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Introduction Introduction
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The Need for Transforming Early Mathematics Education The Need for Transforming Early Mathematics Education
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Children’s Mathematical Minds Children’s Mathematical Minds
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The Content of Early Mathematics Education The Content of Early Mathematics Education
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Thinking Thinking
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Metacognition Metacognition
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Mathematizing Mathematizing
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Positive Disposition Positive Disposition
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A Basic Pedagogical Principle: Building a Synthesis of the Everyday and the Formal A Basic Pedagogical Principle: Building a Synthesis of the Everyday and the Formal
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What Computers Can Afford What Computers Can Afford
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Goal-Driven Activities Goal-Driven Activities
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Virtual Objects Virtual Objects
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Tools Tools
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Representations Representations
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Scaffolds Scaffolds
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Pedagogical Agents Pedagogical Agents
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Feedback Feedback
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Interaction, Fantasy, Challenge, and Flow Interaction, Fantasy, Challenge, and Flow
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Communication and Collaboration Communication and Collaboration
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Record Keeping and Reporting Record Keeping and Reporting
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Current Educational Software Misses the Mark Current Educational Software Misses the Mark
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The Development Process The Development Process
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Stage 1: Humble Theory-Based Design Stage 1: Humble Theory-Based Design
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Goal-Driven Activities and Virtual Objects Goal-Driven Activities and Virtual Objects
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Tools Tools
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Representations Representations
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Scaffolds Scaffolds
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Pedagogical Agents Pedagogical Agents
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Feedback Feedback
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Interaction, Fantasy, Challenge, and Flow Interaction, Fantasy, Challenge, and Flow
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Communication and Collaboration Communication and Collaboration
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Record Keeping and Reporting Record Keeping and Reporting
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Stage 2: Formative Research: Usability and Learning Stage 2: Formative Research: Usability and Learning
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Stage 3: Revision Stage 3: Revision
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Stage 4: Learning Studies Stage 4: Learning Studies
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Stage 5: Evaluation Stage 5: Evaluation
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Representative Sample Representative Sample
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Standard Measures of Achievement Standard Measures of Achievement
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Scalability Scalability
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Conclusions Conclusions
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Early Childhood Education Early Childhood Education
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Software Design and Analysis Software Design and Analysis
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Research and Development Research and Development
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References References
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56 New Possibilities for Early Mathematics Education: cognitive guidelines for designing high-quality software to promote young children’s meaningful mathematics learning
Get accessHerbert P. Ginsburg, Teachers College Columbia University
Rachael Labrecque, Teachers College Columbia University
Kara Carpenter, Teachers College, Columbia University
Dana Pagar, Teachers College Columbia University
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Published:01 July 2014
Cite
Abstract
Mathematics instruction for young children should begin early, elaborate on and mathematize children’s everyday mathematics, promote a meaningful integration and synthesis of mathematics knowledge, and advance the development of conceptual understanding, procedural fluency, and use of effective strategies. The affordances provided by computer programs can be used to further these goals by involving children in activities that are not possible with traditional methods. Drawing on research and theory concerning the development of mathematical cognition, learning, and teaching, high quality mathematics software can provide a productive learning environment with several components: (1) useful instructions and demonstrations, scaffolds, and feedback; (2) mathematical tools (like a device that groups objects into tens); and (3) virtual objects, manipulatives and mathematical representations. We propose a five-stage iterative research and development process consisting of (1) coherent design; (2) formative research; (3) revision; (4) learning studies; and (5) summative research. A case study of MathemAntics, software for children ranging from age 3 to grade 3, illustrates the research and development process. The chapter concludes with implications for early childhood educators, software designers, and researchers.
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