doi:
10.1016/j.childyouth.2017.09.012
The Pennsylvania Department of Education. PSSA Results. (n.d.). Retrieved November
10, 2019, from
https://www.education.pa.gov/DataAndReporting/Assessments/Pages/PSSAResults.aspx.
Ruff, S. E., & Boes, S. R. (2014). The sum of all fears: the effects of math anxiety on
math achievement in fifth grade students and the implications for school
counselors. Georgia School Counselors Association Journal, 21(1). Retrieved
from https://files.eric.ed.gov/fulltext/EJ1084441.pdf
Sarrell, D. M. (2014). The effects of reflex math as a response to intervention strategy to
improve math automaticity among male and female at-risk middle school

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

96

students (doctoral dissertation). Retrieved from
https://www.semanticscholar.org/paper/The-effects-of-Reflex-math-as-aresponse-to-to-math-Sarrell/f7b795a49a34a12b5ffb39e3060afdca8b7d8918
Tran, N. A., Schneider, S., Duran, L., Conley, A., Richland, L., Burchinal, M., Martinez,
M. E. (2012). The effects of mathematics instruction using spatial temporal
cognition on teacher efficacy and instructional practices. Computers in Human
Behavior, 28(2), 340–349. doi: 10.1016/j.chb.2011.10.003
Ulichnie, S. (2011). The effects of math intervention on student achievement (master’s
thesis). Retrieved from ED560695
Uribe-Flórez, L. J., & Wilkins, J. L. M. (2016). Manipulative use and elementary school
students’ mathematics learning. International Journal of Science and
Mathematics Education, 15(8), 1541–1557. doi: 10.1007/s10763-016-9757-3
Waite, R. D. (2000). A study of the effects of everyday mathematics on student
achievement of third-,fourth-, and fifth- grade students in a large north texas
school district (doctoral dissertation). Retrieved from
https://pdfs.semanticscholar.org/0548/42b289ef426ebf4ca720d95a4339e95ff37e.
pdf
Wendt, S., Rice, J., Nakamoto, J. (2019). A cross-state evaluation of Mind Research
Institutes ST Math program and math performance. San Francisco, CA: WestEd.
Ysseldyke, J., Spicuzza, R., Kosciolek, S., & Boys, C. (2003). Effects of a learning
information system on mathematics achievement and classroom structure. The

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

Journal of Educational Research, 96(3), 163–173. doi:
10.1080/00220670309598804
Zank, A. A. (2015). Teaching strategies for effective fifth grade math intervention
(dissertation). Retrieved from
https://eric.ed.gov/contentdelivery/servlet/ERICServlet?accno=ED557579

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APPENDICES

98

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99

Appendix A
IRB Approval

Institutional Review Board
California University of Pennsylvania
Morgan Hall, 310
250 University Avenue
California, PA 15419
instreviewboard@calu.edu
Melissa Sovak, Ph.D.

Dear Kristopher,

Please consider this email as official notification that your proposal titled
“Math Intervention Effectiveness in the Elementary PSSA Grades”
(Proposal #18-090) has been approved by the California University of
Pennsylvania Institutional Review Board as amended.

The effective date of approval is 8/15/19 and the expiration date is 8/14/20.
These dates must appear on the consent form.

Please note that Federal Policy requires that you notify the IRB promptly
regarding any of the following:

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100

(1) Any additions or changes in procedures you might wish for your study
(additions or changes must be approved by the IRB before they are
implemented)

(2) Any events that affect the safety or well-being of subjects

(3) Any modifications of your study or other responses that are
necessitated by any events reported in (2).

(4) To continue your research beyond the approval expiration date of
8/14/20 you must file additional information to be considered for continuing
review. Please contact instreviewboard@calu.edu

Please notify the Board when data collection is complete.

