ABSTRACT

What sorts of mathematics competencies must teachers have in order to teach the discipline well? This book offers a novel take on the question. Most research is focused on explicit knowledge–that is, on the sorts of insights that might be specified, catalogued, taught, and tested. In contrast, this book focuses on the tacit dimensions of teachers’ mathematics knowledge that precede and enable their competencies with formal mathematics. It highlights the complexity of this knowledge and offers strategies to uncover it, analyze it, and re-synthesize it in ways that will make it more available for teaching. Emerging from 10 years of collaborative inquiry with practicing teachers, it is simultaneously informed by the most recent research and anchored to the realities of teachers’ lives in classrooms.

chapter |15 pages

Teachers' Mathematics

Framing The Question

chapter |18 pages

Knowing and Learning (Mathematics)

Some Game-Changing Insights

chapter |14 pages

Substructing Emergent Mathematics

Cultivating an Open Disposition

chapter |28 pages

Concept Study

Teachers Co-Constructing Mathematics

chapter |18 pages

Pedagogical Problem Solving

The Emergence of a Community of Experts

chapter |16 pages

Concept Study in the Classroom

Enacting an Open Way of Being

chapter |17 pages

The Mathematics Teachers (Need to) Know

Profound Understanding of Emergent Mathematics