Key arithmetic word problems to assess children's understanding

Structured abstract Background Solving arithmetic word problems is an essential mathematical skill that many children find challenging. The difficulty often depends on how well the problem framing aligns with children's prior knowledge, which can either support or hinder its interpretation. The ability to extract meaningful information even from counterintuitive problems indicates a profound understanding and mastery of problem-solving. Aims This study investigated how problem framing influences children's individual performance on arithmetic word problems, aiming to identify tasks most effective for diagnosing students needing additional support. A further aim was to explore how improvements in solving non-intuitive addition problems carry over to later-introduced subtraction problems. Sample The sample consisted of 544 children using an application designed to help first graders solve arithmetic word problems. Methods Latent Profile Analysis was applied to identify distinct response patterns across problems that differed in contextual congruency. Subsequent analyses examined performance on subtraction problems after addition practice. Results The analysis revealed three distinct profiles that varied most significantly for specific problems, for which the framing did not match the solver's intuition, namely problems incongruent with the substitution and scenario analogy. Such problems could thus be used to identify children who have difficulties fully integrating mathematical concepts. Evidence that improvement in performance on non-intuitive addition problems was related to later-introduced subtraction performance was also observed for specific problem types. Conclusion These findings support the SECO model, showing that children's performance depends on how well problems align with different analogies, offering a new way to understand variation of problem difficulties within traditional problem frameworks. Counterintuitive problems are good candidates to efficiently identify children who have difficulty fully integrating mathematical concepts.