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Mathematic Psychology and Students
It is no secret that math is not a very popular subject in school. In fact, during the hours I
have spent observing different math classes I have noticed a majority of the students would have
a look of confusion or boredom on their faces. Something else that I observed in the classrooms,
especially in the average level classes, was the different level of understanding between each of
the students with the material, even though they were in the same level class. There would be the
students that would understand the information once it was written on the white board, but there
were also those students that would need it repeated a dozen times before the lightbulb went off.
Then, going off of the students that understand the material, some of them would not do well
when they were tested on the subject, even though their homework and classwork had very little
errors. After some research I came across math anxiety among students, as well as math
disabilities, and how teachers can help those students or prevent them from developing those
issues. With this research I wish to find out ways to make math more enjoyable for the students
and how to help them be more relaxed with the information that is presented to them.
The subject of math anxiety has come farther out of the shadows throughout the years.
Some might think that math anxiety must turn up around the high school level because that’s a
very stressful time for students. The classes are more challenging, they’re starting to think about
their future, and not to mention all the extracurricular activities that they have after school.
Surprisingly, math anxiety starts to show in students at the elementary school level, roughly
around the fourth grade and “escalates in junior high school, when students experience
increasing social pressures” (Perina, 2002). With this information, teachers need to be more
aware of what to look for in order to point out the students that are starting to show signs of math
anxiety or find some exercises to help them be more comfortable with math early on. We will
talk more about what teachers can do to help the students with math anxiety later, but one thing
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that teachers can look out for to point out students that may be perceptible to math anxiety are
students with a low level of working memory. Working memory is, “what allows you to keep
several things in mind simultaneously, and to manipulate them in order to think and solve
problems” (Beilock & Willingham, 2014). In other words, when given a problem, working
memory helps the student keep in mind the information they need and the order of the steps
taken to solve that problem. For example, when the students are taught the order of operations
they are given the abbreviation PEMDAS, which stands for Parenthesis, Exponent,
Multiplication, Division, Addition, and Subtraction, this is also the order in which to solve the
equation. So, when the students are given the problem(2 + 4) × 63
− 12, their working memory
helps the students remember PEMDAS to perform the right steps to get the correct answer. They
would work in the parenthesis first, then the exponent to get6 × 216 − 12, then the students
would first multiply 6 × 216 to get 1,296-12, and finally subtract 1,296-12 to get the solution
1,284. If a student who suffers from math anxiety were to see this on a test or quiz their working
memory would probably fail to remember PEMDAS and therefore solve the equation in the
wrong order, which would lead them to most likely receive the wrong answer.
Another key characteristic that can be found with students that have math anxiety ties in
with their social life. According to Mark Ashcraft, he believes that math anxiety and regular
anxiety are separate from one another, he also states that “if you’re math anxious, there’s a
greater likelihood that you’re test anxious and maybe also socially anxious” (Pernia, 2002). Also
recall earlier that it was is shown that math anxiety tends to escalate at the junior high school
level. Students around that level are starting find the social groups that they belong to, whether
it’s playing sports, joining the drama club, or playing in the band. So, if students are already
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showing signs of being anxious when it comes to math and then they go through the social
pressure of fitting in and finding their group of people, their math anxiety may increase.
Math anxiety may be the most common reason for a student’s struggle in math, however
teachers should not just assume that anxiety is the only reason why they are struggling. Math
disabilities (MD), also known as math dyslexia, are something an instructor should look into as
well. In a study done by N.A. Badian it was found that “6.4% of elementary school and junior
high school children showed some form of MD, as compared with 4.9% who showed some form
of reading disability” (Geary, 1993). Even though students with reading disabilities had a smaller
percentage, they are the students that get the most attention. If a student were to show trouble in
reading, they would most likely be tested or evaluated to see if they needed special help or put in
a certain program. If a student were to show trouble with mathematics, the supervisors would
presumably not take any further actions. Just like how a student that has a disability with reading
cannot read literature that relates to their peers, a student that can be categorized as having a
math disability may have trouble performing the simplest of problems. Working memory comes
into play when dealing with math disabilities as well because the students have trouble
remembering how to perform those simple problems that come so easily to their peers. In a study
done with a class of first graders, there was a mix of MD students and normal students and they
were asked to perform a series of counting tasks to test their understanding of the three how-to-
count rules they were given. The end of this study resulted that, “The MD group committed more
than twice as many computational errors as the normal group on the addition task, and when they
counted to solve an addition problem, they were less likely to use the min procedure” (Geary,
1993). They also found that over half of the errors were because the MD students received fewer
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facts than the normal students, which was suggested that was because the students had an
undeveloped understanding of the essentials of counting.
In that study, the MD students proved to have poor working memory, for the reason that
they didn’t perform the task that was described to them and they did not remember the process of
how to perform it correctly. However it is important to point out that “working memory does not
appear to be a unitary skill but involves a number of component skills- such as rate of decay, the
ability to allocate attention, the level of activation association with problem encoding, and so on”
(Geary, 1993). That is important to mention so people do not think that working memory is
something that you either have or not. It is a combination of different skills that helps the mind
remember the knowledge context to help solve any problem, it does not have to just be in math.
