An Information Processing Analysis of the Function of Conceptual Understanding in the Learning of Arithmetic Procedures.

Abstract : School children learn arithmetic procedures by rote, rather than by constructing them on the basis of their understanding of numbers. Rote learning produces lack of flexibility, nonsensical errors, and other difficulties in learning. Mathematics educators have proposed that if arithmetic procedures were constructed under the influence of conceptual understanding of the principles of arithmetic, then procedure acquisition would not suffer from these difficulties. However, little effort has been investigated in conceptual analysis of this hypothesis, or in proving its viability. We propose a theory of conceptual understanding and its role in the learning and execution of arithmetic procedures. The basic hypothesis of the theory is that principles constrain the possible states of affairs, and thereby enable the learner to monitor his/her own performance and to correct his/her errors. We propose a new knowledge representation, the state constraint, which captures this view of principled knowledge. Keywords: Computerized simulation, Machine learning.

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