## Abstract

Informal strategies reflecting the representation of a situation described in an arithmetic word problem mediate students’ solving processes. When the informal strategies are inefficient, teaching students to make way for more efficient ways to find the solution is an important educational issue in mathematics. The current paper presents a pedagogical design for arithmetic word problem solving, which is part of a first-grade arithmetic intervention (ACE). The curriculum was designed to promote adaptive expertise among students through semantic analysis and recoding, which would lead students to favor the more adequate solving strategy when several options are available. We describe the ways in which students were taught to engage in a semantic analysis of the problem, and the representational tools used to favor this conceptual change. Within the word problem solving curriculum, informal and formal solving strategies corresponding to the different formats of the same arithmetic operation, were comparatively studied. The performance and strategies used by students were assessed, revealing a greater use of formal arithmetic strategies among ACE classes. Our findings illustrate a promising path for going past informal strategies on arithmetic word problem solving.

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## Notes

- 1.
Inversion is also a term used to describe the subtraction as addition relation (e.g., 7 − 3 = ? can be solved by considering 3 + ? = 7).

- 2.
In order to display the distribution of the strategies among the correct answers in Fig. 2, we counted the number of occurrences of informal strategies and the number of occurrences where no strategy was written down.

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## Funding

Funding was provided by Fonds d’expérimentation pour la jeunesse (Grant no. ACE_HAP_10).

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Gvozdic, K., Sander, E. Learning to be an opportunistic word problem solver: going beyond informal solving strategies.
*ZDM Mathematics Education* **52, **111–123 (2020). https://doi.org/10.1007/s11858-019-01114-z

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### Keywords

- Arithmetic word problem solving
- Informal strategies
- Arithmetic knowledge
- Mathematics education
- Adaptive expertise
- Semantic recoding