How Wording and Context Can Transform Problem Solving
education exchange
Have you ever had a pupil tell you that they need "3.2 buses" to transport a class? This common issue, often called "mindless calculation", happens when pupils ignore real-world logic in favour of purely mathematical operations. A recent study involving 127 Year 7 pupils1 has revealed that simple changes to how we frame and word our problems can significantly increase the number of "realistic" solutions pupils provide.
The Research: What Was Tested?
The study looked at two specific factors to see if they would encourage pupils to use their common sense:
The Scenario: Whether the problem was presented as part of a Maths Test or a School Trip.
- The "Maths Test" Scenario: pupils in this group were told they were solving problems as part of a school mathematics test.
- The "School Trip" Scenario: pupils in this group were given the exact same mathematical problems, but the work was framed as "planning a summer sports week".
- The Question Wording: Whether the question used standard wording (e.g., "How many buses are needed?") or emphasized an Imminent Action (e.g., "How many buses do the teachers need to order from the bus company?").
Key Findings: Why Context Matters
The researchers found that pupils often provide unrealistic answers because they believe the "rules" of the maths classroom demand a single, precise number above all else. However, the data showed that:
- Context doubles the odds: pupils in the school trip scenario had 2.38 times higher odds of providing a realistic solution than those in the maths test group.
- Wording is a powerful lever: Simply changing the question to imply a real-world action (like ordering the buses) led to 2.80 times higher odds of pupils giving a sensible, realistic answer.
- Expectations shift with the setting: In the school trip scenario, pupils were 9.01 times more likely to expect that a realistic solution was what was actually wanted.
Quick Wins for the Classroom
The study suggests that pupils do not necessarily lack the ability to think realistically; rather, they are often just trying to follow what they perceive to be the "socio-mathematical norms" of your classroom. You can help them bridge this gap with these easy-to-implement strategies:
- Rephrase for Action: Instead of asking "How many...?", try asking "How many should be ordered?" or "What should the manager decide?" This signals that the answer has a practical consequence.
- Change the Frame: Occasionally move maths problems out of the "test" format. Framing a set of problems as "Planning our next excursion" can prompt pupils to engage their real-world knowledge more naturally.
- Explicitly Discuss Validation: Encourage pupils to add a final step to their working where they ask, "Does this answer make sense if I were actually there?".
- Reward "Realistic" Thinking: Make it clear that in certain problems, a rounded or estimated answer that accounts for real-world constraints is worth more than a mathematically "exact" but impossible one.
The 127 seventh-grade pupils who participated in this study came from two different schools and seven different classes. While the report does not name the specific institutions, the data collection was approved by the Directorate of Education for Lower Austria. The participants were approximately 12.6 years old on average, and the group consisted of 70 girls, 50 boys, and 7 students who either identified as "other" or did not specify their gender.
References
- Wisenöcker, A.S. and Große, C.S. (2026) ‘It matters how you ask: how scenario and question wording influence problematic word problem solving’, Contemporary Educational Psychology, 84, p. 102443. Available at: https://doi.org/10.1016/j.cedpsych.2026.102443.
