Running head: IMPLICATIONS FOR INTERVENTION STRATEGIES AS IT RELATES TO
MATH ANXIETY
Tyneshia A. Tolbert
Vanderbilt University
Learning & Instruction Capstone Essay
Implications for Intervention Strategies as it Relates to Math Anxiety
IMPLICATIONS FOR INTERVENTION AS IT RELATES TO MATH ANXIETY
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ABSTRACT
Math anxiety is a major influence in low math performance in America’s public educational
system. Math anxiety can be a result of several different factors. Some of those key factors
include low self-efficacy, cognitive factors, and timed tests. Low self-efficacy affects the
student’s ability to perform well on a math task due to a lack of belief in the student’s personal
capabilities. Cognitive factors influence math anxiety by causing tension in students who have
higher working memory capacity to reason about math, but suffer from cognitive overload.
Timed tests are naturally anxiety provoking and can result in terrible math performance. In order
to improve math performance, math anxiety, as one of many influences, should be reduced in
students in the K12 system who have generally underperformed when it comes to the likes of
assessments. Through examination of the three factors shown to have a causal relationship with
math anxiety, the following recommendations have been made: To transform low self-efficacy
into high self-efficacy, Social Emotional Learning (SEL), a new learning approach that has
gained popularity in the U.S for its unique ability to consider the whole child in the daily routines
of the learning environment, can be enacted in classrooms as an intervention strategy. To
consider cognitive factors in an attempt to reduce math anxiety, teachers must be mindful about
the selection of mathematical tasks and the ways in which they’re presented to reduce the
chances of students dealing with cognitive overload. Last, but not least, timed tests should not be
thrown to extinction, but should be administered in variable assessment approaches to reduce
stress and tension in students ultimately leading to less math anxiety. This in turn will move the
public educational system in the U.S. one step closer to math achievement for all students.
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INTRODUCTION
“Without mathematics, there's nothing you can do. Everything around you is mathematics.
Everything around you is numbers.” -Shakuntala Devi
Mathematics is a content area of high regard to American society. It is a critical skill in
the Kindergarten through Twelfth grade (K12) lifespan of a student. It can be argued that it is a
crucial element in navigating the daily aspects of life. Being that math is such an essential part of
both life and educational curriculum, efforts must be made to ensure students achieve in math to
the highest level of their potential. Ways to improve mathematics achievement for all learners
must be continuously examined. In order to improve, math achievement for a K12 student in the
United States public educational setting must be defined.
Math Achievement
For the purpose of this paper, the definition of math achievement will be informed by the
provisions of the No Child Left Behind Act (2001), which measures academic proficiency in
Reading and Mathematics through the practice of standardized testing. Math achievement is
being able to score at a proficient level of mastery for Mathematics at grade level on statemandated assessments. According to the Center of Education Policy (2007), state test scores in
math has improved over the years since No Child Left Behind was enacted in 2002. However,
the goal of every teacher, school, and school district is to have every learner achieve at Math.
Why isn’t it that every child is successful at math? There is a plethora of reasons that can range
from teacher effectiveness to socioeconomic status. While there are many factors to consider
when discussing potential inhibitors of math achievement, one factor that has been widely
research as being linked to math achievement is math anxiety. This paper will specifically
examine mathematics anxiety as it relates to mathematics achievement.
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Math Anxiety
Math anxiety is defined as "the feeling of tension and anxiety that interferes with
manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary
life and academic situations" (Richardson & Suinn (1972) p. 551,” as cited by Tsui & Mazzocco
(2006). In other words, math anxiety is an influx of affective influences, which could include
tension and anxiety, along with worry and emotionality (Wigfield & Meece, 1988), negatively
associated with Math that can play a substantial role in the lives of students by interfering with
their ability to reason about Mathematics. Using this definition, the construct of math anxiety
will be analyzed within the realms of math achievement, as defined earlier.
