In order to find the unknown angle of a triangle, an elementary school student will use a protractor to measure it. But once in high school, students are expected to find the answer through deductive reasoning. They need to understand that, given two angles of a triangle, they can then calculate the third.
Students are ill-prepared for this abrupt transition from a purely practical approach to theory-based deductive reasoning.
This example clearly illustrates the shift in reasoning required by students once they reach high school.
According to Stéphane Cyr, research professor of mathematics teaching at Université du Québec à Montréal, students are ill-prepared for this abrupt transition from a purely practical approach to theory-based deductive reasoning. When they reach high school, they have difficulty writing proofs and providing well-structured arguments tosupport their answers when solving problems.
For three years, the researcher tested the possibility of gradually introducing the difference between measurement and deductive reasoning in sixth-grade classes. Using short, simple exercises, he began by demonstrating that measurements are inaccurate and that deductive reasoning makes it possible to obtain more precise results. The students understood the difference, and began spontaneously resorting to a deductive approach when a measurement gave them an inaccurate answer.
Cyr believes that his study clearly demonstrates that young students have the skills necessary for making the gradual transition towards a deductive approach to problem solving.