The link between deductive reasoning and mathematics

Morsanyi, Kinga; McCormack, Teresa; O'Mahony, Eileen

doi:10.1080/13546783.2017.1384760

Cited by 43 publications

(40 citation statements)

References 60 publications

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“…In the field of mathematics education, the study of deductive reasoning has been mainly associated with mathematical proof, leaving the understanding of deductive reasoning, per se, in the background [20,21]. This may have to do with the diverse ways of conceiving deductive thinking by the protagonists involved in mathematics education.…”

Section: Logical Reasoning and Mathematics Learningmentioning

confidence: 99%

Venues for Analytical Reasoning Problems: How Children Produce Deductive Reasoning

2020

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The research on deductive reasoning in mathematics education has been predominantly associated with the study of proof; consequently, there is a lack of studies on logical reasoning per se, especially with young children. Analytical reasoning problems are adequate tasks to engage the solver in deductive reasoning, as they require rule checking and option elimination, for which chains of inferences based on premises and rules are accomplished. Focusing on the solutions of children aged 10–12 to an analytical reasoning problem proposed in two separate settings—a web-based problem-solving competition and mathematics classes—this study aims to find out what forms of deductive reasoning they undertake and how they express that reasoning. This was done through a qualitative content analysis encompassing 384 solutions by children participating in a beyond-school competition and 102 solutions given by students in their mathematics classes. The results showed that four different types of deductive reasoning models were produced in the two venues. Moreover, several representational resources were found in the children’s solutions. Overall, it may be concluded that moderately complex analytical reasoning tasks can be taken into regular mathematics classes to support and nurture young children’s diverse deductive reasoning models.

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Section: Logical Reasoning and Mathematics Learningmentioning

confidence: 99%

Venues for Analytical Reasoning Problems: How Children Produce Deductive Reasoning

2020

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“…Yet, acquiring math skills also involves understanding relations between quantities and drawing inferences based on these relations (Singley and Bunge 2014). In keeping with this idea, recent behavioral studies suggest that understanding relations of transitivity may significantly contribute to math learning in children (Handley, Capon et al 2004, Morsanyi, Devine et al 2013, Morsanyi, Kahl et al 2017, Morsanyi, McCormack et al 2017). Here we tested whether the brain representations of transitive relations may predict current and future math skills in children.…”

Section: Discussionmentioning

confidence: 94%

Neural representations of transitive relations predict current and future math calculation skills in children

et al. 2020

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A large body of evidence suggests that math learning in children is built upon innate mechanisms for representing numerical quantities in the intraparietal sulcus (IPS). Learning math, however, is about more than processing quantitative information. It is also about understanding relations between quantities and making inferences based on these relations. Consistent with this idea, recent behavioral studies suggest that the ability to process transitive relations (A > B, B > C, therefore A > C) may contribute to math skills in children. Here we used fMRI coupled with a longitudinal design to determine whether the neural processing of transitive relations in children could predict their current and future math skills. At baseline (T1), children (n=31) processed transitive relations in an MRI scanner. Math skills were measured at T1 and again 1.5 years later (T2). Using a machine learning approach with cross-validation, we found that activity associated with the representation of transitive relations in the IPS predicted math calculation skills at both T1 and T2. Our study highlights the potential of neurobiological measures of transitive reasoning for forecasting math skills in children, providing additional evidence for a link between this type of reasoning and math learning.

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“…For example, Handley et al (2004) showed that numeracy and arithmetic skills are positively correlated with logical (including transitive) reasoning performance in 10-year-olds. Morsanyi and colleagues further found a specific relationship between transitive reasoning performance and mathematical abilities in adolescents and adults (Morsanyi et al, 2017; Morsanyi et al, 2018). Therefore, the literature suggests that inter-individual differences in math skills may relate to inter-individual differences in transitive reasoning skills.…”

Section: Discussionmentioning

confidence: 99%

Impaired neural processing of transitive relations in children with math learning difficulty

Schwartz

Epinat-Duclos

Léone

et al. 2018

NeuroImage: Clinical

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Math learning difficulty (i.e., MLD) is common in children and can have far-reaching consequences in personal and professional life. Converging evidence suggests that MLD is associated with impairments in the intraparietal sulcus (IPS). However, the role that these impairments play in MLD remains unclear. Although it is often assumed that IPS deficits affect core numerical abilities, the IPS is also involved in several non-numerical processes that may contribute to math skills. For instance, the IPS supports transitive reasoning (i.e., the ability to integrate relations such as A > B and B > C to infer that A > C), a skill that is central to many aspects of math learning in children. Here we measured fMRI activity of 8- to 12-year-olds with MLD and typically developing (TD) peers while they listened to stories that included transitive relations. Children also answered questions evaluating whether transitive inferences were made during story comprehension. Compared to non-transitive relations (e.g., A > B and C > D), listening to transitive relations (e.g., A > B and B > C) was associated with enhanced activity in the IPS in TD children. In children with MLD, the difference in activity between transitive and non-transitive relations in the IPS was (i) non-reliable and (ii) smaller than in TD children. Finally, children with MLD were less accurate than TD peers when making transitive inferences based on transitive relations. Thus, a deficit in the online processing of transitive relations in the IPS might contribute to math difficulties in children with MLD.

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The link between deductive reasoning and mathematics

Cited by 43 publications

References 60 publications

Venues for Analytical Reasoning Problems: How Children Produce Deductive Reasoning

Venues for Analytical Reasoning Problems: How Children Produce Deductive Reasoning

Neural representations of transitive relations predict current and future math calculation skills in children

Impaired neural processing of transitive relations in children with math learning difficulty

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