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Mathematics scores of middle school students are a major concern for educators, community leaders, parents, and other stakeholders. The purpose of this qualitative case study was to examine the perceptions of teachers regarding (a) Voyager Math (VM) as a tool to improve students’ academic performance and (b) their ideas about its implementation. The theoretical foundation was guided by the theories of discovery learning, sociocultural theory, expectancy theory, and social constructivism. The research questions addressed how teachers in Grades 6-8 implemented the VM program and perceived mathematics learning effectiveness.
1.
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Teachers' Perceptions of the Impact of a Remedial
Math Program on Student Success
Wintter Naitalya Samuel
Walden University
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2.
Walden University
College of Education
This is to certify that the doctoral study by
Wintter Naitalya Samuel
has been found to be complete and satisfactory in all respects,
and that any and all revisions required by
the review committee have been made.
Review Committee
Dr. Fatima Mansur, Committee Chairperson, Education Faculty
Dr. Mario Castro, Committee Member, Education Faculty
Dr. Paul Englesberg, University Reviewer, Education Faculty
Chief Academic Officer
Eric Riedel, Ph.D.
Walden University
2018
3.
Abstract
Teachers’ Perceptions of the Impact of a Remedial Math Program on Student Success
by
Wintter Naitalya Samuel
MED, Georgia College and State University, 2007
BS, Albany State, 2004
Doctoral Study Submitted in Partial Fulfillment
of the Requirements for the Degree of
Doctor of Education
Walden University
April 2018
4.
Abstract
Mathematics scores of middle school students are a major concern for educators,
community leaders, parents, and other stakeholders. The purpose of this
qualitative case study was to examine the perceptions of teachers regarding (a)
Voyager Math (VM) as a tool to improve students’ academic performance and (b)
their ideas about its implementation. The theoretical foundation was guided by the
theories of discovery learning, sociocultural theory, expectancy theory, and social
constructivism. The research questions addressed how teachers in Grades 6-8
implemented the VM program and perceived mathematics learning effectiveness.
Data collection included administrator and teacher interviews, classroom
observations, and related documents of one middle school in a single southeastern
school district. Twelve purposefully selected 6-8 grade mathematics teachers and
2 administrators participated in classroom observations and semistructured
interviews at the research site to provide triangulated data. Data were recorded
and transcribed, then analyzed and coded for themes. Teachers and administrators
agreed that the VM program was an effective remedial mathematics program. The
results revealed differences in remedial mathematics teaching strategies, how
students are grouped according to mathematics scores, and an overall emphasis
placed on mathematics throughout the school. The implications for social change
include educational leaders implementing relevant professional development
classes and understanding teachers’ experiences.
5.
Teachers’ Perceptions of the Impact of a Remedial Math Program on Student Success
by
Wintter Naitalya Samuel
MED, Georgia College and State University, 2007
BS, Albany State, 2004
Doctoral Study Submitted in Partial Fulfillment
of the Requirements for the Degree of
Doctor of Education
Walden University
April 2018
6.
Dedication
This study is dedicated to my mother Cheryl who has inspired me to reach beyond
the stars because there is an entire universe awaiting my arrival. To my oldest son, CJ,
you are the reason I have so much determination to continue when the road gets tough.
To my husband, Charles, I am thankful for all the encouragement you have given me and
I love you. To Keron and Jayden, your resilience and excitement helped me through this
process. To my dad James, brother, and sisters thank you for teaching me how to survive.
Thank you for the love and support.
7.
Acknowledgements
A huge thank you to Demetria because without you I would have truly given up
on this process. To Dr. Mansur, thank you for everything. You helped me overcome so
many challenges and obstacles. Thank you Dr. Castro for sticking with me throughout the
years and challenging me to become better. Dr. Mansur, Dr. Castro, and Dr. E. this would
not be possible without your support and guidance.
8.
Table of Contents
Section 1: The Problem ........................................................................................................1
Introduction ..................................................................................................................... 1
Statement of the Problem .................................................................................................4
Nature of the Study ..........................................................................................................6
Research Questions ..........................................................................................................6
Purpose of the Study ........................................................................................................7
Conceptual Framework ....................................................................................................7
Operational Terms ...........................................................................................................8
Assumptions.....................................................................................................................9
Scope and Delimitations .................................................................................................9
Limitations ......................................................................................................................9
Significance of Study .....................................................................................................10
Summary ........................................................................................................................10
Section 2: Review of the Literature ...................................................................................12
Introduction ....................................................................................................................12
Literature Search Strategy .............................................................................................13
Literature for Conceptual Framework ...........................................................................14
Literature Review Related to Key Variables and Concepts ..........................................19
Gaps in Achievement ....................................................................................................19
Student Achievement and Race .....................................................................................22
Gender Gap ....................................................................................................................25
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9.
Remediation ....................................................................................................................28
Factors that Influence the Achievement of Students .........................................................30
Student Preparation ....................................................................................................31
Teacher Perceptions ..................................................................................................34
Mathematics Anxiety .................................................................................................37
Technology and Its Effectiveness ..................................................................................40
Voyager Mathematics Program .........................................................................................45
Literature Related to the Use of Differing Methodologies ................................................47
Literature Related to the Study Methods ...........................................................................50
Summary ............................................................................................................................53
Section 3: Methodology .....................................................................................................55
Introduction ....................................................................................................................55
Research Design ............................................................................................................56
Research Questions ........................................................................................................58
Contexts for the Study ..................................................................................................58
Setting ....................................................................................................................58
Criteria for Selection of Participants......................................................................59
Measures for Ethical Protection of Participants ............................................................60
Role of the Researcher ...................................................................................................62
Data Collection ..............................................................................................................62
Classroom Observation ..........................................................................................64
Semi-Structured Interviews ...................................................................................67
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10.
Related Documents ................................................................................................68
Data Analysis .................................................................................................................69
Coding ............................................................................................................................71
Interpretation ..................................................................................................................73
Trustworthiness ..............................................................................................................74
Ethical Procedures .........................................................................................................75
Summary ........................................................................................................................75
Section 4: Results...............................................................................................................77
Introduction ....................................................................................................................77
Descriptive Data ............................................................................................................77
Data Generating and Gathering .....................................................................................77
Interview Data................................................................................................................80
Observation Data ...........................................................................................................81
Related Documents ........................................................................................................81
Findings .........................................................................................................................82
Discrepant Data..............................................................................................................96
Evidence of Quality .......................................................................................................99
Summary ........................................................................................................................99
Section 5: Discussions, Conclusions, Recommendations ................................................101
Introduction ..................................................................................................................101
Interpretations of Findings ...........................................................................................101
Discovery Learning .....................................................................................................102
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Social Constructivism ......................................................................................................103
Expectancy Theory ..........................................................................................................104
Summary of Findings .......................................................................................................104
Implications for Social Change ........................................................................................108
Recommendations for Actions .........................................................................................109
Recommendations for Further Study ...............................................................................110
Summary ..........................................................................................................................112
Reflections .......................................................................................................................112
References ........................................................................................................................115
Appendix A ......................................................................................................................137
Discussion Questions for Teachers .............................................................................137
Appendix B ......................................................................................................................138
Observation Protocol ...................................................................................................138
Appendix C ......................................................................................................................139
Interview Protocol: Teacher Perspectives on VM .......................................................139
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1
Section 1: The Problem
Introduction
For many years, much emphasis has been placed on closing the achievement gap.
Yet it remains one of the most pressing educational policy challenges that states currently
face (National Governors Association Center for Best Practices [NGACBP], 2013), as the
gap remains wide. This achievement gap is true for African American and European
American students, especially in mathematics. Although educational administrators and
teachers are held accountable for preparing students for standardized assessments in
mathematics (Bahr, 2008; Rosas & Campbell, 2010; Ottmar et al., 2013), academic
frameworks that ensure students are progressing in the content areas, particularly in
mathematics, are needed (Bahr, 2008; NGACBP, 2013). Additionally, educators must
work to create invigorating, challenging, and engaging lessons that promote successful
learning outcomes so that the achievement gap can be closed.
