Computation
Strategies
The
computation strategies and approaches described below can be used by
parents and teachers to foster students' understanding of a variety
of math problems. They are not all inclusive nor mandates for instruction,
but are presented merely as a resource.
Algorithmic Thinking
Algorithms (step by step operational procedures) are often taught in
the following manner:
First, young children explore and experiment with concrete models of
numbers and operations. Students then gradually move beyond concrete
representations to pictorial representations. At the concrete and pictorial
stages, number symbols (numerals) are used along with their concrete
or pictorial counterparts. Finally, students are ready to work with
symbols only.
We continue to build students’ understanding of numeration, basic
facts, and operations from the concrete to the pictorial to the symbolic.
Our goal is to have students eventually learn the most efficient standard
paper and pencil algorithms for addition, subtraction, multiplication,
and division of whole numbers, decimals, and fractions.
We also view computational algorithms as more than rote processes. Students
can actively participate in the analysis of various alternative algorithms
and then develop new ones. The established belief is when students create
and share their own problem-solving methodologies, instead of simply
learning a prescribed (and limited) set of standard algorithms, they
become active and enthusiastic participants in their learning processes
and take risks, think logically, and reason analytically.
Everyday
Mathematics, 2002, Everyday Mathematics Operations Handbook, SRA/McGraw
Hill, Chicago, Il.
Addition
Everyday
Mathematics
a.
Partial-Sums Algorithm for Addition
b.
Column-Addition Algorithm for Addition
c.
Short Algorithm (Standard) for Addition
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