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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