October 27, 2003

This paper was written as an assignment for Ian Walton's Math G - Math for liberal Arts Students - at Mission College. If you use material from this paper, please acknowledge it.

Math Anxiety

Math anxiety is real. When I first began to research the subject of math anxiety I was not convinced that it existed. I thought perhaps it was a neurosis that human beings used for an excuse to not have to do math. Since my research began, I’ve found that math actually frightens, terrifies and causes much turmoil in people’s lives. However, I have also found that math anxiety can be overcome and managed—and if done so, human beings can discover an entirely new view of mathematics and how remarkable it really is.

Math anxiety is common to all of us to some degree. It’s not necessarily math, but the symptoms of the anxiety are generally the same.

Essentially, math anxiety is a feeling of intense frustration and helplessness. It paralyzes some people and can also be an emotional (learned) response to loathing mathematics. Mathematics can be disabling, causing humiliation, resentment and panic.

For example, a random group of students, when asked how they feel about math have said, “when I look at a math problem, I feel stupid”, “when I was 9, I was grounded because I couldn’t learn multiplication”, “In math; there is always one right answer. If you can’t find it, you fail.” “Math exams terrify me.”

It’s not difficult to understand why mathematics has such a bad rap. Mathematics has a tarnished reputation to begin with. For years the perception has been that math is difficult, incomprehensible, and only those people who are characterized as “nerds” and “geeks” like it. There is also a stigma that people who are good at math actually may have something seriously wrong with them. It’s just not normal to like math or be good at it.

Another cause for math’s reputation has to do with teaching…many teachers actually communicate this attitude to their students, (whether consciously or not). For nearly seventy years teaching methods have focused on memorization and repetition. Once the problem is solved, the student is expected to move on to the next one and solve it as well. This method of teaching bypasses the very premise of math, “Students must learn that mathematics is the most human of endeavors…” J.D. Phillips [from: www.mathacademy.com/pr/minitext/anxiety/index.asp].

Thankfully, teaching methods are changing – although there remains no widely accepted teaching methodology for implementing any reform efforts. I think teachers need to embrace an attitude similar to Russian or German cultures whereby mathematics is viewed as an essential part of literacy. And an educated person would be embarrassed to confess not to understand mathematics.

Society has also played a part in the negative perception of mathematics. Even at the start of the 21^st century, girls continue to be discouraged by parents, peers and teachers. They face a barrier that communicates messages, such as -- mathematics isn’t something girls do; mathematics isn’t feminine; mathematics is considered a masculine field to study, etc.

Winifred Edgerton Merrill, the first American woman to receive her Ph.D. in mathematics from Columbia University faced huge challenges in being accepted. After earning her B.S. degree from Wellesley College in 1883, and after studying mathematics and astronomy at Columbia University, she petitioned to receive a Ph.D. degree. She had fulfilled all of her required credits and written an original thesis that dealt with geometric interpretations of multiple integrals and translations and relations of various systems of coordinates (I feel my math anxiety accelerating). Her work in mathematical astronomy included computation of the orbit of the comet of 1883. All that, and the Board of Trustees refused to accept her application. Finally she convinced a friend to speak to each of the trustees individually and the effort proved successful. She was awarded her Ph.D. degree in mathematics from Columbia University in 1886 with highest honors.

On the 50^th anniversary of Winifred’s graduation from Wellesley, a portrait of her was presented to Columbia and now hangs in one of the academic buildings with the inscription, “she opened the door.” [a little information is directly quoted from: www.agnessscott.edu/lriddle/women/merrill.htm].

Although women will continue to struggle in all male dominated fields, I think with the help of parents, teachers, and certainly people like Winifred Merrill, women and young girls alike will continue to contribute remarkable ideas and energy in the field of mathematics.

One of the fascinating discoveries I’ve had throughout the process of researching this assignment is realizing that yes, math does require logic, BUT that’s just the beginning. Math and the ability to do math is in all of us. It doesn’t require a special genetic makeup, nor does it require a super charged “geek” brain. Besides, logic means only that we want things to make sense. And, as John Locke once said, “Logic is the anatomy of thought.” [from: www.mathacademy.com]. Mathematics has elevated logic almost to an art form, but this is because logic itself is a kind of structure…an idea.

“The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver.”…I.N. Herstein [from: www.mathacademy.com]. These and other quotes that I’ve discovered have personally helped me to view mathematics in an entirely different light. I’m finding that mathematics actually encompasses what I love: logic, ideas, thought, imagination, creativity and, I must admit, when I find a solution it feels incredibly satisfying just knowing I was able to go through the process of finding the solution…getting “it right” is just the icing on the cake.

Augustus DeMorgan, a mathematician once said, “The moving power of mathematics is not reasoning but imagination.” [from: www.mathacademy.com]. DeMorgan was an important innovator in the field of logic. He also had many contributions to the field of mathematics.

