Affective processes in interactive construction of understanding in mathematics

Year: 1994

Author: Owens, Kay, Perry, Bob, Geoghegan, Noel, Howe, Peter

Type of paper: Abstract refereed

This paper reports on affective processes that emerged during a study of an adult mathematics class that used a teaching approach compatible with a social constructivist theory of knowing. The study was part of a larger research project on the effects of using a cyclical teaching model based on the premise that learning occurs through participation in the phases of experiencing, discussing, generalising, and applying. Paired groups worked through the phases by way of a series of mathematical problems with many opportunities for discussion. Whole- class student-led sharing sessions allowed students to continue their collaborative construction of meaning and solutions.

Goldin (1988) provides a model of affective pathways that may occur when students undertake mathematical problems. Goldin's model indicates certain links and pathways between descriptors of affective states. However, the nature of these links is not elaborated. The present study suggests that affective states are not as clear-cut as Goldin's model might suggest. Students with negative affects such as fear and anxiety about mathematical problem-solving in fact have a range of affective states relating to areas of knowing (such as teaching primary school mathematics) that are associated with the target area (mathematical problem-solving). These related affects assisted students to move away from negative affective states about mathematical problem-solving. Students who had high levels of risk- taking, high verbal analytical skills, or positive experiences with teaching primary mathematics were able to link knowledge and attitudes and feel more positive about mathematical problem-solving despite their initial negative feelings.

The research procedure used was itself compatible with constructivist theories of knowing and involved viewing tape-recordings of all teaching sessions (totalling 36 hours). The researchers then collaborated in drawing conclusions from the observations.