Math Anxiety & Math Achievement
Math anxiety and math achievement have been studied for correlation in K12 schools over
many decades through the works of authors such as Ramirez, Gunderson, Levine, & Beilock,
2013; Wu, Willcut, Escovar, & Menon, 2014; Lee, 2009. The authors focus on different factors
that may bring about math anxiety in the K12 classroom and how they might influence academic
achievement. Through much of the research, the correlation between math achievement and math
anxiety has proven to be a negative one. However, in a study produced by Tsui & Mazzocco
(2006), academically talented students tended to perform better on assessments that were anxiety
provoking. Due to the nature of this paper, the identity of the learner is that of a K12, public
education student who is underperforming, or not able to reach proficiency on math standardized
test, in math. Learners who have not been recognized as academically talented or gifted are more
apt to perform worse on assessments when facing math anxiety (Tsui & Mazzocco, 2006).
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Need for Intervention
In an effort to transform the negative association between math achievement and math
anxiety, for underperforming learners into a positive one, intervention strategies must be
proposed to extinguish the factors that may lead to math anxiety. Intervention, after all, is an
attempt to intervene in a situation to produce more favorable results than those that have
historically happened. The first step in preventing or remediating a phenomenon is to understand
what causes it to happen. In a review of the reading list, three key factors, low self-efficacy,
cognitive factors, and timed tests, have been identified as having an effect on math anxiety.
Throughout the remainder of this paper, these three factors of math anxiety will be
examined in depth. The thorough examinations will allow for a suggestion of remediation and
intervention strategies specific to each of these factors in hopes of removing math anxiety in
underperforming K12 learners. With the use of intervention strategies, math achievement will
become more prominent in K12 schools allowing students to reach their highest level of
potential, excluding other factors that may hinder math achievement. This paper will conclude by
discussing the limitations and implications of this research with my current teaching context and
what it will mean for my learners.
LOW SELF-EFFICACY
Self-efficacy is a widely used concept in the field of psychology. It can be defined as
one’s own belief in possessing the capabilities to organize and implement a course of action that
would ultimately lead to success (Bandura, 1997). Self-efficacy is most often synonymously
referred to as self-concept, which involves reflecting upon one’s capacity and capability to
overcome the demands of an environment or situation (Ahmed, Minnaert, Kuyper, & van der
Werf, 2012). Both constructs, self-efficacy and self-concept, focus on beliefs about competence.
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It is not that an individual cannot achieve or be successful at a particular goal, it is more about
the individual having confidence in their abilities, or lack thereof, rather. It is a personal attribute
that is developed in individuals based on a number of influences that include the environment,
previous experiences, peers, content, and so forth. This means that it can be shaped by both
internal and external factors. Considering that there are other factors, it is safe to say that
educators, an external factor, can play a huge part in helping students develop either high selfefficacy or low self-efficacy as it pertains to their subject of expertise.
One limitation that occurs with aiding in this development is being able to measure selfefficacy. It is not directly visible to sensory muscles. In order to get a sense of the self-efficacy of
an individual, you must be able to understand how they feel about themselves and their abilities.
To do so, subtle questionnaires are often constructed to have individuals answer questions
directly related to concepts of self-efficacy. The questions are designed to ask individuals to
predict their own performance on a certain task or in a specific situation. For example, in a study
designed to investigate the relationship between anxiety and self-efficacy by Griggs, RimmKaufman, Merritt, & Patton (2013), students were asked to rank statements, such as “I know I
can learn the skills taught in math this year (p. 364),” adapted from the Academic Efficacy
subscale of the Patterns of Adaptive Learning Scales. There is not a prescribed way to measure
self-efficacy, and the manner in which you would go about doing so differs based on the
intentions of using the questionnaire as a measuring tool. The intended outcome is to get a better
grasp of the level of self-efficacy within an individual.
Being able to measure self-efficacy allows for the comparison of this concept to math
anxiety. Self-efficacy can vary from individual to individual and from task to task. For instance,
an individual may have high self-efficacy when it comes to sports and low-self-efficacy to
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academics. There are a number of factors that could be considered. The intention of this paper is
to examine factors of math anxiety in relation to math achievement, as measured by standardized
tests in the classroom. With that in mind, the element of interest is self-efficacy as it relates to
math anxiety.
Self-efficacy in math and math anxiety, as well as self-concept, have been argued to be
indistinguishable. If that is the case, one would not be able to make case of comparing concepts
that are to be used interchangeable. In light of this debate, Lee (2009) presented a study to
determine if the three constructs are indeed the same idea. Through this study, it was found that
math anxiety and self-efficacy are dissimilar in many ways and have sizable variances across the
constructs and countries. Knowing that the two have been thought of as one, it is important to
survey the aspects of each construct to determine their relationship if it is not a synonymous one.
