| home | stands | games | about | mpjournal | back | links |
It never fails. Someone asks me what my major is. I reply "mathematics." The ensuing (resulting) reaction is the same old story. A nervous laughter trailing behind a doubtfully expressed, "oh." Perhaps a comment with the likes of "I was never any good at math" or "I used to be good at math..." or maybe just a trembling and a fear-filled shaking of the head. Naturally, the topic is not pursued (followed), at least not in this conversation.
I am not the first to make this observation. I, as well as others, have noticed that this somewhat averse (reluctant) reaction toward mathematics is not only very common, but more curiously, quite intense. For years, this reaction has baffled (puzzled) and intrigued (fascinated) me for exactly these reasons. Thus, I decided to study and research a bit into the topic of why students, particularly during adolescence (teenage), begin to lose interest and even begin to dislike mathematics.
This is not to say that everyone hates mathematics. To propose such a thing would be ridiculous (absurd). However, the reality remains that a relatively large number of students would admit that mathematics was not exactly one of their favorite subjects during school. Yet, these same students would agree that mathematics is important. With the pace at which technology in this country is progressing, one could argue that since mathematics is the foundation for all this progress, mathematics is therefore an important subject in education. Hence, we must build a strong foundation of mathematics in our children so that they can become the great scientists and researchers in the world to make the world a better place. On the other hand, one can argue that this advancement of technology has, in a sense, created a catch-22 effect, where the increased accessibility to computers and calculators equipped with high-powered functions has actually decreased the need for children to pedantically (thoroughly) learn traditional mathematics through means such as times tables, flashcards, and memorization. This paradox raises the question of what the purpose of teaching mathematics really is. The most common response is that the purpose of teaching mathematics is to get a "good job". In other words, a fairly strong background in mathematics is, in a sense, essential to survival (continue existence) in a modern society such as ours. Besides getting a "good job", one needs mathematics in order to know how to balance a checkbook and how much to tip the waiter at your favorite restaurant, for instance; that is, it has a very specific, concrete, utilitarian purpose. But how often is mathematics seen as a vessel in which to achieve greater means, like learning how to think, or enriching one's personal life, one's soul?
Keep in mind that the objective of this editorial research paper is not to find ways to make math more interesting for students. I would like to merely examine the reasons behind this fascinating phenomenon of the widespread (extensive) "lack of enthusiasm (strong desire)" (to put it mildly) for mathematics. By examining these reasons, I believe we create a little window into the mystery of what causes our likes and dislikes, what causes those "walls" to come up when we are faced with certain things.
First, one may even question the necessity and validity of studying a topic such as emotions related to math. After all, math is often seen as an emotionless, cold discipline. Well, for such an emotionless field, it certainly evokes (reminds) quite an intense emotional reaction for many. It is a strange phenomenon that while most people can recall their feelings about math when they were in school, sometimes even with great detail, they remember almost none of the content of the subject. A lot of research has already been done on what is learned in school, but not on what is liked. However, what is liked is just as important as what is learned; to an extent, one depends on the other. What we learn may sometimes shape what we like and vice versa. Furthermore, it is ideally what we like now that shapes what we may become later.
One of the most common reasons for disliking math pointed to the rigidity and lack of creativity in mathematics. Most people see math as a discipline where an answer is either right or wrong. There is no room for personal interpretation as there is in other fields such as the humanities. Unfortunately, many times, answering right or wrong may sometimes translate to YOU are right or wrong. English math educator, Laurie Buxton, proposes that the intense negative feelings we get from answering incorrectly or doing poorly in math may have something to do with the moral connection of right and wrong.
At first when I read this theory, I was quite skeptical (disbelieving). But examining closer into this theory, I can see how our system of over-emphatic rewarding of accuracy may treat errors as a cause for shame. This common attitude raises some deeper issues of how the black and white image of mathematics affects our feelings of personal worth.
