Acquiring Arithmetic Knowledge in a Computer-Based Learning Environment for Long Division

Abstract

This paper reports on the acquisition of arithmetic knowledge in successive stages of expertise, and on the types of instruction that are needed to make that learning possible. The domain is that of integer arithmetic and the target skills and concepts of the learning system relate to long division with remainder. We studied students' learning performance using a computer-based learning environment representing division as repeated subtraction from the dividend and facilitating the exploration and construction of multiples of the divisor to be subtracted. The learning environment also took over the subtasks of multiplication, addition and subtraction from the student. In particular, we studied the extent to which students were constrained in their freedom to construct solution paths and the effect of this factor on learning performance. Results showed that students profited from this learning environment, but the more optimal solutions reached under constrained problem solving could not be demon strated in a pre-post test comparison using only paper-and-pencil type problems. It appears that this performance can only be reached if the learning environment assists the student with lower-level subtasks and that more advanced strategic knowledge is required in order to reach the same level of performance without this support.