Prof. Dr. Marzita Puteh and the students. |
SME6044 - CONTEMPORARY ISSUES IN MATHEMATICS EDUCATION. THIS BLOG IS CREATED WITH THE GUIDANCE OF OUR COURSE COORDINATOR PROF. DR. MARZITA PUTEH FROM UPSI. PLEASE BROWSE THROUGH OUR BLOG TO FIND MORE INFORMATION ABOUT MATHEMATICS ANXIETY. LAST BUT NOT LEAST, PLEASE BE A FOLLOWER TO OUR BLOG. THANK YOU VERY MUCH.
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Self-help Techniques
Students have the big indeed to learn the self-help techniques for combating
math anxiety. These techniques include:
1. learn stress management and
relaxation techniques
2. combat negative thinking, visualize yourself succeeding
3. do
“easiest” problems first, start preparing early before the examination
4. try to
understand the “why” of math concepts rather than memorizing
5. find a support
group do math every day and study smart
6. utilize all your resources
7. reward
yourself for hard work!
Shift Toward Assessing Students
Schools really need to shift toward
assessing students' full mathematical power by giving students multiple
opportunities to demonstrate their full mathematical understanding, aligning
assessment with curriculum and instruction, and regarding assessment as
continual and recursive (NCTM, 1995). Teachers need to employ alternative forms
of assessment in math classes, such as: observations, questioning, interviews,
performance tasks, self-assessments of students, work samples, portfolios,
writing samples, paper and pencil tests, and standardized tests. By carrying
out the authentic assessment, students will be more likely to be problem
solvers for the real life situations.
Teachers also need to emphasize more communication in the classroom
through discussion, problem solving, discourse, and writing.
Students are very crucible of math anxiety because the
math exams represent a do-or-die challenge that can inflame all one’s doubts
and frustrations. Here are some techniques and strategies that the teachers
must teach to improve students’ test-taking experience, such as note-taking skills, test-taking skills, relaxation techniques, tell the importance of homework or studying,
the way to read and use the textbook, address the positive “I” messages and also
guiden students on visualization
of success in math.
Collaborative Learning
Students who collaborate can develop a
synergy among themselves which supports their learning, helping them to learn
more, more quickly, and more lastingly. Another practical idea for teacher
is having the cooperative group work so
that able to provide
students a chance to exchange ideas. Cooperative
groups provide students a chance to exchange ideas, to ask questions freely, to
explain to one another, to clarify ideas in meaningful ways and to express
feelings about their learning (Furner & Berman, 2002) . These skills
acquired at an early age will be greatly beneficial throughout their adult
working life.
Different Teaching Approaches
According to
Spikell (1993), students learn best when they are active rather than passive
learners. Hence, teachers must employ
best practices for teaching mathematics in their classrooms by addressing different
learning style. We should accept the truth that everyone is
capable of learning, but may learn in different ways. The theory of multiple intelligences
addresses the different learning styles which the lesson can be presented for
visual/spatial, logical/mathematics, musical, body/kinesthetic, interpersonal
and intrapersonal and verbal/linguistic.
Young children enjoy jokes and cartoons. With all the tension and anxiety,
math humor is greatly needed. The
cartoons may be used to introduce a concept or for class discussion whereas the
jokes are typical case of real life problems. Apart from that, some games that are beneficial to
learners and are enjoyed are cards playing, Life, Yahtzee, Battleship and
Tangrams.
This video below show a fantastic idea that imply the math formulae in a song! I guess that your students might interest your lesson when you play this video.
Use the computer, scientific or graphing calculators,
internet and all technology! There are vast resources out there to help
students learn math as well as conquer their math anxiety. Many teachers and
professors around the world have developed web-sites dedicated to helping
students succeed at all levels of math.
This video below show a fantastic idea that imply the math formulae in a song! I guess that your students might interest your lesson when you play this video.
Relation of Math
Teachers have
the responsible to help students to see
the important of math. Pupils should learn
to value and see application for learning math inside and outside the classroom
since math surrounds us, everything in life is a problem (many involve math).
This will able to help students realize that it is not something from which
they can escape, but a tool they need to learn how to use and apply in
real-life situations. It is important for
students to become confident in their ability to do math.
