There is ample evidence that reasoning about stochastic phenomena is often subject to systematic bias even after instruction. Few studies have examined the detailed learning processes involved in learning probability. This paper examines a case study drawn from a large corpus of data collected as part of a research project that dealt with the…

Our main goal in this study is to exemplify that a meticulous design can lead pre-service teachers to engage in productive unguided peer argumentation. By productivity, we mean here a shift from reasoning based on intuitions to reasoning moved by logical necessity. As a subsidiary goal, we aimed at identifying the kinds of reasoning processes…

We present a view of knowledge construction processes, focusing on partially correct constructs. Motivated by unexpected and seemingly inconsistent quantitative data based on the written reports of students working on an elementary probability task, we analyze in detail the knowledge construction processes of a representative student. We show how…

The transition from arithmetic to algebra in general, and the use of symbolic generalizations in particular, are a major challenge for beginning algebra students. In this article, we describe and analyze students' learning in a "computer intensive environment" designed ad hoc and implemented in two seventh grade classrooms throughout two…

Studies of knowledge constructing often focus on the analysis of a single episode, without considering enough the history of the learners, or the future learners' trajectories with regard to the concepts learned. This paper presents an example of knowledge constructing within the context of peer learning. We show how the design of the task and the…

Describes two activities that led students to contradictions between conjectures and findings. Analyzes the conjectures, working methods, and explanations given by students when faced with the contradictions that arose. (Author/MM)

Attempts to extend the range of application of the emergent perspective to middle and high school classrooms. Identifies some practices rooted in such rich environments from which several sociomathematical norms stemmed. Concludes that sociomathematical norms do not rise from verbal interactions only but also from computer manipulations as…

Investigates processes involved in visual estimation and processes of judgment in visual estimation situations involving proportional reasoning. Exposure to a unit in the Agam project, designed to enhance visual estimation capabilities, resulted in changes in the nine-year-old subjects' strategies, reflecting processes by which children overcome…