Reports has shown that self-efficacy and math anxiety, are indeed related (Griggs, RimmKaufman, Merritt, & Patton, 2013). Self-reported high anxiety equals less self-efficacy. The
relationship is reciprocal (Ahmed, Minnaert, Kuyper, & van der Werf, 2012). If a student’s selfefficacy is improved, more success at math will generate as a result of less math anxiety. The
same is true for the complement of that statement. If math anxiety is reduced, students will
develop a higher sense of self-efficacy. Math self-efficacy plays a part in achieving higher math
grades (Ahmed, Minnaert, Kuyper, & van der Werf, 2012). This means that student’s levels of
self-efficacy can be a determinant in both math anxiety and math achievement as we have
defined.
Not only does student’s self-efficacy play a part in math anxiety, but a teacher’s selfefficacy can also. Research has been conducted to determine whether or not a female teacher’s
anxiety carries negative consequences for the learners (Beilock, Gunderson, Ramirez, & Levine,
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2010). The study was conducted with the likes of female teachers because it has been known that
females tend to have more negative attitudes towards the STEM fields than males (Gunderson,
Ramirez, Levine, & Beilock, 2012). It was found that at the beginning of the year, the teacher’s
anxiety had no effect on student performance as it pertained to math tests compared over a short
period of time. However, during the middle of the year and the end of the year, the more anxious
the teacher became, the more the test scores started to decrease for female learners. Math anxiety
for the teachers was measured using questionnaires based on the self-efficacy of the teacher
when performing math tasks. This shows a relationship between self-efficacy in teachers and
math anxiety in students.
A teacher’s influence on math anxiety and self-efficacy is grounded in more than the
teacher’s own self-efficacy. Teacher’s attitudes in the classroom, whether negative or positive,
have been known to influence the success of learners for decades now (Aiken Jr., 1970).
Teachers may also encourage low self-efficacy in math, unknowingly, by the way in which they
visualize intelligence. Those teachers who view the brain as having fixed limitations on
intelligence tend to promote lower self-efficacy in students who have generally been labeled as
underperforming by holding them to lower standards as expectations than their peers (Fennema,
Peterson, Carpenter, & Lubinski, 1990). If a teacher is to analyze the brain as a muscle, then their
beliefs about under-performing students is not affected in a way that would lower a student’s
self-efficacy (Beilock, Gunderson, Ramirez, & Levine, 2010).
Teachers are not the only adults in a child’s life that may influence math self-efficacy.
Parents can be viewed as having the most influence on a child during certain stages of
development. Parents have seen the student firsthand evolve in the learning process over time.
Parents have precedent in many of the biggest decisions concerning their child. Students often
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assume or heavily consider the beliefs and values, including educational, of their parents. This
type of influence can be present throughout a child’s K12 career. “By sixth grade, parents
believe that boys have more natural talent in math, anticipate that boys will have greater future
success in careers requiring math skills, and rate the importance of math as greater for boys than
for girls, and rate math as more difficult for girls than for boys (Eccleset al. 1990),” as cited in
(Gunderson, Ramirez, Levine, & Beilock, 2012). Parent’s beliefs, for the most part, are apparent
to students and made visual through actions. For instance, if a parent does hold higher
expectations for their male child (ren) in Math than they do for their female (child) ren, then
parents would be more accepting of a lower grade from the female child (ren) than the male
siblings of the child. Parent’s holding low expectations for a child can result in the child
lessening their beliefs about their own educational abilities, which results in low self-efficacy.
Low self-efficacy in students is problematic in attempts to achieve math success in the
classrooms.
Social-Emotional Learning
One approach to supporting high self-efficacy in the classroom is the Social-Emotional
Learning (SEL) approach. SEL is an instructional method that has gained popularity in school
districts around the US in the last few years (Collaborative for Academic, 2013). It is described as
an approach to learning that designs the classroom in a way that is conducive to academic learning,
while incorporating the social and emotional needs of the student as well (Griggs, Rimm-Kaufman,
Merritt, & Patton, 2013). Teachers can approach this methodology from a number of different
angles. Schools have designated times for morning meetings in which the teacher is able to address
personal concerns of the classroom that students may not see as directly related to their learning.
