Experimental studies on concrete analogues for algebra

Year: 1994

Author: Quinlan, Cyril

Type of paper: Abstract refereed

Several experimental studies are being undertaken to contribute to ongoing research on mental processes in early algebra. In each study, a comparison is made of two teaching approaches for some aspect of junior secondary algebra. The intervention teaching stage includes the use of concrete analogues for one class, while another class follows a parallel concept sequence without the analogues. Both classes are taught by their regular mathematics teacher and both are in the same Year level. The dates for the studies are November 1993, August 1994, and September 1994.

In November 1993, two Year 7 mixed ability coeducational classes were each taught with the aim of developing an understanding of algebraic generalisations which included the distributive law. One class used arithmetic examples leading to generalisations. The other used an objects-and-containers model to assist. Significantly better gains were recorded by the latter class on attitudes and content-specific achievement. No significant differences were detected before the four periods of teaching intervention. A delayed post-test showed that the advantages persisted, although not at a significant level. The evidence from this field study pointed to the likelihood that the chosen concrete analogue assisted cognitive development.

The September study examines the use of unit cubes for representing exponential growth, leading to an exploration of properties of indices. The August study investigates the effect of using an area approach for finding the factors of first and second degree algebraic expressions.