new approach builds on them (Hiebert, 1984; Cobb, 1985; Baroody & Ginsburg, 1986; Resnick,
Lesgold, & Bill, 1990). For example, young children often use counting strategies to solve
problems. By encouraging the use of such strategies and by teaching even more sophisticated
counting techniques, the new approach helps children become proficient at computation while
also preserving their belief that mathematics makes sense. This new approach to computation is
described in more detail below.
Reducing the emphasis on complicated paper-and-pencil computations does not mean that paperand-
pencil arithmetic should be eliminated from the school curriculum. Paper-and-pencil skills
are practical in certain situations, are not necessarily hard to acquire, and are widely expected as
an outcome of elementary education. If taught properly, with understanding but without demands
for "mastery" by all students by some fixed time, paper-and-pencil algorithms can reinforce
students' understanding of our number system and of the operations themselves. Exploring
algorithms can also build estimation and mental arithmetic skills and help students see
mathematics as a meaningful and creative subject.
3
Algorithms in Everyday Mathematics
Everyday Mathematics includes a comprehensive treatment of computation. Students learn to
compute mentally, with paper and pencil, and by machine; they learn to find both exact and
approximate results; and, most importantly, they learn what computations to make and how to
interpret their answers. The following sections describe in general terms how Everyday
Mathematics approaches exact paper-and-pencil methods for basic operations with whole
numbers. For details about particular algorithms and for information about how the program
teaches mental arithmetic, estimation, and computation with decimals and fractions, see the
Everyday Mathematics Teacher's Reference Manual.
In Everyday Mathematics, computational proficiency develops gradually. In the beginning,
before they have learned formal procedures, students use what they know to solve problems.
They use their common sense and their informal knowledge of mathematics to devise their own
procedures for adding, subtracting, and so on. As students describe, compare, and refine their
approaches, several alternative methods are identified. Some of these alternatives are based on
students' own ideas; others are introduced by the teacher or in the materials. For each basic
operation, students are expected to become proficient at one or more of these alternative
methods.
The materials also identify one of the alternative algorithms for each operation as a focus
algorithm. The purpose of the focus algorithms is two-fold: (i) to provide back-up methods for
those students who do not achieve proficiency using other algorithms, and (ii) to provide a
Algorithms in Everyday Mathematics
Start from the beginning
