I recall one assignment I assigned my students earlier this year which drew heavily upon students’ in-depth understanding of how to apply abstract mathematical concepts to real-world situations. After having spent a day on teaching my students the formula for calculating the volume of a cylinder and doing a huge number of abstract problems involving finding the volume of hypothetical cylinders on a sheet of paper, the next day I brought in a Coke can, a coffee mug, and a water bottle and had my students calculate their volumes using nothing but a ruler and a TI-84. I feel that this boosted my students’ overall comprehension of computing cylinder volumes since the formulas were no longer used for vague, inapplicable purposes. Instead, this one formula I taught them could be used to solve for any cylinder in the known universe. This amazed my students. Soon they were using their ruler to calculate the volume of not just the items I brought in but also of other cylindrical objects around the classroom (such as a can of soup a student had brought). Using this as an exemplar case, I have learned that bringing palpable objects for my students onto which my students can apply their geometrical knowledge has proven to be one of the most effective means of boosting my students’ mathematical problem solving skills.
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