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 isreal. When I first began toresearch the subject of math anxiety I was not convinced that it existed. I thought perhaps it was a neurosisthat human beings used for an excuse to not have to do math. Since my research began, I’vefound that math actually frightens, terrifies and causes much turmoil inpeople’s lives. However, Ihave also found that math anxiety can be overcome and managed—and if doneso, human beings can discover an entirely new view of mathematics and howremarkable it really is.

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

Essentially, mathanxiety is a feeling of intense frustration and helplessness. It paralyzes some people and can alsobe an emotional (learned) response to loathing mathematics. Mathematics can be disabling, causinghumiliation, resentment and panic.

Forexample, a random group of students, when asked how they feel about math havesaid, “when I look at a math problem, I feel stupid”, “when Iwas 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 examsterrify me.”

It’s notdifficult to understand why mathematics has such a bad rap. Mathematics has a tarnished reputationto begin with. For years theperception has been that math is difficult, incomprehensible, and only thosepeople who are characterized as “nerds” and “geeks”like it. There is also a stigmathat people who are good at math actually may have something seriously wrongwith them. It’s just notnormal to like math or be good at it.

Another cause formath’s reputation has to do with teaching…many teachers actuallycommunicate this attitude to their students, (whether consciously or not). For nearly seventy years teachingmethods have focused on memorization and repetition. Once the problem is solved, the student is expected to moveon 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 ofendeavors…” J.D. Phillips[from: www.mathacademy.com/pr/minitext/anxiety/index.asp].

Thankfully, teaching methods are changing – although there remainsno widely accepted teaching methodology for implementing any reformefforts. I think teachers need toembrace an attitude similar to Russian or German cultures whereby mathematicsis viewed as an essential part of literacy. And an educated person would be embarrassed to confess notto understand mathematics.

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

Winifred EdgertonMerrill, the first American woman to receive her Ph.D. in mathematics fromColumbia University faced huge challenges in being accepted. After earning her B.S. degree fromWellesley College in 1883, and after studying mathematics and astronomy atColumbia University, she petitioned to receive a Ph.D. degree. She had fulfilled all of her requiredcredits and written an original thesis that dealt with geometricinterpretations of multiple integrals and translations and relations of varioussystems of coordinates (I feel my math anxiety accelerating). Her work in mathematical astronomyincluded computation of the orbit of the comet of 1883. All that, and the Board of Trustees refusedto accept her application. Finallyshe convinced a friend to speak to each of the trustees individually and theeffort proved successful. She wasawarded her Ph.D. degree in mathematics from Columbia University in 1886 withhighest honors.

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

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

One of the fascinating discoveriesI’ve had throughout the process of researching this assignment isrealizing that yes, math does require logic, BUT that’s just thebeginning. Math and the ability todo math is in all of us. Itdoesn’t require a special genetic makeup, nor does it require a supercharged “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 toan art form, but this is because logic itself is a kind of structure…anidea.

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

Augustus DeMorgan, amathematician once said, “The moving power of mathematics is notreasoning but imagination.” [from:www.mathacademy.com]. DeMorgan was an important innovator inthe field of logic. He also had many contributions to thefield of mathematics.

He was born inMandura, 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 Collegein 1823 he was trying to decide what he wanted to do with his life. His experience at college was not ahappy one. He was disillusioned byeducation in general and had no desire to pursue a master’s degree.

DeMorgan decided tobecome a mathematician. He taughtmathematics and was well liked. His student’s found that his teaching style made mathematics aliveand interesting. He wrotethousands of books and articles on mathematics, logic and philosophy.

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

Mathematicalinduction is:

A tool tocheck conjectures about the patterns and outcomes of a process that repeatsitself in a sequence. Thissequence tends to follow a fixed pattern, which enable the conjecture to beproven true or false by using Mathematical Induction.

Theprinciple is used mainly in:

Identities

Inequalities

Number Theory

Geometry

Set Theory

The Principle ofMathematical Induction states that:

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

Suppose the following two statements are true:

1. P(a) is true.

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

Thenthe statement for all integers greater or equal to “a”, P(n) istrue.

The principle ofMathematical Induction is widely accepted and used as a tool for provingstatements. Mathematical Inductionis to mathematics what argumentation is to writing. People use writing as a means to make and defend theirpoints of view. MathematicalInduction does the same…it allows us to “argue” whether astatement 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 enjoymathematics. I do not think hedecided to become a mathematician because of text book knowledge, but becausehe believed in imagination and creativity. He helped me to understand that math anxiety can sometimesbe 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), ifone accepts their feelings and realizes that they are not uncommon and thattheir feelings do not indicate that something is wrong – then I thinkmath anxiety can be overcome.

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

Journalthe experience and include the reasons why you wish to overcome math anxietynow.

Onceyou’ve managed those feelings, I think it’s your responsibility totake the bull by the horns. Thefollowing are suggestions to implement in an effort to help overcome theanxiety:

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

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

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

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

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

Insummary, I believe math anxiety is alive and well. However, I also believe that with determination, a positiveattitude and a little help, human beings can find the “power” ofmathematics 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 andsincerely changing my perception and feelings about math. I also have a great deal more respectfor mathematics and all that it does.

October 27, 2003

Kathy Phelan

Midterm

Math Anxiety

Sources:

· Mathematics and theSearch 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.htmand 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 BedrickBooks, 1985

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