The link between deductive reasoning and mathematics

ABSTRACT

Recent studies have shown that deductive reasoning skills (including transitive and conditional inferences) are related to mathematical abilities. Nevertheless, so far the links between mathematical abilities and these two forms of deductive inference have not been investigated in a single study. It is also unclear whether these inference forms are related to both basic maths skills and mathematical reasoning, and whether these relationships still hold if the effects of fluid intelligence are controlled. We conducted a study with 87 adult participants. The results showed that transitive reasoning skills were related to performance on a number line task, and conditional inferences were related to arithmetic skills. Additionally, both types of deductive inference were related to mathematical reasoning skills, although transitive and conditional reasoning ability were unrelated. Our results also highlighted the important role that ordering abilities play in mathematical reasoning, extending findings regarding the role of ordering abilities in basic maths skills. These results have implications for the theories of mathematical and deductive reasoning, and they could inspire the development of novel educational interventions.

KEYWORDS:

• Arithmetic skills
• conditional reasoning
• number line task
• order processing
• transitive inference

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Although Handley et al. (2004) did this, they combined the scores of the two types of reasoning task, and did not report the individual results.

² The results regarding the links between ordering abilities and basic mathematics skills were already reported in Morsanyi, O'Mahony, and McCormack (2017). However, the main focus of that paper was on a detailed analysis of number and month ordering performance and the domain-specificity of the link between ordering abilities and mathematics skills.

³ The availability of counterexamples was established on the basis of the findings of McKenzie, Evans, and Handley (2010).

⁴ See the Results section for analyses regarding reliability.

⁵ We have considered the possibility of analysing the results separately for different types of problems. However, when we computed the reliability of the task, we found that reliability was the highest when all problems were included together.

⁶ On a theoretical basis, combining the scores from the MP, AC and DA inferences would seem appropriate. Nevertheless, we decided against this on the basis of our empirical findings, which showed that performance on the MP problems was at ceiling, and that including these scores would have somewhat reduced the reliability of our conditional reasoning measure.

⁷ Given the large number of variables, we have checked the robustness of these correlational patterns using a bootstrapping procedure with 10,000 bootstrap samples. All significant correlations remained significant when a bootstrapping procedure was used, with the exception of the relationship between the CRT-long and fluid intelligence, and mathematical reasoning and performance on the number line task.

⁸ We have also tested the robustness of the regression results by using a bootstrapping procedure with 10,000 samples. The same results were obtained as with the traditional analyses (i.e., transitive and conditional inferences, as well as ordering ability were significant predictors of cognitive reflection, but fluid intelligence was not).

⁹ The correlation coefficients for DA and AC inferences with a high availability of counterexamples were relatively low (0.18 for both DA and AC), and non-significant. The correlation coefficients for DA and AC inferences with a low availability of counterexamples were stronger (0.30 for DA and 0.29 for AC), and significant at the p < 0.01 level. This seems to suggest that the relationship with maths was stronger in the case of conditionals where the retrieval of counterexamples required more effort. Nevertheless, when we obtained confidence intervals for these correlations using a bootstrapping procedure with 10,000 samples, we found that these correlation coefficients were not significantly different.