It encourages the likes of the classroom as being seen by students as safe havens. It is a place in
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which students feel comfortable being themselves, and everyone in the classroom is aware and
appreciative of the differences of others in the classroom. There is also a research based approach,
known as the Responsive Classroom (RC), that has been proved to lead to a better school climate
and greater student achievement (Children, 2010). It has been founded on the four foundational
basis of positive community, developmental awareness, effective management, and engaging
academics. One central goal of this approach to SEL is to improve self-efficacy in students through
the vision of a more positive school and classroom climate. Given the relationship between selfefficacy and math anxiety, the RC approach was implemented amongst classes in the elementary
grades to determine if the RC approach would bring about a significant difference in math anxiety
and self-efficacy of learners (Griggs, Rimm-Kaufman, Merritt, & Patton, 2013). In this study, math
and science anxiety and self-efficacy was measured in students at the beginning of the year using
self-reported methods and then again at the end of the year. Students who reported more anxiety,
reported less self-efficacy. Teachers were trained to convert their classrooms into a responsive
classrooms through a number of instructional methods designed to promote SEL. At the end of the
year, those students who were exposed to the RC approach had their end of the year self-reports
compared to those students who had not. The results indicated that the students in the RC had less
negative associations between math anxiety and self-efficacy than students in non-RC.
Implementing SEL into the classroom using the RC approach did prove to have a positive impact
on both math anxiety and self-efficacy in students. Although this study was completed in
elementary grades, “middle and high schools optimize youth development when educators
personalize educational and social emotional learning opportunities for the changing needs of
youth (Battistich, 2010; Deci & Ryan, 2002; Eccles & Roeser, 2010; Lapan, Gysbers, & Petroski,
2001),” as cited in (Davis, Solberg, de Baca, & Gore, 2014). By helping students develop socially
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and emotionally throughout their K12 careers, educators can inspire more academic success as
well. Not only does SEL improve self-efficacy in students, teacher’s perceptions about SEL can
also influence a teacher’s self-efficacy (Collie, Shapka, & Perry, 2012). Teacher’s with positive
views about SEL and who enact SEL tend to have higher self-efficacy. Impacting the teacher’s
self-efficacy impacts a student’s self-efficacy as discussed earlier.
COGNITIVE FACTORS
In addition to self-efficacy impelling math anxiety, cognitive factors can play a role as well.
Two cognitive factors that have been linked to math anxiety are spatial processing ability and
working memory capabilities (Maloney, Waechter, Risko, & Fugelsang, 2012) (Ramirez,
Gunderson, Levine, & Beilock, 2013). Working memory capabilities vary by age and
developmental level and describe the ability to store information while actively working with other
information. Spatial processing ability is a trait that is more positively associated with male
learners and describes the process of visualizing geometric aspects and dimensions. Both cognitive
factors can be analyzed and used as indicators of math anxiety in K12 learners.
Working Memory
Working memory capacity increases over time through the different developmental levels
of learners. “Lower-WM individuals are thought to have limited capacity for problem
computations to begin with, which means that anxiety-induced consumption of WM may shrink
this available capacity below the level needed to successfully solve difficult math problems
(Ramirez, Gunderson, Levine, & Beilock, 2013).” In other words, younger students, or students
who have lower working memory as well, have difficulty completing computations because of the
limits placed on working memory. Anxiety consumes working memory consumption, leaving even
less room for computation. Students become overwhelmed and even more anxious.
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Working memory is seen more of as an indirect contributor to anxiety because it has a
reciprocal relationship with math anxiety just as self-efficacy does. Many authors have argued that
anxiety affects working memory capabilities, while others have argued the opposite, working
memory capabilities affect anxiety. However, it has been shown that working memory capabilities
can be used as a predictor of math anxiety (Ho, et al., 2000). Using this information, it can be
concluded that working memory capabilities must be considered in the discussion of reducing
math anxiety for learners.