Regards,

Melissa Sovak, PhD.
Chair, Institutional Review Board

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Appendix B
Letter of Participation

Benner Elementary School
490 Buffalo Run Road
Bellefonte, PA 16823
Telephone: (814) 355-2812

Fax: (814) 353-5339

Mr. Kristopher M. Vancas,
Principal / Attendance Compliance Officer
Bellefonte Area
School District

March 6, 2020
To the Math Teachers of 3rd, 4th, and 5th Grade Students at BASD,
Over the past several years Bellefonte Area School District has experienced little growth,
or even a decline, in student Math scores over time at the elementary level. Elementary
PSSA proficiency rates were 66% in 2015-16, 59% in 2016-17, 63% in 2017-18, and
61% in 2018-19. For the past two years I have been completing coursework as a doctoral
student with the California University of Pennsylvania. I am working on completing my
action research project to answer the following questions:
What instructional strategies are teachers using across the district to increase the growth
in student math skills?
How has departmentalization in the elementary schools aided the students in their math
growth or hindered their progress?
What professional learning opportunities does the district need to provide teachers to
ensure more consistent use of data protocols, as well as appropriate intervention
strategies?

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102

As part of the research project I would like to identify instructional practices and
intervention strategies and programs that teachers are using across the district. My hope is
to be able to identify which instructional practices aided students in achieving significant
gains in their math fact automaticity and overall math growth and achievement. Once
those instructional strategies are identified, I plan on working with the teachers and math
coaches to provide professional learning for all elementary professional staff members.
I am writing to invite you to participate in a survey that will help to identify your use of
data and instructional practices in regards to math achievement and growth. Please know
that the survey is voluntary and you may withdraw from the survey at any time. All
answers to the survey will be kept confidential and only used as part of this research
project. I would expect the survey to take approximately fifteen (15) minutes to
complete. The research project has been approved by the California University of
Pennsylvania Institutional Review Board and the Bellefonte Area School District. This
approval is effective 08/14/19 and expires 08/14/20.
Please let me know if you have any questions about my action research project and how I
plan to utilize the data that I am asking you to provide. I am hopeful that we will be able
to expand on the findings of the research project and offer all teachers of the school
district strategies to engage our students and enrich their learning. If you have any
questions please contact me at 814-280-5029 or van7236@calu.edu. Thank you in
advance for your time and consideration.
Sincerely,

Kristopher M. Vancas
Doctoral Student, California University of PA

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Appendix C
Questionnaire

Elementary Math Interventions Survey
This survey is designed to collect your ideas and instructional practices that you are
utilizing in the classroom with students. The survey is completely optional and all
responses will be kept confidential. I hope to be able to identify the instructional practices
and interventions that our math teachers are using to increase student growth and
achievement in math across grades 3, 4, and 5 in the district. Your information will help to
provide professional learning opportunities for your peers in the future.
Your email address (kvancas@basd.net) will be recorded when you submit this form. Not
you? Switch account
* Required

Please use provide your current elementary building assignment. *
Choose

Please provide the grade level you currently are teaching. *
Choose

How do you deliver your math lessons?
primarily whole group instruction
math workshop model
a combination of the two approaches
Other:

Do you assign math homework? If so, how often?
1-2 days a week
3-4 days a week
everyday
no homework given

What data are you utilizing to inform your instruction?

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

104

Your answer

How many times a week do you review data to inform your instruction?
1 to 2 times
2 to 3 times
3 to 4 times
Each Day

How effective do you feel your data analysis process is in informing your instruction.
Not Very Effective
1
2
3
4
5
Very Effective

How many times a week do you meet in small groups or with individual students during
math class?
2 to 3 times a week
3 to 4 times a week
4 to 5 times a week

How do you feel about the effectiveness of your differentiated instruction for math?
Not Very Effective
1
2
3
4
5
Very Effective

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

105

What components of the Everyday Math program are you using daily in your
instruction?

Your answer

What are your impressions on the strengths and weaknesses of EDM?
Your answer

What instructional strategies are you using with ALL students that are outside of the of
the Everyday Math program? Please indicate how often you utilize the strategy.
Your answer

What math interventions are you using with your students that you have found to be
successful in promoting student growth?
Your answer

What math basic fact automaticity interventions are you using with your students that
you have found to be successful in promoting student growth?
Your answer

What technology programs do you find helpful and how often do students use these
programs?

