Avoid teaching strategies that link key words to specific operations.
Consider the use of the word ‘more’ in the following word problems:
- Michelle had 4 pencils and was given 3 more. How many does she have now?
- Michelle has 8 pencils and I have 5 pencils. How many more pencils does Michelle have?
In the first example the implication is to add. Many students reading the word ‘more’ in the second example will automatically add the 8 and 5 to obtain an answer of 13. However, subtracting 5 from 8 will provide the correct answer of 3.
The assumption being made is that students actually read the question in full and understand the situation. Swan, no relation, (1990) noted that most word problems might be solved by cues, which he listed as:
- If there are more than two numbers, add them;
- If the two numbers are of similar magnitude, subtract the smaller from the larger;
- If one number is relatively large compared to a second number, divide; and
- If the answer has a remainder, cross out your work and multiply. (p. 60)
While these were written somewhat ‘tongue in cheek’ a review of many primary textbooks and worksheets indicates that in many cases these cues hold true. Swan concludes with a piece of advice:
“We now have considerable research evidence to suggest that to understand a mathematical concept it is better to work through a few well-chosen problems, than to work through lists of exercises. These problems must embody key concepts and be discussed and tackled in depth …” (p, 60).
Polya said something similar in his book, “How to Solve it”.
“It is better to solve one problem five ways than five problems one way.”
A single NAPLAN Style word question may be discussed as part of a warm up.
The good news is that there is a better approach to teaching students how to solve NAPLAN-style word problems. We have made a professional learning course that further delves into this.
Reference:
Swan, M. (1990). Becoming numerate: developing conceptual structures. In S. Willis (Ed). Being numerate: what counts? Victoria: ACER.