One route, in view of working memory, to intervene is to be cognizant of cognitive
overload. Cognitive overload is the process of challenging the brain’s ability to process
information by overworking it (Fong, Lily, & Por , 2012). Breaking information into chunks can
be a method for reducing cognitive overload, freeing up working memory capacity. Fong, Lily,
and Por (2012) have found that segmented animations also reduce cognitive overload, as it is
another form of chunking information. Segmented animation can be thought of as the way in which
educators present lessons. When covering a new topic, or reviewing previous learnings, teachers
can plan the lesson into shorter segments in which smaller concepts are addressed one at a time
instead of in a continuous lecture or presentation.
Spatial Processing Ability
Another cognitive factor that is essential to the discussion math anxiety is spatial
processing ability. As with working memory, it is something that develops in students at varied
rates because of multiple reasons. However, cognitive factors can still be addressed in the
classroom although they are not of direct influence of the teacher. In a study conducted by
Maloney, Waechter, Risko, & Fugelsang (2012), the researchers noted the sex difference in math
anxiety and examined the role of spatial processing ability in the disparities. In this study math
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anxiety, as reported through questionnaires, and student’s ability to solve problems involving
spatial configuration and schematic images are shown to have a strong correlation. Students who
had higher scores on the spatial configuration test self-reported having higher math anxiety. Spatial
skills emerge in early grades of school. This lends to the idea of intervening and exposing students
of younger ages to more spatial processing skills and problems to enhance and build foundation
for these skills to develop as students age.
TIMED TESTS
The last factor that will be analyzed in relation to math anxiety is timed tests. Naturally,
placing a time limitation on anything can be anxiety provoking. National tests that have been
administered in schools across the US are timed, with the exception of special accommodations
for learners with recognized learning abilities (No Child Left Behind Act of 2001, 2001). Timed
tests are not going anywhere anytime soon. While timed tests have proven anxiety provoking for
most students, anxiety can lead to very different results for different learners. It was found that
gifted learners in a middle school classroom saw anxiety as a facilitative measure and produced
positive results on timed tests as opposed to learners who had not been recognized as gifted (Tsui
& Mazzocco, 2006). For those students who under-perform on timed tests, it is important to
consider alternative solutions for assessment.
Variable Assessment Approaches
While timed tests are a reality, there are variations that can be considered to convert the
conditions of the timed test to low-pressure conditions. For instance, tests are most often
administered in a sterile environment that consists of the student, paper, and a writing utensil. It is
a room of silence in which the teacher monitors the moves of every student. The environment itself
plays a critical role in testing. Including soft classical or jazz music can be a calming incentive to
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the testing environment, allowing students to feel less pressure and less anxious about completing
the test.
Also, during timed tests, students are often reminded of the time constantly. Instead of
placing a timer in the front of the room, teachers can remind students of the time allotted for the
exam in increments or even individually. It depends on the audience. Teachers will recognize the
ways in which to keep students cognizant of the time frame of the assessment as they get to know
their students and students’ learning preferences better throughout the year.
Besides changing the conditions in which timed tests occur, teachers have autonomy, in
most cases, on how many times students are exposed to timed tests or how they are tested. In
previous experiences, my students tend to test better on the retest because they have a sense of
what the test will look like and what to expect. If the goal is to master the subject being taught, it
shouldn’t matter that students have seen the design of the test as long as they are able to effectively
solve the problems. Students aren’t being tested on how to take a test, but rather what is actually
on the test.
Another variable approach to assessment is group testing. Group testing is not very popular,
due to the amount of monitoring it requires from teachers. However, if SEL is incorporated and all
students feel as though the classroom climate is a positive one, students may feel more
accountability to make sure every member of the learning community plays their part in the test.
Timed tests are a form of assessment that students will encounter, but the way in which the students
are exposed to the timed tests is within the locus of control of the teacher and should be considered
in math classrooms.
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IMPLICATIONS
Timed tests, self-efficacy, and cognitive factors are all considerations that will be helpful
given the context of my learners. Beginning the 2015-2016 school year, I will be teaching a Middle
School Math Connections course at Morgan County Middle School. Math Connections is a Routeto-Intervention (RTI) program that will be implemented the start of this school year in an attempt
to support math learners who have generally been labeled as under-performing through the results
of the Georgia Milestones Assessments. My learners are all in either 6th, 7th, or 8th grade and the
classes are no larger than 15 students.
