| Contents |
1. Teachers' mathematics: framing the question : Mathematics-for-teaching: a working definition ; What's the question? Three framings of mathematics-for-teaching ; The bigger picture: making sense of M₄T by grappling with why math matters ; Where are we going with this? -- 2. Knowing and learning (mathematics): some game-changing insights : "Thou shalt not": a teacher dares to divide by zero ; Complexity science ; Knowing ; Learning ; Where are we going with this? -- 3. Substructing emergent mathematics: cultivating an open disposition : Is 1 prime? ; Concept study ; Substructing ; Emergent mathematics ; Open dispositions ; Where are we going with this? -- 4. Concept study: teachers co-constructing mathematics : Pulling together, not just pulling apart ; Collective cognition ; Structures of concept study ; Emphasis 1: Realizations ; Emphasis 2: Landscapes ; Emphasis 3: Entailments ; Emphasis 4: Blends ; Where are we going with this? -- 5. Pedagogical problem solving: the emergence of a community of experts : Pedagogical problem solving ; A community of experts ; Mathematics teaching and listening ; A depth and breadth of mathematical knowledge ; Knowledge of how mathematics is produced ; Where are we going with this? -- 6. Concept study in the classroom: enacting an open way of being : A concept study of circles ; Four quadrants of M₄T ; What's interesting about circles? Emergent problem solving ; Do circles exist? Student agency in mathematical knowledge production ; Rope around the equator: cultural mathematics ; Are circles efficient? An open way of being ; Where are we going with this? -- 7. The mathematics teachers (need to) know: profound understanding of emergent mathematics : Zero and function ; Profound understanding of emergent mathematics ; All that and more ; Where are we going with this? |
| 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"-- Provided by publisher. |
| Bibliography note | Includes bibliographical references (pages [129]-136) and index. |
| LCCN | 2013006056 |
| ISBN | 9780415858434 (hbk : acid-free paper) |
| ISBN | 0415858437 (hbk : acid-free paper) |
| ISBN | 9780415858441 (pbk : acid-free paper) |
| ISBN | 0415858445 (pbk : acid-free paper) |