For example, if a mother were to give their child a list of errands to run, working memory helps
the child remember the tasks they were given and how to perform them. In other words, just
because the student’s working memory may be poor when dealing with math that does not mean
that they have no working memory at all. It simply means that the student’s anxiousness is taking
up the space for that working memory, kind of like how a cloud covers the sun and blocks the
rays of sunshine on a cloudy day.
But how can the teachers help these students? Well, there are a number of things that
they can do. First, they can get to know their students by forming a formative assessment, which
is “generally defined as assessment for the purpose of instruction” (Ginsburg, 2009). This would
presumably be the most organized way to understand how the student absorbs the information
given to them and whether it is an MD or math anxiety. There are four parts to a formative
assessment; performance, which observes the child’s behavior toward the context, thinking,
which asks the question why the student is having trouble, learning potential, which questions
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whether the student is ready for the material, and motivation, which is how the teacher will get
the students more interested in the information that is being given the them. With those
categories the teachers will be able to make a detailed assessment on how to help the student. In
order to get that information Piaget believes that “There are fundamentally three basic methods
for assessment: observation, task, and clinical interview” (Ginsburg, 2009). When the teacher is
observing the student, they should keep in mind the different types of learners there are. Every
student is different and absorb the information at different rates.
There are four different categories to classify the students in; expert, mechanical learner,
ordinary learner, and the lost mathematical soul. The expert learner not only understands the
information as the text describes it, but they can also relate the information to real life. For
instance, if the student was taught addition, the expert learner would be able to explain the
process and explain how to use it outside of the classroom. When it comes to the mechanical
learner, they take that information and will try to go above and beyond with it even though they
do not comprehend it. In other words, “He may parrot the teacher’s explanation, but when
pressed does not really understand it, either in purely formal mathematical terms, or with respect
to his own everyday knowledge” (Ginsburg, 2009). So if a mechanical student were to be taught
addition, they hear what the teacher is telling them and mimic the teachers instructions on how to
perform the solution, but they just cannot wrap their head around how and why they took those
steps. Then there is the ordinary student who can perform the context fairly well and understands
a good portion of the information, however they make sloppy mistakes. These students just don’t
pay attention to the little details in solving the problems even though they have a fairly good
understanding on the information given to them. Finally there are the lost mathematical souls.
These students do not have the skill or the understanding of the information to perform. These
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students are the ones in which the teachers should probably further evaluate to see if they have a
math disability.
Something else the teachers could do is keep the math lessons in class light and fun.
Students become more engaged and motivated with the topic when the instructor makes the
lessons fun and has a game that goes with them. If the class is just spent reading from the
textbook the students may not understand the material, especially if the student is more of an
auditory learner or needs more visuals than the textbooks provide. In fact, “One of the biggest
obstacles to learning mathematics is the textbook, which in the USA at least is often more
colorful and lengthy than informative” (Ginsburg, 2009). Since math textbooks are seen as a
slight problem when teaching the students math, then the teachers should try and find ways to
teach the students using it as little as possible. With the rise of technology there are thousands of
programs, websites and videos that can be used to assist the teacher in their lessons. Even regular
board games can be used for teaching the students math because it keeps the class fun and also
works on the student’s strategy skills and playing by the rules. However, “some teachers and
parents are apprehensive about using games to reinforce mathematics because they feel as
though time spent on games could be better spent on drill and practice problems in the
classroom” (Lazaros, 2013). Of course not every class should be spent playing games or spent on
the computer, but it is important to remember that most students are sitting all day and their
attentions starts to drift away if they sit for too long. Especially if the kids are at the elementary
school level, that’s the whole reason why they have recess, because the students need to get their
jitters out from sitting in class all day. By setting aside a day where the students can put what
they have learned to the test through a game the students will become more involved. If the
teacher sees their students every day, perhaps they could have a game day once a week. If the
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students meet every other day, perhaps their game day could be once a month. Giving the
students something to look forward to excites them and if the games are based on the information
they are given, then they will pay more attention in class so that they have the skills needed to
perform well on game day.
By keeping the classes’ fun and doing different activities that test the students on what
they have learned also strengthens their spatial thinking. Spatial thinking “concerns the locations
of objects, their shape, their relations to each other, and the paths they take as they move”
(Newcombe, 2010). Like working memory, spatial thinking is not a learning technique, it is a
way the student thinks. One example of this is when the students are working with 3-D objects
and the teacher hands them the 2-D visual of the shape and the student sees where to fold the
paper in order to get the 3-D shape. These special activities best helps the students at the
elementary level to help them think out of the box when working with math problems. It is
important that, “In the elementary school years, teachers need to supplement the kinds of
activities appropriate for preschoolers with more focused instructions in spatial thinking”
(Newcombe, 2010). One example is a measuring activity where the students measure a picture of
a bear. The student first places the bear at a random part of the ruler and record the measurement,
then they measure the bear again by placing it at the start of the ruler to check their answer. This
exercise helps the students read the hash marks on the ruler more carefully. Even though
measuring the bear is seen as a task for a preschooler, by having the students measure the bear at
a random spot on the ruler it got the students thinking at a higher level.