He was born in Mandura, India on June 27, 1806. He was introduced to mathematics as a young boy in private schools – this is also where he acquired his dislike of exams. After graduating from Trinity College in 1823 he was trying to decide what he wanted to do with his life. His experience at college was not a happy one. He was disillusioned by education in general and had no desire to pursue a master’s degree.

DeMorgan decided to become a mathematician. He taught mathematics and was well liked. His student’s found that his teaching style made mathematics alive and interesting. He wrote thousands of books and articles on mathematics, logic and philosophy.

DeMorgan contributed many accomplishments to the field of mathematics. In addition to formal logic, system of notations for symbolic logic and the famous DeMorgan laws, [Abbott, David Ph.D. Ed “DeMorgan, Augustus”. The Biographical Dictionary of Sciences: Mathematics. New York: Peter Bedrick Books, 1985 and Dubbey, John M. “DeMorgan, Augustus.” Dictionary of Scientific Biography. New York: Charles Scribner’s Sons, 1970. vol. 3], DeMorgan perfected and made the principle of Mathematical Induction easier to understand.

Mathematical induction is:

A tool to check conjectures about the patterns and outcomes of a process that repeats itself in a sequence. This sequence tends to follow a fixed pattern, which enable the conjecture to be proven true or false by using Mathematical Induction.

The principle is used mainly in:

Identities

Inequalities

Number Theory

Geometry

Set Theory

The Principle of Mathematical Induction states that:

Let P(n) be a predicate that is defined for integers, n and let “a” be a fixed integer.

Suppose the following two statements are true:

1. P(a) is true.

2. For all integer, k that is greater or equal to “a”, if P(k) is true, then P(k+1) is true.

Then the statement for all integers greater or equal to “a”, P(n) is true.

The principle of Mathematical Induction is widely accepted and used as a tool for proving statements. Mathematical Induction is to mathematics what argumentation is to writing. People use writing as a means to make and defend their points of view. Mathematical Induction does the same…it allows us to “argue” whether a statement is true or false. [from: Interactive Real Analysis, ver. 1.9.3 © 1994-2000, Bert G. Waschsmuth].

DeMorgan, to me, seemed to be a man who was bright, thoughtful and happened to enjoy mathematics. I do not think he decided to become a mathematician because of text book knowledge, but because he believed in imagination and creativity. He helped me to understand that math anxiety can sometimes be a “learned” emotional response. Yet if one manages it constructively, as opposed to unconstructively, ( i.e., do not rationalize, suppress or deny the reality of the anxiety), if one accepts their feelings and realizes that they are not uncommon and that their feelings do not indicate that something is wrong – then I think math anxiety can be overcome.

A few methods of dealing with math anxiety and trying to overcome the symptoms may be to try and remember what factors contributed most to your frustration regarding math.

Journal the experience and include the reasons why you wish to overcome math anxiety now.

Once you’ve managed those feelings, I think it’s your responsibility to take the bull by the horns. The following are suggestions to implement in an effort to help overcome the anxiety:

· Take lectures-it’s YOUR job to get the most out of them.

· Self study and homework-remember the reasons you do this…YOU are the reason.

· Take math problems…one step at a time; do not look at the problem as a “whole”— break it down into manageable steps.

· Story Problems…They are in the real world--everyday life. View them that way.

· PREPARE for your math exams; do not cram and do not wait until the last minute to study.

In summary, I believe math anxiety is alive and well. However, I also believe that with determination, a positive attitude and a little help, human beings can find the “power” of mathematics and be fueled by it.

Math anxiety is alive and well.

Personally, this class has fueled me. I don’t feel so stupid – I am truly and sincerely changing my perception and feelings about math. I also have a great deal more respect for mathematics and all that it does.

October 27, 2003

Kathy Phelan

Midterm

Math Anxiety

Sources:

· Mathematics and the Search for Knowledge, Kline, Morris 1985 Oxford University Press

Rara Arithmetica – Fourth Edition, Smith, David Eugene 1970 Chelsea Publishing Company

· http://mathacademy.com/pr/minitext/anxiety/index.asp - viewed on October 8, 2003 @ 8:00 p.m.

· http://www.shu.edu/projects/reals/history/demorgan.html - viewed on October 16, 2003 @ 10:00 p.m.

· http://www.geocities.com/jespinosa57/induction.htm - viewed on October 18, 2002 @ 8:00 p.m.

· http://www.agnesscott.edu/lriddle/women/merrill.htm and http://www.agnesscott.edu/lriddle/women/smithk.htm - viewed both on October 19, 2003 @ 3:00 p.m.

· Abbott, David Ph.D. Ed “DeMorgan, Augustus”. The Biographical Dictionary of Sciences: Mathematics. New York: Peter Bedrick Books, 1985

· Dubbey, John M. “DeMorgan, Augustus.” Dictionary of Scientific Biography. New York: Charles Scribner’s Sons, 1970. vol. 3