Chapter
Part I Doing and Learning Mathematical Talk
2 Language Socialization in the Mathematics Classroom: Discourse Practices and Mathematical Thinking
The Process-Product Tradition
Sociocultural Theory of Mind
Mathematical Cognition and Discourse Practices
Mathematical Modes of Cognition
What Is a Social Practice?
Discourse Practices and Social Practices
Protoforms of Mathematical Discourse Practices
Mathematical Discourse Forms and Protoforms: Two Examples
Argument: Claims, Warrants, and Opposition
Conflict Versus Oppositional Argument
Unwanted Transfer: Social Image and Credibility
Negotiated Defining and Other MetalinguisticActivities
What Do You Mean by "Even"?
Protoforms of Negotiated Defining
3 The Role of Imagery and Discourse in Supporting Students' Mathematical Development
The Folding Back of Discourse
Taken-as-shared Basis for Communication
4 Building a Context for Mathematical Discussion
Texts As Knowledge Constructing Contexts
Establishing a Mathematical Context: Data Examples
5 Disciplined Perception: Learning to See in Technoscience
Disciplined Perception and Coordination
Comparing Cases of Disciplined Perception
Case 1: The Tutoring Interaction: Learning to See in Cartesian Space
Thought Experiment I: Taking Adam and His Grid Calculus to School
Case 2: Using Cartesian Space to See
1. Is Perception Socially Constructed?
2. Is Conceptual Change Asymmetric in Interaction Between People?
3. How Do Accountabilities Shape Disciplined Perception?
Thought Experiment II: Taking Adam and His Equationsto Work
Part II Teaching Mathematical Talk
6 Investigating Teaching Practice
How Does the Teacher "Help" Students Learn toTalk Math?
Who Is This Teacher and What Does She Think She Is Doing?
Research Methods and Procedures
Tools and Strategies for Analysis
7 The Teacher's Role in Mathematical Conversation: Stepping In and Stepping Out
Understanding Mathematical Literacy
Talk As a Way to Learn Mathematics Content
Why Look at Teacher Talk?
Back to Gee: Or What Is a Discourse and Where Do I Get One?
What's a Teacher to Do?: Comprehensible Input and Mathematical Discourse
Apprenticeships and Participation
Stepping In and Stepping Out: Lampert's Multiple Roles
Participating in Mathematical Conversations: Modeling andScaffolding
Modeling Requests for Information
Scaffolding Students' Talk with One Another
Commenting on Mathematical Conversations: Talking About the Talk
8 Teacher Talk About How to Talk in Small Groups
Why Work in Small Groups?
What and Who Are Small Groups?
How to Work in Small Groups
9 Teaching and Learning Politeness for Mathematical Argument in School
Face-Threatening Acts in the Lesson
The Classroom Record: September 11,1989
Face-Threatening Acts in the Classroom Record
Positive Face-Threatening Acts: Criticism and Challenge
Limitations and Directions for Future Work
10 Closing Reflections on Mathematical Talk and Mathematics Teaching
Implications of Research on Language and Literacy
Talking Mathematics in School
：Studies of Teaching and Learning
( Learning in Doing: Social, Cognitive and Computational Perspectives )
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