Rethinking “Concrete” Manipulatives

Douglos H. Clements · Sue McMillen

197 citations0/0 files storedTeaching Children Mathematics

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Mathematics Education and Teaching Techniques Mathematics Education and Pedagogy History and Theory of Mathematics

Abstract

Close your eyes and picture students doing mathematics. Like many educators, the mental pictures may include manipulative objects, such as cubes, geoboards, or colored rods.

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2009“Concrete” Computer Manipulatives in Mathematics Education 2011Teaching with concrete and abstract visual representations: Effects on students' problem solving, problem representations, and learning perceptions.2009The Challenge of Formative Assessment in Mathematics Education: Children’s Minds, Teachers’ Minds 2000From exercises and tasks to problems and projects 2006Virtual Manipulatives in Mathematics Education: A Theoretical Framework.2013Usability of concrete and virtual models in chemistry instruction 2016Physical and Virtual Manipulatives: What Is “Concrete”?2004Comments on the Use of Learning Trajectories in Curriculum Development and Research

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