One day while I was teaching math to a class of twenty-four seventh graders over the summer, other teachers and I presented our students with the question: "How important do you think it is to get the right answer?" Most students agreed that ideally, the right answer is not as important as learning about the problem and thinking critically and seriously about the problem. However, many students responded that it is still very or even most important to get the right answer. The reason, they explained was because most of the time in their math classes in school, the class is conducted in such a way that the right answer is the most important thing. So while most of the students felt that inside, getting the right answer was not as important, the reality is, material is presented in a way such that the right answer is most important.
Math anxiety is another factor that seems to make math more unpleasant. Math anxiety happens at all levels, from learning fractions in 6th grade to taking an exam for a masters degree. Anxiety in general happens when survival is at stake (risk). However, what has that got to do with math? Doing poorly in math certainly will not kill you physically. Yet, not succeeding in math can feel like a metaphorical or internal death. From day one of high school, we have driven into our minds that math is necessary in order to get a "good job", and a "good job" points to greater chances of survival in our modern society. So, in fact, subconsciously, we may realize that our survival IS at stake if we do not succeed in math. How our performance is connected to our feelings of self worth may also help explain these feelings of the metaphorical death.
· Time pressure : The pressure caused by time restrictions when doing math can be debilitating (weakening) to the point where one cannot think clearly. The ticking of the clock hovers above one's head like the cloud that clouds one's mind. Sometimes, this sense of urgency can even defeat the objective of learning the material. As Buxton points out, "ideas in math...seem immensely difficult before they are grasped, and sometimes easy to the point of triviality when they are understood." The reality is that some students simply take longer than others to understand a concept.
I remember as a young child, I absolutely loathed (hated) those flashcards my mother would whip out (practiced) regularly to sharpen our math skills. Even when mom did not express any negativity when I answered incorrectly or when I was slower than my siblings, I still felt horrible. The negativity was inherent in the purpose of the flashcards.
· Authority : Authority can take shape in the form of rules, teachers, and parents. Math is often seen as a set of rules, impenetrable (impassable) and final. Normally, one would not panic when faced with rules; perhaps one may react with slight annoyance (irritation), but certainly not panic. According to psychologist Richard Skemp, panic occurs when we do not know which rules we must follow. In mathematics, this is often the case.
Attached to our memories of math anxiety are our math teachers. Math teachers have an image of being intimidating, the creator of all our suffering in math. This happens for many reasons. First of all, teachers are the authority on the subject matter. Hence, it is naturally thought that everything the teacher says is right, and you are wrong if you do not say exactly what she says. Second of all, it is common for students to feel the threat of judgment from the teacher. True, it is not the job of a teacher to judge a child, at least not in today's world of political correctness. However, the student cannot help but feel the threat of judgment. We have some silly idea that our performance in math says something about our self-worth; and we would not like to be seen as worthless in the eyes of those we respect and care about. For me, it is my desire to not disappoint those whom I respect and care about, such as my parents and certain teachers, which drive this particular type of anxiety.
Some students may mention "difficulty" and "complexity" of math as reasons for not liking math. These vague nouns to mean math became more difficult because: 1) of changes in the material 2) old methods of learning are not enough anymore 3) genetics.
· Change in material : Like any other subject, learning mathematics is not a static process. The first time this hits students in a large way usually happens when they start doing pre-algebra or algebra. Math does not have just numbers anymore! Now it has letters called variables, and sometimes, these letters aren't even English!! What are these crazy math teachers trying to do to us? Letters should be kept with letters and numbers with numbers -- no mixing! These sentiments (feelings) reflect the difficulty of symbol translation for many students in mathematics. Some have said that learning math is analogous (similar) to learning a foreign language. Any foreign language is filled with a myriad (countless) of terms filled with meaning; but sometimes, we are unsure of what those meanings are. Often one can define with exquisite (beautiful) precision (accuracy) a symbol (i.e. d/dx (f(x)) the derivative of f(x) taken with respect to x), but whether or not the meaning of that symbol is fully swallowed, digested, and understood is another story. Sometimes, it just takes time for these definitions to sink in. However, the way our curriculum is structured often does not allow the absorption time that is needed so that each definition is understood in a consecutive linear fashion.
