Rigorous Mathematical Thinking Conceptual Formation in the Mathematics Classroom 1st Edition by James Kinard, Alex Kozulin ISBN 0521700264 978-0521700269

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Product details:

ISBN 10: 0521700264
ISBN 13: 978-0521700269
Author: James Kinard, Alex Kozulin

This book demonstrates how rigorous mathematical thinking can be fostered through the development of students’ cognitive tools and operations. Though this approach can be applied in any classroom, it seems to be particularly effective with socially disadvantaged and culturally different students. The authors argue that children’s cognitive functions cannot be viewed as following a natural maturational path: They should be actively constructed during the educational process. The Rigorous Mathematical Thinking (RMT) model is based on two major theoretical approaches allowing such an active construction – Vygotsky’s theory of psychological tools and Feuerstein’s concept of mediated learning experience. The book starts with general cognitive tools that are essential for all types of problem solving and then moves to mathematically specific cognitive tools and methods for utilizing these tools for mathematical conceptual formation. The application of the RMT model in various urban classrooms demonstrates how mathematics education standards can be reached even by the students with a history of educational failure who were considered hopeless underachievers.

Rigorous Mathematical Thinking Conceptual Formation in the Mathematics Classroom 1st Table of contents:

1 Culture of Mathematics

Sociocultural Needs Systems

Historical Evolvement of the Sociocultural Needs Systems

From Symbolic Thought to Mathematical Expression: Historical Footprints of the Mathematics Culture

Mathematical Learning Activity

Mathematical Knowledge

Need for Mathematically Specific Psychological Tools

Mathematical Rigor

2 Goals and Objectives of Mathematics Education

The Standards Movement in Mathematics and Science in the United States

The Need for Rigorous Thought in Mathematics and Science Education

3 Vygotsky’s Sociocultural Theory and Mathematics Learning

Mediated Character of Human Learning

Symbolic Tools and Their Internalization

Zone of Proximal Development

Learning Activity

Learning Activity and Math Curriculum

4 Mediated Learning and Cognitive Functions

Mediated Learning Experience

Development of Cognitive Functions

Cognitive Functions in RMT Paradigm

Instrumental Enrichment Program

IE Program as a System of Psychological Tools

Instrumental Enrichment and Math Problem Solving in Immigrant Students

Study 1

Study 2

5 Mathematical Concept Formation and Cognitive Tools

Mathematically Specific Psychological Tools

Symbols and Codes

Number System with Its Intrinsic Place Values

Number Line

Table

Cartesian Coordinate System

Mathematical Language

Standards-Based Conceptual Formation Through RMT

Conceptual Nature of Cognitive Functions

The RMT Process for Concept Formation

Strategic Planning to Teach Through the RMT Process

Conceptual Formation in Basic Mathematics Through RMT

Basic Mathematics Operations

Mathematical Activity A on Quantity

Mathematical Activity B on Quantity

Understanding and Comparing Fractions with Unlike Denominators

Conceptual Formation in Algebra Through RMT

6 RMT Application, Assessment, and Evaluation

Lesson Planning

Mediation During the Lesson

Assessment

RMT Program Research in Primary School

RMT Research with Cultural Minority Students in the Middle School

High School Dropouts

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Tags: James Kinard, Alex Kozulin, Rigorous Mathematical, Mathematics Classroom