“Whiteboxing” the Content of a Formal Mathematical Text in a Dynamic Geometry Environment

In this article, we provide an empirical example of how digital technology; in this case, GeoGebra may assist students in uncovering—or whiteboxing—the content of a mathematical proof, in this case that of Proposition 41 from Euclid’s Elements. In the discussion of the example, we look into the impact of GeoGebra’s “dragging” functionality on students’ interactions and the possession and development of students’ proof schemes. The study and accompanying analysis illustrate that, despite the positive whiteboxing effects in relation to the mathematical content of the proposition, whiteboxing through dragging calls for caution in relation to students’ work with proof and proving—in particular, in relation to students seeing the necessity for formal proof. Moreover, caution must be paid, e.g., by teachers, so that students do not jump to conclusions and in the process develop inexpedient mathematical proof schemes upon which they may stumble in their future mathematical work

Towards a definition of "mathematical digital competency"

Due to the embeddedness of digital technologies in mathematics education of today, we often see examples of students simultaneously using their mathematical competencies and digital competencies. In relevant literature, however, these are not seen as a connected whole. Based on reviewing existing competency frameworks, both mathematical and digital, and by exploring an empirical example, this article addresses the question of how to think about and understand a combined Bmathematical digital competency^ (MDC). In doing so, the article relies on the two theoretical frameworks of the instrumental approach and conceptual fields to Bbridge^ the mathematical and digital competency descriptions

On the relations between historical epistemology and students’ conceptual developments in mathematics

There is an ongoing discussion within the research field of mathematics education regarding the utilization of the history of mathematics within mathematics education. In this paper we consider problems that may emerge when the historical epistemology of mathematics is paralleled to students’ conceptual developments in mathematics. We problematize this attempt to link the two fields on the basis of Grattan-Guinness’ distinction between “history” and “heritage”. We argue that when parallelism claims are made, history and heritage are often mixed up, which is problematic since historical mathematical definitions must be interpreted in its proper historical context and conceptual framework. Furthermore, we argue that cultural and local ideas vary at different time periods, influencing conceptual developments in different directions regardless of whether historical or individual developments are considered, and thus it may be problematic to uncritically assume a platonic perspective. Also, we have to take into consideration that an average student of today and great mathematicians of the past are at different cognitive levels

Survey team on : conceptualisations of the role of competencies, knowing and knowledge in mathematics education research

This paper presents the outcomes of the work of the ICME 13 Survey Team on 'Conceptualisation and the role of competencies, knowing and knowledge in mathematics education research'. It surveys a variety of historical and contemporary views and conceptualisations of what it means to master mathematics, focusing on notions such as mathematical competence and competencies, mathematical proficiency, and mathematical practices, amongst others. The paper provides theoretical analyses of these notions-under the generic heading of mathematical competencies-and gives an overview of selected research on and by means of them. Furthermore, an account of the introduction and implementation of competency notions in the curricula in various countries and regions is given, and pertinent issues are reviewed. The paper is concluded with a set of reflections on current trends and challenges concerning mathematical competencie