144 research outputs found

    M 133.02: Geometry and Measurement for Elementary School Teachers

    Get PDF

    M 326.01: Number Theory

    Get PDF

    Editorial: The Planet’s Pandemic Pandemonium

    Get PDF

    Historiography of Mathematics from the Mathematician’s Point of View

    No full text
    Mathematicians used to be highly invested in the study of the history of their own field, but their voice in historiographical discussions has diminished in influence in the past century. One prominent narrative paints this as a justified fall from grace: mathematicians wedded to present mathematical values looked at the past with prejudiced eyes, whereas a new generation of historians were better able to appreciate the past proper, in its own terms. But the best internalist mathematical historiography of old needed no such external corrective. It was already committed to avoiding presentism and anachronism, for reasons that were not in opposition to mathematical values but rather derived directly from a positive vision of the role that history could play in the mathematical community. In this vision, a historical understanding of how a field developed is a proxy for first-hand research experience in that field. It follows that it is essential for historical accounts to thoroughly convey the scope and limitations of alternative conceptions and approaches, including dead-end developments, since this is precisely what sets the critical knowledge gained by first-hand research experience apart from the doctrinal knowledge gained merely from a textbook. Hence, from this point of view, presentist historiography is not the natural outlook of the mathematician, but rather a direct antithesis of the mathematician’s most fundamental reason for studying history. To study past mathematics precisely as it appeared to active researchers at the time is not foreign to the mathematician, but a direct corollary of the mathematician’s core conviction that only those with first-hand research experience in a field of mathematics truly understand it. A sophisticated internalist historiography derived from these ideals was articulated to a greater extent in the past than is commonly recognized today. By going back to its roots, the mathematician’s historiography could revive some of the virtues that have been neglected in recent years

    Prospective teachers constructing dynamic geometry activities for gifted pupils : Connections between the frameworks of Krutetskii and van Hiele

    No full text
    The Swedish educational system has, so far, accorded little attention to the developmentof gifted pupils. Moreover, up to date, no Swedish studies have investigated teachereducation from the perspective of mathematically gifted pupils. Our study is based on aninstructional intervention, aimed to introduce the notion of giftedness in mathematics andto prepare prospective teachers (PTs) for the needs of the gifted. The data consists of 10dynamic geometry software activities, constructed by 24 PTs. We investigated theconstructed activities for their qualitative aspects, according to two frameworks: Krutetskii’s framework for mathematical giftedness and van Hiele’s model of geometricalthinking. The results indicate that nine of the 10 activities have the potential to addresspivotal abilities of mathematically gifted pupils. In another aspect, the analysis suggests thatKrutetskii’s holistic description of mathematical giftedness does not strictly correspondwith the discrete levels of geometrical thinking proposed by van Hiele

    M 439.01: Euclidean and Non-Euclidean Geometry

    Get PDF

    M 609.50: Research Methods in Mathematics Education

    Get PDF

    Creativity in problem solving: Integrating two different views of insight

    Get PDF
    Even after many decades of productive research, problem solving instruction is still considered inefective. In this study we address some limitations of extant problem solving models related to the phenomenon of insight during problem solving. Currently, there are two main views on the source of insight during problem solving. Proponents of the frst view argue that insight is the consequence of analytic thinking and a sequence of conscious and stepwise steps. The second view suggests that insight is the result of unconscious processes that come about only after an impasse has occurred. Extant models of problem solving within mathematics education tend to highlight the frst view of insight, while Gestalt inspired creativity research tends to emphasize the second view of insight. In this study, we explore how the two views of insight—and the corresponding set of models—can describe and explain diferent aspects of the problem solving process. Our aim is to integrate the two different views on insight, and demonstrate how they complement each other, each highlighting diferent, but important, aspects of the problem solving process. We pursue this aim by studying how expert and novice mathematics students worked on two ill-defned mathematical problems. We apply both a problem solving model and a creativity model in analyzing students’ work on the two problems, in order to compare and contrast aspects of insight during the students’ work. The results of this study indicate that sudden and unconscious insight seems to be crucial to the problem solving process, and the occurrence of such insight cannot be fully explained by problem solving models and analytic views of insight. We therefore propose that extant problem solving models should adopt aspects of the Gestalt inspired views of insight
    • …
    corecore