# When masters of abstraction run into a concrete wall: Experts failing arithmetic word problems

## Abstract

Can our knowledge about apples, cars, or smurfs hinder our ability to solve mathematical problems involving these entities? We argue that such daily-life knowledge interferes with arithmetic word problem solving, to the extent that experts can be led to failure in problems involving trivial mathematical notions. We created problems evoking different aspects of our non-mathematical, general knowledge. They were solvable by one single subtraction involving small quantities, such as 14 – 2 = 12. A first experiment studied how university-educated adults dealt with seemingly simple arithmetic problems evoking knowledge that was either congruent or incongruent with the problems’ solving procedure. Results showed that in the latter case, the proportion of participants incorrectly deeming the problems “unsolvable” increased significantly, as did response times for correct answers. A second experiment showed that expert mathematicians were also subject to this bias. These results demonstrate that irrelevant non-mathematical knowledge interferes with the identification of basic, single-step solutions to arithmetic word problems, even among experts who have supposedly mastered abstract, context-independent reasoning.

## Keywords

Encoding effects Mathematical cognition Mental models Semantics## Notes

### Acknowledgments

We sincerely thank Pernille Hemmer and two anonymous reviewers whose insightful feedback helped improve and clarify this manuscript. We also acknowledge gratefully Pierre Barrouillet, Katarina Gvozdic, and Maxime Maheu for helpful comments on previous versions of this work.

This research was supported by grants from the Regional Council of Burgundy, Pari Feder Grants (20159201AAO050S02982 & 20169201AAO050S01845, JPT), from the Experimental Fund for the Youth and French Ministry of Education (HAP10-CRE-EXPE-S1, ES), and from the French Ministry of Education and Future Investment Plan (CS-032-15-836-ARITHM-0, ES). HG was further supported by a doctoral fellowship from the Paris Descartes University.

### Open practices statement

The data and materials for all experiments are available at (https://osf.io/fxgqh/?view_only=ed1374ef4d204c90a0cb03a30cb0a099).

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