Math need relevant to students’ everyday life. Thus, students today need for practical math too. Students enjoy experimenting and engaging in exploring, conjecturing, and thinking rather than, engaged only in rote learning of rules and procedures. So, the use of manipulative will able to make learning math concrete. Some of the abstract ideas can be model or represent by the pictures and symbols. This also provides a chance of hand-on activity for students to enjoy their learning in math.
Math need relevant to students’ everyday life. Thus, students today need for practical math too. Students enjoy experimenting and engaging in exploring, conjecturing, and thinking rather than, engaged only in rote learning of rules and procedures. So, the use of manipulative will able to make learning math concrete. Some of the abstract ideas can be model or represent by the pictures and symbols. This also provides a chance of hand-on activity for students to enjoy their learning in math.
Math anxiety happens in the classroom due to the lack of consideration of different learning styles of students. Math must be looked upon in a positive light to reduce math anxiety. Teachers must change their teaching approaches from traditional teaching methods which often do not match students’ learning styles. Once young children see math as fun, they will enjoy it, and, the joy of mathematics could remain with them throughout the rest of their lives. The teachers begin a cycle that will produce less math-anxious students for generations come.
Assess Students' Attitude
How can math anxiety prevent? Schools can help
prevent math anxiety from occurring in students because teachers play a
critical role in helping to develop positive attitudes toward math. According
to Tobias (1987), one way for students to reduce math anxiety is to recognize
when panic starts, to identify the inactiveness in their analytic and retrieval
systems, and to clear up the static without ceasing to work on the problem.
“Mathitude Survey” is a practical idea for teachers and students to assess
their attitudes toward math at the beginning of a school. Hackworth (1992)
suggested that discussing and writing about math feelings will assist in
reducing math anxiety.
Intellectual
As mentioned before, teachers normally
are being trained on the pedagogy of teaching and learning rather than to understanding
the concept itself. Therefore, we are sure that every teacher knows how to
perform the calculation and pass it in the same way the application to the
students without knowing the actual concept of the formulas and where or how it
is coming from.
When some of the high curiosity students
expecting to learn more than simply the application itself, teacher find that
it is hard to analyse and elaborate the concept, and letting students to be
more easily relating the understanding they are performing, into the real world
of application. This is because mathematics does not come by itself without any
reason. By looking through how those mathematicians creating those formulas, we
can see that most of them are stranded into a real world situation, which inspire
them to design and manipulate suitable formula to be use by everyone else.
The
intelligence in overcoming difference learning background also is a big
challenges to a teacher especially in local, there are three main different
learning background and each of them are conducting their own creativity so
help students improving their understanding. When all of them are gathered into
one same teacher, the teacher will found that one same question will lead to
many difference applications which come to the same answer. So it is depending
on ones intellectual to judge the marking scheme. Any inappropriate action will
undermines confidence students’ confidence in performing the same calculation
in future.
Cultural Misconception
Issues relating with
the cultural matter happened all around the world. The misconceptions are
usually deeply implanted in the basic understanding and affecting ones perception, even in the mind of the
teacher which also coming from the same background.
“If
interaction always has a purpose, it also has meaning for those involved. At
its broadest, the teacher-student interaction is probably interpreted as
having some form of educational meaning (as opposed to other forms of meaning
that could exist between adults and young people). However, when we dig down to
specific individual meanings for the interaction that takes place “in the
school” there can, once again, be a wide variety of meanings for those
involved. For the teacher, for example, these can range from “education” being
a vocation – their mission is to influence and change lives for the better – to
the idea that education is “just a job”; something that is to be endured
because it pays the bills”
(Chris
& Tony, n.d)
From what have quoted from Chris and
Tony, it is the matter of what the teacher is thinking about the teaching and
that will be the matter of how he or she performs the teaching process.
Another
misconception is where, from the research of Sian Beilock, teachers
who are anxious about their own math abilities are translating some of that to
their kids (Karen Kaplan, 2010). The research are saying that the anxiety that
pass through from the teacher to the students may lead to a misunderstanding
that male can do better mathematics than female.
Environment
The issues related to the environment,
we are pointing towards the facilities and school management abilities which
are not in the hand of control by teachers; where we may call it as the
spontaneous event or dilemmas.