This section will cover the following topics: (a) legislation surrounding
educational reform efforts, emphasizing closing the achievement gap; (b) student
achievement in mathematics at the study site; (c) nature of the study, the research
questions to be answered, the conceptual framework, significance of the study are
In January of 2002, President George W. Bush signed into law the No Child Left
Behind Act (Monks, 2014). This legislation sought to determine not what schools were
teaching or implementing, but how the schools performed (Monks, 2014). National
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mandates were established that demanded: (a) school accountability for student
outcomes, (b) flexibility for state and local school districts, (c) emphasis on evidence-
based education methods, and (d) alternative options for parents of children in failing
schools (White, Loker, March, & Sockslager, 2009). In efforts to improve the academic
achievement levels of American students, the NCLB Act required states to set the same
performance targets for all students (Trolian & Fouts, 2011). In general, it made
American school systems accountable for helping students improve test scores (Rowley
& Wright, 2011). Shirvan (2009) and Trolian & Fouts (2011) also noted it made districts
accountable for improving standardized assessment scores of at-risk and low-achieving
students. Specifically, it mandated that states and school districts must improve the
achievement level of low-performing students in the subject areas of mathematics and
reading before 2014 (Shirvani, 2009; Trolian & Fouts, 2011).
Educational supporters challenged Congress to reform the NCLB Act (Meyer,
2013; Posey, 2014). This challenge resulted in President Obama granting states waivers
in 2011, which offered more flexibility in complying with the burdensome requirements
of the NCLB Act (Posey, 2014). The acceptance of waivers by states allowed the U.S.
Department of Education to implement changes in education to include student
performance on state assessments tied to teacher evaluation (Posey, 2014). States that
accepted the initial waivers during the 2012-2013 school year were required to explain
the initiatives that they implemented with the use of waiver to improve student
achievement (Posey, 2014). The options included states working to narrow the
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achievement gap that exists between at-risk subgroups and regular education students in
math and reading (McNeil, 2012). Closing this achievement gap will help to have all
students at a proficient math and reading level by 2020 (McNeil, 2012). States that
accepted the initial waiver were allowed an extension to the waiver but had to request it
before the renewal deadline of February 21, 2014 (Posey, 2014). The state of Georgia
implemented an achievement target in mathematics of 92% for all students, which would
close the achievement gap by 2017 (House, 2013; McNeil, 2012). The waiver was
accepted and a new statewide accountability system, the College and Career Ready
Performance Index (CCRPI), was implemented. It measures the achievement of schools
in Georgia on assessments and other indicators, and replaces AYP (Georgia Department
of Education, 2014). The CCRPI report attempts to provide an easier representation to
parents and the public on the performance of students (Georgia Department of Education,
In 2009, President Obama and his administration created the Federal grant
program, Race to the Top (RT3), which required states to compete against other states in
implementing new ideas to improve student achievement (Abbott, 2013; Lee & Wu,
2017; Tanner, 2013). RT3 is an extension of NCLB with the goal of preparing students
for success and financially rewarding schools that meet the challenge of the program (Lee
& Wu, 2017; Tanner, 2013). The RT3 and NCLB challenge educators to implement
programs that improve achievement and close the achievement gap between students,
especially among minorities (Abbott, 2013; Lee & Wu, 2017). Georgia was awarded
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$400 million to help reform education (Badertscher & McWhirter, 2010). Twenty-six
counties, including the county in which this study was conducted, were selected to
participate in the RT3 initiative (Badertscher & McWhirter, 2010). The next section
describes the specific problem this study was designed to address in the context of a
south Georgia school.
Statement of the Problem
Continuous low student achievement levels in mathematics over the years have
become a major concern of administrators, teachers, and all stakeholders across America
(Robinson et al., 2014). Low proficiency levels in mathematics not only adversely affect
student and school performance, they adversely affect society and the economy in general
because mathematics is needed in virtually every career (Change the Equation, 2010;
Robinson et al., 2014). Thus, educational administrators, teachers and other stakeholders
are searching for strategies to reverse this downward trend. Educators in the school at the
site of this study are no exception.
The school has experienced fluctuations in progress on student math achievement.
For instance, the school experienced gains in mathematics in 2009 and 2010, resulting in
AYP success. However, in 2011, the school did not make AYP in mathematics (Georgia
Department of Education, 2011). Under the new accountability measurement, CCRPI, the
school experienced gains in 2012, 2013, and 2014 with the CCRPI score, but failed to
meet the academic performance target (Georgia Department of Education, 2014). The
most points a school can receive with CCRPI is 110. The targeted schooled earned a
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score of 54.8 points with a score of 19.8 out of 50 in the category of achievement and the
category of progress a score of 31.2 out of 40 (Governor's Office of Student
Achievement, 2017). With regard to mathematics, the school's assessment scores in
mathematics, on the CRCT, declined for two consecutive years and did not meet
Performance Indicator 3 (percent of students meeting or exceeding in mathematics). The
scores were 72.2% in 2012, 67.8% in 2013, and 66.4% in 2014 (Georgia Department of
Education, 2014). Under the new student performance end of grade (EOG) assessment,
Georgia Milestones, the school was graded with the following performance categories (a)
beginning, (b) developing, (c) proficient, and (d) distinguished learner. The student must
perform in the proficient and distinguished learner category to pass the assessment.
During the 2014-2015 school year, 6.9% of students performed as proficient and 0.8%
performed as distinguished learners while 2015-2016 school year 6.6% of students
performed as proficient and 0.8% performed as distinguished learners (Governor's Office
of Student Achievement, 2017). This decline resulted in school administrators, teachers,
and other stakeholders agreeing that mathematics remediation was needed to help low-
achieving students and would help in accomplishing the requirements of NCLB and RT3
(Governor’s Office of Student Achievement, 2017).
As a result, school personnel determined that mathematics remediation was
needed to accomplish the goal of the NCLB and RT3 requirements (Governor’s Office of
Student Achievement, 2017). This school implemented a Voyager Math (VM)
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remediation program for its low-achieving students. VM was implemented to help
students improve their level of achievement in mathematics.
Nature of the Study
This study examined teachers' perceptions of the mathematics program VM. It is a
math intervention system that helps students with basic skills and concepts in math.
Cambium (2013) explained that the VM program integrates small group interventions
with the instructional modules (Voyager Sopris Learning, 2014). This study used a
qualitative approach to focus on the exploration of teachers’ perceptions of the VM
program, the benefits and limitations of the program, and the implementation of the
Qualitative data were collected in the form of transcribed interviews and field
notes from observations of Vmath classroom instruction. The semi-structured interviews
helped to understand teachers’ perceptions. The interviews were conducted using a one-
on-one session with each participant. Teachers were asked to meet at an agreed-upon
time for a minimum of 20 minutes. The meetings were recorded and transcribed. The
transcripts were read and coded to identify key themes. A detailed explanation the
research method and design is provided in Section 3.
Research Question
The guiding research question that addressed the study was: How do teachers
implement the VM program and perceive mathematics learning effectiveness? Two
subquestions helped answer the guiding question: (a) What are teachers’ perceptions
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about the effectiveness of the VM remediation program? (b) What is the teacher’s role in
the delivery of the VM remediation program?
Purpose of the Study
Student achievement among at-risk students has become a major concern for
educators, community leaders, and parents. The purpose of this qualitative study was to
examine the perceptions of teachers about VM, the selected math remediation program
used at the middle school study site. Specifically, the purpose was to examine the
perceptions of teachers regarding VM as a mathematics tool to improve academic
performance and to review their ideas on its implementation. The findings are expected to
contribute to existing research studies on teachers’ perceptions of the use of remediation
programs, such as VM, as a tool to improve mathematics skills.
Conceptual Framework
The conceptual framework for this study focuses on teachers’ perceptions and
how the behaviors and actions of teachers may influence student achievement in
mathematics. Teachers’ attitudes and behaviors not only influence curriculum and
instruction; they influence the implementation of strategies that enhance student
performance and achievement. Thus, to guide the research in this study, the following
theories were used: (a) discovery learning theory, (b) sociocultural theory, (c) expectancy
theory, and (d) social constructivist theory. These theories were selected because they
explain perceptions that influence student learning and impact student academic
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Discovery learning permits the teacher to help students discover learning via
strategies such as scaffolding and other methods (Bruner, 1960). Teachers also encourage
the students to become self-motivated and independent while working on challenging
assignments (Alfieri, Brooks, Aldrich, & Tenenbaum, 2011). The idea of sociocultural
theory relies on one’s understanding, which develops from experiences and cultures
(McBride, 2011). Teachers create lessons which evolve from their culture and
understanding of the culture of their students. The expectancy theory is based on the
premise that effort results in positive results. The student should expect that the
assignment is achievable before considering putting forth the necessary effort. Teachers
who focus on instruction and student learning believe the students have the ability to
complete the assignment; otherwise, it may be that they do not understand the
assignment. The social constructivist theory is based on the principle that students are
actively engaged in the learning process and receive encouragement and support from
teachers. Detailed information on the conceptual framework and the selected theories are
included in Chapter 2.
