Classroom strategies for expressing generalities from patterns

Year: 1994

Author: Robertson, Margaret, Taplin, Margaret

Type of paper: Abstract refereed

This paper reports on a pilot study that considers the relevance of recent theoretical conceptualisations of intelligence to mathematical problem-solving related to patterns and relationships. Psychologists believe that a wide range of mental processes are available to humans as a power factor in intelligence which can be enhanced with appropriate instructional strategies. By analysing children's preferred modes of problem-solving some recommendations may be possible for improving thinking skills through relevant teaching strategies.

Expressing generality from patterns is a notion that is fundamental to the development of mathematical concepts in algebra. It is one of the three sub-headings in the algebra section of the National Statement on Mathematics for Australian Schools. How best to implement these ideas in the classroom is the concern of this research.

Our conjecture is that there is a mismatch between teachers' preferred mode of delivery and the intelligences that students are most likely to apply to the task. This paper reports, first, on the identification of tasks that enable students to express generalisations from patterns, and second, on the quality of observed outcomes based on the SOLO Taxonomy. Using this information our aim is to gain insight into the preferred processing mode of a small sample of junior high school students. From these findings a further aim is to generate hypotheses for a major investigative study into children's thinking related to mathematical problem-solving.