OVERCOMING MATH ANXIETY
Math Anxiety: Author's Update
As reported in Overcoming Math Anxiety (1978, 1993, 2nd edition) in 600 interviews with college-age and older returning students, Tobias found three significant variables in her subjects' inability to do college-level mathematics: fear of mathematics, the conviction that mathematics is a white male domain, and the conviction that one is either good in mathematics or in language arts but never both. The students' lack of coping skills in dealing with mathematics classes and with their own anxieties appeared to be the main barrier to their attempting mathematics one more time. Subsequently, Tobias focused her research on entering college students. Her second book, Succeed With Math: Every Student's Guide to Conquering Math Anxiety (1987) was commissioned by the College Board. What follows is a selection of excerpts from that book.
Two myths about mathematics need to be put to rest. One is that college-level mathematics is too difficult for otherwise intelligent students to master. Another is that without mathematics anyone can live a productive intellectual and professional life.
Mathematics is no longer just an entry-level prerequisite for engineering, the physical sciences, and statistics. Its principles and techniques, along with computers, have become part of almost all areas of work, and its logic is used in thinking about almost everything. This is a big change from the days when a number of professions were virtually math-free. Today, many occupations that do not require college-level calculus or statistical skills at the outset do demand them later on for anyone aiming toward promotion into management or work in more interesting technical areas.
Mathematical expressions such as "the slope of the curve," "zero sum," "normalized distribution," and "asymptotic" are no longer just the mutterings of bearded thinkers who cannot remember to wear socks the same color. They have become part of the basic vocabulary of business, politics, library science, health care, and even social work. One important reason is that mathematical expressions give us a way of thinking about relationships that would otherwise be unavailable to us. Just as college students' ability to think more complex thoughts is enhanced every time they learn a new word or phrase, so their ability to understand abstract concepts will be enriched when they master such mathematical constructs as "limits, "nonlinear," and "exponential growth."
Where Does Math Anxiety Come From?
I have interviewed hundreds of people who have math anxiety.
They can all remember the moment when they began to doubt that
they had what it takes to learn math. In some cases, it was because
someone had told them "girls don't do math" or "blacks don't become
engineers." Others came to the conclusion that they would either
be good with numbers or with words but that they could not be
good with both. Because our American culture is ambivalent about
mathematicians' role models, some students decided they did not
want to enter the field. Besides, math seemed dreary, never fun.
None of these widespread assumptions are true. First, if there are still few females and blacks in the top tiers of working mathematicians and scientists, it is not because they are genetically inferior; it is because social and institutional barriers exist that are only now slowly disappearing. Second, while some writers do not like math and some mathematicians do not like to write, no evidence exists, whatsoever, that writing ability and mathematics ability are mutually exclusive. In fact, people who show high capability on both the mathematical and verbal sections of the SAT are more likely to succeed in math than those who have a severely skewed score, strong only in quantitative skills. And, finally, while elementary mathematics may indeed be repetitive, it is a skill that must be practiced to get to the creative part later on.
Another source of trauma for many people is the style of the mathematics classroom. Students complain that math offers little opportunity for debate or discussion. Teachers say they liked English and social studies better than math because they could participate more in class and because there was no pressure to find the one right answer. Mathematics does depend on right answers but it can also be experienced as a series of discoveries that we all make for ourselves. More often than not, however, math is presented as a fixed set of rules to be digested whole and without dispute, which may discourage students from learning.
Few people can think clearly and well with a clock ticking away. It is hard to perform at the blackboard with thirty sets of eyes watching you. No one likes a subject that is presented rigidly and uncompromisingly. And most people do not do well when they are scared. Some years ago, my colleagues and I came to suspect that math inability may not be the result of a failure of intellect but rather of nerve.
How Does Math Anxiety Work?
We think of math anxiety as causing an emotional "static" in the
brain. It might be best to begin by thinking about the brain
(entirely hypothetically) as consisting of three parts: an input
area, a memory bank, and some kind of understanding and recall
pathways connecting the two. If the system is working well, upon
looking at a math problem or trying to fathom a new piece of mathematical
information, the math-healthy person will call up from memory
the right formula and the right approach. He or she will move
back and forth effortlessly along the recall and understanding
pathways of the brain until the problem is solved or the new mathematical
idea is understood. If stuck, he or she can return to the memory
bank or get some more information from the problem, draw a diagram
or put some hypothetical numbers into the problem to make it more
concrete. But whatever he or she chooses to do, the learner will
be busy moving along the pathways of the brain, activating memory,
using analytical skills, learning, and doing.
