After reading Skemp's article, I fully stood on the side of relational understanding of mathematics and hence was surprised to discover a good number of the class in support of the instrumental approach. Throughout the discussion, some stressed teaching students instrumentally first so that they would gain confidence in learning math; however, others contended that it is more important to present students with the relational understanding before showing them the shortcuts/formulas.
For example, on teaching angles in polygons, one could easily give out the formulas for computing the sum of the interior angles (180 degrees*(n-2)) and calculating each interior angle of a regular polygon (180 degrees*(n-2)/n). Nevertheless, it is much more helpful to have students start by looking at the sum of interior angles in a triangle, which is 180 degrees. Then, we see that a square/rectangle is composed of two triangles and that a pentagon can be divided into three triangles, etc. From this point, the students can come up with the formula themselves about the sum of the interior angles in a polygon. Furthermore, they can also figure out each interior angle in a regular polygon.
I now feel that both instrumental and relational learning are crucial to mastering mathematics and that it is the teacher's responsibility to discern how to integrate both approaches with regards to specific lessons.
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