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

106

Your answer

What are your feelings about the effectiveness of departmentalization for math
instruction in grades 4 and 5?
Your answer

What professional learning opportunities do you feel would be beneficial to you and the
other staff members of the Bellefonte School District?
Your answer

Submit
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Forms

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

107

Appendix D
Questionnaire Responses
Survey Question
What data are you utilizing to inform your
instruction?

Teacher 2
mini quizzes, summative assessments,
observation

How many times a week do you review data
to inform your instruction?

1 to 2 times

How effective do you feel your data analysis
process is in informing your instruction.

3

How many times a week do you meet in
small groups or with individual students
during math class?

1 to 2 times

How do you feel about the effectiveness of
your differentiated instruction for math?

3

What components of the Everyday Math
program are you using daily in your
instruction?

warm-up, focus, homework

What are your impressions on the strengths
and weaknesses of EDM?

I like that it provides many practice problems to
enhance student understanding. I also like that
the warm-up always leads into the focus of the
lesson. I do not find it allows for much
differentiation.

What instructional strategies are you using
with ALL students that are outside of the of
the Everyday Math program? Please indicate
how often you utilize the strategy.
What math interventions are you using with
your students that you have found to be
successful in promoting student growth?

I do small group reteaching based on quick
formative assessments when time allows. This
has proven to be most successful for me.

What math basic fact automaticity
interventions are you using with your
students that you have found to be successful
in promoting student growth?

Reflex Math

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108

What are your feelings about the
effectiveness of departmentalization for math
instruction in grades 4 and 5?
What professional learning opportunities do
you feel would be beneficial to you and the
other staff members of the Bellefonte School
District?

A math workshop approach

How do you deliver your math lessons?

a combination of the two approaches

Do you assign math homework? If so, how
often?

3-4 days a week

What technology programs do you find
helpful and how often do students use these
programs?

Reflex Math (daily for morning work) and
SplashMath (several times a week depending on
time)

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

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Survey Question
What data are you utilizing to inform your
instruction?

Teacher 7
Daily google quizzes, unit quizzes and
assessments

How many times a week do you review data
to inform your instruction?

3 to 4 times

How effective do you feel your data analysis
process is in informing your instruction.

4

How many times a week do you meet in
small groups or with individual students
during math class?

1 to 2 times

How do you feel about the effectiveness of
your differentiated instruction for math?

4

What components of the Everyday Math
program are you using daily in your
instruction?

Math message, Lesson parts 1&2, games, math
boxes, sometimes readiness and enrichment
when needed,

What are your impressions on the strengths
and weaknesses of EDM?

Strengths- spiraling, incorporating all math
concepts in showing how they are connected,
using real world problem solving,

What instructional strategies are you using
with ALL students that are outside of the of
the Everyday Math program? Please indicate
how often you utilize the strategy.

Weakness- focus on fact automaticity, need
more work with fractions and measurement.
Timed fact sheets three times a week so
students can master foundational facts and
higher by the end of third grade

What math interventions are you using with
your students that you have found to be
successful in promoting student growth?

fact timed sheet, reflex math, IXL

What math basic fact automaticity
interventions are you using with your
students that you have found to be successful
in promoting student growth?

giving timed fact sheets three times a week that
focus on mastery of foundational facts first.

What are your feelings about the
I cannot comment since I teach third grade.
effectiveness of departmentalization for math
instruction in grades 4 and 5?

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

110

What professional learning opportunities do
you feel would be beneficial to you and the
other staff members of the Bellefonte School
District?

More on teaching kids through a math
workshop approach and using a flipped
classroom approach to teaching.

How do you deliver your math lessons?

a combination of the two approaches

Do you assign math homework? If so, how
often?

3-4 days a week

What technology programs do you find
helpful and how often do students use these
programs?

Reflex and IXL 2-3 times a week.

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

Survey Question
What data are you utilizing to inform your
instruction?
How many times a week do you review data
to inform your instruction?

111

Teacher 11
I use a google form to assess each lesson. This
allows me to differentiate my instruction every
day.
Each Day

How effective do you feel your data analysis
process is in informing your instruction.

4

How many times a week do you meet in
small groups or with individual students
during math class?

1 to 2 times a week

How do you feel about the effectiveness of
your differentiated instruction for math?

4

What components of the Everyday Math
program are you using daily in your
instruction?

