Intro
Preface
Contents
Chapter 1: Disturbance as a Driving Force
1.1 Form and Sources of Disturbance
1.2 A Framework of Professional Responding to Disturbing Encounters
1.2.1 Responding to Disturbance as a Problem Solver
1.2.2 Responding to Disturbance as a Teacher in Search for a Good Explanation
1.2.3 Responding to Disturbance as a Teacher in Search of Ways of Teaching Difficult Problems While Preserving Student Autonomous Learning
1.2.4 Responding to Disturbance as a Teacher-Educator Teaching Mathematics

1.2.5 Responding to Disturbance as a Teacher-Educator Teaching How to Teach
1.2.6 Coda: Response to Disturbance as a Teacher-Educator-Researcher
References
Chapter 2: A Fictional Dialogue on Infinitude of Primes
2.1 Introduction
2.2 Theoretical Underpinnings
2.2.1 Duoethnography
2.2.2 Virtual Monologue
2.3 Introducing and Exemplifying Virtual Duoethnography
2.3.1 What is Virtual Duoethnography?
2.3.2 Lakatos' Dialogue as an Example of Virtual Duoethnography
2.4 Virtual Duoethnography: Situating a Fictional Dialogue

2.4.1 Learning and Teaching by Scripting Instructional Interactions
2.4.2 Background and Task
2.5 Fictional dialogue on Infinity of Primes
2.5.1 Same Theorem?
2.5.2 On Number and Unit
2.5.3 On "Measured"
2.5.4 Prime or Not Prime
2.5.5 Absurd?
2.5.6 The essence and the difference
2.5.7 The Gap
2.6 Discussion
References
Chapter 3: Encounters with Euclidean Propositions
3.1 Introduction
3.2 How It Started
3.3 Leaving the Choice to Students
3.4 On Continued Proportions
3.4.1 Warm-Up Tasks

3.4.2 Proposition 4 from Book IX, Its Proof, and Students' Script
3.4.3 Solid Numbers and Similar Solid Numbers
3.4.4 On Mean Proportional Numbers
3.4.5 Interpreting Euclid's Proof of Proposition IX. 4
3.4.6 Geometric Sequences and Geometry
3.5 New Proposition VIII. 6
3.6 On the Euclidean Algorithm
3.6.1 Proposition X.2 and Mike's Script
3.6.2 Which Proposition Is Euclid's Algorithm?
3.6.3 Detour on Applicability
3.6.4 On Rational and Irrational
3.7 Concluding Remarks
References
Chapter 4: Stories on Problem-Solving Instruction
4.1 Introduction

4.2 Explore
Launch
Re-explore
Relate
4.2.1 Explore
4.2.2 Launch
4.2.3 Explore
4.2.4 Relate
4.3 Launch
Explore
Re-launch
Re-explore
Relate
4.3.1 Launch
4.3.2 Explore
4.3.3 Re-launch
4.3.4 Re-explore
4.3.5 Relate
4.4 Launch
Get Stuck
Intervene
Relate
4.4.1 Background
4.4.2 Launch
4.4.3 Get Stuck
4.4.4 Intervene
4.4.5 Relate
4.4.6 Follow-Up
4.5 Launch
Intervene
Re-launch
Explore
Relate
4.5.1 Background
4.5.2 Launch
4.5.3 Intervene (Formalize)
4.5.4 Detour: Types and Effects of Teacher Interventions