Algorithms in Everyday Mathematics
Algorithms in School Mathematics .............................................................................................1
Algorithms in Everyday Mathematics .........................................................................................3
Invented Procedures................................................................................................................3
Alternative Algorithms ...........................................................................................................5
Focus Algorithms....................................................................................................................6
Algorithmic Thinking .................................................................................................................7
References .................................................................................................................................8
An algorithm is a step-by-step procedure designed to achieve a certain objective in a finite time,
often with several steps that repeat or "loop" as many times as necessary. The most familiar
algorithms are the elementary school procedures for adding, subtracting, multiplying, and
dividing, but there are many other algorithms in mathematics.
Algorithms in School Mathematics
The place of algorithms in school mathematics is changing. One reason is the widespread
availability of calculators and computers outside of school. Before such machines were invented,
the preparation of workers who could carry out complicated computations by hand was an
important goal of school mathematics. Today, being able to mimic a $5 calculator is not enough:
Employers want workers who can think mathematically. How the school mathematics
curriculum should adapt to this new reality is an open question, but it is clear that proficiency at
complicated paper-and-pencil computations is far less important outside of school today than in
the past. It is also clear that the time saved by reducing attention to such computations in school
can be put to better use on such topics as problem solving, estimation, mental arithmetic,
geometry, and data analysis (NCTM, 1989).
Another reason the role of algorithms is changing is that researchers have identified a number of
serious problems with the traditional approach to teaching computation. One problem is that the
traditional approach fails with a large number of students. Despite heavy emphasis on paper-andpencil
computation, many students never become proficient in carrying out algorithms for the
basic operations. In one study, only 60 percent of U.S. ten-year-olds achieved mastery of
subtraction using the standard "borrowing" algorithm. A Japanese study found that only 56
percent of third graders and 74 percent of fifth graders achieved mastery of this algorithm. A
principal cause for such failures is an overemphasis on procedural proficiency with insufficient
attention to the conceptual basis for the procedures. This unbalanced approach produces students
