The Cognitive Acceleration (or Let's Think) approach to mathematics teaching is a Piagetian programme drawing on Vygotsky's research, developed at King's College London over 30 years ago, along with its associated professional development (PD) programme. This project sought to replicate the original studies conducted 10-15 years earlier and before…

With the development of personalized learning in technological platforms, more data and information are given to instructors on what contents are appropriate for a learner's next step, with an aim of helping them support their students in navigating an optimized learning path that can promote an enhanced learning outcome. In this study, we…

Though the No Child Left Behind Act of 2001 requires secondary students with Asperger's syndrome (AS) to take high-stakes mathematical tests, many students with AS exhibit weaknesses in mathematical and executive functioning skills. The purpose of this mixed-methods case study was to explore the use of differentiated mathematical strategies with…

The theory of conceptual fields is a developmental theory. It has two aims: (1) to describe and analyse the progressive complexity, on a long- and medium-term basis, of the mathematical competences that students develop inside and outside school, and (2) to establish better connections between the operational form of knowledge, which consists in…

This paper describes application of innovative practice and procedures in relationship to recognized principles and theory of adult education used in college math instruction. Adult learning principles provide the theoretical constructs and foundation of the practice supporting a learner-centered approach to learning. The purpose was to explore…

The developmental psychology of mathematical thinking and the clinical interview method can make major contributions to education by transforming the process of formative assessment--the attempt to use information concerning student performance, knowledge, learning potential, and motivation to inform instruction. The clinical interview is a…

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

Mathematics education is viewed as a process imbedded in social interaction. Alternatives to seven widely recognized modeling perspectives that provide conceptual foundations for mathematics learning are discussed. (MP)

A case for theoretical development of advance organizers that aid in the learning and transmission of knowledge is presented. (MP)

The texts gathered in this document come from work done in the framework of two postgraduate courses at the Faculte des Sciences de l'Education, Geneva: (1) "Learning: Meta-cognitive et socio-cognitive dimensions" course; and (2) "Didactical analysis of the interactions in class: Case study of mathematics at school" course. The problematics dealt…

This paper describes the application of theories underlying research-in-progress intended to enhance substantially the cognitive development of children in the first two years of Primary school. The intervention is delivered partly in the context of mathematics, and partly through an existing Y1 intervention focused on Piaget's concrete…

The concept of equivalence is shown to be an elusive one that provides difficulty for preschoolers through college students. The idea persists that the equal sign is a "do something," or operator symbol, rather than a symbol for an equivalence relation. (MP)

Demonstrates that Vygotskian theory can support two opposing interpretations: supporting reform and undermining reform. Discussion is organized by: sociocultural perspectives, Marxist influences on historical analysis and the role of labor, semiotics and psychological tools, dialectic of thought and language, conceptual development, and learning…

Discusses why improvements in teaching mathematics are needed, including discussion of students, human development, knowledge and learning, structure of schools and instructional programs, and mathematics. Also discusses a need for two theories: (1) how young people form self-concepts and (2) classification of approaches to curricula and…

The article describes creative ways to interest children in mathematics. (CD)