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.
"This book argues convincingly that teaching mathematics is a complex process and teachers need to reflect on fundamental ideas. It raises important questions, provides practical examples, and offers invaluable insights into mathematics teaching. Summing up: Recommended." - H.P. Koirala, Eastern Connecticut State University, in CHOICE, January 2014
1. Teachers’ Mathematics: Framing the Question 2. Knowing and Learning Mathematics: Some Game-Changing Insights 3. Substructing Emergent Mathematics: Cultivating an Open Disposition 4. Concept Study: Co-Constructing Teachers’ Knowledge of Mathematics 5. Pedagogical Problem Solving: The Emergence of a Community of Experts 6. Concept Study in the Classroom: Enacting an Open Way of Being 7. The Mathematics Teachers (Need To) Know: Profound Understanding of Emergent Mathematics