Children’s Reasoning While Building Fraction Ideas / / edited by Carolyn A. Maher, Dina Yankelewitz.

• Superior document: Mathematics Teaching and Learning
• HerausgeberIn: Maher, Carolyn A.; Yankelewitz, Dina.
• Place / Publishing House: Rotterdam : : SensePublishers :, Imprint: SensePublishers,, 2017.
• Year of Publication: 2017
• Edition: 1st ed. 2017.
• Language: English
• Series: Mathematics Teaching and Learning
• Physical Description: 1 online resource (CCXXII, 16 p.)

This book may be used for research, graduate and undergraduate teacher education, and teacher development. It presents an integrated set of studies of a heterogeneously grouped class of twenty-one nine-year olds, engaged in exploring fraction ideas prior to classroom instruction under conditions that supported investigation, collaboration and argumentation. It demonstrates with text and video narrative how young children can reason about mathematics in surprisingly sophisticated ways when provided the opportunity to do so in the proper classroom environment. In this volume, fourth grade students’ reasoning about fraction concepts is described through careful analysis and accompanying video excerpts showcasing the variety and originality of their thinking. These children will serve as an inspiration for educators to encourage the development of reasoning and argumentation in their students as part of a mathematics curriculum designed to produce critical thinkers.

Table of Contents

Preliminary Material / Carolyn A. Maher and Dina Yankelewitz -- The Experiment / Carolyn A. Maher and Dina Yankelewitz -- Establishing A Mathematical Community / Miriam Gerstein -- A Problem With No Solution / Dina Yankelewitz and Esther Winter -- Designing A New Rod / Dina Yankelewitz and Miriam Gerstein -- Reasoning by Cases While Exploring Fractions as Numbers / Esther Winter and Dina Yankelewitz -- Developing the Foundation for Proportional Reasoning / Esther Winter -- Establishing the Importance of the Unit / Cheryl K. Van Ness and Alice S. Alston -- Switching the Unit / Alice S. Alston and Cheryl K. Van Ness -- Justifying the Choice of the Unit / Cheryl K. Van Ness and Alice S. Alston -- Determining Fraction Equivalence / Miriam Gerstein and Dina Yankelewitz -- Using Reasoning to Resolve Conjectures / Suzanne Reynolds and Elizabeth B. Uptegrove -- The Development of Upper and Lower Bounds Arguments While Comparing Fractions / Dina Yankelewitz and Esther Winter -- Using Generic Reasoning to Compare Fractions / Dina Yankelewitz -- Recursive Reasoning / Dina Yankelewitz and Baila Salb -- From Rod Models To Line Segments / Suzanna Schmeelk -- Students’ Argumentation About Ahe Density Of Fractions / Cheryl K. Van Ness -- Comparing And Ordering Fractions / Kenneth Horwitz and Suzanna Schmeelk -- Extending Fraction Placement From Segments To A Number Line / Kenneth Horwitz -- Epilogue / Carolyn A. Maher , Alice S. Alston and Dina Yankelewitz -- Fraction Tasks And Activities By Chapter / Carolyn A. Maher and Dina Yankelewitz -- Fraction Dissertations From The Colts Neck Intervention / Carolyn A. Maher and Dina Yankelewitz -- Video Narratives By Chapter And Author(s) / Carolyn A. Maher and Dina Yankelewitz -- Index / Carolyn A. Maher and Dina Yankelewitz.