Sometimes teachers have prepared well on
thing that he or she is going to teach but suddenly things does not going well
as expected. It could be the events arise in the middle of teaching such as
announcement of gathering teachers of science and mathematics for the meetings,
or announcement of the clubs meeting that student’s representative will ask for
the permissions to give their announcement in meeting of few students in the
class. These all are quite interrupting the process of teaching.
Now talk about the facilities, accidents
could happen most of the time without expected. The faultiness of facilities
such as computer, projectors, clashes schedule of laboratory arrangement and so
on. All of these accidents was not able to be predicted, and the lesson might
not going well even though teacher has planned and organize everything well.
Another issue that happened in most of
the school in town area, which is one class, hold large number of students and
some even reaching in the number of fifty or more. The class is too large until
not every student will get the fully attention from the teacher. There are
research proving that smaller classes can shrink the achievement gap
and lead to reduced grade retention, fewer disciplinary actions, less dropping out,
and more students taking college entrance exams (Jeremy & Charles, 2003).
Personality
Roseman
and Smith believe that emotions
are caused by the interpretations of events, rather than events themselves.
(Mei-Lin Chang, 2009) Emotional can be affected by any of the following, it
just the matter of how a person manage the emotion with tactful and not
involving third party, which are the students in school. Emotion regulation
refers to “the processes by which we influence which emotions we have, when we
have them, and how we environment and express them”, said Gross (Mei-Lin Chang,
2009)
Mostly
emotion was distracted by surrounding such as family matter, financial
difficulty, and physiological imbalance, which a person, without oneself
awareness being brought forward into the life, and then to the works in school.
Lastly, this imbalance emotion will be carry on into classes especially when
facing students which we mostly know of their active behaviour. This normally
will end up with either punishment and/or low performance of teaching and
learning process.
The
failure to monitoring classes will also affecting ones emotion and having the
feeling of did not wanted to get in to particular classes. From Nixon
understanding, Emotional valences can extend to other aspects
of the communication environment. For instance, negative experiences with
emotion work can result in an overall negative emotional valence (Scott,
Margaret & Joseph, 2010).They
are sometime give up on trying to manage the class or only choose a few of the
talent students to be concern more so that at least this particular students
will have a better chance in scoring the paper. This action will lead to the
misunderstanding on how the students think on the teacher by what the teacher
may look on them. Students actually are a very simple in sensation of someone’s
reaction. What the teacher done will let them having thought of that teacher
did not likes them, and therefore as to rebel that action, they tend to dislike
the teacher, following by hating the subject that teacher taught.
We
all know that learning mathematics is an on-going process, where mathematics is
related in every single topic. Distributing mathematics into few topics is to
let teaching to be convenient. But now days, teachers have been given so much
of works until themselves having the difficulty in managing time. Mostly the
classes will be taking over by temporary teachers or new teacher to continue
the lessons. When they return to the class, they will find they it is hard to
follow back what have been planned and the interruption of new scheduling will
only make things getting worse.
Personal experiences are also the main
reason on influencing teaching anxiety. Normally this happened to those who are
new in teaching field. Mostly, Pre-service teachers learn majority about the
pedagogy of teaching and learning, rather than to be tested the understanding
on mathematics concepts and how pedagogy took place in understanding those
concept ideas. Therefore, when they approaching the real teaching situation,
they are merely wanted students to score high in examination and increasing
their own reputation in teaching field. So they tend to teach in the form of
memorising formulas and application. This was because they still lack of
experience and suitable creativity in creating interesting lessons which fit to
the students and the situation.
Furthermore, new and normally young
teacher will be assigned to teach those who are less talented students which
usually, the class align at the back of the rank. The reason of this kind of
arrangement was because these classes normally need more attention and afford
to guide compare to the others which aligned at the front rank. This has cause
the new teachers, who are usually being blamed to be no experience and less
professionals, facing the tough challenges at the mean while they might also
being assigned to the others new activities of school rather than simply
teaching in class.
Teaching Anxiety
As every issues were pointed to teachers, we are here to
claim a little more justice for the teachers where even at the end, teachers
still cannot avoid to be the party who should be the most responsible for the
entire anxiety issues in math, but at least, to be given a little bit
forgiveness.