While getting a detailed assessment on the students and giving them a positive
environment in the classroom are important, making sure the teacher is well informed on the
context is something that should not be over looked. Sometimes when a child is having a hard
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time, they say that it is because the student just does not understand what is being put in front of
him and the problem is too hard. But what about the teacher? Did they teach it to the students
correctly? Do they understand the context? If the teacher is not comfortable with the material
they are teaching then they show their own math anxiety, which makes the students more
anxious. With this being said, “Researchers have found that a course focused on how to teach
math concepts was more effective in addressing math anxiety among pre-service teachers than a
course focused directly on the math concepts themselves” (Beilock & Willingham, 2014). When
future teachers go through their training as an undergraduate they most likely are taught how to
teach and then they are taught the subject they are going to go into. It is very rare to find a course
that will teach the future instructors on how to teach the subject they are going to pursue.
In one study, they found that 2.15% of instructors’ rating the importance of specific
topics to the preparations of future teachers of elementary mathematics said that basic learning
processes were not important at all, whereas 51.611% said that it was important (Laski, Reeves,
Ganley, Mitchell, 2013). Even though 2.15% is a small percentage, it still shows that there are
instructors out there that skipping the basics when training other teachers, which implies that
those teachers may skip out on teaching the basics to their students. Whether the teachers focus
on the basics or not, “Just as students must practice mathematics, educators must also practice
regularly to be capable enough to teach the subject matter and help students solve problems they
encounter” (Lazaros, 2013). It is important for the teachers to fully understand the information
they are teaching the students because if the students ask the teachers questions they need to able
to answer them effectively. Also, like we discussed earlier about how the schools textbooks are
seen as an obstacle, the teacher needs to sure that they are able to break down the information
given by the textbook. If a teacher bases their lesson primarily on the textbook and the student
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asks a question, the teacher should be able to think of an answer without having to back to the
book every time. Which also ties with courses that teach the undergraduates on how to teach
their subject should be available because they may not be comfortable answering the students
questions, due to the fact that they are not comfortable with the subject themselves.
Formative assessment, positive and fun environments, and knowledgeable teachers are
three ways to help decrease a student’s math anxiety and to catch if a student has a math
disability. The formative assessments are an organized way for the teacher to map the student’s
performance and will allow the teacher to determine if the student has a math disability or if the
student is starting to show signs of math anxiety. Keeping a positive and fun environment in the
classroom gets the students excited to go to class and it keeps them interested in the lesson.
Giving them a day to look forward to, by having designated days set for games and activities
based on the context they are learning will also keep the students interest because it is that
knowledge that will help them participate in the set day for games. Finally keeping the teachers
knowledgeable of their subject will decrease the anxiety of the students because when they see
that their instructor fully understands the topic they may become more open to ask questions and
trust the process more. These simple steps could really help students become more affectionate
towards the subject. Starting at the elementary level, showing the students that math is fun and
useful outside of the classroom they will become more attentive of what they learn in the
classroom.
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Work Cited:
Beilock, S., & Willingham, D. (2014). Math Anxiety: Can Teachers Help Students Reduce It?
American Educator.
Geary, D. (1993). Mathematical Disabilities: Cognitive, Neuropsychological, and Genetic
Components. Psychological Bulletin, 114.
Ginsberg, H. (2009). The Challenge of Formative Assessment in Mathematics Education:
Children’s Minds, Teachers’ Minds. Human Development.
Laski, E., Reeves, T., Ganley, C., & Mitchell, R (2013). Mathematics Teacher Educators’
Perceptions and use of Cognitive Research. Mind, Brian, and Education, 7(1), 63-74.
Lazaros, Edwards, J. “Promoting the study of mathematics by using Internet resources in the
technology and engineering classroom.” Children’s Technology and Enineering: A
Journal for Elementary School Technology and Engineering Education, Mar. 2013,
p.10+. Psychology Collection,
libraries.state.ma.us/login?gwurl=http://go.galegroup.com/ps/i.do?p=PPC&sw=w¨in
_c_nichols&v=2.1&id=GALE%7CA322026755&it=r&asid=8f3f558852b66fe90235e52
3f8940d2b. Accessed 7 Nov. 2016.
Newcombe, N. (2010). Increasing Math and Science Learning by Improving Spatial Thinking.
American Educator.
Perina, Kaja. “The sum of all fears: what makes people mathphobic? (Education).” Psychology
Today, Nov.-Dec. 2002, p19. Psychology Collection,
libraries.state.ma.us/login?gwurl=http://go.galegroup.com/ps/i.do?p=PPPC&sw=w&u=m
lin_c_nicols&v=2.1&id=GALE%7CA92849347&it=r&asid=7aa4cc051860353fe7b21c4
146cfbd28. Accessed 7 Nov. 2016
WETA. (2015). Math learning disabilities. Retrieved December 13, 2016, from
http://ldonline.org/article/5896/.