Operational Definitions
Some terms included in the context of this study are fundamental but may not be
readily understood. Thus, for purposes of clarity, they need to be defined. The selected
terms and their corresponding definitions are listed below.
Adequate Yearly Progress: A measure which makes schools and districts
accountable for the performance of all students under Title 1 (Klein, 2015).
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Enrichment. A class that builds on the skills already learned. This class practices
and extends the skills in mathematics or other subjects (Georgia Department of
Education, 2011).
Assumptions
Three assumptions were made about the work conducted for this study: (a) the
teachers were honest and would provide reliable data; (b) during the one-on-one
interview, the participants would cooperate; (c) participants would present a positive
attitude whereas self-efficacy affected their role in the remediation process.
Scope and Delimitations
The scope of this study was confined to one school in a school district in Georgia.
Student’s grade point averages, academic grades in math, and discipline reports were not
considered in this study. Not all participants had the same math experiences before
middle school.
Limitations
This study was limited to one technology program, VM, which was used to
support the strengths and weaknesses of low-achieving students in Grades 6-8. Since this
study was limited to student performance in mathematics, the findings cannot be
generalized to other subjects. Data were collected from teachers of one school in one
Georgia school district, and the sample size was limited to 12 teachers and two
administrators. Two classroom observations were observed and data was collected from
the observations. There was no detailed information about the participants, teachers or
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administrators working experiences and how their experiences may influence their
opinions. The study was also limited to five lesson plans and six VM student progress
reports. Data were collected for the period of one academic school year.
Significance of the Study
This study was significant for six reasons. (a) Findings from this study could
contribute significantly not only to educators at the targeted site and school district at
large but also to other school districts utilizing math remediation programs. (b) The
findings could aid middle school teachers and future educators in addressing emerging
concerns about low student performance in mathematics. (c) They could also aid middle
school educators in identifying, reducing or alleviating student deficiencies in
mathematics and provide information that would help fill gaps identified in the existing
literature. (d) The findings could benefit students because teachers would be able to draw
conclusions and provide learning environments that would meet the needs of individual
students. (e) The noted benefits and patterns established could also provide community
leaders with information to help them understand how struggling students learn
mathematics. (f) Most importantly, the nation benefits when students perform well in
school because they are then equipped with the necessary skills to be productive citizens
and to meet the needs of the workforce in a modern and global society.
Summary
The academic achievement of students is an important issue in a global society.
Thus, it is critical that students reach proficiency in [name the subject or subjects]. Levels
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of achievement can determine if students are successful in their career choices. This study
focused on the perceptions of teachers about a mathematics remediation program, VM,
which the site chose to help improve the success of its low-performing students. The
purpose of this qualitative study was to explore teachers’ perceptions of the VM
remediation program and to take a close look at teachers’ perceptions of the benefits and
limitations of the program, ideas on the implementation of the program, and patterns in
its effectiveness.
A review of existing literature on student achievement and the factors that
influence student achievement in general and mathematics, in particular, is presented in
Chapter 2. Section 3 is used to provide the details about the methodology that was used in
the investigation. The research design and data collection techniques are described in
Section 3. Lastly, Sections 4 and 5 are used to present, respectively, the results of the
study, and the conclusion and recommendations based on the findings.
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Section 2: Literature Review
Introduction
Many American students are falling below average in mathematics, especially in
middle school, a critical grade level in the teaching–learning process (Legewie &
DiPrete, 2012; Cheryan, 2012). Therefore, school administrators and teachers are in
search of strategies to reverse the downward trend. The purpose of this qualitative study
was to examine the perceptions of teachers about the mathematics remediation program
implemented at the study site along with the benefits, limitations, and implementation of
the program. One guiding question, with two subquestions, was addressed.
Legewie and DiPrete (2012) and Cheryan (2012) suggested that mathematics
achievement in elementary and secondary school may help determined one’s success in
post-secondary education, math-related careers, and the work force. Because of the
NCLB Act, many schools have implemented several initiatives to help improve student
achievement and motivation (NGACBPNGACBP, 2013). Student motivation and
achievement toward mathematics involve factors such as ability, motivation, positive
teacher interactions, and home factors (Cheryan, 2012; Schwery, Hulac, & Schweinle
(2016); Naizer, Hawthorne, & Henley, 2014). Burton (2012), Fulmer and Turner (2014),
and Zwiep and Benken, (2013) proposed that educators’ perceptions of the curriculum
and content, and their expectations of students may affect student performance.
Topics researched to aid in answering the questions established are included in
this study. This section covers the following topics: (a) achievement gaps among
American students are presented generally and specifically by race and gender, (b)
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remediation is defined and the purpose is provided, (c) a description on how students
have been remediated in the educational system (d) research related to factors that impact
student success in the classroom and their career choices, (e) the importance of student
and teacher preparation, the impact of mathematics anxiety on student performance,
research designs, and methodologies, (f) VM is described and research related to
technology that highlights the success of the program, (g) a summary of key points that
will be made to provide the rationale for the study.
Literature Search Strategy
The subjects of the literature review were as follows: academic achievement,
remediation, gender gap, and the factors that influence student achievement. The review
includes summaries of the literature that validate the study’s framework. A search of
databases in the Walden University Library included SAGE Journals, Education Source,
Academic Search Complete, Education Research Complete, and ERIC. The government
websites were used to obtain information and copies of studies from the Department of
Education and NGACBP. The keywords used in searching online materials, both alone
and in combination, were as follows: teacher, perceptions, mathematics, achievement,
gender gap, remediation, middle school, cognitive theory, constructivism, online,
remediation, technology, and achievement.
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Literature on the Conceptual Framework
The theory of discovery learning has been linked to the teaching and learning of
mathematics (Bruner, 1960). Discovery learning provides opportunities for the students
to use prior knowledge to discover the target information for learning.
In’am & Hajar (2017) suggested that teachers should teach students how to use
their critical thinking skills to become discovery learners and investigators. Janssen,
Westbroek, and van Driel (2014) asserted that students should be given support to aid in
developing the necessary skills that will inspire them to be successful in the classroom.
Bruner (2006) contended that the teacher should teach so that the student gains
information and skills to use in future learning. Mukherjee (2015) discussed discovery
learning as allowing students to discover the learning by asking questions, evaluating
information, and thinking critically. The student and teacher should share the role of
teaching and learning to assure a balance of “cognitive functioning” (Bruner, 1960, p.
612). When the teacher removes manipulation, the student has an opportunity to discover
learning independently. For example, Bruner described a young boy who used critical
thinking skills to discover the learning of mathematics while playing with snail shells.
The young boy learned that, through discovery, he could find a new way to complete a
mathematics task and was able to apply his learning of mathematics to another situation
(Bruner, 1960). Bruner and In’am and Hajar (2017) emphasized that teachers should
implement scaffolding and critical thinking skills, so students can apply their prior
knowledge to any task.
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The idea of sociocultural theory relies on an individual’s understanding and
cognition that develops from experiences and cultures (McBride, 2011). Vygotsky’s
sociocultural theory explained that an individuals’ culture and history may influence their
teaching and learning (Allahyar & Nazari, 2012; Mansour, 2013). Vygotsky’s theory
connects human behavior to critical thinking skills that may be used in the classroom
(Cicconi, 2014; Petrova, 2013). What teachers observe in the classroom is linked to their
beliefs and values to create a perception or idea about a phenomenon. When determining
the perceptions of teachers in education, researchers must understand the influences of
the teachers who develop curriculum and instruction. Mansour (2013) suggested that
teachers’ perceptions are influenced by pedagogy training, historical and societal
experiences, and other educational influences such as colleagues. The students’ behavior,
teacher beliefs and values, and educational knowledge impact teachers’ perceptions.
Teacher perception is created when teachers develop an awareness of the events
or situations that develop in the classroom, and they are connected to the cognitive
functioning of the teacher. Teachers' experiences in the classroom with student behaviors
and pedagogical knowledge create an idea of what may or may not occur and affect
teacher behavior and thoughts (Allahyar & Nazari, 2012; Barak, 2014; Wang, 2012).
Teachers’ behaviors affect student performance and beliefs in the classroom because of
past understandings and experiences (Robinson-Cimpian, Lubienski, Ganley,& Coput-
Gencturk, 2014). Allahyar & Nazari (2012) explained that to understand the perception of
teachers in the classroom regarding instruction, pedagogy, attitudes, and beliefs toward
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students, the teachers’ experience, cultural experiences, and cognitive functioning must
be observed.