Here we are
looking into three main factors that arise in approaching the teachers’
anxiety, which more suitable, the teaching anxiety. Therefore, we categorize it
into three main categories, which are view from the personality, environment
and intellectual.
The Effects Of Mathematics Anxiety On Matriculation Students As Related To Motivation And Achievement
Based on the review of literature by
Effandi Zakaria & Norazah Mohd Nordin (2008), the results of their study
provide evidence that mathematical anxiety has an important effect in
mathematics education. When the mathematics anxiety is high, students’
achievement is low, when the anxiety is low, students’ achievements is high.
Therefore, teacher should be thinking on how to reduce students’ anxieties by
finding a better way to teach mathematics. Implication on this, Woodard (2004)
suggested techniques to reduce students’ anxiety towards mathematics. Firstly,
create an environment in which students do not feel threatened and allowing
them to relax. Secondly, teachers can use cooperative grouping to encourage
teamwork in problem solving. Thirdly, teachers must teach at a slower pace as
to let the students comprehend better of what the learning is all about. Last
but not least, teachers can provide extra tuition session to build up the
students’ understanding towards learning mathematics.
How Negative Expectancies And Attitudes Undermaine Females’ Math Confidence And Performance
Societies as a whole believe females are less
mathematically capable than males. This belief is communicated to parents and
teachers, who pass it along to students. Girls come to view their failures in
mathematics as evidence that they are indeed inferior and to view their
successes as flukes. This belief reinforces the belief that females are not
capable of doing well in mathematics. Females stop taking advanced mathematics
courses in high school or college, believing them too difficult. In the end,
the expectancies of their parents and teachers are fulfilled and society was
further “proof” of females’ inferior mathematical ability. Refer Diagram 1 as
Cycle of Low Expectancy on Female Students by Parents and Teachers
The findings by researchers further found
that the differences between males’ and females’ performance is quite small.
There is no significant difference between boys and girls mathematical
achievement in elementary school and few differences at any age (Feingold,
1988, NAEP, 1983; Shipman, Krantz & Silver, 1992). These differences are
getting smaller over time (Hyde & Linn, 1988).
In future, as differences decrease, parents
and teachers will see more of that female are capable of performing well in
mathematics. This will lead to more parental and academic support, further
enhancing females’ ability. In this way, the cycle may be broken
Math Anxiety In Elementary And Secondary School Students
Studies have documented the negative
effects of mathematics anxiety on mathematics performance and achievement.
Students’ mathematics anxiety may impact on their ability to learn Mathematics
more effectively. According to Liebert and Morris (1967), they had
distinguished two components of test anxiety. Worry is the cognitive
component of anxiety, consisting of self-deprecatory thoughts about one’s
performance. Emotionality is the affective component of anxiety,
including feelings of nervousness, tension, and unpleasant physiological
reactions to testing situations.
The purpose of this study is to examine the
age and gender difference in mathematics anxiety. In regards to gender
differences, there were no differences in the structure of boys’ and girls’
responses to the Math Anxiety Questionnaires which indicates that they were
answering the items in similar ways. Boys and girls also did not differ in
their reports of math worry, which indicates that they were equally concerned
about doing well in mathematics. However girl reported experiencing more
negative affective reactions to mathematics than boys. These implicate that
that as math courses get harder, girls will be more likely to stop taking math
when they have that option. The suggestion by researchers is that intervention
programs to alleviate the affective and cognitive aspects of math anxiety must
deal with both affective and cognitive aspects. These programs should be
implemented during the elementary school years, before children’s anxiety about
math becomes too strongly established.
Parental And Peer Group Influences Towards Mathematics
According
to Poffeenberger and Norton (1959), parents affect on child’s attitude and
performance can be in 3 ways; Parental encouragement will have a
positive impact towards students’ mathematics interest thus relieving their
anxieties towards that subject. Parent’s own attitudes and trust in
encouraging and motivating their child towards mathematics does significantly
improve their attitude towards the subject generally. Parental expectations
of child’s achievement may put a lot of pressure on them to do well
in mathematics. High expectations towards mathematics from parents will develop
the students’ interest and confidence in the subject. However, too high of an
expectation will create anxiety and avoidance toward the subject. Peer group
can play an important role in either reinforcing or removing their negative
attitude and behaviour towards mathematics. These two factors have great impact
on students’ performance and also math anxiety that should not be taken
lightly.