Furthermore, learning math in schools is a cumulative process for the most part. In order to advance to higher levels of math, one must have a strong foundation in order to be able to tackle the new material later on. Actually, there has been some argument over this point. Some say that Trigonometry can be learned without Algebra, or Calculus can be learned without algebra. But common opinion is that learning mathematics is a process of building. If one does not have a firm grasp on the elementary concepts and ideas first, one can become so lost later on that one can feel such an impenetrable feeling of despair and loss of hope. That is when one often throws in the towel. A foundation of hollow wooden sticks cannot support the tons of concrete built on top of it. The foundation is merely crushed and the concrete falls and shatters into a million useless rocks.
Things simply do not make sense anymore! When we learned multiplication in grade school we learned 2*3 to mean take 2 and add it to itself 3 times. Then with the introduction of rational and negative numbers, that rule just got blown out of the water. What does Sqrt(2)*Sqrt(3) mean? How can you take Sqrt(2) and add it to itself Sqrt(3) times? Or what about -2*-3? How do you add -2 to itself -3 times? What does -3 times mean? The old friendly rules we learned simply don't work anymore. How do we know if we can trust what we are being told anymore? The problem really is, even if we were to teach our students the meaning of -2*-3, that does not guarantee that math will be any easier to understand at that stage. The problem is not whether to teach a student the algorithm for solving the equation 3x+15=0 or to teach the abstract meaning of 3x+15=0. The problem lies in creating that connection in the student's mind between the algorithms to the meaning. Sometimes that connection has to come months or even years later.
· Old tricks don't work anymore : Some have said that the reason they have lost interest in math is simply because learning the formulas, following the examples, and praying for the curve to work for you, just don't work anymore. The result is that one must put more effort into learning the material, and for some, the material is not worth the trouble. One "can work for hours and still not understand," said one student of a survey. Many feel that those hours can be used more efficiently somewhere else.
· "I just can't do math" : In other words "I wasn't born with the ability to do math." Blaming biology for our total lack of ability to do math comes from the sentiment that "if we haven't learned something so far, it is probably because we can't." It is dangerous to accept such a sentiment, for it is thoughts like these that cause us to limit ourselves far more than we should. The existence of the math gene is uncertain. Personally, I do believe that some people have more mathematical talent (ability) than others; however, this talent does not depend solely on biology. Some have made the generalization that Asians tend to be better at math than Americans. Does this imply that Asians are born with a "math gene" that makes them "better" at math than Americans? Hardly. When asked why some students do better in math than others, Asian children, their teachers, and parents pointed to hard work, while their American counterparts pointed to ability.
The most compelling (convincing) reason for losing interest in math that I have seen so far is the one that asks, "Why do I have to do this? What does it have to do with me ?" This inquiring attitude (approach) is usually formed during adolescence. During this critical time in a person's life, one filled with endless questions about life and identity, an adolescent may often conclude that mathematics lacks human insight. Math simply does not apply to things they care about at that time when one is finding oneself, one's self-identity. Hence, mathematics merely becomes a nuisance (bother).
Students may also complain of boredom. That "math is just numbers -- no drama," as one respondent succinctly put it. However, this boredom may result from the fact that much of the teaching of mathematics in K-12 is based a lot on repetition and memorization. One can be bored with these ideas even if the ideas that are repeated or memorized are not fully understood.
To the comment, "I'm never going to use this stuff anyway," a respond may be in this way: Certainly when one is in subjects such as algebra or geometry, a student could easily be contradicted. However, for subjects like Calculus and higher math, contradictions do not come quite as easily. For economists, statisticians, engineers, physicists, etc. higher math is definitely useful. However, if one aims to be a journalist, lawyer, artist, or ambassador, it is hard to give an answer, other than an abstract one:
Many mathematicians would attest (inform) that they find great pleasure in swimming in the sea of human logic; that mathematics as a language, with its precision and foundation is quite beautiful. In every math teacher who appreciates the discipline, there is a part of him or her that wants to impart (teach) the knowing of this beauty and appreciation to his or her students, just as an art or music teacher would like to impart the appreciation of art and music to his or her students.
