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 t ook part in an experimental 'realistic arithmetic' program participated in the study. Results showed that students' preference for certain mathematica l procedures depended on the number characteristics of the problems. This i ndicates that the students had a good conceptual understanding of numbers a nd procedures. Their actual use of these procedures, however, was somewhat limited. Most problems were solved within a sequential structure, A complet ely 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 oc curred after the introduction of this procedure in the mathematics curricul um. Students' preference for this procedure also increased, although to a l esser extent. Another finding of the study was that students exhibited more flexible strategic behaviour with context problems than with numerical-exp ression problems. (C) 2000 Elsevier Science Ltd. All rights reserved.