The problem with Mathematics teaching – Algorithm vs Concept
In one of the previous articles I have written about a simple problem with Fractions and how the teachers are not able to make the students appreciate what is happening when you are adding two Fractions.
What typically gets taught in schools is the algorithm. If we have to add two fractions take the LCM of the denominators and do the corresponding multiplication.
But to the question why can’t we add the numerator and denominator we need to approach this from a concept viewpoint.
What is the concept of a fraction ? What does the numerator represent ? What does the denominator represent ?
A fraction represents a portion of something. It represents a part of a whole. The numerator speaks of the number of parts under consideration and the denominator represents the parts which the whole is divided into.
With this understanding now if we stop and look back at the addition of the fractions when the denominators are different, we are looking at adding two different fractions whose wholes have been sub divided into different number of parts. How can we add two things that are different. So the solution is to make them the same. If we have to make them the same we need to find the LCM of the denominators and hence the rest of the argument follows.
This is the concept.
When the child went and asked the teacher this question at the school, as to why should we do this algorithm the teachers response was this was not for his level and he would learn when he grew up. We are all grown up and we still don’t know.
This is the irony of the education. It was interesting to observe that the teacher did not make an attempt to go back home and learn the concept. This system of education has to change.
We should change this world, a thought at a time.