Toward Computational Fluency in Multidigit Multiplication and Division
Traditionally in the United States and Canada, students have first learned how to compute with whole numbers and then have applied that kind of computation. This approach presents several problems. First, less-advanced students sometimes never reach the application phase, so their learning is greatly limited. Second, word problems usually appear at the end of each section or chapter on computation, so sensible students do not read the problems carefully: They simply perform the operation that they have just practiced on the numbers in the problem. This practice, plus the emphasis on teaching students to focus on key words in problems rather than to build a complete mental model of the problem situation, leads to poor problem solving because students never learn to read and model the problems themselves. Third, seeing problem situations only after learning the mathematical operations keeps students from linking those operations with aspects of the problem situations. This isolation limits the meaningfulness of the operations and the ability of children to use the operations in a variety of situations.