Proportional reasoning: Reducing the interference of natural numbers through an intervention based on the problem-solving framework of executive functions

According to the problem-solving framework of executive functions, the first step is to construct a problem space, i.e., the representation of the problem and its possible solutions. We explored how different problem spaces affect students' proportional reasoning. Proportional reasoning is important in school and in everyday life. It involves the comparison of ratios and is known to be difficult. Previous studies have shown that difficulties in proportional reasoning may stem from the interference of the automatic comparison of the salient natural numbers that comprise the ratios. We designed two equivalent comparison of ratios tests that were visually very similar, the Drops test and the Juice test. In the Drops test, tenth graders were asked to compare the intensity of colour of
mixtures of red and white paint drops. In the Juice test, they were asked to compare the amount of juice each child receives when equally dividing the contents of cups of juice among children in each group. The Juice test
was aimed at presenting the task in a mode leading to a problem space that directs students to calculate “rate per unit,” thereby reducing the interference of the automatic comparison of the salient natural numbers. The findings
indicated that success in the Juice test was higher than in the Drops test. Moreover, success in the Drops test was higher when performed after the Juice test. The current study suggests using modes of presentation that lead to problem spaces that direct students to use appropriate solution strategies, hence aiding them in overcoming difficulties. Using modes or orders of presentation could serve as important tools for educators in science and mathematics and could lead to higher academic achievements among their students.