Reflection: Integrating Instrumental and Relational Learning

Based on the class discussion, I realized that as an educator, there is no need to choose between two methods when teaching students. Rather than using one method, integrating both relational and instrumental learning is an effective way of teaching students. However, the order of methods does not matter in teaching as long as students understand logically and construct their own way of thinking to solve problems. For example, when introducing arithmetic series, a teacher can use both methods as below.

Ex) What is the sum of all the odd numbers between 1 and 100?

1+3+5+......+95+97+99 = ?

●Relational method:

è  (1+99)+(3+97)+(5+95)+...  = 100+100+100+...

Since they are odd numbers between 1 and 100, so there are 50 odd numbers.

But two of the odd numbers are added together, so there are 25 of them.

è  100 * 25 = 2500

Therefore, the sum is 2500.

●Instrumental method:

With a formula:

Sn=(n(a1+a2))/2 ,     where Sn=the sum of n terms, a1=first term, an=nth term.

So, when applying this formula to the problem,

S50=(50*(1+99))/2 = (50*100)/2=2500

Without a formula:

1=1=1^2

1+3=4=2^2

1+3+5 =9=3^2

1+3+5+7=16=4^2

We see patterns of n^2. Since there are 50 terms, n=50. -> 50^2=2500.

Not only applying a formula to the problem (instrumental learning), but showing why it works (relational learning) will help students understand the principle, so they will be able to branch out to similar problems. Moreover, even if the formula is not given, a teacher can help them find their own way to solve the problem by making pattern rules.