The perception of students is important and influential in the educational process
(Allahyar & Nazari, 2012; Firmender, Gavin, & McCoach, 2014). Jansen and Bartell
(2013) asserted student achievement and performance play a major role in how teachers
perceive activities and events that occur in the educational setting. Teacher perception
may influence the student’s learning and achievement in mathematics. For example,
some teachers continue to use traditional methods of teaching instead of using mobile
devices that improve higher level and abstract thinking in the classroom (Barak, 2014).
According to Barak (2014), teacher perception of the use and implementation of
technology in the classroom influences student achievement and performance. The
traditional methods of teaching such as lectures and note-taking may not permit students
to take an exploratory approach to learning, actively participate, or for students to take
responsibility for their learning. The perceptions teachers hold about instruction and
curriculum may be influenced by standardized assessment or student behaviors.
Many teachers’ instruction may not evolve with the implementation of new ideas
(Barak, 2014). For example, they may not offer students challenging or higher-level
instruction because they believe the students are unmotivated and do not have the ability
to complete the task and student performance may harm student achievement on
standardized assessments (Fulmer & Turner, 2014). The perceptions teachers have of
students indicate their expectations and may result in the development of positive or
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negative ideas about the students (Allahyar & Nazari, 2012). Thus, student expectations,
behaviors, and performances must be discussed when discussing teachers’ perceptions.
Student motivation and engagement in the classroom may be influenced by
teachers’ perceptions and attitudes (Wang, 2012). The attitudes teachers display toward
students impact their learning and motivation in the classroom. Classroom instruction that
supports student independence and intrinsic motivation builds competence in the
mathematics classroom (Senko & Hulleman, 2013).
To understand teachers’ perceptions, I will explore student achievement and
performance through the expectancy theory. The expectancy theory is a belief that an
individual puts forth effort that will produce a positive outcome useful to the individual
(Lambright, 2010; Legewie & DiPrete, 2012). The individual believes the task is
achievable to put forth the effort (Robinson-Cimpian et al., 2014). A student’s decision to
take advanced mathematics courses will be determined by his or her expectation to be
successful in the class (Andersen & Ward, 2014). Teacher support is important for the
student to gain motivation and competence.
Wang (2012) explained that the support provided by teachers may impact the
student’s competence and influence his or her future academic goals. Wang (2012)
suggested that student achievement in mathematics will influence whether students take
advanced math courses in the future. Minority students may not believe mathematic
careers are suited for them because of the low number of minorities in those career fields
(Anderson & Ward, 2014). Research has revealed that girls are more likely to perform
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lower than boys on mathematical examinations because of the beliefs they have about
mathematics (Ross, Scott, & Bruce, 2012). Wang (2012) reported that girls are expected
to have low performance in mathematics, although they need more extrinsic motivation.
Self-efficacy, an important quality related to expectations, impacts student
success and achievement. It is the degree of motivation or confidence one has about
himself or herself (Orange & Murakami-Ramalho, 2013). When students who have low
self-efficacy are presented with challenging assignments, they need a supporter to
provide encouragement.
Self-efficacy stereotype threat is seen in students who do not take challenging
math courses or avoid STEM majors or careers (Schwery et al., 2016). This threat has
been seen in peer culture where boys develop anti-school behaviors and attitudes
(Legewie & DiPrete, 2012). This behavior, which has been seen more often in low
quality schools, results in underperformance in boys and disruptive behaviors in the
classroom (Legewie & DiPrete, 2012; Orange & Murakami-Ramalho, 2013). Research
suggested that girls perform lower on standardized assessment than boys. This results in
girls needing immediate feedback and motivation on assignments to help build the
confidence needed to continue working toward mastery in math (Legewie & DiPrete,
2012; Robinson-Cimpian et al., 2014; Schwery et al., 2016).
If students are not provided the necessary support, their performance in the
classroom, as well as achievement on standardized assessments, may be below average
(Crosnoe et al., 2010; Fulmer & Turner, 2014). However, students who have high self-
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efficacy in mathematics seek challenging assignments. They are likely to take advanced
mathematic courses or pursue mathematic career choices (Andersen & Ward, 2014).
They possess confidence and motivation.
The social constructivist theory includes instructional goals that encourage and
support learners through coaching, modeling, scaffolding, or collaborative work to
develop their own learning experience (Schreiber & Valle, 2013). Collaboration allows
students to gain a deeper understanding from other student’s perspectives (Ahn, Ingham,
& Mendez, 2016). Stearns (2017) found that students were able to use conversations with
other students to seek clarity and knowledge for their learning. Flint (2015) reported that
student experiences can contribute to the classroom learning environment impacting peer
learning. Since social learning supports the remediation approach of guiding students to
their academic potential, the problem of low academic achievement in mathematics relies
on remediation to reinforce the concepts so teachers and support teachers can guide
students to understanding and learning.
Literature Review Related to Key Variables and Concepts
Gaps in Achievement
The achievement gap between students has been an important issue in America as
well as countries throughout the world. Academic achievement is an important issue for
teachers, parents, and students in the United States (Reardon, Greenberg, Kalogrides,
Shores, & Valentino, 2012). Many students are not meeting standards as set by the NCLB
Act (Peterson & Kaplan, 2013). National Assessment of Educational Progress (NAEP)
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reports 65% of the United States’ 8th graders were not proficient in mathematics in 2011,
which leaves only 35% being proficient (Peterson & Kaplan, 2013). This percentage is of
importance because it has implications for the percentage of students who enter high
school and become prepared for college. Moller et al. (2013) reports the importance of
mathematics in technological careers and the daily usage of mathematical concepts.
Mathematics preparation is important for longitudinal accomplishment as twenty-first
century citizens and workers (Moller et al., 2013; Roschelle, Feng, Murphy, & Mason,
2013). Thus, early preparation improves the chances of students being successful in
college and developing high paying careers.
Hansen and Gonzalez (2014) stated that when compared to other academically
challenging countries, American students were performing academically below other
students in mathematics. Ottmar et al. (2013) reported that United States schools still
performing below other countries although there has been an increase in mathematics
achievement. Zhang, Trussell, Gallegos, and Asam (2015) stated that the mathematics
performance of students in the K-12 educational system indicates a need to improve
mathematical ability. Zhang et al. (2015) reported that approximately 10% of students in
Grades 1-6 are successful in solving problems found in the number and operations
mathematics domain.
The NCLB Act was established to close the achievement gap between high and
low performing students (Goodman, 2014). The focus was placed on low-achieving
students by requiring schools to increase student achievement. To meet this goal of
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student achievement schools were tasked to experience annual progress for their low
performing students in percentages between 5% and 7% (Shirvani, 2009). A major
feature of NCLB required student assessments each year on standardized tests and results
reported to the public in various ways (Goodman, 2014; Rosas & Campbell, 2010;
Monks, 2014, Sun, Saultz, & Ye, 2016; Trolian & Fouts, 2011).
To monitor how students are performing nationwide, educators and policyholders
rely on results of the National Assessment of Educational Progress (NAEP) assessments.
The NAEP is also known as the Nation’s Report Card, which includes standardized
mathematics and reading assessments administered to a random sample of students across
the country (Rosas & Campbell, 2010; White et al., 2009). The NAEP assessments for
mathematics measure student achievement in Grades 4, 8, and 12. This instrument is also
the only ongoing assessment of mathematics achievement in the United States (Goodson-
Espy et al., 2014; Rosas & Campbell, 2010).
The Nation’s Report Card (as cited in Gottfried, Marcoulides, Gottfried, & Oliver,
2013) revealed students in Grades 4, 8 and 12 performed below proficiency. Only “40%
fourth, 35% eighth, and 26% 12th graders” (p. 68) met grade level proficiency. Thus,
American students must improve their mathematics skills. Specific reasons are listed
1. The United States falls behind many countries in mathematics capabilities,
including Japan, Korea, and Canada (Peterson, Woessmann, Hanushek, &
Lastra-Anadon, 2011; Vigdor, 2013).
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2. Students cannot move to the next academic level in school if they do not
achieve proficiency level.
