Teaching Math: What's the Learning For?

If students spend their time in class doing something over and over, with an emphasis on memory and recall, can we blame them for wondering, "What am I doing this for?"

Learning is a process best driven by inquiry rather than a grade. Focusing on the learner's questions and interests is just as important in logic-driven fields such as mathematics as in expressive fields.

Traditionally, students take numerous sequential courses before getting to the math which scientists and engineers apply in relevant, interesting ways. Or, as we might express that at Hampshire, before they can start putting their ideas into action.

We challenge that tradition, and have tried to turn the teaching process upside down. The what that the student is learning for shapes the process. By way of example, I'll share some background from a curriculum development project of the Five Colleges (Hampshire, Amherst, Mt. Holyoke, Smith, and University of Massachusetts). The project, called Calculus in Context and supported by the National Science Foundation, is based in Hampshire's approach to math:

Early on, Hampshire students grapple with primary sources in all fields. If a mathematical argument is needed, it is used. Students in the life and social sciences found that they needed calculus to explore the questions that drove them in their chosen fields. However, the calculus they needed was not, by and large, the calculus that was actually being taught. Hampshire professors in the mid-1970s developed a calculus course for these students: "The core of the course was calculus, but calculus as it was used in contemporary science. Mathematical ideas and techniques grew out of scientific questions . . . Hence, calculus in context." (Source: Five College Calculus Website)

Students don't just look at a problem and ask, "How would I solve this?" Professors expect them to master the concept and then use it to analyze, innovate, go further, and possibly go in a different direction, based on what they need to know. Rather than relying on recall, this approach demands and develops the critical capacity to intuit, experiment, and connect.

When students pursue individualized academic programs, someone else's linear, sequential model is not the best way to meet their needs. One size does not fit all: They don't enter a course with the same backgrounds, or with the same questions. They don't compete with one another for grades. They work to learn what they need to know in order to accomplish their goals.

This approach demands much of the student. It also demands much of the teacher. In my next post I plan to share some specific ideas and approaches used when working with students who, to quote math professor Sarah Hews, "are not traveling in the same direction. They're on their journey. We're not making them go on ours."