Now, suppose the learner's memory bank is intact and understanding and recall skills are well developed, but every time he or she looks at some new mathematical materials, negative emotions come into play. There is panic. "This is just the kind of problem I can never solve." Tension develops that comes from time pressure and uncertainty, as well as from lack of confidence. At this point, the understanding and recall pathways will become cluttered by emotions. This is what we mean by "static." There is an inability to think, but not because the hardware is inadequate. The input, memory, and understanding and recall systems are as good as they were before. But, because the pathways have been blocked, the student cannot remember. Soon the pencil stops moving; the brain seems to stop functioning altogether. The student thinks, "I cannot work because I cannot think." In fact, it is just the reverse. The student cannot think because she or he has stopped working.
Self-Monitoring
To reduce and eventually overcome math anxiety, we recommend that
people, college-age students and even teachers, learn first to
recognize when panic starts, then to identify the static as precisely
as possible, and finally, to clear it up without ceasing to work
on the mathematical problem. How can they do all this at once?
The essence of math-anxiety therapy is self-monitoring. We have
learners practice while doing homework and even while in class
by using the divided-page exercise. They are taught to draw a
line down the center of the page they are working on. On one
side they record their feelings and thoughts, however random and
seemingly disconnected they are. On the other side, they keep
their notes, calculations, and problem-solving steps. Exclusive
feelings and thoughts are not easy to capture, especially the
first time students try. But, in time, they learn to observe
the messages they give themselves under stress. This is the way
they discover the obstacles they are creating when they work at
math.
For example, if a person writes on the left side of the page, "This is just the kind of problem I can never solve," we teach him or her, instead of quitting, to ask, "What is making this problem difficult for me, and what can I do to make it easier for myself?"
Self-Permission
The point of the divided-page exercise is to teach the math-anxious
to give themselves permission to explore their own confusions
and to find out what is making the problem or the new material
seem difficult. We find that, as they become more and more familiar
with their own learning styles, learners become more adept at
discovering flaws in their thinking. Most important, doing the
exercise permits them to keep on working.
One purpose of the divided-page exercise is this: when learners are stuck and not able to put anything down on the right-hand side of the page, they can still be writing their thoughts and feelings on the left. That means they can continue working, even if they are not doing math calculations.
So long as they are writing, they are thinking, and thinking in mathematics (doing, writing down random feelings and thoughts) breaks the tension and their sense of isolation. Soon their ability to analyze their own problems becomes a source of insight into the math problem itself. In time, the two mental processes become so entwined that no one can say with certainty whether the insights that finally crack a problem come from the problem itself or from the learner's self-assessments.
Best of all, the tuning-in process teaches learners about their idiosyncracies. In talking with people who are successful in math, I have found that they are not necessarily smarter than the rest of us but that they seem to know themselves better. They can anticipate the difficulties they are going to have. They know what kinds of questions and actions will give them the power and confidence to continue. They know when to skim and when to focus on a paragraph, sometimes for hours at a time. They are never bored because they are busy. They never quit because they recognized long ago that progress in mathematics very often involves making just a little headway, one step at a time. They do not judge themselves as harshly as we judge ourselves when answers do not come out right. They are patient, tenacious, and rarely very fast.
The goal of all this training is not to turn out mathematical geniuses but to offer students (and teachers) math mental health, which involves the willingness to learn the math they need when they need it.
Math-anxiety workshops can be organized for teachers as well as for students. There is no blueprint, but it is advisable to include at least some of the following:
1) the solicitation of every participant's "math autobiography" in a one-on-one interview.
2) the creation of six or more sessions of math-anxiety reduction, including relaxation training, group discussion of difficulties in confronting mathematics, and training in keeping a journal and divided-page work.
3) the development of traditional slow-paced math sessions where no more than twenty minutes of new material is introduced by math instructor, and this instruction is folowed by at least as many minutes for processing lead by a counselor. (Each participant should be assessed in an exit interview before being encouraged to enroll in a mainstream math class.)
4) a return to mainstream mathematics with a weekly group session to discuss feelings and "left-hand side of the page" comments, and
5) assertiveness training to transform the passive learner into
an active and demanding one.
NACADA Journal
Volume 10 (1) Spring 1990 47-50
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