Different types of hierarchies in the learning of mathematics and criteria by which they might be judged are examined. Current works on mathematical learning hierarchies are illustrated and in particular the work of the mathematics team of the research project "Concepts in Secondary School Mathematics and Science" is examined. (MP)

Task performance experiments concerning properties of mathematical groups with 10 and 11 year-old children are discussed including transfer effects, effects of structural relations, individual differences, and memory (both short and long term). (JG)

In everyday teaching, the mathematical meaning of new knowledge is frequently devalued during ritualized formats of communication and replaced by social conventions. Specific aspects of the problem of meaning development were investigated in two second-grade teaching cases. These were used to develop decisive requirements for maintenance of an…

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…

Based on the premise that body experiences interfere inconveniently with scientific ideas in mechanics instruction. Suggests that learning processes start with body experiences and, with guidance, transform them into something scientific. Discusses this process for the static and kinetic aspects of force and for measurement. (MDH)

Sketches a theory for designing teaching based on mathematical activity, situations, tasks, and interventions, exposing and resolving cognitive conflicts, changes of structure and context, feedback, reflection and review. Reviews the main psychological principles underlying this theory, then considers some examples of teaching designs in light of…

An analysis of a 10-minute episode in which 7-year-old students (n=3) engage in collaborative small group activity is presented to explore the relationship between individual learning and group development. Students learned as they interactively constituted situations for justification or validation, yielding an institutionalized solution method.…