Most components

What are your impressions on the strengths
and weaknesses of EDM?

It allows students to have a deeper
understanding of math, however the spiraling
component is unnecessary in my opinion.
Reflex, extra practice on occasion, mini
quizzes, modified assessments

What instructional strategies are you using
with ALL students that are outside of the of
the Everyday Math program? Please indicate
how often you utilize the strategy.
What math interventions are you using with
your students that you have found to be
successful in promoting student growth?

Reflex

What math basic fact automaticity
interventions are you using with your
students that you have found to be successful
in promoting student growth?

Reflex

What are your feelings about the
NA
effectiveness of departmentalization for math
instruction in grades 4 and 5?
What professional learning opportunities do
you feel would be beneficial to you and the
other staff members of the Bellefonte School
District?

NA

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

How do you deliver your math lessons?

Primarily whole-group instruction

Do you assign math homework? If so, how
often?

3-4 days a week

What technology programs do you find
helpful and how often do students use these
programs?

Reflex, 3 times per week

112

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

113

Survey Question
What data are you utilizing to inform your
instruction?

Teacher 13
Small Group Observations, Exit Tickets,
Multiple Choice Tests, Open Response Tests

How many times a week do you review data
to inform your instruction?

Each Day

How effective do you feel your data analysis
process is in informing your instruction.

5

How many times a week do you meet in
small groups or with individual students
during math class?

1 to 2 times a week

How do you feel about the effectiveness of
your differentiated instruction for math?

5

What components of the Everyday Math
program are you using daily in your
instruction?

Problem Sets, Math Boxes, Journal Pages,
Open Tasks

What are your impressions on the strengths
and weaknesses of EDM?

Not well aligned to PA Core

What instructional strategies are you using
with ALL students that are outside of the of
the Everyday Math program? Please indicate
how often you utilize the strategy.
What math interventions are you using with
your students that you have found to be
successful in promoting student growth?
What math basic fact automaticity
interventions are you using with your
students that you have found to be successful
in promoting student growth?

Reflex

What are your feelings about the
I think it has been very effective. I am a more
effectiveness of departmentalization for math knowledgeable teacher and all of my
instruction in grades 4 and 5?
professional learning opportunities are used to
make me a more effective teacher.
What professional learning opportunities do
you feel would be beneficial to you and the
other staff members of the Bellefonte School
District?

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

114

How do you deliver your math lessons?

Primarily whole-group instruction

Do you assign math homework? If so, how
often?

3-4 days a week

What technology programs do you find
helpful and how often do students use these
programs?

Zearn, E-Spark, Quizziz - 2-3 Times per week
during Workshop Time

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

Survey Question
What data are you utilizing to inform your
instruction?

How many times a week do you review data
to inform your instruction?

115

Teacher 16
I use a combination class work, my own created
formative assessments/exit tickets,
observations, mini-quizzes, and summative
assessments at the end of units to drive
instruction.
1 to 2 times

How effective do you feel your data analysis
process is in informing your instruction.

3

How many times a week do you meet in
small groups or with individual students
during math class?

1 to 2 times a week

How do you feel about the effectiveness of
your differentiated instruction for math?

3

What components of the Everyday Math
program are you using daily in your
instruction?

I use the manual as a guide, but often make the
lesson my own that fits my own style and what
my kids need. This looks differently each year,
because each group of kids is different.
Strengths-teaching concepts in a conceptual
manner as opposed to straight procedures. A
major weakness in my opinion is that concepts
don't spiral as much as they should and can be
difficult to revisit content to make sure students
are retaining what has been taught.
I use Khan Academy almost daily.

What are your impressions on the strengths
and weaknesses of EDM?

What instructional strategies are you using
with ALL students that are outside of the of
the Everyday Math program? Please indicate
how often you utilize the strategy.
What math interventions are you using with
your students that you have found to be
successful in promoting student growth?
What math basic fact automaticity
interventions are you using with your
students that you have found to be successful
in promoting student growth?

I use Khan Academy and my own created
materials. I also utilize my classroom aide and
Learning support teacher when they are pushing
in to help my students grow.
Math Reflex

What are your feelings about the
I think it has helped me to become a better math
effectiveness of departmentalization for math teacher because it has allowed me to focus more
instruction in grades 4 and 5?

