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# Deductive reasoning impairments in math learning difficulties: Behavioral and neural correlates – REASOMATH

## Deductive reasoning impairments in math learning difficulties

Behavioral and neural correlates

### What is the role of deductive reasoning in math learning?

One of the most remarkable features of the human brain is its ability to reason, that is, to infer new conclusions from known information. Reasoning can be applied to many different types of information. For example, the conclusion Moscow is north of New-York can be inferred from the linear-ordering relations Moscow is north of Paris and Paris is north of New- York. Similarly, the conclusion All humans are animals follows from the set-inclusion statements All humans are mammals and All mammals are animals. These sorts of arguments are often called “deductions” because the conclusion is a logical consequence of the premises and cannot be disputed (i.e., the conclusion is always true if the premises are true). <br />Despite the importance of deductive reasoning for math education, very little attention has been paid to the role of reasoning impairments in math difficulties. Yet, it is necessary to further our understanding of the factors contributing to such difficulties. Indeed, the OECD estimates that about 22.5% of 15-year-old students in France have poor achievements in mathematics, and this has disastrous consequences for both individuals and nations. The sources of math difficulties in the population are likely to be heterogeneous. For example, some math learning difficulties might be due to specific impairments in the acquisition of math concepts and the manipulation of spatial information (with no language deficits), a condition called developmental dyscalculia (DD). Other difficulties might be caused by deficits in the production and reception of language that also impairs some aspects of math learning, such as specific language impairment (SLI).

This project will use behavioral and neuroimaging measures to examine the relationship between (1) math learning difficulties in DD and SLI and (2) impairments in deductive reasoning in 10-year-old children. Specifically, we will test whether DD and SLI are associated with impairments in different forms of deductive reasoning (i.e., linear-ordering versus set-inclusion). We will also evaluate whether measuring the behavioral and neural correlates of deductive reasoning in 10- year-olds with and without math learning difficulties has potential for predicting future improvements in math ability 18 months later. This project will have implications for the diagnosis and remediation of math learning difficulties in children with DD and SLI.

Most studies to date that have examined the factors underlying math achievement in children have focused on basic numerical knowledge. Yet, math skills are clearly not limited to basic numerical knowledge and recent behavioral studies suggest a relationship between math and deductive reasoning skills. The goal of the present study was to determine the neural mediators of this relationship. We asked 24 typically-developping children from 9 to 12 to complete a standardized math achievement test and measured their brain activity while they processed deductive arguments that were embedded in stories. In line with previous behavioral studies, we found a behavioral correlation between reasoning performance and math skills. We further found that activity in the intra-parietal sulcus (IPS) and rostrolateral prefrontal cortex (RLPFC) during deductive reasoning predicts math skill across participants. This relationship, however, appears to be modulated by the type of deductive argument processed (linear-ordering versus set-inclusion). To our knowledge, this study is the first to demonstrate a neural link between deductive reasoning and math achievement.

The project will continue with an examination of the behavioral and neural impairments in deductive reasoning of children with DD and SLI, as well as with a longitudinal assessment. The findings will have implications for advancing our understanding of math disability, which affects about 5% of children worldwide.

Gardes, M.L. & Prado, J. (2016). Entre neurosciences et éducation : les chainons manquants. Cahiers pédagogiques. 527, 35-38.

One of the most remarkable features of the human brain is its ability to reason, that is, to infer new conclusions from known information. Reasoning can be applied to many different types of information. For example, the conclusion Moscow is north of New-York can be inferred from the linear-ordering relations Moscow is north of Paris and Paris is north of New-York. Similarly, the conclusion All humans are animals follows from the set-inclusion statements All humans are mammals and All mammals are animals. These sorts of arguments are often called “deductions” because the conclusion is a logical consequence of the premises and cannot be disputed (i.e., the conclusion is always true if the premises are true). Over the course of Western intellectual history, deductive reasoning has always been considered the most advanced form of human reasoning and a hallmark of mathematical thinking. Educators often emphasize the critical role of deductive reasoning in math education, and many school systems consider deductive reasoning a key competence to be acquired by students. This is because deductions are critical for learning and understanding many fundamental math concepts during childhood, such as quantity, ordinality, measurements, geometry, class inclusion, and logical proof.
Despite the importance of deductive reasoning for math education, very little attention has been paid to the role of reasoning impairments in math difficulties. Yet, it is necessary to further our understanding of the factors contributing to such difficulties. Indeed, the OECD estimates that about 22.5% of 15-year-old students in France have poor achievements in mathematics, and this has disastrous consequences for both individuals and nations. The sources of math difficulties in the population are likely to be heterogeneous. For example, some math learning difficulties might be due to specific impairments in the acquisition of math concepts and the manipulation of spatial information (with no language deficits), a condition called developmental dyscalculia (DD). Other difficulties might be caused by deficits in the production and reception of language that also impairs some aspects of math learning, such as specific language impairment (SLI).
This project will use behavioral and neuroimaging measures to examine the relationship between (1) math learning difficulties in DD and SLI and (2) impairments in deductive reasoning in 10-year-old children. Specifically, we will test whether DD and SLI are associated with impairments in different forms of deductive reasoning (i.e., linear-ordering versus set-inclusion). We will also evaluate whether measuring the behavioral and neural correlates of deductive reasoning in 10-year-olds with and without math learning difficulties has potential for predicting future improvements in math ability 18 months later. This project will have implications for the diagnosis and remediation of math learning difficulties in children with DD and SLI.

## Project coordination

Jérôme Prado (Laboratoire sur le Langage, le Cerveau et la Cognition)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

## Partner

L2C2 Laboratoire sur le Langage, le Cerveau et la Cognition

Help of the ANR 239,720 euros
Beginning and duration of the scientific project: September 2014 - 48 Months