The SimCalc Vision and Contributions



Abstract:
This volume provides essential guidance for transforming mathematics learning in schools through the use of innovative technology, pedagogy, and curriculum. It presents clear, rigorous evidence of the impact technology can have in improving students learning of important yet complex mathematical concepts - and goes beyond a focus on technology alone to clearly explain how teacher professional development, pedagogy, curriculum, and student participation and identity each play an essential role in transforming mathematics classrooms with technology. Further, evidence of effectiveness is complemented by insightful case studies of how key factors lead to enhancing learning, including the contributions of design research, classroom discourse, and meaningful assessment. The volume organizes over 15 years of sustained research by multiple investigators in different states and countries who together developed an approach called "SimCalc" that radically transforms how Algebra and Calculus are taught.

Table of Contents

PART I: Philosophy and Background
Ubiratan D'Ambrosio

  1. Introduction: Major Themes, Technologies, and Timeline
    Jeremy Roschelle and Stephen Hegedus
  2. The Mathematics of Change and Variation from a Millennial Perspective: New Content, New Context
    James J. Kaput and Jeremy Roschelle
  3. From Static to Dynamic Mathematics: Historical and Representational Perspectives
    Luis Moreno-Armella and Stephen Hegedus
  4. Intersecting Representation and Communication Infrastructures
    Stephen Hegedus and Luis Moreno-Armella

PART II: Aspects of Design

  1. Reflections on Significant Developments in Designing SimCalc Software
    James Burke, Stephen Hegedus, and Ryan Robidoux
  2. Designing for Generative Activities: Expanding Spaces for Learning and Teaching
    Nancy Ares
  3. SimCalc and the Networked Classroom
    Corey Brady, Tobin White, Sarah Davis, and Stephen Hegedus

PART III: Impacts from Large-Scale Research
Jinfa Cai

  1. SimCalc at Scale: Three Studies Examine the Integration of Technology, Curriculum, and Professional Development for Advancing Middle School Mathematics
    Jeremy Roschelle and Nicole Shechtman
  2. Learning and Participation in High School Classrooms
    Sara Dalton and Stephen Hegedus
  3. Development of Student and Teacher Assessments in the Scaling Up SimCalc Project
    Nicole Shechtman, Geneva Haertel, Jeremy Roschelle, Jennifer Knudsen, and Corinne Singleton
  4. Sustainable Use of Dynamic Representational Environments: Toward a District-Wide Adoption of SimCalc-Based Materials
    Phil Vahey, George J. Roy, and Vivian Fueyo
  5. Impact of Classroom Connectivity on Learning and Participation
    Stephen Hegedus, Luis Moreno-Armella, Sara Dalton, Arden Brookstein, and John Tapper

PART IV: Impacts from Small-Scale Research

  1. Mathematical Discourse as a Process that Mediates Learning in SimCalc Classrooms
    Jessica Pierson Bishop
  2. Scaling Up Innovative Mathematics in the Middle Grades: Case Studies of "Good Enough" Enactments
    Susan B. Empson, Steven Greenstein, Luz Maldonado, and Jeremy Roschelle
  3. Changing from the Inside Out: SimCalc Teacher Changes in Beliefs and Practices
    John Tapper
  4. Connection Making: Capitalizing on the Affordances of Dynamic Representations Through Mathematically Relevant Questioning
    Chandra Hawley Orrill
  5. "They Need to Be Solid in Standard Skills First": How Standards Can Become the Upper Bound
    Margaret Dickey-Kurdziolek and Deborah Tatar

PART V: International Contributions

  1. Developing and Enhancing Elementary School Students' Higher Order Mathematical Thinking with SimCalc
    Demetra Pitta-Pantazi, Paraskevi Sophocleous, and Constantinos Christou
  2. Adapting SimCalc to Different School Mathematics Cultures: A Case Study from Brazil
    Rosana Nogueira de Lima, Lulu Healy, and Tânia M.M. Campos
  3. Mathematical Modeling with SimCalc: Enhancing Students' Complex Problem Solving Skills Using a Modeling Approach
    Nicholas G. Mousoulides
  4. Approaching Calculus with SimCalc: Linking Derivative and Antiderivative
    Patricia Salinas

PART VI: Extensions, Commentaries, & Future Visions

  1. You Can Lead a Horse to Water. . .: Issues in Deepening Learning Through Deepening Teaching
    John Mason
  2. Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age
    Richard Lesh, Lyn English, Serife Sevis, and Chanda Riggs
  3. The Kaputian Program and Its Relation to DNR-Based Instruction: A Common Commitment to the Development of Mathematics with Meaning
    Guershon Harel
  4. The Evolution of Technology and the Mathematics of Change and Variation: Using Human Perceptions and Emotions to Make Sense of Powerful Ideas
    David Tall
  5. Conversation About SimCalc, Its Evolution and Lessons Along the Way
    Eric Hamilton and Nora Sabelli

 

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