Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds: The Global Evolution of an Emerging Field of Research and Practice

Description

This book highlights new developments in the teaching and learning of algebraic thinking with 5- to 12-year-olds. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for teaching early algebra. Building on the work of the ICME-13 (International Congress on Mathematical Education) Topic Study Group 10 on Early Algebra, well-known authors such as Luis Radford, John Mason, Maria Blanton, Deborah Schifter, and Max Stephens, as well as younger scholars from Asia, Europe, South Africa, the Americas, Australia and New Zealand, present novel theoretical perspectives and their latest findings. The book is divided into three parts that focus on (i) epistemological/mathematical aspects of algebraic thinking, (ii) learning, and (iii) teaching and teacher development. Some of the main threads running through the book are the various ways in which structures can express themselves in children’s developing algebraic thinking, the roles of generalization and natural language, and the emergence of symbolism. Presenting vital new data from international contexts, the book provides additional support for the position that essential ways of thinking algebraically need to be intentionally fostered in instruction from the earliest grades. Front Matter ....Pages i-xiii Front Matter ....Pages 1-1 The Emergence of Symbolic Algebraic Thinking in Primary School (Luis Radford)....Pages 3-25 Implementing a Framework for Early Algebra (Maria Blanton, Bárbaras M. Brizuela, Ana Stephens, Eric Knuth, Isil Isler, Angela Murphy Gardiner et al.)....Pages 27-49 New Words and Concepts for Early Algebra Teaching: Sharing with Teachers Epistemological Issues in Early Algebra to Develop Students’ Early Algebraic Thinking (Nicolina A. Malara, Giancarlo Navarra)....Pages 51-77 Seeking, Using, and Expressing Structure in Numbers and Numerical Operations: A Fundamental Path to Developing Early Algebraic Thinking (Carolyn Kieran)....Pages 79-105 Cultivating Early Algebraic Thinking (David W. Carraher, Analúcia D. Schliemann)....Pages 107-138 Front Matter ....Pages 139-139 Characteristics of Korean Students’ Early Algebraic Thinking: A Generalized Arithmetic Perspective (JeongSuk Pang, JeongWon Kim)....Pages 141-165 Function Tasks, Input, Output, and the Predictive Rule: How Some Singapore Primary Children Construct the Rule (Swee Fong Ng)....Pages 167-193 Algebraic Understanding of Equalities in Primary Classes (Ralph Schwarzkopf, Marcus Nührenbörger, Carolin Mayer)....Pages 195-212 Observations of Structure Within Shape Patterns (Aisling Twohill)....Pages 213-235 Generalizing Fractional Structures: A Critical Precursor to Algebraic Thinking (Catherine Pearn, Max Stephens)....Pages 237-260 First Encounter with Variables by First and Third Grade Spanish Students (Marta Molina, Rebecca Ambrose, Aurora del Rio)....Pages 261-280 Front Matter ....Pages 281-281 Making Implicit Algebraic Thinking Explicit: Exploiting National Characteristics of German Approaches (Anna S. Steinweg, Kathrin Akinwunmi, Denise Lenz)....Pages 283-307 Early Algebra as Analysis of Structure: A Focus on Operations (Deborah Schifter)....Pages 309-327 How Early Is Too Early for Thinking Algebraically? (John Mason)....Pages 329-350 Cycles of Generalizing Activities in the Classroom (Susanne Strachota, Eric Knuth, Maria Blanton)....Pages 351-378 Scaffolding Teacher Practice to Develop Early Algebraic Reasoning (Jodie Hunter, Glenda Anthony, David Burghes)....Pages 379-401 Preservice Teachers’ Knowledge to Teach Functional Thinking (Sharon Mc Auliffe, Cornelis Vermeulen)....Pages 403-425 Back Matter ....Pages 427-443