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Problem-Solving Before Instruction (PS-I): A Protocol for Assessment and Intervention in Students with Different Abilities

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Arithmetic problems at school: when there is an apparent contradiction between the situation model and the problem

Danièle Coquin-Viennot¹, Stéphanie Moreau

¹Laboratoire Langage, Mémoire, et Développement Cognitif (LMDC), University of Poitiers, France. daniele.coquin@mshs.univ-poitiers.fr

The British Journal of Educational Psychology

|April 7, 2007

Summary

Contradictions between qualitative situation models (QSMs) and problem models (PMs) hinder problem-solving, particularly when formal representations aren't automatic. This impacts younger students and specific problem types, showing QSMs can impede performance if inconsistent with PMs.

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Area of Science:

Cognitive psychology
Educational psychology
Problem-solving research

Background:

Problem-solving involves both logico-mathematical (problem models/PMs) and qualitative (qualitative situation models/QSMs) representations.
PMs contain numerical data, while QSMs use everyday language to describe situations.

Purpose of the Study:

To investigate if contradictions between PMs and QSMs negatively affect problem-solving performance.
To examine the role of automatic activation of formal representations in this effect.

Main Methods:

Third and fourth-year primary school students (ages 8-9) in France participated.
Participants solved change and compare problems presented in consistent and inconsistent QSM-PM versions.

Main Results:

Inconsistent versions led to more errors, especially for younger students on change problems.
Inconsistent versions increased errors for all students on compare problems.

Conclusions:

Qualitative situation models (QSMs) act as intermediate representations, particularly when problem schemas are not automatically activated.
Performance deteriorates when QSMs contradict problem models (PMs), highlighting the importance of representational consistency in learning.