Presents the way in which language issues have become a relevant factor in research that aims to study the socio-cultural aspects of mathematics education in classrooms with a high percentage of immigrant students. Illustrates the fact that, even if the mathematical language can be considered universal, the language of doing mathematics within the…

Discusses the features of East Asian mathematics education and its underlying values in contrast to features and values in the West. Presented in terms of six dichotomies: (1) product versus process; (2) rote learning versus meaningful learning; (3) studying hard versus pleasurable learning; (4) extrinsic versus intrinsic motivations; (5) whole…

Describes, in a case study, the growth in reasoning ability with fractions of one student in a newly developed program of 30 lessons during one whole school year. Indicates that the program and its teaching stimulated the progress of an average performer in mathematics. (Author/MM)

Reports on a case study of one student's pattern of engagement in an 8th grade algebra class. Argues both empirically and theoretically that none of the current theories of engagement and motivation serve to characterize the core of this student's decision about engagement: his affective assessment of mathematics. (Author/MM)

Synthesizes the literature on mathematics learning and provides research-based recommendations, advice, and guidance and develops an elaborated view of mathematical literacy termed 'mathematical proficiency' in the study report. The study demonstrated how research could be synthesized so that evidence from research might be used more productively…

Describes the recent evolution of Portuguese basic education in which the concept of competence and the process of curriculum development became major aspects of an innovative movement at a national level. Describes the context and explores the concept of competence, and presents a formulation for the characteristics of mathematical competence for…

Describes the success, the methods (mental, informal written, standard algorithm) and the strategies of informal written arithmetic to be observed when 300 elementary students worked on six addition and six subtraction problems with three-digit numbers. (Author/MM)

Reports on a study of 10 middle grades teachers' uses of manipulatives for teaching mathematics using interviews and observations to explore how and why the teachers used the manipulatives as they did. Concludes that using manipulatives was little more than a diversion in classrooms where teachers were not able to represent mathematics concepts…

Reports on a study comparing the use of Multi-base arithmetic blocks (MAB) and an alternative, LAB (linear arithmetic blocks) on the basis of epistemic fidelity and accessibility for students. Use of LAB was associated with more active engagement by students and deeper discussion. (Author/MM)

Surveys recent literature on the use and value of the history of geometry in mathematics education. Makes the case that arguments can be divided into conceptual, (multi-) cultural and motivational ones. Details about content and purpose of the literature surveyed are presented in two appendices. (Author/MM)

Discusses the place of infinity in the history and epistemology of mathematics. (Author/MM)

Considers examples of aspects of the infinitely small and large as they unfolded in the history of calculus from the 17th through the 20th centuries. Presents didactic observations at relevant places in the historical account. (Author/MM)

Develops an epistemological and didactic view of the genesis of Cantorian set theory. (Author/MM)

The construction of both natural and formal infinities are products of human thought and may be considered in terms of embodied cognition. Forwards the viewpoint that formal deduction focuses as far as possible on formal logic in preference to perceptual imagery, developing a network of formal properties that do not depend on specific embodiments.…

Considers young peoples' views of infinity prior to instruction in the methods mathematicians use in addressing the subject of infinity. Presents a partially historical account of studies examining young peoples' ideas of infinity. Four sections address potential pitfalls for research in this area and the work of Piaget, issues concerning the…