Multiple Solutions: A Key to Strengthening the Generalization Skill in Mathematic-Like Thinking

Emphasizing multiple solutions can help with the strengthening of the generalization skill. To test this hypothesis, a group of high school students in math and experimental sciences was selected in order to see if the chosen method would have a differential effect on different levels of mathematic-related skills. The group was divided into two, one of which was subjected to the multiple solutions approach. The measure used as both pre- and posttest assessed three basic skills in generalization: immediate, close, and distant generalization. The results show that using the multiple solution approach does lead to improvement in all three types of generalization in both math and experimental sciences students. Further analyses of the responses reveal that students are not familiar with the concept of variable, and the gap between algebraic and arithmetic thinking, as they are weak in the expression of generalization and mathematical discourse.