3. Students with high standardized test scores make more money in careers.
There is a disparity in skill level among students entering school because
many enter with various mathematical abilities (Simms, 2012; Smith, Cobb,
Farran, Cordray, Munter, & Dunn, 2010). Some enter with some knowledge
of math facts while many are not able to perform simple arithmetic, such as
counting objects (Simms, 2012; Smith, Cobb, Farran, Cordray, Munter, &
Dunn, 2010). The difference in skill levels, such as counting and reciting the
alphabet, can be visible as early as kindergarten (Robinson-Cimpian et al.,
2014). These differences can widen the achievement gap about one-fourth of a
standard deviation each year in regard to gender and race (Robinson-Cimpian
et al., 2014). The gap in achievement tends to widen as students transition
from elementary to middle school (Cheema & Galluzzo, 2013; Legewie &
DiPrete, 2012). These gaps are attributed to factors such as attendance,
economic status, and parental involvement (Nidich et al., 2011; Schwery et
al., 2016; Smith, Cobb, Farran, Cordray, Munter, & Dunn, 2010).
Student achievement and race. The achievement gap that educators across the
nation are trying hard to close is an important issue. Cheema and Galluzzo, (2013)
reported that race is an important factor in math achievement. A Nation at Risk, a report
written almost 35 years ago, explained that the United States lagged behind many high
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achieving countries and explained that many factors that affected and continue to affect
the U.S. Low test scores are one factor (Ornstein, 2010). Hines and Kritsonis (2011)
stated that the gap is the result of racial disparities in student achievement on
standardized assessments. When comparing the achievement gap in relationship to race,
European American students outperform African-American and Hispanic students in the
United States. (Cheema & Galluzzo, 2013; Hines & Kritsonis, 2011). The achievement
gap between minorities and their European American peers continues to exist, although
minorities are represented in higher levels or advanced placement math classes (Cheema
& Galluzzo, 2013; Riegle-Crumb & Grodsky, 2010). Findings with regards to racial
achievement report that European Americans outperform Hispanics and Hispanics
outperform African Americans (Cheema & Galluzzo, 2013; Hines & Kritsonis, 2011).
When reviewing scores extracted from the 2013 Nation’s Report Card, the NAEP
reported that Grades 4, 8, and 12 on students in the United States assessed in
mathematics. The NAEP scores over a four-year test period (2003-2007) revealed a
maximum math increase of less than 3% for minority students, which is little progress in
closing the gap between minorities and European Americans in over 90,000 public
schools (Shirvani, 2009). The Council of the Great City Schools (2010) reported that
achievement of African-American males in Grades four and eight on the NAEP
The NAEP reported that fourth-grade African-American males’ achievement
remained consistent between 2011 and 2013; however, European American males’
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achievement increased one point between 2011 and 2013 on the mathematics
achievement assessment (NAEP, 2013). Regardless of the academic gain, fourth grade
African-American males continued to remain around 25% to 26% percent below
European American male students who performed at proficient levels (NAEP, 2013). At
the Eighth grade level, African-American males who met the standard increased 1% over
a 2-year period (2011-2013) and 26% between 1990 and 2013. Conversely, European
American males improved from 26% on the mathematics assessment within 23 years
(1990-2013), which showed growth for African-American males but still left them at
least 31% lower than European American males (NAEP, 2013).
The Nation's Report Card reported that fourth and eighth grade students had
experienced growth in mathematics. However, females have shown the most growth in
these grades, with males remaining consistent in performance (NAEP, 2013). On the
contrary, when reviewing students during the 2013 testing year, male students have a
higher percent of students who are reaching or exceeding proficiency (NAEP, 2013).
The Nation’s Report Card (NAEP, 2013) reported that mathematics score gaps in
2013 as 14% of African-American students meeting proficiency in mathematics and 45%
of European American students meeting proficiency. Hispanic students were in the
middle, with 21% at or above proficiency (NAEP, 2013). The National Center for
Educational Statistics (NCES) reported that 68% of Georgia’s students met the standard,
which remained consistent from 2011 (NCES, 2013). The National Center for
Educational Statistics (NCES) (2013) reported that Georgia students had mathematics
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score gaps in 2013 with African-American students being 29 points lower than European
American students and Hispanic students only 16 points lower than European American
Riegle-Crumb and Grodsky (2010) suggested that if the United States wants to
produce highly qualified workers then there should be an improvement in the educational
knowledge and performance expectations for all youths. Ornstein (2010) reported that the
McKinsey consulting firm discovered the decline in product output and skilled workers
was because of achievement gaps in mathematics and science. For example, if the United
States had improved student achievement by closing the gap in mathematics and science
from 1983 to 1998 and raised its performance to the level of top performing countries, the
gross domestic product (GDP) would have been tremendously higher (Ornstein, 2010).
Gender gap. There are several explanations concerning the male and female gap
in subjects such as mathematics in the classroom. Sociocultural factors can be used to
show students how to think and learn in a scholastic setting (Voyer & Voyer, 2014).
These factors can threaten an individual’s knowledge and performance when he or she is
not expected to perform well in subjects. An individual’s expectations of a task and one’s
behavior can predict how well he or she will value that task (Cheema & Galluzzo, 2013;
Voyer &Voyer, 2014).
Ross, Scott, and Bruce (2012) referred to the gender gap as one gender having an
“advantage” over the other in a subject (p. 278). It can be considered one of the most
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common gaps that appears during elementary school affecting student achievement in
Robinson-Cimpian et al. (2014) suggested that the gender gap does not exist at the
beginning of kindergarten; rather, it develops based on the school experiences of each
boy and girl. Cimpian et al. (2016) reported the gap emerging in the first 3 to 4 years of
school learning. Niederle and Vesterlund (2010) claimed that boys are more competitive
than girls, and they learn better when they are receiving a grade on an assignment. Girls,
however, perform best when they are working in cooperative learning groups on math
Regardless of the differences, attitudes toward mathematics are affected during
the middle school years (Naizer et al., 2014). During the junior high or middle school
years, this gap seems very minute, but by the end of high school, boys are leading girls in
mathematics, which may have an impact on college major and career decisions (Cheema
& Galluzzo, 2013). Ellison and Swanson (2010) reported a wider gender gap with higher
achieving students.
Girls are underrepresented in higher-level math courses as well as STEM fields
and careers that are important to our economy (Ellison & Swanson, 2010; Schwery et al.,
2016). Similarly, as females progress in school their confidence in math tends to diminish
and the success that they once saw in elementary and middle school declines (Naizer et
al., 2014). The achievement gap tends to increase with girls falling behind due to low
motivation and peer pressure (Cheema & Galluzzo, 2013; Schwery et al., 2016).
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Many girls tend to shy away from mathematics courses because they do not feel
they may have the ability to perform the tasks. Research suggests girls excel on
assessments that are not quantitative. In contrast, boys excel on quantitative assessments
because of their development of spatial skills (Hansen & Jones, 2011; Niederle &
Vesterlund, 2010). Teacher perception continues to play a significant role in how boys
and girls feel toward math. Robinson et al. (2014) asserted teachers have higher
expectations for boys because of the perception boys are naturally talented in
mathematics. Cimpian et al. (2016) found evidence that when both genders’ behavior and
performance are similar teachers give girls lower scores than boys. Thus, believing that
girls must work harder than boys for mathematics achievement (Cimpian et al., 2016).
Robinson-Cimpian et al. (2014) cited two studies, Study A and Study B. Study A
confirmed girls put forth more effort than boys, although boys have the mathematical
ability to be successful.
Study B suggested that teachers believe girls outperform boys in mathematics, as
they have higher grades in math, even when data reveal boys are more successful
(Robinson-Cimpian et al., 2014). During the elementary and middle years, girls and boys
may receive different messages from teachers or parents about math performance, which
affects their confidence and feeling of competency in mathematics (Legewie & DiPrete,
2012; Schwery et al., 2016). Stereotypes such as mathematics being a masculine subject
and girls lacking the ability to be successful in mathematics results in girls believing they
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will not perform successfully in mathematics (Cheryan, 2011; Ross, Bruce, & Scott,
Although the gender gap in mathematics achievement has decreased, stereotypes,
as well as differences and similarities, continue to exist (Ross, Scott, Bruce, 2012).
Stereotypes such as girls perform behind their male peers and girls are not successful in
mathematics has narrowed over the years (Ross, Scott, & Bruce, 2012; Cimpian et al.,
2016). Cheryan (2011) asserted that a gender gap does not exist because females perform
better than males on assessments and receive better grades in math classes. Rather it is
due to the parallel success of boys and girls in mathematics, females continue to be
underrepresented in STEM or mathematics career fields (Cheryan, 2011; Cimpian et al.,
Many schools are implementing programs to help their low-achieving students
improve mathematics performance. Implementing remedial interventions to improve
achievement provides the low-achieving student more opportunities to achieve, even
when early prevention measures have been instituted (Fuchs et al., 2010). Mathematics
remediation is intended to provide a ladder of basic skills that lead up to the minimum of
math competency of knowledge (Bahr, 2007).
