The History and the

Story of Math Egyptian Fractions in 4th Grade by Houman Harouni

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ately, a good portion of my reading is dedicated to the history of mathematics. I have found we have more readings on the topic than I had thought, and less than we should.

There are, for example, some fascinating but intemperately dull pieces on Sumerian and Babylonian scribe schools, writings on Ancient Chinese approaches to problem-solving, original texts from Medieval Iran, and many textbooks from the early United States. I con- sider the time I spend trying to understand math from these earlier perspectives as prep time for my elementary school classes. They prepare me for teaching by ushering me into the mystery of mathematics, and when I manage to find a good artifact for my students to explore, they in turn find similar gateways into the topic. Exploring the history of math has a second, seemingly contradictory effect on my students:

it demystifies mathematics. As they read about others inventing and reinventing mathematics, the topics begin to seem doable, without becoming trivial. The history connects to their own process of learning: they see firsthand that there have been many ways of expressing and solving the same problems, and all these ways, whether efficient or long-lasting, are wonderfully intel- ligent.

Math Stories

Ancient Egyptian hieroglyphic numerals

1 10 100 1,000 10,000 100,000

1,000,000 ½ 1⁄3

reciprocal Page 20 • Connect

( 1⁄4 ) +( 1⁄28 ) 2⁄7

My fourth-grade public school ESL students have had enough experience with the boxed- in, mystifying, and un-mysterious form of math to appreciate the potential in this approach. They describe it in rather articulate terms. The shorthand they use to talk about it is the phrase “math stories.” It took about five months of work before it became obvious to them that there are “stories” in mathematics, and that these are different from the traditional word problems they encounter in textbooks. The most salient sign of this developing under- standing is that whenever I introduce a new topic, they demand to hear stories about it. Sometimes they are more explicit about the historical aspect of their demand: “Who did it this way first?” they want to know, or, “But how did the Chinese do it?” As a teacher I find the phrase “math stories” compelling. One reason is that it allows me

to be more creative in my presentations. A story is not an answer, nor is it a problem with a single answer. Stories are chock-full of myster- ies: they are spaces for the imagination to grow and test itself. At the same time, stories, no matter how fantastic, must always be rooted in real inter- actions, or otherwise they will not make sense. Classroom math is in deep need of such real inter- actions. I want to briefly describe how history can func-

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tion in a math lesson, using an example from my classroom. This particular example begins two or three weeks after the fourth-grade students were introduced to fractions. It begins when the students noticed that I refer to common fraction notations as “Arabic fractions.” It made them interested in knowing what other forms of frac- tions have existed.

©synergy learning • 800-769-6199 • May/June 2011