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

What professional learning opportunities do
you feel would be beneficial to you and the
other staff members of the Bellefonte School
District?

How do you deliver your math lessons?

116

on math and has given me more time to develop
different activities to help engage students.
Integrating technology in a meaningful and
useful way into math instruction. Sometimes I
do not feel like I get the most out of a 1:1
setting. I think this could be a very powerful
differentiation tool that I do not think I use to
the fullest potential.
Primarily whole-group instruction

Do you assign math homework? If so, how
often?

1-2 days a week

What technology programs do you find
helpful and how often do students use these
programs?

Math Reflex and Khan Academy-they use these
tools almost daily.

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117

Survey Question
What data are you utilizing to inform your
instruction?

Teacher 17
Unit Assessments, CDTs, daily check-ins

How many times a week do you review data
to inform your instruction?

2 to 3 times

How effective do you feel your data analysis
process is in informing your instruction.

3

How many times a week do you meet in
small groups or with individual students
during math class?

2 to 3 times a week

How do you feel about the effectiveness of
your differentiated instruction for math?

4

What components of the Everyday Math
program are you using daily in your
instruction?

All of them

What are your impressions on the strengths
and weaknesses of EDM?

StrengthsPresentations with tools
Manipulatives
Spiraling curriculum
Justifying solutions
Problem-solving
WeaknessesCertain content topics covered in depth, while
others receive weak coverage

What instructional strategies are you using
with ALL students that are outside of the of
the Everyday Math program? Please indicate
how often you utilize the strategy.

Additional organizers and manipulatives, one
on one and small group learning, peer teaching,
reviewing and reteaching of lessons

What math interventions are you using with
your students that you have found to be
successful in promoting student growth?

Learning Support teachers and I work together
to create assignments and assessments together.
We have often used the documents in the
Shared Drive-Fourth Grade Math Curriculum
and revised them using DocHub. We use
graphic organizers, manipulatives, explicit
instruction and lots of visual representations.
Reflex

What math basic fact automaticity
interventions are you using with your

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

118

students that you have found to be successful
in promoting student growth?
What are your feelings about the
I feel it is very effective. This was my first-year
effectiveness of departmentalization for math teaching in a departmentalized grade and I
instruction in grades 4 and 5?
thought it was beneficial to focus on teaching
just math and science.
What professional learning opportunities do
None at this time
you feel would be beneficial to you and the
other staff members of the Bellefonte School
District?
How do you deliver your math lessons?

a combination of the two approaches

Do you assign math homework? If so, how
often?

3-4 days a week

What technology programs do you find
helpful and how often do students use these
programs?

Daily- EDM, Khan Academy, Zearn, Reflex,
Math Antics videos
I have heard great things about eSpark.

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

Survey Question
What data are you utilizing to inform your
instruction?
How many times a week do you review data
to inform your instruction?

119

Teacher 18
Student responses in small group instruction,
homework problems, quizzes and informal
assessments throughout my lessons
1 to 2 times

How effective do you feel your data analysis
process is in informing your instruction.

2

How many times a week do you meet in
small groups or with individual students
during math class?

3 to 4 times a week

How do you feel about the effectiveness of
your differentiated instruction for math?

4

What components of the Everyday Math
program are you using daily in your
instruction?

I often use the math journal pages to assess how
well my students understand the concepts and
to give them some practice with the skill. I use
the Teachers Manual to guide what concepts
need to be taught and then usually determine
how I am going to do that in a small group
setting when I plan the week before.
I feel it gives too many different strategies that
the students become confused and blend them
together. It also spends time on unnecessary
skills instead of spending more time on one
skill so that students have time to really digest
and understand what they are doing. It doesn't
allow for practice.
I teach mostly in a guided math structure where
I differentiate the strategies depending on the
group. I have found students are getting the
individualized instruction needed to help them
grow.
By teaching in a guided math structure, I can
spend more time with my struggling students
while giving my more advanced students more
advanced tasks to complete. I have found that
this has motivated my on-level students to push
themselves more so that they can try to work on
the more challenging tasks, all while I can be
giving more guided practice to my struggling
learners.

