Why do good maths students still trip over tricky word problems?
Even children who were good at maths made many errors when a word problem said 'less than' but actually required adding, and those with better reading comprehension were less affected.
Source
Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training
Study at a glance
- Design
- Human experiment — 2 x 2 x 2 design: consistency and markedness of the relational term manipulated within subjects; successful vs less successful solvers (median split on a national maths test) between subjects.
- N
- N=80 · 80 Dutch sixth graders from eight schools, split into 39 successful and 41 less successful word problem solvers.
- Population
- Dutch sixth-grade children (mean age about 11.7) taught with Realistic Mathematics Education
- Outcome
- Accuracy on eight two-step compare word problems; correlations with standardised reading comprehension
Structured fields used in claim comparison tables when every cited study has a complete layer.
What they did
Eighty Dutch sixth graders solved eight two-step shopping word problems in which the wording either matched the needed operation (consistent) or pointed the wrong way (inconsistent), and used either 'more than' (unmarked) or the harder 'less than' (marked). Children were split into successful and less successful solvers by their score on a national maths test, and their reading comprehension was measured with a standardised national test.
What they found
Overall, children were less accurate on inconsistent than consistent problems, a medium-to-large consistency effect. Less successful solvers showed this effect for both 'more than' and 'less than' problems, whereas successful solvers showed it only for 'less than' problems, where they had to add despite the wording. Among successful solvers only, better reading comprehension was linked to a smaller consistency effect on these marked problems (r about -0.40); no such link appeared for less successful solvers.
The limits
What it doesn't show
The claim that the curriculum under-teaches reading comprehension is the authors' interpretation, not something the study measured; no classrooms or instruction were observed or compared. Each child solved only two problems per type, the solver groups came from a median split, and reading comprehension was correlated with performance rather than trained, so it cannot be shown to cause better problem solving. The sample was from one country and one curriculum.
Key terms
- Consistency effect
- More errors on word problems where the relational word (e.g. 'more') suggests the wrong operation than on problems where it suggests the right one.
- Lexical markedness
- The idea that one member of an antonym pair, like 'less' in more/less, is harder to process than the other, default member.
- Compare word problem
- A problem describing one quantity in relation to another, such as a price being 3 euro more than at another shop.
- Problem-model strategy
- Building a mental picture of the situation described in the text before deciding which calculations to do, instead of grabbing the numbers and keywords.
- Realistic Mathematics Education
- The Dutch approach to maths teaching that puts word problems and real-life contexts at the centre.
Flashcards
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Quiz yourself
Which problem type caused errors even for successful solvers?
Common questions
What makes an inconsistent problem hard?
The keyword points to the wrong operation, for example 'less than' when you must add, so a child who translates keywords directly gets it wrong.
Does this show reading lessons would improve maths?
It suggests it, but the study only found a correlation; an intervention that trains reading comprehension would be needed to show a causal benefit.
Why only look at reading in successful solvers?
Less successful solvers already fail inconsistent problems because they do not build a mental model, so reading skill can only make a difference once that basic step is in place.
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