Through this research, it has been found that under-performing students can possess math
anxiety when approaching math tasks or tests. Reducing math anxiety can be the transformation
technique used to turn under-performing learners into excelling learners. As far as self-efficacy,
there are multiple approaches to increasing self-efficacy in students. SEL is a proven, researchbased approach that helps students develop socially, emotionally, and academically. Taking time
at the beginning of the class, when allotted, to discuss schematics of how students are represented
in the classroom will help me to get to know my students better and get a sense of their personal
development. When lesson planning, I can be sure to chunk information instead of presenting loads
of information as once in an attempt to reduce cognitive overload. This can also be done through
multiple representations of information. Modeling different ways to solve a problem and allowing
them to choose which solution pathway is most feasible for their individualized preferences. Last,
but not least, I’ll be able to allow students to take timed tests in different ways, through the likes
of group testing or chunked testing. Working with a partner or sectioning a test based on time can
be of major influence to the amount of math anxiety a student has. These are all practical changes
or additions that can be made in a K12 classroom to help reduce math anxiety in students.
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LIMITATIONS
Furthermore, these implications should be considered in light of the limitations presented
in the research and context. Throughout the research presented in this paper, there has been
reference through many different age groups of learners in the K12 system. Earlier studies
focused on high school learners’ math anxiety only. However, much research has been done to
include elementary and middle school learners in the recent years. The research is varied and
math anxiety is simulated by different factors according to certain age groups. For example,
working memory capabilities is often only considered in elementary learners who have not
developed a high working memory capacity. Middle and high school learners tend to have more
working memory capacity. Implications for younger learners would be to have shorter tasks, or
less extensive tasks, as for older learners it would be to break assignments into shorter parts, but
not necessarily make the task shorter. As with any instructional method, it must be catered to the
unique needs of the learners in the classroom.
As with age grouping, the research presented also narrowly focuses on female learners in
instances where male learners are not considered. This is due largely in part to the amount of
research that shows female learners tend to have more negative attitudes about math due to a
number of reasons which include math anxiety, as well as gender stereotype, parental, teacher,
and community influences, and perceptions of mathematical tasks.
Another limitation of all the studies researched in this paper is the tools of measurement.
Math anxiety, self-efficacy, and self-concept are not characteristics that can be viewed. The
measurement used is often self-reporting, which could be questionnaires, surveys, or interviews.
It is based hugely on qualitative research, rather than quantitative. There is no value on one or
the other, but there is not a triage of resources that has been used, making the research limited.
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The relationship found between these three factors and math anxiety have not been
solidly identified in a specific causal direction, meaning math anxiety could cause low selfefficacy, poor performance on timed tests, and the ability to process information, or low selfefficacy, timed tests, and cognitive factors are reasons for the occurrence of math anxiety. The
research varies in the direction of cause, but the correlation is still apparent.
CONCLUSION
In conclusion, math anxiety is a construct that can affect K12 learners. Math anxiety
tends to lead to less success on math tasks and assessments, which are used as indicators of math
achievement. Reducing math anxiety will lead to a positive impact on math achievement, so
intervention strategies must be implemented in hopes of decreasing the level of math anxiety in
learners. In order to intervene, factors of math anxiety must be examined and remedied, or even
prevented, if applicable. Three factors that have been concluded to have a major influence in
math anxiety are cognitive abilities or factors, timed tests, and low self-efficacy. By being aware
of cognitive overload, working memory capacity, and spatial processing ability, cognitive factors
that induce math anxiety can be examined and considered in the planning of daily lessons to
reduce math anxiety. Timed tests are an inevitable part of K12 learners’ lives and are known to
be anxiety-provoking. By reducing the amount of timed tests administered to students, using
variable assessment approaches, such as group testing, individual testing, and low-pressured
testing environments, and conducted untimed tests, math anxiety can be lessened, also leading to
greater math achievement. Also, improving self-efficacy in students can lead to less math
anxiety, due to the negative associations found between the two.
Math anxiety is only one of many factors that influence math achievement. To increase
math achievement in learners, math anxiety must be reduced, but more intervention strategies
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must be enacted as well to combat all the internal and external factors contributing to math
achievement. However, one teacher can make a difference in a classroom of learners by making
strides to reduce math anxiety.
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