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PrefaceAcknowledgmentsAbout the AuthorsChapter 1. Mathematical Argumentation: Why and What Argumentation Is Important! What Argumentation Is-and Is Not A Four-Part Model of Argumentation About Truth Teaching as Disciplined Improvisation Improvisation for Argumentation and Norm Setting Sharing Mathematical Authority Getting Started With Argumentation Argumentation Lessons Versus Argumentation in Lessons Working TogetherChapter 2. Generating Cases What Does It Mean to Generate Cases? An Activity Rich in Argumentation and Content Vignette: Small Groups Generate Cases Teaching Moves Establishing Norms Planning Tasks Working TogetherChapter 3. Conjecturing What Does It Mean to Conjecture? Vignette: Conjecturing Together Teaching Moves Establishing Norms Planning Tasks Working TogetherChapter 4. Justifying What Does It Mean to Justify? Vignette: Justifying Multiple Conjectures Teaching Moves for Eliciting Justifications Vignette: Critiquing and Connecting Arguments Teaching Moves for Critiquing and Connecting Arguments Establishing Norms Planning Tasks Working TogetherChapter 5. Representations in Justifications What Are Representations? Vignette: Visual Representations Foster Participation Vignette: Gestures Enable a Unique Contribution Teaching Moves Using Dynamic Digital Tools Establishing Norms Planning Tasks Working TogetherChapter 6. Levels of Justification Four Levels of Justification Level 0: No Justification Level 1: Case-Based Justifications Level 2: Partially Generalized Justifications Based on Cases Level 3: Fully Generalized Justifications A Rubric for Levels Teaching Moves for Transitions Between Levels Working TogetherChapter 7. Concluding What Does It Mean to Conclude? Vignettes: Concluding Teaching Moves Establishing Norms Planning Tasks Working TogetherChapter 8. Planning How Can You Plan for Students' Argumentation? Written Lesson Plans Visualizing a Lesson Vignette: Visualizing Justification Digital Tools Updating and Sharing Lesson Plans Advice on Planning Working TogetherGlossaryReferencesIndex