Pre-service elementary teachers' reasoning in introducing multidigit subtraction

摘要

Ideally, mathematical concepts must be justified rather than simply stated. This study examined the reasoning expressed by pre-service elementary teachers when asked to describe how they would introduce the concept of multidigit subtraction to their students. The sample consisted of 230 pre-service elementary teachers from six Philippine universities located in various regions of the country. The reasoning in each response was classified to be of high- or low-quality, on the basis of whether they were anchored to intrinsic mathematical properties. Repeating phrases were also identified and were analysed qualitatively. The findings show that more than 90% of the reasoning produced by teachers relied heavily on rules and procedures, without connections to the quantities involved in the problem. The existence of responses that were repeated across a large number of participants also suggests that the pre-service teachers' reasoning's were influenced by a 'cultural script' they learned over a lifetime of participation in rule-dominated classrooms. The paper concludes by offering recommendations and future directions.