Teaching Operation Metaphors 2

Countable & Measurable Quantities

Further, in Primary School, normally teachers restrict themselves to problems dealing only with discrete things like pencils, chocolates, tokens etc. But right from Class 1, examples using various units of measurement with which children are familiar with, can also be used. These are weights, volumes, areas, lengths, time, age, money etc.

Children are familiar with life experiences of rice being 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 like this one. “I went to a shop with an empty bag. First I purchased 2 kgs of rice and then 1 kg of sugar. What will be the weight of the bag?”. Such examples will strengthen their belief in the relevance of Math to their daily life.

Teachers possibly think that when they introduce units of measurement, they should also teach all the different units and conversions between them and that children are not yet ready. But these basic units can be used without going into conversions. If they are familiar with the use of these units, they may find unit conversions easy to learn in higher classes.

Confusions Caused by Terminology

Some of the metaphors carry the same name as a particular procedure used in certain operations. This often causes confusion between metaphors & procedures.

For example, any addition can be carried out by “putting together” procedure. Any subtraction can be carried out by “taking away” procedure. Any multiplication (with whole numbers) can be carried out by “repeated addition”. Any division can be carried out by “repeated subtraction”. They indicate a procedure by which a particular operation can be done.

While looking at operation metaphors, the terms used above are found to be one of the several metaphors. But they have been so thoroughly identified with the operations themselves that the existence of other metaphors has been disappeared from our conscience.

Operational terms like ”repeated addition” & “repeated subtraction” are wrongly termed as concepts. They are just procedures. Such issues have obscured the real concepts behind the multiplication & division processes.

A Caveat

We would like to clarify here that the above “operational metaphors” are meant mainly for introducing techniques of problem-solving primary school (K-5) students. Problems in 6thgrade upwards would involve scenarios related to banking, commerce, work, speed, time etc and may involve a multiplicity of metaphors. These would require more practice in problem solving per se.