Mental computation and conceptual understanding

The goal of this study was to assess the strategic flexibility of students in mental arithmetic up to the number 100. Sixty Dutch second-graders who took part in an experimental 'realistic arithmetic' program participated in the study. Results showed that students' preference for certain mathematical procedures depended on the number characteristics of the problems. This indicates that the students had a good conceptual understanding of numbers and procedures. Their actual use of these procedures, however, was somewhat limited. Most problems were solved within a sequential structure, A completely different procedure was used for solving subtraction problems that had a very small difference between the two numbers. Furthermore, it was found that a substantial increase in the students' use of a base-ten procedure occurred after the introduction of this procedure in the mathematics curriculum. Students' preference for this procedure also increased, although to a lesser extent. Another finding of the study was that students exhibited more flexible strategic behaviour with context problems than with numerical-expression problems. (C) 2000 Elsevier Science Ltd. All rights reserved.