Bahr (2010) defined remediation as a remedy that seeks to restore opportunity to
those who may be “relegated to meager wages, poor working conditions, and other
consequences of socioeconomic marginalization” (p. 209). The intention of remediation,
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as discussed by Bahr (2008; 2010), is to provide a balance between the advantaged and
disadvantaged groups. Additionally, the students who consist of these groups would
benefit from remediation and eventually become college attainment participants.
Preparing students for advanced math courses will ensure they are seeking competitive
careers in the global workforce as well as helping to improve the U.S. economy.
Researchers suggest that mathematics is the subject which requires many students
to receive the most assistance in remediation (Adelman, 2004; Bahr, 2008; Bahr, 2010).
As a resolution, many states are developing curricula that are aligned from elementary to
high school (Howell, 2011; Hoyt & Sorensen, 2001).
Oregon implemented a relationship between secondary and postsecondary
institutions to help bridge the transition to post-secondary education (Howell, 2011).
Other states followed by implementing dual enrollment between high school and college
(Howell, 2011; Hoyt & Sorensen, 2001). Dual enrollment permits students to take classes
at a postsecondary institution while completing high school. This relationship has been
effective in providing minorities opportunities to take college courses and pursue
postsecondary education (Howell, 2011). Postsecondary institutions provide feedback to
secondary schools about their previous students, which enables them to adjust or improve
the curricula, if necessary, for upcoming students (Hoyt & Sorensen, 2001).
Many schools and colleges are working to develop programs to provide
opportunities for the students to experience college life (Howell, 2011). The middle
school level is of concern for educators because this is the level that many detrimental
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factors affect student lives (Nidich et al., 2011). Because of the concern that develops
during this educational level, an urban middle school attempted a peculiar intervention
that remediated the students in math.
The intervention involved mediation that proved to increase the academic
achievement of low performing students (Elder et al., 2011; Nidich et al., 2011). This
form of mediation involved settling down the mind and experiencing “a state of restful
alertness” (Nidich et al., 2011, p. 558). This program was implemented by successfully
showing the students how to meditate and allowing them time throughout the day to
practice this intervention (Elder et al., 2011; Nidich et al., 2011).
Forty-one percent of the students who used this approach showed significant
gains in mathematics (Nidich et al., 2011). Although this is not a program that helps
recall or reteach information, it allows the student to repair or improve an area that will
help them move toward academic success. “The transcendental meditation program
increases the electroencephalographic brain integration and coherence that is responsible
for higher order processing” and allows the student to use this higher order processing to
improve on mathematics skills (Nidich et al., 2011, p. 558). Young et al. (2012)
suggested teachers should connect mathematics to students’ prior knowledge and use real
world scenarios to make learning meaningful and significant.
Factors that Influence Student Achievement
When students transition to middle school and high school, there is a decrease in
academic achievement due to several factors that may affect the student’s life. Middle
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school is a period in an adolescent’s life where his or her physical and cognitive abilities
are undergoing constant changes (Cimpian et al., 2016). This developmental stage
represents a critical period for life skills development in children (Cimpian et al., &
Moller et al., 2013). This is a period when peer pressure and a sense of belonging are of
importance. These students also are at risk for a decline in achievement (Mowrey &
Farran, 2016; Nidich et al., 2011).
Students’ gender, race, behavior, ability level, and attitudes account for the
student differences seen in the education system (Burton, 2014; Ross, Scott, &Bruce,
2012). As students enter the educational system and transition through the levels, their
academic attitudes about school, subjects, and teachers are developed. Many students can
overcome many obstacles, but some students are not able to move past factors that may
influence their ability to be successful.
Student Preparation
Being prepared is an important asset that can prepare students for success in the
academics and in a career. Students enter the education system at different skill levels.
Many students receive some form of instruction in daycare centers, at home, or at
preschool. Parents who value education tend to prepare their children by introducing
concepts and imparting knowledge early on, before they enter the school system, as they
are their children’s first teacher (Crosnoe et al., 2010). These early learning experiences
give the students an academic edge over other students who may not have received any
type academic instruction before entering school (Crosnoe et al., 2010). Hansen and
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Jones (2011) agreed that early learning at home or in a structured environment prepares
students and widens the gap between prepared and non-prepared students.
Home is a child’s first environment of learning. This environment can determine
how successful a child should or should not be in academics. Family influences on the
education of their children have been investigated and have been identified as factors
which continue to operate throughout the early school years and can explain a great deal
of the achievement gap between children in school (Armor, Duck, & University of
Arkansas, 2007). Hansen and Jones (2011) discussed the family’s decision of who should
be educated based on the family’s cultural belief. Many cultures have customs or
standards that forbid a woman to work outside of the home; thus, education should not be
wasted on a girl (Hansen & Jones, 2011). This idea has caused many families to only
focus on the boys because girls are needed at home.
Many children use media as models of how life should be; therefore, the media
should begin to project more images to support mathematics as well as other STEM
careers (Cheryan, 2011). Ross, Scott, and Bruce (2012) explained that when children,
especially girls, do not see women in STEM career fields as engineers, scientists, or
mathematicians, they may feel those jobs are not for women. Cimpian et al. (2016) stated
that girls are underrepresented in mathematics fields which creates a gender imbalance in
STEM careers. Many adolescents see images on television that influence their ideas
about individuals who are portrayed to have successful careers in STEM. However,
students may feel intimidated because they may not see many individuals of who this can
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identify with that have prestigious positions in STEM (Cheryan, 2011; Cimpian et al.,
2016, & Ross, Scott, & Bruce, 2012).
Children enter school with different achievement levels of exposure. Opitz et al.
(2017) reported student deficiencies in basic mathematic concepts began during the early
years of school in Germany. Research reported that girl’s early learning may influence
their perception of mathematics and their ability level (Cimpian et al., 2016). These levels
of exposure result in a class placement where the more advanced student will be assigned
to a classroom with more advanced learners, and the less advanced student will be placed
in a class where there are more students with lower achievement levels of exposure
(Crosnoe et al., 2010). The advanced class may have higher expectations for students and
more rigorous lessons, which will move the advanced student to an increased level of
learning. These differences may widen the academic gap and continue as the student
transitions from one grade level to the next (Crosnoe et al., 2010).
Many students who have lower achievement levels of exposure receive a
curriculum that is less advanced (Crosnoe et al., 2010). If students are placed into classes
regardless of their academic levels, teachers can differentiate the lessons, considering the
different achievement levels, and all students will be exposed to the same lesson.
Otherwise, students will continue to fall behind if they are constantly differentiated by
skill level (Crosnoe et al., 2010; Robinson-Cimpian et al., 2014).
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Teachers’ Perceptions
Teachers’ perceptions about educational programs can influence how well the
program is implemented. Firmender, Gavin, and McCoach (2014) asserted that the
strategies and instructional practices that teachers use in the classroom influence student
learning. The task of a classroom teacher is to identify student deficiencies and prepare
lessons that will help fill in the learning gap between students who are on target and
students who have not yet reached their full potential (Crosnoe et al., 2010). This task
may be difficult for teachers if they are not familiar with the program (Burton, 2012;
Fulmer & Turner, 2014).
Teachers reported that their self-efficacy prevented them from implementing new
strategies in the mathematics classroom due to lack of training (Burton, 2012; Fulmer &
Turner, 2014). The ideas teachers present to their students in the mathematics classroom
are based on their understanding and knowledge of the content, which can impact a
student’s achievement in the subject (Akpan, & Saunders, 2017; Burton, 2012; Fulmer &
Turner, 2014; Zwiep & Benken, 2013). Teacher competency in mathematics classrooms
has been one of many issues that the NCLB Act attempted to improve (Rosas &
Campbell, 2010).
Rosas and Campbell (2010) reported that many schools in the United States have
mathematics teachers who lack a major or minor in math education. For example, Rosas
and Campbell (2010) reported “61% of middle school students were taught by teachers
who did not have a minor in mathematics or a related field” (p. 103). This issue results in
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many students not being instructed by a highly qualified teacher, which may adversely
impact their performance in the classroom and achievement on standardized assessments
(Rosas & Campell, 2010).
