Teaching syllogistic reasoning is often perceived as teaching pupils the purely formal rules of deductive inference. According to this common conception, such reasoning is a highly abstract skill, one that is carried out by the processing of syntactically encoded representations of the premises. This paper argues that syllogistic reasoning may,…

The paper focuses on student-teachers' geometric diagrams to mediate the emergence of different proofs for a geometric proposition. For Peirce, a diagram is an icon that explicitly and implicitly represents the deep structural relations among the parts of the object that it stands for. Geometric diagrams can be seen as epistemological tools to…

Introduction: Scientific and technological areas include tuition based on highly visuo-spatial specialization and problem solving. Spatial skills and problem solving are embedded in a curriculum that promotes understanding of Science and technical subjects. These abilities are related to the development of executive functions (EFs). We aim to…

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

Literature on relational reasoning mainly focuses on the performance question. It is typically argued that problem difficulty relies on the number of ''mental models'' compatible with the problem. However, no study has ever investigated the wording of conclusions that participants formulate. In the present work, we analyze the relational terms…

A two-year study randomly assigned children (K-grade 2) with advanced mathematical skills (n=276) to two groups, an intervention group reflecting a constructivist approach or a control. Boys gained more than girls on quantitative and visual-spatial measures in the control, whereas the intervention group made greater gains in quantitative measures…

This study tested the hypothesis that children with weaker speech ability have greater difficulties in perception, powers of reasoning and spatial orientation than children with better speech ability, and assessed the value of Apgar scores as a predictive measure of later linguistic disorders. Subjects were 100 children born in 1970 who attended…

A review of Piaget's theory and research on children's cognitive development is presented, including a discussion of the psychological structures of intelligence, developmental constructivism, and the evolution of knowledge as a subject-object relation. Piaget's assessment techniques are summarized, including moral development, number…