Addition Metaphors 1

There are 2 metaphors for addition. 

Join situations (commonly known as “put together”)

In Join situations, two collections are joined together by putting together, collecting, mixing etc. What are the things which can be joined? Apart from discrete things (like pencils, erasers, tokens) even weights, volumes, areas, lengths, time, age, money, angles etc can be joined.

Such examples can be given from the life experiences of children themselves; rice is bought in Kgs, milk in Litres, distances measured in Cms, Mtrs and Kms, school vacations measured in weeks etc. These can be used in word problems without converting within the units. The conversions themselves can be taught in higher classes. Right now, the intention is to make students think about things they can join together.

Join situations can be taught from Class 1 as they can be demonstrated in the classroom by role play where things can be put together in a basket. It is by many such activities of different situations that the concept of “Join” gets internalised.

Teachers also should train children in using vocabulary like “How many in total?”, “What is the total?”, “How much is it altogether?” etc .

Counter Examples

Children should be given counter examples of “entities” which either cannot be “joined” or make no sense to join them. A glass of milk at 30deg when added to a glass of milk at 40 deg does not result in milk at 70deg!! Entities like speed & price cannot be added in a simple way!

Also it makes no sense to add the ages of 2 brothers, except if asked in a textbook problem!

One litre of sugar when added to one litre of milk does not give 2 litres of sweet milk! This is because some sugar “enters” the spaces between milk. Hence addition can be used only when the Join operation does not “overlap” the collections. This is also a good introduction to set theory (in Middle School) when the Join operation is called Union. AUB is not equal to A + B, except when A & B do not have common elements i.e AпB =0

Unnecessary Use of the Word “more”

Since most teachers are not conscious about the “More Than” metaphor, they tend to use the word “more” unnecessarily in “put together” situations.

Take the following example – “Ram had 3 pencils. His father gave him 2 more pencils”. The problem can be rewritten as “Ram had 3 pencils. His father also gave him 2 pencils”.

Many teachers even teach children that if the word “more” comes in the word problem then it is a hint that addition needs to be performed. This can be very misleading since, as we will see later, even a subtraction problem can have the word “more” in it.

It is best to teach students to understand the “context” of the problem and figure out the operation.