When teachers assigned to teach math do not have a solid understanding of
mathematics, they are not preparing students to solve mathematical problems beyond the
classroom (Burton, 2012; Zwiep & Benken, 2013). Rather, they are simply teaching how
to memorize rules and how to use an abstract way of thinking. Furthermore, the students
are not learning how to apply rules to the real world or non-math classrooms, but rather
how to pass the class. Teachers' perception of the mathematics should be positive; this
may help students to value math and to ensure success in the classroom (Zwiep &
Benken, 2013). Teacher attitudes often contribute to student success in any subject.
With the pressures of high stakes testing and daily challenges of the classroom,
many teachers may feel bound by the textbook or may not want to implement new
strategies into the classroom (Burton, 2012; Fulmer & Turner, 2014). This lack of
mathematic content may negatively impact students’ learning as early as elementary
school because of teachers’ limited understanding (Burton, 2014). Zwiep and Benken
(2013) explained that the mathematics curriculum requires teachers “that promote and
integrate, a connected view of content” (p. 300) which will allow them to connect these
concepts to real world experiences and non-math applications. Teachers need
professional development classes that will challenge their content knowledge to help
bridge their understanding with their instruction (Burton, 2014; Zwiep & Benken, 2013).
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Zwiep and Benken (2013) conducted a study where teachers participated in professional
development classes that focused on content knowledge in the mathematics and science
classroom. Zwiep and Benken (2013) discovered many mathematics teachers’
perceptions of what they understood as mathematics learners are strengthened after
participating in a professional development class.
Teacher expectations of their students’ performance have a great impact on
teacher instruction as well as student achievement. Many teachers may feel their students
are not motivated and unable to complete challenging assignments. This leads them to
use basic teaching strategies and not incorporate higher-level thinking strategies into the
lessons (Fulmer & Turner, 2014).
Fulmer and Turner (2014) reported that although teachers desire to incorporate
higher-level thinking strategies and challenging instruction into the lessons, they were
cautious of the motivation and ability that students display in the classroom. This belief
in student motivation may result in wasted time in the classroom, which may impact
student achievement on standardized assessments (Fulmer & Turner, 2014; Zwiep &
Benken, 2013). This expectation of student motivation and interest can be related to
student autonomy and independence (Fulmer & Turner, 2014; Zwiep & Benken, 2013).
Many students may not believe they are able to complete the assignments and
thus rely heavily on their teachers for support. Teachers must be competent to teach
challenging assignments and support students when they feel there is a lack of
motivation, interest, or effort. For example, a math teacher reported that many of her
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students relied on others to complete assignments or would constantly ask questions to
help solve a problem. The mathematics teacher increased the student autonomy and
independence by requiring them to think on their own to achieve the assignment (Fulmer
& Turner, 2014). Less guidance will be needed in mathematics classes if teachers
increase independence in mathematics by providing challenging and higher-level
thinking questions that require open ended response answers (Fulmer & Turner, 2014;
Zwiep & Benken, 2013).
Mathematics Anxiety
Another problem that has been shown to have a negative impact on achievement
in mathematics is mathematics anxiety. The negative attitude toward mathematics
develops as young as elementary school and continues to grow over the years (Finlayson,
2014). Finlayson (2014) informed that children develop an idea toward mathematics as
they enter the classroom environment and begin to interact with others and their
environments. These ideas are often turned into negative experiences as early as
elementary school and are related to achievement in math (Beilock & Maloney, 2015;
Finlayson, 2014; Ramirez, Gunderson, Levine, & Beilock, 2013).
Finlayson (2014) defined mathematics anxiety as a feeling one experiences that
he or she will not be able to perform efficiently in situations where mathematics will be
used. Finlayson (2014) also described anxiety as a feeling of tension that is related to
mathematics. Math anxiety can result in poor cognitive and reasoning thinking when
having to complete a task (Beilock &. Maloney, 2015).
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The fear of mathematics develops from the anticipation of getting the answers
wrong and fear of failure (Beilock & Maloney, 2015; Finlayson, 2014; Ramirez et al.,
2013). Ramirez et al. (2013) stated this fear impacts the achievement and performance of
students in the classroom. When elementary students begin school, the ideas they
developed about mathematics are replaced with other factors such as time testing,
teaching from the textbooks that may suggest only one way to solve a problem, and the
idea of failure (Beilock & Maloney, 2015; Ramirez et al., 2013).
According to Burton (2012), students began to have negative interactions as early
as elementary school because they are taught how to solve a problem for the answer
rather than how to understand and interpret the concepts in mathematics. Burton
indicated that the teacher’s role in the classroom may impact a student’s classroom
experience. Teacher behavior in the classroom may be negative or positive, but teachers
who do not meet the student’s needs or present hostile environments contribute to student
anxiety of mathematics. These factors not only affect student confidence, but also change
student ideas of the importance of math in the classroom, which impacts student
Beilock and Maloney (2015) described mathematical anxiety as a fear that may be
experienced in the classroom and while completing daily tasks. Daily tasks can include
healthcare workers calculating medication or financial planning. Math anxiety appears as
early as elementary school and increases until high school. It can influence a student’s
learning and understanding of mathematics (Young &Young, 2016). Students who suffer
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with mathematics anxiety will try to avoid tasks related to mathematics (Beilock &
Maloney, 2015; Young & Young, 2016). This avoidance may result in negative
consequences such as avoiding math and STEM careers, poor math performance, and
poor math attitudes (Beilock & Maloney, 2015). However, students can be taught how to
manage their behavior and attitudes to improve basic mathematics skills. Strategies such
as scaffolding and spatial activities can be used to help prevent children from being
anxious about doing math. Teachers can teach students how to learn from their faults in
the math class (Beilock & Maloney, 2015).
Mathematics anxiety is a very complex issue in society today. Furner and
Gonzalez-De-Hass (2011) reported that more than two-thirds of all Americans have a
phobia in mathematics that may result in math anxiety. These phobias lead to many
adults not seeking STEM careers and students not achieving success in the mathematics
classroom (Beilock & Maloney, 2015).
Many students do not understand the math concept, as they use rote memorization
to learn rules and procedures for completing mathematics (Finlayson, 2014). Ramirez et
al. (2013) suggested that math anxiety may affect students’ working memory and impact
performance in mathematics. Ramirez et al. (2013) explained that working memories “are
resources that are crucial for successful math problem solving” (p. 188). When students
experience math anxiety, the working memory is influenced and the anxiety may be
compared to an eraser because it erases or deletes the resources needed to complete the
math problem and students find it difficult to continue. A person with more working
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memory capacity will be more successful in mathematics courses but may have more
math anxiety than a person who has little working capacity (Ramirez et al., 2013). For
example, people who show advanced mental ability to retrieve information instead of
relying on counting objects such as fingers or other objects may have less anxiety in math
(Ramirez et al., 2013).
Teacher behaviors impact the way students feel about math. Finlayson (2014)
found that teachers are responsible for the math anxiety that their students feel and
develop in elementary grades. The ideas and concepts students have for math may be
passed from their teachers due to their uncomfortableness or confidence in math when
they are instructing their students (Beilock & Maloney, 2015; Finlayson, 2014).
The instruction implemented in the classroom may have a negative effect on
students’ ideas about math (Aksu et al., 2016; Beilock & Maloney, 2015; Finlayson,
2014; Cheryan, 2011; Ross, Scott, & Sibbald, 2012). Math anxiety is a social anxiety
most often learned in school (Beilock & Maloney, 2015; Finlayson, 2014). For example,
if the teacher relies on the textbook or strategies that are not challenging, then students
may not see the usefulness of mathematics in their lives.
Technology and Its Effectiveness
The National Mathematics Advisory Panel (NMAP) reported that in 2008 the
mathematics achievement of youths, when compared to other countries, had declined
(Rave & Golightly, 2014). Many students need assistance in improving basic
computation, skills, and problem solving in mathematics (Beal, Rosenblum, & Smith,
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2011). Many schools are implementing innovative technology programs to facilitate
learning in the classroom which will encourage the new generation of an advanced
technological population that will eventually enter the workforce.
Technology should be used as a tool to teach students and to guide curriculum
(Bottge, Grant, Stephens, & Rueda, 2010). It has been found to improve student
performance and achievement in mathematics (Barak, 2014; Zhang et al., 2015). Bryant
et al. (2011) found the NMAP encouraged early interventions that provide effective
instructional practices for at risk students. Lopez and Patron (2012) contended teaching
should include various techniques that include different learning styles to ensure students
are gaining the most from the learning experience.