Mathematics is often seen as a very private activity. One is in her own little world, wrapping herself in this "web of mystique" called mathematics. To some, mathematics is an esoteric field, a sort of Garden of Eden on the other side that has denied them and is reserved for only the elite few. Such denial may make them resentful (offended) toward the discipline.
I used to think that anyone who used the word "math" and "beautiful" in the
same sentence was crazy. But, as the old cliché goes "beauty is in the eye of
the beholder," and in my mind, it would not make sense to believe otherwise. To
me, there is no hierarchy among the emotional, mental, spiritual, or physical.
All areas must be given attention. The purpose of teaching mathematics in
schools is not just to employ the future citizens of this country will the
skills of physical survival. If that were the case, then it is possible at
this stage in American history that calculators and computers could take care of
that purpose for us. However, while calculators give us the ability to
compute, they do not give us the ability to understand what one is
computing. Therein lies the difference and the greater reason behind why one
should learn math. I believe that the greater purpose of why math is taught in
schools is to teach one to think about thinking, to invite one into exploring
how one thinks. Just as one may find a divinity (spirituality) in love, in
god, in dancing, one may also find divinity in thinking.
· Know thyself: We all would like to learn math well enough so that we do not become victims of our fear; that is, we would like to reach the point where our fear or distaste for math does not make our decisions for us. The best way that I think one could reach this stage is to know oneself. When the wall comes up, your first reaction may be to close your eyes and turn away. First, realize that you are closing your eyes and you are turning away. Then reflect and critically think about why you react the way you do when the wall comes up. Sometimes walls can lead to windows to one's understanding. The trick may be to poke around, examine the wall. Try to observe it upside down, sideways, standing on your head. One way to reflect may be to keep a journal in which you can vent, reflect, and otherwise critically think about what you are feeling when your wall comes up.
· Group talk: Another method that will surely alleviate (ease) your pain is simply to talk to others about what you are thinking and feeling when doing a problem. I have found that communication is a bridge that makes working on math such an enjoyable and fulfilling experience. Even finding out that you are not alone can excise (remove) a great acidic tumor out of your stomach, which allows you to focus more on the work and not your discomfort. Most people who do not like math do not like to talk about math. Hence, that bridge of communication that makes life so much nicer may never be built, and doing math then seems so much harder.
· Learn to read math: Learning to read math is a very useful skill that will aid your understanding. Reading a math textbook is not like reading a novel or even a history textbook. One can read along in a novel and not fully understand every line, yet still grasp the essential parts of the novel such as the theme, plot, etc. However, one cannot do this when reading math. For instance, most of the time every single line in a proof must be understood in order to convince me why a theorem is true. I will often spend an hour just reading a page or two in a math textbook. Thus, if you are find yourself attempting to read a math textbook and not understanding the third sentence, do not be alarmed; this is normal. Now all you must do is reserve some patience for tearing apart each statement. Also, I've found that stating things your own way helps a lot. Once you start writing things your way, you will find that math actually allows quite a bit of room for creativity, and you may even find yourself losing the constant tendency to ask the teacher for confirmation, for by then, you will have already confirmed it yourself through your own logic.
Certainly there are many other ways to cope with negative feeling about math. However, these three are some of the most helpful ones for me.
A famous stage actress was once asked if she had ever suffered from stage fright, and if so how she had gotten over it. She laughed at the interviewer’s naive (inexperienced) assumption that, since she was an accomplished actress now, she must not feel that kind of anxiety. She assured (certained) him that she had always had stage fright, and that she had never gotten over it. Instead, she had learned to walk on stage and perform - in spite of it.
Like stage fright, math anxiety can be a disabling condition, causing humiliation, resentment, and even panic. Consider these testimonials from a questionnaire given to students in the past several years:
à When I look at a math problem, my mind goes completely blank. I feel stupid, and I can’t remember how to do even the simplest things.
à I've hated math ever since I was nine years old, when my father grounded me for a week because I couldn’t learn my multiplication tables.
à In math there’s always one right answer, and if you can’t find it you've failed. That makes me crazy.
