Mathematical and Analogical Reasoning of Young Learners

by English, Lyn D.; Alexander, Patricia A.; Buehl, Michelle; Chiu, Shuhui

• ISBN13: 9780805849455
• ISBN10: 0805849459
• Format: Paperback
• Copyright: 2004-05-07
• Publisher: Lawrence Erlbau

Summary

Mathematical and Analogical Reasoning of Young Learnersprovides foundational knowledge of the nature, development, and assessment of mathematical and analogical reasoning in young children. Reasoning is fundamental to understanding mathematics and is identified as one of the 10 key standards for school mathematics for the new millennium. The book draws on longitudinal and cross-cultural studies, conducted in the United States and Australia, of children's reasoning development as they progressed from preschool through the end of second grade. The multifaceted analysis of young children's development of mathematical and analogical reasoning focuses on individual learners, their learning environments, and the interaction between the two. The multidisciplinary team of authors present multiple perspectives and multiple methodologies, and provide valuable information on organizing and sustaining interdisciplinary and cross-cultural inquiry. Key issues addressed include: *the relationship between mathematical and analogical reasoning; *how changes in children's reasoning relate to the implicit instruction they receive in their classrooms; *analyses of the participating teachers' knowledge, beliefs, and practices with respect to mathematical and analogical reasoning of young learners; and *ways in which we might promote development of mathematical and analogical reasoning in young children. This volume is highly relevant for mathematics educators, researchers in mathematics education, educational psychologists, early childhood teachers, and others interested in mathematical development of young children, in particular, the development of their reasoning processes.

Table of Contents

Preface	ix
1 Mathematical and Analogical Reasoning in Early Childhood	1	(22)
Lyn D. English
2 Seeing the Possibilities: Constructing and Validating Measures of Mathematical and Analogical Reasoning for Young Children	23	(24)
Patricia A. Alexander and Michelle M. Buehl
3 Longitudinal and Cross-Cultural Trends in Young Children's Analogical and Mathematical Reasoning Abilities	47	(28)
Michelle M. Buehl and Patricia A. Alexander
4 Classroom Discourse and the Development of Mathematical and Analogical Reasoning	75	(22)
Shuhui Chiu and Myriam O. Tron
5 Portraying Mathematical and Analogical Reasoning in the Young: Three Case Studies	97	(30)
Debby Deal and Shanon Hardy
6 Teachers' Knowledge, Beliefs, and Practices and Mathematical and Analogical Reasoning	127	(26)
C. Stephen White, Debby Deal, and Carla Baker Deniz
7 Case Studies of Teacher Beliefs, Knowledge, and Practices	153	(16)
C. Stephen White and Debby Deal
8 Commentary: Analogical Reasoning and Mathematical Development	169	(18)
Usha Goswami
9 Commentary: Toward a Cognitive-Sociocultural Psychology of Mathematical and Analogical Development	187	(14)
Giyoo Hatano and Tomomi Sakakibara
10 Promoting the Development of Young Children's Mathematical and Analogical Reasoning	201	(14)
Lyn D. English
Author Index	215	(6)
Subject Index	221