Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof

This book aims to advance debates in mathematics and mathematics education by analyzing classroom practice across grade levels using different conceptions of argumentation,justification,and proof. It considers the implications of each conception for research and practice and includes a synthesis chapter from an expert in the field.

Format: Paperback / softback
Length: 333 pages
Publication date: 05 March 2023
Publisher: Springer Nature Switzerland AG

This book aims to delve deep into the ongoing discussions in the realm of mathematics and mathematics education, focusing on the conceptions of argumentation, justification, and proof. By conducting comprehensive analyses of classroom practices across different grade levels, researchers explore the profound implications of these constructs on empirical outcomes. Organized by grade bands, the authors adopt specific conceptions of argumentation, justification, and proof, and analyze one data set from each perspective. Additionally, each section features a synthesis chapter by an esteemed expert in the field, highlighting potential implications and raising intriguing new questions. The culmination of the book examines the application of each conception across grade bands and data sets, shedding light on their diverse roles and potential applications. This scholarly work strives to advance our understanding of argumentation, justification, and proof in mathematics education, paving the way for innovative research and practice.

Introduction:
The study of argumentation, justification, and proof has been a central focus in mathematics and mathematics education for decades. These constructs play a crucial role in developing students' logical reasoning abilities, critical thinking skills, and problem-solving capacities. However, the conceptions of argumentation, justification, and proof have varied widely across different cultures, educational systems, and mathematical traditions. This book aims to advance ongoing debates in the field by exploring the consequences of applying particular conceptions of each construct in research and practice.

Chapter 1:
In this chapter, the authors introduce the conceptions of argumentation, justification, and proof and their historical development. They discuss the different perspectives on these constructs, including logical, epistemic, and social perspectives, and their implications for mathematics education. The chapter also highlights the need for a comprehensive understanding of these constructs to promote effective teaching and learning.

Chapter 2:
In this chapter, the authors analyze classroom practices across grade levels using different lenses, such as particular conceptions of argumentation, justification, and proof. They examine how these conceptions shape students' thinking, reasoning, and problem-solving abilities. The chapter also explores the challenges and opportunities that arise when applying different conceptions in the classroom.

Chapter 3:
In this chapter, the authors synthesize the findings from the previous chapters and present potential implications for research and practice. They discuss the strengths and weaknesses of each conception and their potential impact on students' learning outcomes. The chapter also raises new questions that need to be addressed in future research.

Chapter 4:
In this chapter, the authors consider the use of each conception across grade bands and data sets. They discuss the challenges and opportunities that arise when applying different conceptions in different contexts. The chapter also explores the potential benefits and limitations of using each conception in mathematics education.

Conclusion:
In conclusion, this book aims to contribute to the ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof. By conducting comprehensive analyses of classroom practices across grade levels, the authors provide valuable insights into the implications of these constructs on empirical outcomes. The book also raises new questions that need to be addressed in future research to further enhance our understanding of argumentation, justification, and proof in mathematics education.

Weight: 539g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030800109
Edition number: 1st ed. 2022