Concept Mapping in Mathematics: Research into Practice

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Concept Mapping in Mathematics: Research into Practice is the first comprehensive book on concept mapping in mathematics. It provides the reader with an understanding of how the meta-cognitive tool, namely, hierarchical concept maps, and the process of concept mapping can be used innovatively and strategically to improve planning, teaching, learning, and assessment at different educational levels. This collection of research articles examines the usefulness of concept maps in the educational setting, with applications and examples ranging from primary grade classrooms through secondary mathematics to pre-service teacher education, undergraduate mathematics and post-graduate mathematics education. A second meta-cognitive tool, called vee diagrams, is also critically examined by two authors, particularly its value in improving mathematical problem solving.

The theoretical underpinnings of concept mapping and of the studies in the book include Ausubel’s cognitive theory of meaningful learning, constructivist and Vygotskian psychology to name a few. There is evidence which suggests that students’ mathematical literacy and problem solving skills can be enhanced through students collaborating and interacting as they work, discuss and communicate mathematically. This book proposes the meta-cognitive strategy of concept mapping as one viable means of promoting, communicating and explicating students’ mathematical thinking and reasoning publicly in a social setting as they engage in mathematical dialogues and discussions.

Concept Mapping in Mathematics: Research into Practice is of interest to researchers, graduate students, teacher educators and professionals in mathematics education.

Author(s): Joseph D. Novak, Alberto J. Cañas (auth.), Karoline Afamasaga-Fuata'i (eds.)
Edition: 1
Publisher: Springer US
Year: 2009

Language: English
Pages: 220
Tags: Mathematics Education; Learning & Instruction

Front Matter....Pages i-xiv
Front Matter....Pages 1-1
The Development and Evolution of the Concept Mapping Tool Leading to a New Model for Mathematics Education....Pages 3-16
Front Matter....Pages 1-1
Analysing the “Measurement” Strand Using Concept Maps and Vee Diagrams....Pages 19-46
Concept Mapping as a Means to Develop and Assess Conceptual Understanding in Primary Mathematics Teacher Education....Pages 47-57
Using Concept Maps and Vee Diagrams to Analyse the “Fractions” Strand in Primary Mathematics....Pages 59-86
Concept Maps as Innovative Learning and Assessment Tools in Primary Schools....Pages 87-113
Front Matter....Pages 1-1
Evidence of Meaningful Learning in the Topic of ‘Proportionality’ in Second Grade Secondary Education....Pages 117-135
Concept Mapping as a Means to Develop and Assess Conceptual Understanding in Secondary Mathematics Teacher Education....Pages 137-147
Concept Mapping a Teaching Sequence and Lesson Plan for “Derivatives”....Pages 149-169
Curricular Implications of Concept Mapping in Secondary Mathematics Education....Pages 171-188
Using Concept Maps and Gowin’s Vee to Understand Mathematical Models of Physical Phenomena....Pages 189-216
Applying Concept Mapping to Algebra I....Pages 217-234
Front Matter....Pages 1-1
Enhancing Undergraduate Mathematics Learning Using Concept Maps and Vee Diagrams....Pages 237-257
Concept Mapping: An Important Guide for the Mathematics Teaching Process....Pages 259-277
Concept Mapping and Vee Diagramming “Differential Equations”....Pages 279-297
Using Concept Maps to Mediate Meaning in Undergraduate Mathematics....Pages 299-326
Front Matter....Pages 1-1
Implications and Future Research Directions....Pages 343-329
Back Matter....Pages 335-339