We are interested in understanding how university students learn to use programming as a tool for "authentic" mathematical investigations (i.e., similar to how some mathematicians use programming in their research work). The theoretical perspective of the instrumental approach offers a way of interpreting this learning in terms of…

This paper examines mathematical meaning-making from a phenomenological perspective and considers how a specific dynamic digital tool can prompt students to disclose the relationships between a function and its antiderivatives. Drawing on case study methodology, we focus on a pair of grade 11 students and analyze how the tool's affordances and the…

The initial assumption of this article is that there is an overemphasis on abstraction-from-actions theoretical approaches in research on knowing and learning mathematics. This article uses a critical reflection on research on students' ways of constructing mathematical concepts to distinguish between abstraction-from-actions theoretical…

In this paper we describe learners being asked to generate examples of new mathematical concepts, thus developing and exploring example spaces. First we elaborate the theoretical background for learner generated examples (LGEs) in learning new concepts. The data we then present provides evidence of the possibility of learning new concepts through…

Uses an evolutionary perspective of conceptual change to consider a conception in the domain of linear functions. Summarizes the results of the written assessments and presents an analysis of the discussions for two pairs of students to show that the use of the x-intercept can be framed as a transitional conception. Contains 31 references.…

The author explains what the IOWO is and the reason for the present conference and his part in it. He discusses the observation of learning processes and gives an example of an opportunity he had to observe a learning jump in a small boy. (MN)

The intention of this investigation was to diagnose the retention of some basic skills in some topics in algebra and geometry and to reveal difficult steps in the learning processes in these topics. (MP)

Reports on an intensive study of problem-solving activity of female students at the senior secondary level. Focuses on both the mathematical processing and the underlying cognitive and metacognitive activities that led to that processing. Concludes that all successful groups displayed a high number of key points where metacognitive decisions could…

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…

Describes observations, written samples, and interviews of (n=24) high school teachers learning concepts of group, subgroup, coset, normality, and quotient group in an Abstract Algebra course. General observations are made about the role of errors and misconceptions in light of an action-process-schema framework. (32 references) (MKR)

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)

Used are test and interview data to extract evidence as to what level tenth graders have coordinated the worlds of arithmetic and algebra and can move freely between them. More dissociation is shown than was expected. (Author/MVL)

Divided into two parts, this article analyzes why some pupils feel reserve about instantaneous velocities and instantaneous flows. The second part relates reactions of pupils facing a problem that implicates the instantaneous rate of change. Describes some characteristics of this problem that enables the authors to explain its instructional…

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.…