From Drawings to Buildings; Working with Mathematical Scales

Abstract

School instruction about and daily practice with proportions problems were contrasted with respect to their influences upon students' and construction foremen's performance in a series of problems on scale drawings, which seem to entail the formal operational scheme of proportionality. Foremen's perfomance was more accurate than students' but a greater proportion of students used a generalizable problem-solving strategy of finding and working with a simplified ratio (l/x or x/l). The school-taught proportions algorithm (x/a = b/c) had no significant impact upon students' problem-solving strategies. Students' performance revealed a strong ability to deal with the rule-based aspects of the mathematics in the problem but their ability to deal with meaning was weak; in contrast, job experience seems to enrich measurement with meaning. These differences can be traced to the contexts in which problem solving had been practiced and are suggestive of an educational implication: schools have overlooked the importance of meaning in mathematics, a practice which makes students' performance appear lower than their reasoning skills would lead one to expect.