“I want students to see math, to appreciate it, as part of a quest - another way of trying to make sense of the world,” says Senior Math Teacher Robert Mason. “It’s a body of knowledge important to understand for its own sake, but it’s about thinking - about the analytical process of solving problems.” His Euclid Project, taught to both 7^{th} and 8^{th} grade math students, is the culmination of his efforts to integrate technology into math education, to help the non-intuitive math student, and to make what he sees as real connections between math and the humanities.

Mason believes strongly that the early Middle School years must be spent solidifying computational and problem-solving skills. The 6^{th} grade includes some pre-algebra as well. With those basics mastered, 7^{th} graders begin the Euclid Project, an informal study of Euclidean geometry which enables students to explore the theorems and definitions of plane geometry without having to write the formal proofs that are a part of high school math. Half of the project is completed in 7^{th} grade; 8^{th} graders complete the rest before moving on to Algebra I.

Responding to a recommendation by the NCTM that more stress on geometry was needed in eary math education, Mr. Mason saw the opportunity to give students the chance to explore two-dimensional space in an informal, child-centered fashion. The 7^{th} grade course begins with an investigation of the process of analysis itself, ranging from defining the word to its application in studying the humanities as well as math or science. (His Core colleagues participate in this conversation in their classes at the same time.)

Next, the scientific method is introduced: hypothesis, testing and conclusion. Using familiar Euclidean theorems, Mason facilitates the development of hypotheses, offers models of experiments to test them, and guides the independent explorations of students for findings that will support the hypotheses. Stressing the cause and effect relationships basic to most learning, he says he “tries to give students the same analytical learning structure that is fundamental to all thinking, whether in Math, Social Studies or English.”

The use of computer technology, he asserts, is a crucial tool. *Geometer’s Sketchpad*, the software program he uses to support the curriculum, contains “certain tools one can use to build shapes and move them around the computer screen, which enhances the ability to visualize and review one’s thinking. It provides an environment in which 7^{th} and 8^{th} graders can play with geometric concepts like they did as toddlers, playing with blocks.” A confirmed constructivist, he says, “You learn best when you are actively participating in learning. “ Computers have made it possible “to create learning situations in which students are first taught about the tools they’ll use and then can use the tools to make meaning of their explorations.”

Then comes the writing. Students are required to record what they’ve done and to describe their thinking during the process: “Describe what you did; what are your findings, why does it make sense?” These “mini-essays” not only help students clarify and verbalize the process they have experienced, but help them to look more broadly at the mathematical concepts involved. He asks them to “look for relationships between problems that will help them grasp concepts at a high level; “to “take inventory” of a problem, search for familiar elements, and to use information cumulatively, instead of storing it in “discrete chunks.”

The last component of the program is an application of the knowledge they have mastered. Mason explains that, while they use the same models to show that they understand both the content and concepts of the course, in this case they are “paper and pencil” exercises; in reality, old-fashioned tests.

The program, he explains, not only empowers the students, but “frees the teacher to work on the thinking rather than the mechanics, to communicate more with the students about the thinking process involved in this kind of work.” He asserts firmly that though the project is dependent on the availability of technology, computers are a tool, not the driving force at work in the curriculum. Without appropriate software, for example, the eighth grade algebra curriculum relies on a traditional textbook. The teacher remains the vital force in the classroom, he maintains; “they need the human guidance only a teacher can give.”

The Euclid Project meshes perfectly with the Dalton Plan. While Mason incorporates many teaching styles, he thinks of himself as a facilitator of the process of learning for his students. Because they work in small groups, many classes become labs where he works with individuals or groups. Students who have difficulty with this methodology are referred to textbooks and given an alternative method of solving the same problems, though he says “they miss the opportunity to have a set of mistakes from which to learn.” Individualization of the process plays a significant role.

His excitement about this curriculum is palpable; not only for teaching mathematics, but the broader use of the process that the project entails. “This program adds a layer of understanding about the world,” he explains. What he omits to say is that it clearly will add a generation of able and competent math students.

Susan Buksbaum, Editor

Connections Magazine

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