What are your impressions on the strengths
and weaknesses of EDM?

What instructional strategies are you using
with ALL students that are outside of the of
the Everyday Math program? Please indicate
how often you utilize the strategy.
What math interventions are you using with
your students that you have found to be
successful in promoting student growth?

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

120

What math basic fact automaticity
interventions are you using with your
students that you have found to be successful
in promoting student growth?

We use Reflex math daily, but unfortunately, I
still have students who are struggling and by
5th grade it is imperative for them to know
these facts so they will often use multiplication
charts and hundreds grids if necessary.
What are your feelings about the
I love it! I feel I spend more time focusing on
effectiveness of departmentalization for math the specific needs of my students and it allows
instruction in grades 4 and 5?
me the freedom to plan intensively for just
math. I have become a better teacher being able
to just focus on math instruction.
What professional learning opportunities do
I would love to have some time dedicated to
you feel would be beneficial to you and the
guided math. To discuss and learn strategies
other staff members of the Bellefonte School that work well and to learn how to implement it
District?
better. It is a fantastic structure for math and I
would love to see others move in this direction.
It is easier for me since math is all I plan for. I
imagine as a 3rd grade teacher it would seem
overwhelming trying to create lessons in all the
different subject areas, but having time in a
professional learning session to create the
structures and the materials would be helpful.
How do you deliver your math lessons?
a combination of the two approaches
Do you assign math homework? If so, how
often?

1-2 days a week

What technology programs do you find
helpful and how often do students use these
programs?

ESpark has been a wonderful tool that
differentiates the practice. I can enrich those
who are ready for 6th grade material and it
takes them to the grade level that they test in to
practice. The program does this automatically
which saves me time and it also will send me
emails with students’ names of kids who may
need a small group session on a specific skill
that they are struggling with. I will sometimes
use Khan Academy to have students practice
specific skills as well.

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Survey Question
What data are you utilizing to inform your
instruction?

Teacher 19
Observations, end of unit assessments, mini
quizzes

How many times a week do you review data
to inform your instruction?

1 to 2 times

How effective do you feel your data analysis
process is in informing your instruction.

4

How many times a week do you meet in
small groups or with individual students
during math class?

2 to 3 times a week

How do you feel about the effectiveness of
your differentiated instruction for math?

3

What components of the Everyday Math
program are you using daily in your
instruction?

All but differentiation options

What are your impressions on the strengths
and weaknesses of EDM?

Strengths - lesson format, spiral, hands-on
learning, materials provided by EDM, online
resources, games

What instructional strategies are you using
with ALL students that are outside of the of
the Everyday Math program? Please indicate
how often you utilize the strategy.
What math interventions are you using with
your students that you have found to be
successful in promoting student growth?

Weaknesses - in third grade too much emphasis
on multiplication fact strategies, odd unit
progression (for example, some units have 2 or
3 lessons on fractions, then move on to
multiplication)
Turn and talk, explain your thinking, share
solution strategies

I was lucky to have learning support and a
student teacher this year. We were able to
divide the class into 3 groups to help
differentiate.
I also pre-taught some lessons to 1 particular
student. I saw a lot of growth with him when I
saw this. However, as stated above, I had a
student teacher who at that point was teaching
most of the day so I had more flexibility with
my time.

MATH INTERVENTIONS IN ELEMENTARY PSSA GRADES

What math basic fact automaticity
interventions are you using with your
students that you have found to be successful
in promoting student growth?

122

Reflex Math

What are your feelings about the
NA
effectiveness of departmentalization for math
instruction in grades 4 and 5?
What professional learning opportunities do
you feel would be beneficial to you and the
other staff members of the Bellefonte School
District?

How do you deliver your math lessons?

I feel that we have a strong foundation when
teaching math to our students. I think
professional learning opportunities could be
more with how to teach the EDM lessons using
a math workshop model and how to use
Mastery Connect to differentiate
Primarily whole-group instruction

Do you assign math homework? If so, how
often?

3-4 days a week

What technology programs do you find
helpful and how often do students use these
programs?

IXL, Reflex Math

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