Kenschaft (1991) reported that parent’s
support or lack of support is an important in students’ attitude and
participation in mathematics instruction. Dossey (1992) considered teachers
important role in shaping attitudes towards mathematics. While Harris (1995),
concluded that peer affiliations become increasingly more influential on
shaping attitudes than parents and teachers.
The Mathematics Anxiety Pattern
Under ‘The Mathematical Anxiety Pattern’ by
(Puteh, 2002) shown in Chart 2, students through negative experiences will
expect failure, and through this pattern each time they avoid or unable to
perform they will again confirm their expectation of failure. Hence, by
restructuring the attitude, this process can be avoided (Mitchell and Collin, 1991,
p.45). Contribution to the formation of negative attitudes towards mathematics
anxiety (Puteh, 2002) are listed below; fear of asking for help, teachers
blaming students for not understanding, teacher ridiculing students. Teacher’s
strictness and fierceness, use of threats and force by teachers, teachers not
showing interest in their students, teaching style which emphasis the transfer
of information and not attention to the learning of the individual.
Relevance - The Usage Of Mathematics In Everyday Life
The most prominent issue raised by the
trainees was that their teachers were using old fashioned way of teaching
(Puteh, 2002). The way of the subject
was being taught led the trainees to perceive the subject as having no links to
everyday life. Thus the process creates
a dislike for the subject and an anxiety by itself.
They cannot relate the theories they have
learnt in mathematics lesson to the real life situation.
Peer Group Influences
Peer
network interactions might operate in a number of ways to develop and encourage
attitudes, values, and behaviours related to learning. Pattison (1994) argues
that social influence can be classified into three categories. Firstly, a
social relationship may determine the type of information a person is exposed
to. Secondly, typical patterns of social interaction may lead to social
influence, i.e., when students develop a shared level of mathematics anxiety to
show affinity to their peer group. And thirdly, social influence may occur when
people perceive that their social position (e.g. as an active or not-active
member of the peer network) has implications for cognition and behaviour.
Students with low performance (slow
learner) try to move the same phase as those with higher achievements in
mathematics, and if they failed to do so, they give up. Students with low
performance’s belief that they will not do better, they then influence friends
in their circle.
Parental Expectations - Their Aspirations And Standards
The students think too much to meet the
expectations and standards of their parents. The pressure from family occurs especially
if any of the family members do better in mathematics. Students could see their
parents as having a job and doing well without a great love for mathematics and
think that they will be successful without an appreciation of mathematics as
well.
Feelings, Worries, Difficulties (Memory, Innate Disability)
Burton, 1979
says that signs on people that have mathematics anxiety are like sweating
palms, queasy stomach, panic, fear, clenched fists, cold sweat, helplessness,
tension, distress, dry mouth, shame and inability to cope and many more just
like other phobia. Students confronted with a difficult mathematical task on
which they are to be assessed may feel nervous and show signs such as tremor in
the limbs and sweating of hands.
A student may, for a variety of reasons,
develop an emotional and intellectual block towards the learning of mathematics
in the course of his school years. Lazarus (1974) describe that a student who
has developed an emotional and intellectual block against mathematics finds
that making progress in mathematics and closely related fields is very difficult.
If student became over-anxious when he or she did not fully understand some
part of the mathematics lesson, they would make greater effort to comprehend.
Such a student actively turns away from mathematics and rapidly develops a
fatalistic attitude about mathematics, fully expecting to do badly. Therefore,
constant failure in solving mathematical problem hence triggers the dislike for
the subject.
Affective Domain - The Self Factor, Such As Personality, Perception
From the affective perspective, Bush (1991)
commented that mathematics anxiety arises from a climate in which negative
attitudes and anxiety are transmitted from adults to children. McMillan (1976) found that teachers’ attitude
and enthusiasm toward a subject had greater impact on student attitudes than
instructional variables.
Lazarus (1974) and Wilhelm and Brooks
(1980) added that negative parental attitudes may be transmitted to their
children and that parents often reinforce their children’s mathematics anxiety.
It could be very difficult for students to like mathematics when their parents
did not do well in mathematics themselves, and thus do not understand it or do
not think it is important.
Students could see their parents as having
a job and doing well without a great love for mathematics and think that they
will be successful without an appreciation of mathematics as well.
