The lesson, of course, is an introduction to fraction addition. There are a few points,

however, that I would like to highlight regarding the students’ work. First, the work began with an informal process of finding a proof, one of the more exciting aspects of math, and one of the least taught. Second, the process invokes mystery because it begins with an answer and seeks to find plausible solutions. It is imaginative in that, unlike the traditional mode of setting an addition problem (½ + ¼ = ? ), it does not confine the stu- dents to one correct answer. Just like the work involved in understanding a story, it is a journey in making sense and meaning. At the same time, the process is not mystifying. In the traditional mode the students not only have to grapple with the underlying con- cepts of fraction equivalency, they must also feel the added anxiety of avoiding wrong answers. Added to this is the complex algorithm for finding common denominators, which is often imposed on students. At no point during this introduction to fraction addition did my students make the

extremely common mistake of trying to add ½ + ¼ by combining the numerators and denominators separately and arriving at the nonsensical answer, 2⁄6. The answer was in front of them the entire time; their challenge was first, to understand the problem, and second, to invent more and more elegant solutions.

Math in Context

There is a danger of reducing an entire civilization to a gimmick.

As we worked on Egyptian fractions, an ongoing debate took place among the students regarding which notation was better. Many explanations were offered. Arabic notations are simpler, easier to understand. On the other hand, there were students who thought that the Egyptian way was more fun to write. Andrew, a student from Eritrea, offered a different argument: “The Arabic way is good, but I like the way my people did it bet- ter . . .” He was, of course, referring to his African heritage. There is a danger in this account of implying that studying Ancient Egyptians, or

any other civilization, is a means for getting the students to learn their basic math skills. The danger here is of reducing an entire civilization to a gimmick, a teacher’s tool for dealing with the inherent problems in teaching mathematics. I am not sure to what extent I have avoided that pitfall. In my class we studied many

other aspects of Egyptian history, and that history tied into our various lessons in math, history, geography, or writing. My purpose in studying the Ancient Egyptians, I think, went somewhat beyond the immediate concerns of these disciplines. Like any good story, the ongoing story of the Egyptians was meant to get the students thinking about the way they conduct their own lives. There is not enough room in the span of this article to discuss this larger, more important side of learning, but an example can serve as a place-holder. During the debate regarding the merits and demerits of Egyptian and Arabic nota-

tions, Ahmad, a rather demure student, held fast to his preference for Egyptian frac- tions. He offered his reasons to me outside the classroom discussion. “The Egyptian way” he explained, “is nice because it’s big. The Egyptians weren’t afraid of doing big things. The pyramids are hard to build, but the Egyptians built them anyway.” Ahmad’s is my favorite learning of this lesson. !

Houman Harouni has taught at elementary, secondary, and post-secondary levels. For now, he is a resident of Cambridge, Massachusetts.

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