Abstract
Conceptual understanding has been emphasized in the national curriculum and principles and standards across nations as it is the key in mathematical learning. However, mathematics instruction in classrooms often relies on rote memorization of mathematical rules and formulae without conceptual connections. This study considers the concreteness fading instruction strategy—starting with physical activities with manipulatives and gradually fading concreteness to access abstract concepts and representations—as a promising and sustainable instructional model for supporting students in accessing conceptual understanding in mathematics classrooms. The results from the case study support the validity of the concreteness fading framework in providing specific instructional strategies in each phase of concept development. This study implies the development of sustainable teacher education and professional development by providing specific instructional strategies for conceptual understanding.
Highlights
While a reform of how mathematics is taught in school is a worldwide issue, the implementation of such a reform in U.S schools has been advocated by the Principles and Standards for School Mathematics [1], and more recently by the Common Core State Standards for Mathematics (CCSS-M) [2]
These standards emphasize the importance of mathematics by learning aspects such as conceptual understanding, communication, and productive disposition in teaching and learning mathematics
The concreteness fading strategy differs from merely providing concrete materials and vTihseuawl areypsriensewnhtaicthionthse
Summary
While a reform of how mathematics is taught in school is a worldwide issue, the implementation of such a reform in U.S schools has been advocated by the Principles and Standards for School Mathematics [1], and more recently by the Common Core State Standards for Mathematics (CCSS-M) [2] These standards emphasize the importance of mathematics by learning aspects such as conceptual understanding, communication, and productive disposition in teaching and learning mathematics. Features of the new approach include story-telling mathematics (i.e., contextualizing the mathematical content and connecting it to history, visualization, music, design, and additional real-life situations) and problem solving In this context, the significance of mathematizing from Realistic Mathematics Education (RME) [3] has been more emphasized. In his method of didactical phenomenology, Freudenthal considers mathematics as a human activity, so
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