Students with low achievement in mathematics
usually those with low self esteem and slow learner, easily giving-up, dislike
of being challenged, low confidence and self blaming for poor mathematics
performance.
Public Examinations And Their Effect
In Malaysia, the Education System is
highly examination-oriented. Many students perceive that getting good grades
will indicate their achievements. There is a perception that getting an A for
mathematics in public examination reflect that the person has better IQ. Good
achievement in Mathematics has also been the basic requirement for the student
to further their studies. In this way, students felt threatened by mathematics
examination.
Morris (1981) stated that mathematics
tends to lend itself to being taught with procedures that unnecessarily build
tension and pressure in some students. She further argue that for example, in a
timed test, many especially the anxious, tend to freeze up under time pressure.
A study by
Betz (1978) revealed that the level of mathematics anxiety reported was related
to scores on a standardized mathematics achievement test. In other words people with high achievement
scores tended to report low mathematics anxiety and vice versa. The trainees here seemed to confirm that high
anxiety about mathematics was predictably liked with poor results in public
examinations.
Teacher Personality And Their Style Of Teaching
Math anxiety is caused by the negative
predispositions of mathematics teacher. Teachers and parents that are afraid of
mathematics pass that on to their students and children (Furner & Duffy,
2002). Teachers with mathematics anxiety transmit their anxiety to their
students (Kelly and Tomhave, 1985; Bulman and Young, 1982 and Lazarus, 1974).
If the
teacher does not value mathematics, his students certainly cannot be expected
to value mathematics either. There are many things the mathematics teacher can
do that will provoke his students to dislike mathematics. The teacher may be
perceived as not caring about students because he is unwilling to give extra
help to students who need it. The students need to know that their teacher is
able and willing to help them.
Most students fear of asking for help and
they feel shy because they do not know how to solve the mathematics problems.
Besides that, the fear of being blamed by their teachers seemed to be a
recurring theme in the students’ response.
This situation created a barrier between the teacher and the student
relationship.
According to (Jackson & Leffingwell,
1999), the teacher needs to be aware of his words, sighs, and overall body
language. This is because the teacher may become angry or frustrated and use
non-proper words when his class does not understand the problems.
Moreover,
covering the textbook problem by problem can turn students off from learning
mathematics. Also, giving written work every day, insisting there is only one
correct way to complete a problem, and assigning mathematics problems as
punishment for misbehaviour can cause students to dislike mathematics (Furner
& Duffy, 2002).
No one
enjoys discipline. Making students do mathematics as a form of discipline could
very likely cause students to dislike mathematics.
What Causes Mathematics Anxiety
From the research conducted by (Marzita
Puteh, 1998), there are several causes of mathematics anxiety. The major cause
of mathematics anxiety was related to teacher personality and their style of
teaching. Besides that, public examination and their effects also lead to
mathematics anxiety. Other than that, it is also related to affective domain or
the self factor such as student’s personality and his perception to
mathematics. Feelings and worries also lead to mathematics anxiety since
students will have difficulties with their memory and innate disability.
Moreover, students were also burden by
parent’s expectation and standards where they must excel in mathematics if they
want to success. Furthermore, it was found that peer group influences and the
relevance of studying mathematics also caused mathematics anxiety.
Myths And Misconception
1. Aptitude for
mathematics is inborn.
2. To be good
at mathematics you have to be good at calculating.
3. Maths
requires logic, not creativity.
4. In
mathematics, what’s important is getting the right answer.
5. Men are
naturally better than women at mathematical thinking.
The Math Anxiety Process
Unpleasant encounters with math in formative years can be
ruinous to subsequent learning. Students who were made to feel bad about math
become wary and prejudiced against it. They mistrust their own abilities. New
experiences in math, seen in light of the old, are tarnished by their troubled
past, which only accentuates and reinforces long-entrenched negativity.
Bad feelings persist. This impairs
prospects for learning new material and generates anxiety and self-doubt. They
say negative things to themselves, such as “I’m stupid”, “I’ll never be able to
do math”, “I’ll fail” and “Why do I need to know math anyway?” Soon a
continuous flood of negative talk about math ensues; before long, anxiety,
overwhelming fears of failing or looking stupid and panic set in.