à Math exams terrify me. My palms get sweaty, I breathe too fast, and often I can't even make my eyes focus on the paper. It’s worse if I look around, because I’ll see everybody else working, and know that I’m the only one who can’t do it.
à I've never been successful in any math class I've ever taken. I never understand what the teacher is saying, so my mind just wanders.
à Some people can do math - not me!
What all of these students are expressing is math anxiety: a feeling of intense frustration or helplessness about one's ability to do math. What they did not realize is that their feelings about math are common to all of us to some degree. Even the best mathematicians, like the actress mentioned above, are prone to anxiety - even about the very thing they do best and love most.
Imagine that you are at a dinner party, seated with many people at a large table. In the course of conversation the person sitting across from you laughingly remarks, “of course, I’m illiterate (uneducated) …!” What would you say? Would you laugh along with him or her and confess that you never really learned to read either? Would you expect other people at the table to do so?
Now imagine the same scene, only this time the guest across from you says, “of course, I’ve never been any good at math…!” What happens this time? Naturally, you can expect other people at the table to chime in cheerfully with their own claims to having “never been good at math” - the implicit message being that no ordinary person ever is.
The fact is that mathematics has a tarnished (discolored) reputation in our society. It is commonly accepted that math is difficult, obscure, and of interest only to “technical people, not a flattering characterization. The consequence in many English-speaking countries, and especially in the United States, is that the study of math carries with it a stigma (shame), and people who are talented at math or profess enjoyment of it are often treated as though they are not quite normal. Alarmingly, many school teachers - even those whose job it is to teach mathematics - communicate this attitude to their students directly or indirectly, so that young people are invariably exposed to an anti-math bias at an impressionable age.
It comes as a surprise to many people to learn that this attitude is not shared by other societies. In Russian or German culture, for example, mathematics is viewed as an essential part of literacy, and an educated person would be chagrined (bothered) to confess ignorance of basic mathematics. (It is no accident that both of these countries enjoy a centuries-long tradition of leadership in mathematics.)
Our jaundiced (skeptical) attitude towards mathematics has been greatly exacerbated (worsened) by the way in which it has been taught since early in this century. For nearly seventy years, teaching methods have relied on a behaviorist model of learning, a paradigm which emphasizes learning-by-rote; that is, memorization and repetition. In mathematics, this meant that a particular type of problem was presented, together with a technique of solution, and these were practiced until sufficiently mastered. The student was then hustled (pushed) along to the next type of problem, with its technique of solution, and so on. The ideas and concepts which lay behind these techniques were treated as a sideshow, or most often omitted altogether. Someone once described this method of teaching mathematics as inviting students to the most wonderful restaurant in the world - and then forcing them to eat the menu! Little wonder that the learning of mathematics seems to most people a dull and unrewarding enterprise, when the very meat of the subject is boiled down to the gristle before it is served.
A host of common but erroneous (mistaken) ideas about mathematics are available to the student who suffers math anxiety. These have the effect of justifying or rationalizing the fear and frustration he or she feels, and when these myths are challenged a student may feel defensive. This is quite natural. However, it must be recognized that loathing of mathematics is an emotional response, and the first step in overcoming it is to appraise one’s opinions about math in a spirit of detachment. Consider the five most prevalent (common) math myths, and see what you make of them:
This belief is the most natural in the world. After all, some people just are more talented at some things (music and athletics come to mind) and to some degree it seems that these talents must be inborn. Indeed, as in any other field of human endeavor (affort), mathematics has had its share of prodigies (masterminds). Karl Gauss helped his father with bookkeeping as a small child, and the Indian mathematician Ramanujan discovered deep results in mathematics without any formal training. It is easy for students to believe that doing math requires a math brain, one in particular which they have not got.
Mathematics is indeed inborn, but it is inborn in all of us. It is a human feature, shared by the entire race. Reasoning with abstract ideas is the province of every child, every woman, every man. Having a special genetic make-up is no more necessary for success in this activity than being Mozart is necessary to humming a tune.
Ask your math teacher or professor if he or she became a mathematician in consequence of having a special brain. Almost certainly, after the laughter has subsided, it will turn out that a parent or teacher was responsible for helping your instructor discover the beauty in mathematics, and the rewards it holds for the student - and decidedly not a special brain.