Using technology techniques can make the learning environment exciting and can
improve student achievement (Bofill, 2013; Lopez & Patron, 2012). Children are better
prepared to complete tasks when they are provided an example and the information is
communicated to them. Students may benefit from classrooms that offer a variety of
instructional practices through the use of technology rather than the teacher using
technology to present classroom lessons (Higgins, Huscroft-D’Angelo, & Crawford,
2017). Bottge et al. (2010) maintained that students prefer to use technology in the
classroom to complete assignments.
Kiger, Herro, and Prunty (2012) explained that students are more engaged when
they are able to use smart phones, iPod, and other mobile technology in the classroom.
These mobile devices offer valuable resources and learning opportunities for students.
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Many educators are implementing them into lessons and class assignments, including
field trips.
They are also using them to engage students in the classroom (Kiger et al., 2012).
When students are given the opportunity to use technology to improve their learning, they
benefit. Bellamy and Mativo (2010) contended that students will be able to learn and
recall the information when they are given the opportunity to use technology.
Mobile learning is becoming very popular with school and teacher instruction.
Teachers must facilitate technology applications into mathematics classrooms to engage
learners and improve student performance (Blair, 2012). When mobile devices are used
as a learning tool, students are able to “create individualized learning environments”
(Kiger et al., 2012, p. 63) that fit the needs of students and adapt to their mathematical
ability. For example, Kiger reported the findings of a study with a comparison group and
a mobile learning intervention (MLI) group. The MLI group performed better than the
comparison group that used daily manipulatives such as flashcards, math games, and
other practice methods while the MLI group used iPod Touch and math apps to practice
mathematics concepts (Kiger et al., 2012).
Many students are very technology motivated. Many students have iPhones, MP3
players, gaming devices, and tablets that they use for entertainment (Kiger et al., 2012).
Kiger et al. (2012) explained that schools are reconsidering technology instruction due to
the availability of the Internet and digital learning resources among students. Educators
have begun to use math applications that provide individual learning and adjust to the
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students’ educational needs (Zhang et al., 2015). Math applications provide immediate
feedback to improve student achievement (Kroeger, Brown, & O'Brien, 2012; Ysseldyke
& Tardew, 2007). For example, Splash Math is a math application that adjusts to student
learning and allows students to work at their own pace (Zhang et al., 2015).
Splash Math provides feedback by summarizing student progress. It allows
teachers to give students clear instruction and activity sheets for a working period (Zhang
et al., 2015). Long Multiplication is another mathematics application program that uses a
scaffolding strategy to break the complex information into simple parts for students
(Zhang et al., 2015). Long Multiplication uses a step-by-step approach so students can
solve the problem using this scaffolding strategy (Zhang et al., 2015). The use of
mathematics applications has proven to improve student performance (Kiger et al., 2012;
Zhang et al., 2015).
Data reported by NMAP reveal many students will need intervention strategies or
accommodations to improve their mathematics achievement scores. The National Center
for Education Statistics (2007) reported that the United States ranked ninth out of 47
countries for eighth graders having high math achievement. Studies have shown that
integrated learning systems have been used to help improve the academic growth and
achievement of students. An integrated learning system can be categorized as computer
software systems that provide academic support in subject areas to students via the use of
a computer-based program (Riordan, Hine, & Smith, 2017).
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Computer-based programs are used to remediate students in the classroom and
provide "efficient intervention delivery" (Burns, Kanive, & Degrande, 2010, p. 2).
Students discover learning by receiving some instruction from the teacher and applying
that learned information to the applications in the computer-based program (Burns et al.,
2010). Via technology, immediate feedback is given to teachers and students on the data,
making it easy for teachers to analyze student progress.
Ysseldyke, Thrill, Pohl, and Bolt (2005) conducted a study on the use of Math
Facts in a Flash (MFF). MFF is a mathematical computer-based program that increases
fluency in mathematics (Burns et al., 2010). This study included 13 elementary schools
and middle schools with a sample size of 4,000 students and 148 teachers (Ysseldyke et
al., 2005). The students for the program were chosen from the general population. The
experimental group used the MFF, and the control group did not use the program. The
experimental group showed more growth and performed better academically. Ysseldyke
et al. (2005) found the students who participated in the program experienced an increase
in math skills.
Burns et al. (2010) conducted a study on the effects of a computer-based math
fluency program on at-risk students. This study was different from Ysseldyke et al.’s
(2005) because the at-risk students were selected for the program study. The MFF was
also used as the intervention of choice. Burns et al. concluded that the MFF program
increased math skills of at-risk students who had some basic math skills. Burns et al.
asserted that a struggling math student should have knowledge and understanding of how
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to complete the math skill independently before the teacher can allow the student to begin
a computer-based program such as MFF independently.
Voyager Mathematics Program (VM)
Educators have implemented many programs into the classrooms, hoping to
improve student achievement. VM is one of many programs educators have and are
implementing in the classrooms to move struggling students to grade level proficiency.
VM is a math intervention program for students in grades 2-8 who have difficulties in
mathematics. It has two components consisting of teacher-led and student-centered online
instruction (Cambium, 2010).
VM is research based and incorporates strategies and effective instruction so that
students are successful. One of the approaches that have been recommended through
research is the explicit approach, which provides clear direct instruction to the learner.
VM has shown positive results nationwide. One teacher who used the program with her
elementary school students expressed VM was easy to use for her struggling students.
She loved the assessments that allow her to target her students’ weaknesses (Voyager
Sopris Learning, 2014). A 2011-2012 report presented information from students in
Grades 2 through 8 who had increased their overall proficiency from .92 to 1.35, which
was considered large and educationally meaningful (Voyager Sopris Learning, 2014).
Poole, Carter, Johnson, and Carter (2012) discussed one school that implemented
VMath as a RTI tier 2 math intervention program. The VMath program was used to target
basic math skills for at risk students in mathematics. The students were placed in a small
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pull-out group for supplemental instruction for 30 minutes four times a week. One
student who showed progress was transitioned out the VMath intervention program, but
returned to the VMath intervention program because he began to show weakness and
struggled in the general education math class. Two more students were able to exit the
program after 12 weeks of successful intervention. The two students saw gains and
growth as a result of the program and improved in the general education program. Poole
et al. (2012) reported that the teachers saw a positive improvement for the 10 third
graders in the program.
The VM program uses the quantile framework, which uses scores that note
deficiencies and growths (Cambium, 2010; Voyager Sopris Learning, 2014). This
framework also monitors the success of the student by reporting the goals toward the next
grade level mastery as well as the student’s learning readiness (Cambium, 2010; Voyager
Sopris Learning, 2014). A Georgia report revealed the students in Grades 2 through 8
increased their overall proficiency from .63 to 2.42, which is considered a large and
educationally meaningful growth in achievement (Voyager Sopris Learning, 2014). As
reported on Voyager Sopris Learning website, VM students experienced gains between
.75 to 1.3 as well as during the 2007-2009 school year students across the United States
showing student success in their problem solving and math skills after 26 weeks (2014).
The VM 2009 - 2010 national results reported that "students who completed at
least one VM module had increased their overall proficiency as measured by the initial
and final assessments" (Cambium, 2010, p. 9). The new generation of students has
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opportunities to use many types of technology as a support in improving academic
achievement. Students can work with authentic situations that reinforcement concepts
learned in the classroom (Bellamy & Mativo, 2010). They can learn math concepts with
the use of technological programs and tools that support and motivate their learning
(Blair, 2012; Cambium, 2010). With the use of technology, school districts will be able to
address the needs of many students while working toward the goal of NCLB.
Literature Related to the Use of Differing Methodologies
Qualitative research uses methodologies that have been used in sociology and
anthropology (Lodico, Spaulding, & Voegtle, 2010). This type of research is used by the
researcher to observe a natural setting to gain a perspective for the researcher’s viewpoint
(Creswell, 2014; Taylor, Bogdan, & DeVault, 2016). Qualitative research connects the
researcher's ideas and viewpoints to the facts that data have been collected while taking a
subjective role (Taylor, Bogdan, & DeVault, 2016). The method most appropriate for this
study was a qualitative design.
The mixed-method design can assist the researcher in gaining a better
understanding by combining qualitative and quantitative methods to confirm findings
from data sources (Creswell, 2014). For example, one study found African-American
males who are motivated and encouraged to participate in STEM fields are more
prepared for college and desire to work in STEM jobs (Strayhorn, 2015). African-
American males who are confident are better prepared for college and are more
successful in STEM fields (Strayhorn, 2015). The data in this sequential mixed-methods
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