Proving in elemental mathematical classroom 1st Edition by Andreas Stylianides 0191034732 9780191034732

Proving in elemental mathematical classroom 1st Edition Andreas J. Stylianides – Ebook PDF Instant Download/DeliveryISBN:  0191034732, 9780191034732

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ISBN-10 :  0191034732 

ISBN-13 :  9780191034732

Author:  Andreas J. Stylianides 

Although proving is core to mathematics as a sense-making activity, it currently has a marginal place in elementary classrooms internationally. Blending research with practical perspectives, this book addresses what it would take to elevate the place of proving at elementary school. The book uses classroom episodes from two countries to examine different kinds of proving tasks and the proving activity they can generate in the elementary classroom. It examines further the role of teachers in mediating the relationship between proving tasks and proving activity, including major mathematical and pedagogical issues that arise for teachers as they implement each kind of proving task. In addition to its contribution to research knowledge, the book has important implications for teaching, curricular resources, and teacher education.

Proving in elemental mathematical classroom 1st Table of contents:

1. Introduction
A Classroom Episode of Elementary Students Engaging With Proving
Description of the Episode
Brief Discussion of the Episode
The Book’s Broad Aim and Intended Audience
The Book’s Structure
2. The Importance and Meaning of Proving, and the Role of Mathematics Tasks
The Importance of Proving
A Philosophical Argument
A Pedagogical Argument
The Meaning of Proving
An Overview of the Situation in the Field
The Definition of Proving Used in this Book
The Definition of Proof Used in this Book
The Place of Proving in Mathematics Classrooms
The Current Place of Proving
Factor 1: teachers’ knowledge
Factor 2: teachers’ beliefs
Factor 3: pedagogical demands
Factor 4: instructional support
The Role of Mathematics Tasks in Elevating the Place of Proving
3. The Set-up of the Investigation
A Categorization of Proving Tasks
Characteristics of Proving Tasks That Can Influence Their Generated Proving Activity
Data Sources and Analytic Method
Data Sources
Analytic Method
4. Proving Tasks with Ambiguous Conditions
Episode A
Description of the Episode
Discussion of the Episode
Tasks 1, 1a, and 1b: An infinite number of cases
Tasks 1c and 1c′: A finite number of cases
Concluding remarks
Episode B5
Description of the Episode
Discussion of the Episode
The work of the class on the proving task
The role played by assumptions in the work of the class
Concluding remarks
General Discussion
The Relationship between Proving Tasks and Proving Activity
The role of assumptions
The nexus between assumptions and definitions
The Role of the Teacher
5. Proving Tasks Involving a Single Case
Episode C
Description of the Episode
Discussion of the Episode
Episode D2
Description of the Episode
Discussion of the Episode
General Discussion
The Nexus between Calculation Work and Proving
The Relationship between Proving Tasks and Proving Activity
The Role of the Teacher
6. Proving Tasks Involving Multiple but Finitely Many Cases
Episode E1
Description of the Episode
Discussion of the Episode
Episode F
Description of the Episode
Discussion of the Episode
General Discussion
The Relationship between Proving Tasks and Proving Activity
The Role of the Teacher
7. Proving Tasks Involving Infinitely Many Cases
Episode G
Description of the Episode
Discussion of the Episode
Episode H3
Description of the Episode
Discussion of the Episode
General Discussion
The Relationship between Proving Tasks and Proving Activity
The Role of the Teacher
8. Conclusion
The Relationship between Proving Tasks and Proving Activity
The Role of the Teacher
Selecting or Designing Proving Tasks
Implementing Proving Tasks

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