• by Jack Dieckmann, M.A. • IDRA Newsletter • September 2005
In the United States, the majority of people report deep, haunting feelings of ineptitude about doing math. Are you one them? Many of us in the general public feel that we are simply not gifted in this area.
Ironically, even highly-accomplished professionals who work in analytic fields report their inability to “get” math, let alone pursue it as a career. In 2002, Stanford University, a leading institution of higher learning with more than 14,000 students, had only seven math majors.
What might account for such an abysmal interest in studying math? Finding the roots of this deep-seated and widespread feeling of inadequacy requires a trip down memory lane. By understanding and confronting some of these root causes, we will be able to give school children the societal purchasing power that knowing math provides and that so few of us have.
As children, most of us learned math in very much the same way we played particular games on the playground. And that is precisely the problem. Games such as Simon Says, races and dodge ball may be innocent child’s play, but they are harmful yet common blueprints for math learning. A closer look at the goals and rules of Simon Says, for example, reveals eerie similarities to most math classrooms, then and now.
As you will recall, to win at Simon Says, you have to do as the leader tells you. The trick is to obey only those commands prefaced with “Simon Says.” Simon’s sole goal is to confuse you by firing commands in rapid succession in the hopes that you will mess up and be eliminated.
What Simon asked you to do is completely inconsequential. Simon says, “Pat your head while you read this article.” (Please humor me as your Simon.) OK, Stop.
Simon did not say, “Stop.” Hooray, you lose!
Now consider a slight switch of names. Mrs. Math Teacher says, “Borrow from the eight and it becomes a seven.” Mr. Math Teacher says, “When you multiply by two digit numbers, skip a space on the second row before you add.” Try it. Multiply 14 and 27 by hand. Did you put a zero or skip a space on the second line?
Implicit in this math instruction (sometimes math is literally reduced to a set of instructions) is to do exactly as the math teacher tells us and only what the math teacher tells us. How many of us could find good reasons for following these seemingly arbitrary rules? With fractions, why can the top numbers be added but not the bottom ones? What would happen to us if we did?
Sense-making is not valued in playing of this game, nor is it in this form of mathematics. One does not question what one is asked to do. The why is not important. In fact, it slows down the game. Imitation without comprehension and technical correctness (always listening for the “Simon says” preface) is what wins the game, i.e., earns both the grade and the approval of the teacher who then confers the status of “smart.” Total authority rests with teacher.
Currently, children learn a distorted form of mathematics that values docility and rote memorization where some people are winners in math and others are losers. And Simon decides.
But, who exactly is the educational Simon and why do we follow him so blindly? Simon is not just the classroom teacher, who is usually very dedicated and caring, is, herself, a product of her own experiences with Simon.
Our Simon is, in fact, a controlling collection of institutional and societal forces. Simon is a stiff and lifeless math curriculum that favors mechanical procedures at the cost of meaning (though these are far from incompatible). He is the tradition of math elitism that operates from a zero-sum mentality where some must win and others must lose. He may even delight in the failure of others.
His most recent incarnation is in the fetishizing of test scores and proclivity to equate measures of learning with learning itself. Simon derives his power from the masses who do not question or do not know how to question their impoverished and shaming math histories, or the price that their experience has exacted on their lives.
Although we hear rumblings of the new “new” math, the truth is, according to studies like the Third International Math and Science Survey (TIMSS), little has changed in a hundred years. Listen. Watch. Mimic. Could it be otherwise? Yes. Here is how.
First, each of us, whatever our station in life, must reflect on the ways in which we have been silent accomplices. Those of us in the field of education, and a few scholars in mathematics, have posed an alternative vision for what it means to know and do mathematics, one that approximates the work of mathematicians. Such a vision includes students posing real math problems (not just solving trivial ones) and understanding deeply. It would mean heated debates of interesting math ideas and near ecstasy at the formulating of elegant solutions!
Imagine children, adolescents, and eventually adults, using math, fluidly and with pleasure, in every aspect of their lives as if it were their birthright. What image of school mathematics would produce this?
If most of us cannot fathom what such mathematics classrooms would look like, it is only because we have so few examples. It is no small task to let go of traditions. Like bad habits, they cling to us and we to them, even when they are harmful to us.
It will take nothing less than the public will, informed by and in partnership with education and math leaders, to stop the hemorrhagic loss of math talent that results from current math instruction. Perhaps each of us as adults cannot re-experience our elementary math training in the way I am calling for here, but we still have generations who are depending on us.
Most children stop playing Simon Says when they realize that it is fundamentally unrewarding. They have the good sense to do so. So should we, especially when so much as at stake.
Together, we have the power to replace Simon Says as our template for math learning with perhaps another childhood activity. Finger painting, anyone?
Online Math Sites and Tools
Algebra Helper
http://www.algebrahelp.com/index.jsp
Algebra Concepts (at MathDork.com)
Basic Math Skills (at AAA Math)
http://www.aaamath.com/index.html
Calculus Interactive Lessons (at Calculus-Help.com)
http://www.calculus-help.com/
Calculus Surfing Man
Cool Math
http://www.coolmath.com/
Creating a Graph
http://nces.ed.gov/nceskids/graphing/
Discovering Motion – Interactive
http://www.mste.uiuc.edu/murphy/MovingMan/MovingMan.html
Free Graphing Software
http://www.mathgv.com/index.html
Go Math
Grapher (Digital Classroom Resources)
http://www.mathdl.org/mathDL/3/
Interactive Math Applets
http://illuminations.nctm.org/
Inverse Functions
Polynomial Grapher
http://www.mathdl.org/mathDL/3/?pa=content&sa=viewDocument&nodeId=405
Quick Math
http://www.quickmath.com/
Jack Dieckmann, M.A., was an education associate in the IDRA Division of Professional Development. He is now a doctoral student at Stanford University. Comments and questions may be directed to him via e-mail at feedback@idra.org.
[©2005, IDRA. This article originally appeared in the September 2005 IDRA Newsletter by the Intercultural Development Research Association. Permission to reproduce this article is granted provided the article is reprinted in its entirety and proper credit is given to IDRA and the author.]
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