Physically, these people may experience
nausea, perspire profusely, develop a headache or tight muscles, or exhibit a
number of other physical symptoms. Mentally, they become confused or
disorganized, make lots of careless errors, and forget formulas they knew,
can’t think clearly, or blank out entirely.
Understanding Math Anxiety
There appear to be three major domains
which are involved with the development of mathematics anxiety. There is naturally
some overlap between and among them and their boundaries are not well defined.
In order to facilitate the development of this model of mathematics anxiety,
the domains will be treated as though they are distinct and well defined.
Associated
with each domain is a continuum on which it is assumed that any student at any
particular time may be found. The extremes of the continua are given and
discussed below. The colour codes associate each continuum with its appropriate
domain.
The Social
/ Motivational Domain include those forces that act upon a person through the
agencies of family, friends, and society as a whole. The continuum associated
with this domain is Behaviour because although choices are influenced by
others, they are ultimately made by the individual. The Behaviour Continuum has
Pursuit and Avoidance as its opposites. These behaviours are logical
consequences of the value place on mathematics, which is influenced by the
attitudes of significant others and by society in general.
The Intellectual
/ Educational Domain are comprised of those influences that are cognitive in
nature. Specifically, they include but are not limited to, the knowledge and
skills an individual has and or is expected to acquire and his or her
perception of success or failure in them. Although others may “grade” an
individual’s performance in this domain, people form their own evaluations of
their performance in this area. The continuum associated with this domain is
Achievement, where individual perception is paramount. Success and Failure are
the extremes of the Achievement Continuum, and are the subjective evaluations
regarding one’s acquisition or use of mathematics skill and concepts.
The Psychological / Emotional Domain are
formed by the faculties that are affective in nature. It is largely comprised
of the individual’s emotional history, reactions to stimuli and arousal states.
Hence, the continuum associated with this domain is Feelings. At either end of
the Feelings Continuum lie Anxiety and Confidence, although it could be argued
that enjoyment in even further removed from anxiety that confidence. The
assumption is that most students would find it puzzling to think of mathematics
as enjoyable. Confidence can be equated with comfortableness, rather than pleasure.
Research indicates that the more confidence a person has in mathematics, the more likely he or she is to be successful in such tasks (Betz, 1977, p22) and the more confidence the individual has toward learning and using mathematics, the more likely he or she is to pursue its study.
Anxiety reactions to mathematical situations may contribute to failure in mathematics (Tobias & Weissbrod, 1980, p63). In fact, a person who has high mathematics anxiety may actually be unable to perform well on test, and may be unable to learn in a mathematics classroom. Mathematics anxiety also directly contributes to avoiding mathematics (Tobias & Weissbrod, 1980, p63).
Research indicates that the more confidence a person has in mathematics, the more likely he or she is to be successful in such tasks (Betz, 1977, p22) and the more confidence the individual has toward learning and using mathematics, the more likely he or she is to pursue its study.
Anxiety reactions to mathematical situations may contribute to failure in mathematics (Tobias & Weissbrod, 1980, p63). In fact, a person who has high mathematics anxiety may actually be unable to perform well on test, and may be unable to learn in a mathematics classroom. Mathematics anxiety also directly contributes to avoiding mathematics (Tobias & Weissbrod, 1980, p63).
Definition Of Mathematics Anxiety
Webster’s New Word Dictionary explains
anxiety as worry or uneasiness about what may happen. Freud (1924) defined
anxiety as “something felt,” a specific unpleasant emotional state or condition
that included feeling of apprehension, tension, worry and physiological
arousal, and equated with fear with objective anxiety, which he considered to
be an emotional in its intensity to a real danger in the external world.
Tobias & Weissbrod (1980) defined
mathematics anxiety as “the panic, helplessness, paralysis and mental
disorganization that arises among some people when they are required to solve a
mathematical problem. Meanwhile, Ashcraft & Faust (1994) also defined mathematics
anxiety as feelings of tension, apprehension, or even dread that interferes
with the ordinary manipulation of number and the solving of mathematical
problems. Like stage fright, mathematics anxiety can be disabling condition,
causing humiliation, resentment, and even panic. Mathematics anxiety can cause
one to forget and lose one’s self confidence (Tobias, S., 1993).
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