Some people count on their fingers. Invariably, they feel somewhat ashamed about it, and try to do it furtively (secretly). But this is ridiculous. Why shouldn't you count on your fingers? What else
is a Chinese abacus, but a sophisticated version of counting on your fingers?
Yet people accomplished at using the abacus can out-perform anyone who
calculates figures mentally.
Modern mathematics is a science of ideas, not an exercise in calculation.
It is a standing joke that mathematicians can’t do arithmetic reliably, and I
often admonish (warn) my students to check my calculations on the chalkboard
because I'm sure to get them wrong if they don’t. There is a serious message in
this: being a wizard at figures is not the mark of success in mathematics.
This bears emphasis: a pocket calculator has no knowledge, no insight, no
understanding - yet it is better at addition and subtraction than any human will
ever be. And who would prefer being a pocket calculator to being human?
This myth is largely due to the methods of teaching discussed above, which emphasize finding solutions by rote. Indeed, many people suppose that a professional mathematician’s research involves something like doing long division to more and more decimal places, an image that makes mathematicians smile sadly. New mathematical ideas - the object of research - are precisely that. Ideas. And ideas are something we can all relate to. That’s what makes us people to begin with.
The grain of truth in this myth is that, of course, math does require logic. But what does this mean? It means that we want things to make sense. We don't want our equations to assert that 1 is equal to 2.
This is no different from any other field of human endeavor, in which we want our results and propositions to be meaningful - and they can’t be meaningful if they do not jive (suit) with the principles of logic that are common to all mankind. Mathematics is somewhat unique in that it has elevated ordinary logic almost to the level of an artform, but this is because logic itself is a kind of structure -an idea- and mathematics is concerned with precisely that sort of thing.
But it is simply a mistake to suppose that logic is what mathematics is about, or that being a mathematician means being uncreative or unintuitive, for exactly the opposite is the case. The great mathematicians, indeed, are poets in their soul.
How can we best illustrate this? Consider the ancient Greeks, such as Pythagoras, who first brought mathematics to the level of an abstract study of ideas.
They noticed something truly astounding: that the musical tones most pleasing
to the ear are those achieved by dividing a plucked string into ratios of
integers. For instance, the musical interval of a “fifth” is achieved by
plucking a taut string whilst pressing the finger against it at a distance
exactly four-fifths along its total length. From such insights, the Pythagoreans
developed an elaborate and beautiful theory of the nature of physical reality,
one based on number. And to them we owe an immense debt, for to whom does not
music bring joy? Yet no one could argue that music is a cold, unfeeling
enterprise of mere logic and calculation.
If you are building a bridge, getting the right answer counts for a lot, no doubt. Nobody wants a bridge that tumbles down during rush hour because someone forgot to carry the 2 in the 10’s place! But are you building bridges, or studying mathematics? Even if you are studying math so that you can build bridges, what matters right now is understanding the concepts that allow bridges to hang magically in the air - not whether you always remember to carry the 2.
That you be methodical and complete in your work is important to your math instructor, and it should be important to you as well. This is just a matter of doing what you are doing as well as you can do it - good mental and moral hygiene for any activity. But if any instructor has given you the notion that “the right answer” is what counts most, put it out of your head at once.
If there is even a ghost of a remnant (trace) of a suspicion in your mind about gender making a whit’s difference in students’ mathematics aptitude, slay (kill) the beast (creature) at once. Special vigilance (care) is required when it comes to this myth, because it can find insidious (dangerous) ways to affect one’s attitude without ever drawing attention to itself. For instance, I’ve had female students confide (tell) to me that - although of course they do not believe in a gender gap when it comes to ability - still it seems to them a little unfeminine to be good at math. There is no basis for such a belief, and in fact a sociological study several years ago found that female mathematicians are, on average, slightly more feminine than their non-mathematician counterparts.
Across the centuries, from Hypatia to Amalie Nöther to thousands of contemporary women in school and university math departments around the globe, female mathematicians have been and remain full partners in creating the rich tapestry of mathematics.
