The Missing Element for Teachers: Learning What Mathematics Is

This chapter argues for fidelity to mathematics in the preparation of elementary teachers by immersing them in doing mathematics—at their knowledge level, of course—by giving them experiences that are true to its investigative, logical, problem-solving, and system-building, curiosity-inspiring nature. Learning to think like a mathematician is very different from learning the facts and procedures that result from that thinking. Mathematics includes both. Doing mathematics—knowing what mathematics is—requires knowledge, but it is not about that knowledge; it is about what you can figure out using that knowledge. Courses for teachers that focus on explaining facts and procedures and how they work miss the heart of mathematics, the thinking. Teachers will naturally perpetuate that message. By contrast, doing mathematics, centered in the discipline of elementary teaching and its contents, cannot help but also include its key facts, affording a more faithful view of the discipline.