By John McAdam

This PDF file presents chapter 17 of The Learning of Mathematics: 69th NCTM Yearbook in a downloadable file that preserves the design and layout of the book while allowing users to search and print selected pages.

Chapter 17: Prospective Teachers’ Use of Concrete Representations to Construct an Understanding of Addition and Subtraction Algorithms. John McAdam (Marist College, Poughkeepsie, New York) offers a glimpse into how prospective teachers in an elementary methods course make meaning of algorithms using base-ten blocks in their procedural and conceptual study of addition and subtraction algorithms. While manipulating these concrete materials, prospective teachers were required to move back and forth between concrete and symbolic representations to explore the meaning of number, place value, and mathematical operations using whole-number algorithms. Constructing algorithms with base-ten blocks provided the context and opportunity for conceptual growth and understanding for the teaching and learning of mathematics for students in kindergarten through grade 8.

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