Using the Relational Paradigm: effects on pupils’ reasoning in solving additive word problems

ABSTRACT

Pupils’ difficulties in solving word problems continue to attract attention: while researchers highlight the importance of relational reasoning and modelling, school curricula typically use short word problems to develop pupils’ knowledge of arithmetic operations and calculation strategies. The Relational Paradigm attributes the leading role in mathematics learning to the development of relational thinking. Using this perspective, we implemented a new approach to teaching additive word problem-solving in primary school, encouraging relational thinking and modelling. We compared the overall results of additive word problems solved by Grade 2 elementary pupils in the experimental group (N = 216) and in the control group (N = 196). Our data show: (a) on average, the experimental group performed significantly better in problem-solving than the control group; and (b) in the control group, there was a considerable lack of success in solving problems that require relational thinking—there was no such effect in the experimental group.

KEYWORDS:

• Mathematics teaching and learning
• problem-solving
• reasoning development
• Relational Paradigm

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 For a detailed analysis of problem classification, see Carpenter et al. (1993), Nesher et al. (1982), Riley et al. (1984) and Vergnaud (1982).

2 We tested the performance of these pupils at the end of Grade 1.

3 Traditional teaching refers to the approach promoted by the school board for the last several years.

4 The 13 pupils who experienced the EDA during their first year sat the test at the end of the first year.

5 The student uses the French word “chiffre” instead of “nombre”.

Additional information

Funding

This research was supported by the Quebec Ministry of Education.