Even though all of us suffer from math anxiety to some degree - just as anyone feels at least a little nervous when speaking to an audience - for some of us it is a serious problem, a burden that interferes with our lives, preventing us from achieving our goals. The first step, and the one without which no further progress is possible, is to recognize that math anxiety is an emotional response. (In fact, severe math anxiety is a learned emotional response.) As with any strong emotional reaction, there are constructive and unconstructive ways to manage math anxiety. Unconstructive (and even damaging) ways include rationalization, suppression, and denial.
By “rationalization,” we mean finding reasons why it is okay and perhaps even inevitable - and therefore justified - for you to have this reaction. The myths discussed above are examples of rationalizations, and while they may make you feel better (or at least less bad) about having math anxiety, they will do nothing to lessen it or to help you get it under control. Therefore, rationalization is unconstructive.
By “suppression” is meant having awareness of the anxiety - but trying very, very hard not to feel it. I have found that this is very commonly attempted by students, and it is usually accompanied by some pretty severe self-criticism. Students feel that they shouldn’t feel this anxiety, that it’s a weakness which they should overcome, by brute force if necessary. When this effort doesn’t succeed (as invariably it doesn’t) the self-criticism becomes ever harsher, leading to a deep sense of frustration and often a severe loss of self-esteem - particularly if the stakes for a student are high, as when his or her career or personal goals are riding on a successful outcome in a math class, or when parental disapproval is a factor. Consequently, suppression of math anxiety is not only unconstructive, but can actually be damaging.
Finally, there is denial. People using this approach probably aren’t likely to see this essay, much less read it, for they carefully construct their lives so as to avoid all mathematics as much as possible. They choose college majors, and later careers, that don’t require any math, and let the bank or their spouse balance the checkbook. This approach has the advantage that feelings of frustration and anxiety about math are mostly avoided. However, their lives are drastically constrained, for in our society fewer than 25% of all careers are, so-to-speak, “math-free,” and thus their choices of personal and professional goals are severely limited. (Most of these math-free jobs, incidentally, are low-status and low-pay.)
People in denial about mathematics miss out on something else too, for the student of mathematics learns to see aspects of the structure and beauty of our world that can be seen in no other way, and to which the “innumerate” necessarily remain forever blind. It would be a lot like never hearing music, or never seeing colors.
Okay, so what is the constructive way to manage math anxiety? I call it “taking possession.” It involves making as conscious as possible the sources of math anxiety in one’s own life, accepting those feelings without self-criticism, and then learning strategies for disarming math anxiety's influence on one’s future study of mathematics. (These strategies are explored in depth in the next section.)
Begin by understanding that your feelings of math anxiety are not uncommon, and that they definitely do not indicate that there is anything wrong with you or inferior about your ability to learn math. For some this can be hard to accept, but it is worth trying to accept - since after all it happens to be true. This can be made easier by exploring your own “math-history.” Think back across your career as a math student, and identify those experiences, which have contributed most to your feelings of frustration about math. For some this will be a memory of a humiliating experience in school, such as being made to stand at the blackboard and embarrassed in front of one’s peers. For others it may involve interaction with a parent. Whatever the principle episodes are, recall them as vividly as you are able to. Then, write them down. This is important. After you have written the episode on a sheet(s) of paper, write down your reaction to the episode, both at the time and how it makes you feel to recall it now. (Do this for each episode if there is more than one.)
After you have completed this exercise, take a fresh sheet of paper and try to sum up in a few words what your feelings about math are at this point in your life, together with the reason or reasons you wish to succeed at math. This too is important. Not until after we lay out for ourselves in a conscious and deliberate way what our feelings and desires are towards mathematics, will it become possible to take possession of our feelings of math anxiety and become free to implement strategies for coping with those feelings.
At this point it can be enormously helpful to share your memories, feelings, and goals with others. You can engage in a group discussion in a classroom setting or find friends or relatives whom you trust to respect your feelings, and induce them to talk about their own experiences of math anxiety and to listen to yours. Once you have taken possession of your math anxiety in this way, you will be ready to implement the strategies outlined below.