Understanding Word Problems 1

Understanding word problems presents several difficulties to students. Most teachers think that the difficulty is mostly with the language in which the problem is written. Another aspect which is not even recognised by teachers is related to the issue of "operation metaphors."

We present some of the difficulties below. An understanding of the difficulties may also reveal several solutions to the issue.

Call Them Math Stories

It is better to call math word problems as “math stories”. Calling them as problems psychologically may reinforce the idea that they are "problems". Let students see them as stories related to life situations which use numbers and other math ideas to improve precision. Instead of saying that Ram is taller than Ramesh, numbers & measurements help us to tell that Ram is 25 cms taller than Ramesh!

Math & Language

Teaching of languages, especially English, is also very weak in Indian schools. Instead of focusing on the skills; listening, speaking, vocabulary, reading and writing, too much emphasis is laid of grammar and memorization of answers to questions. Hence most students cannot really "read and understand" the math word problem and relate it to a life situation.

In addition, there are a lot of words used in daily interactions and math classes with different meanings. For a student who is not very proficient in English, this can present serious problems in understanding a word problem.

Simplify the language

One solution to this problem is to simplify the language used in a word problems. Some options are -

1. Use direct speech instead of indirect speech

2. Shorter sentences.

3. Use "personal names" instead of common nouns & pronouns

4. Provide the actual meaning of the math vocabulary in case there are multiple interpretations.

Math Language

Math itself has a technical vocabulary with precise meanings. Math language also has to be learnt & used correctly.

We have seen the issues of both "math language" and "language & math" in detail Section 14.

Operation Metaphors

A more serious problem, which teachers are not even aware of is the role of "operation metaphors" which we have already covered in detail.

The 4 basic arithmetic operations arise out of a large variety of life situations. But most teachers emphasize only the following "concepts" so much that students find it difficult to think of other situations.

1. Addition as "Put Together"

2. Subtraction as "Take Away"

3. Multiplicati" as "Repeated Subtraction"

Pictorial Representations

Representing a problem pictorially or as a rough sketch is a powerful way to understand a problem. Students should be trained in this skill.