Routledge | 2013 | 150 páginas | rar - pdf | Mb
link (password: matav)
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.
CONTENTSAcknowledgments | vii
1. teachers’ mathematics: framing the question | 1
1 Mathematics-for-Teaching: A Working Definition
5 What’s the Question? Three Framings of Mathematics-for-Teaching
12 The Bigger Picture: Making Sense of M4T by Grappling with Why Math Matters
15 Where Are We Going with This?
2. knowing and learning (mathematics): some game-changing insights | 17
17 “Thou Shalt Not” – A Teacher Dares to Divide by Zero
20 Complexity Science
23 Knowing
27 Learning
33 Where Are We Going with This?
3. substructing emergent mathematics: cultivating an open disposition | 35
35 Is 1 Prime?
39 Concept Study
42 Substructing
44 Emergent Mathematics
47 Open Dispositions
48 Where Are We Going with This?
4. concept study: teachers co-constructing mathematics | 49
49 Pulling Together, Not Just Pulling Apart
53 Collective Cognition
56 Structures of Concept Study
58 Emphasis 1: Realizations
61 Emphasis 2: Landcapes
66 Emphasis 3: Entailments
70 Emphasis 4: Blends
75 Where Are We Going with This?
5. pedagogical problem solving: the emergence of a community of experts | 77
77 Pedagogical Problem Solving
80 A Community of Experts
83 Mathematics Teaching and Listening
87 A Depth and Breadth of Mathematical Knowledge
90 Knowledge of How Mathematics is Produced
93 Where Are We Going with This?
6. concept study in the classroom: enacting an open way of being | 95
95 A Concept Study of Circles
96 Four Quadrants of M4T
99 What’s Interesting about Circles? Emergent Problem Solving
102 Do Circles Exist? Student Agency in Mathematical Knowledge Production
104 Rope around the Equator: Cultural Mathematics
106 Are Circles Efficient? An Open Way of Being
110 Where Are We Going with This?
7. the mathematics teachers (need to) know: profound understanding of emergent mathematics | 111
111 Zero and Function
117 Profound Understanding of Emergent Mathematics
120 All That and More ...
125 Where Are We Going with This?
References | 129
Index | 137
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