Introduction to Mathematical Challenges for All Unraveling the Intricacy of Mathematical Challenge

Abstract

In this introduction I explore multiple dimensions of mathematical challenge, including, but not limited to, mathematical, psychological, social, and instructional dimensions, each of which is complex and all of which are interwoven. I discuss the nature and structure of mathematical challenge and argue that it can serve as a magnifying glass when examining the quality of mathematics instruction. All the chapters in this book describe research-based design principles for mathematical curricular tasks and collections thereof. Some of them perform theoretical analysis of the described phenomena; some describe theoretical developments accompanied by the results of empirical investigation. I argue that this volume opens new avenues of research in mathematics education and pose multiple questions for future research into mathematical instruction rich in mathematical challenge for all. Each section of this book opens with an introductory chapter and concludes with a commentary chapter that addresses the ways in which mathematical challenges are integrated in the analysis of curricular issues, mathematical tasks, and sets of tasks. I use examples from different chapters in the book to illustrate the suggested theoretical framing of mathematical challenge.