Presents a presentation of some tasks regarded as typical sources for forming students' intuitions and first understandings about limiting processes of real sequences. Features an analysis of the formal definition of limit via identifying roles for each symbol that occurs to achieve a mental image consonant with the definition. Describes how this…

Demonstrates how research-based knowledge about students' incompatible answers to different representations of the same task could be used in mathematics instruction. Describes the 'It's the Same Task' research-based activity which encourages students to reflect upon their own thinking about infinite quantities and avoid contradictions by using…

Analyses several examples of tacit influences exerted by mental models on the interpretation of various mathematical concepts in the domain of actual infinity. Specifically addresses the unconscious effect of the figural-pictorial models of statements related to the infinite sets of geometrical points related to the concepts of function and…

Makes a concrete proposal for bridging the gap between theory and practice in mathematics education and establishing a systemic relationship between researchers and teachers. Explains the background and implications of this proposal. Discusses four characteristics of the definition of Substantial Learning Environments (SLE). (Author/LM)

Discusses the changed roles of mathematics and novel representations that emerge from the ubiquity of computational models. Considers the implications for learning mathematics. Contends that a central component of knowledge required in modern societies involves the development of a meta-epistemological stance. Maps out implications for the design…

Proposes a developmental model involving four response levels concerning how students arrange pictures to represent data in a pictograph, how they interpret these pictographs, and how they make predictions based on these pictographs. The model is exemplified by responses from three related interview-based studies. Discusses educational…

Examines the mathematical proof schemes of students starting their studies at the University of Cordoba and relates these schemes to the meanings of mathematical proof in different institutional contexts. Concludes that deductive mathematical proof is difficult for these students. Suggests that the different institutional meanings of proof might…

Undergraduates often are aware of and able to apply the facts required to prove a statement but still fail to prove it. By comparing doctoral students and undergraduates constructing proofs in abstract algebra, four types of strategic knowledge are hypothesized. Found that doctoral students had knowledge of how to choose which facts and theorems…

Reports some examples of teaching experiments based on body-related metaphors. Some of them are carried out by means of technological devices. Calls for legitimacy in school mathematics, both for an embodied cognition perspective and a related use of technology. (Author/MM)

Reports on a study on the construction of examples and counter-examples in a college-level calculus course. Verbal and written productions of the students were classified as one of activity, expression, content, and correctness. Finds two types of strategies, global and local. Analysis also distinguishes between "winning" and "losing" strategies.…

Documents, compares, and analyzes the nature of spatial reasoning by practitioners (plumbers) in the workplace and students in the school setting while constructing solids, with given specifications, from plane surfaces. Results confirm the power of activity theory and its methodology in explaining and identifying the structural differences…

Reports on the design and study of a new computerized environment enabling a variety of metacognitive supports in different phases of the problem-solving process and designed to influence students' metacognition during word problem-solving. Results indicate that learning environments that provide metacognitive support during the solution process…

Follows an earlier study of school students' abilities to draw inferences when comparing two data sets presented in graphical form. Results for individual student development add to the credibility of the cross-age observations as well as support the hierarchical framework suggested by the original study. Documents changes in levels of performance…

Serves as an introduction to a set of articles on constructing meanings from data. Takes the viewpoint that internal mental processes, epistemological considerations, and pedagogical contexts are deeply connected, each providing structuring forces upon the others. (MM)

Traces some aspects of the development of stochastics education and research to provide a background for understanding the place of the Psychology of Mathematics Education (PME) Stochastics Group in the research process. (MM)