Reflection on Integrating Instrumental & Relational Learning

I like the idea of relational understanding because the student learns both the "what" and "why" of Mathematics but for students who naturally find maths difficult, teachers might feel that relational learning is not the appropriate method.

Thus after Wednesday’s debate on instrumental and relational learning, I see that we should integrate both together. Visual representation is a good way to incorporate relational understanding and afterwards we can come up with any formula or theory.

I would like to take the example of how to calculate the sum of interior angles of a regular polygon. Here we would take pentagon as example.

Instrumental method:

Sum of Interior angle of a regular polygon = 180^◦ (n-2), where n is the number of sides.

Therefore, Sum of Interior angle of a pentagon = 180^◦ (5-2)

                                                                            =540^◦ 

Relational method:

Let us draw a regular pentagon. 

Start from any corner and draw a triangle.Continue drawing triangles but always start from the same starting point.

Here we can observed that the pentagon is made up of 3 triangles and since we know that in a triangle, the sum of angle of the interior angles is 180^◦.

Therefore, we can easily calculate the sum of interior angles of a regular pentagon

= 3 X 180^◦ 

=540^◦ 

Note that a pentagon has 5 sides and 3 triangles. So, we can see that the number of triangles will be 2 less than the number of sides.

            This pattern can be used for all regular polygons.

Our system of teaching Mathematics tends to favor instrumental understanding but still we should incorporate both as there is always a proof behind a formula. It is very easy to forget a formula but if we understand the concept, we can slowly derive the formula.