Den matematikhistoriske dimension i undervisning – generelt set

Denne artikel tilbyder en strukturel ramme for diskussionen af hvorfor og hvordan matematikhistorieskal eller bør inddrages i undervisningen, samt hvorledes en sådan undervisning kan organiseres ogstruktureres. Artiklen foreslår to sæt af kategorier i hvilke henholdsvis argumenterne for at inddragehistorie og tilgangene til inddragelsen kan kategoriseres. Argumenterne inddeles i to kategorier afformål som en inddragelse af historie kan tjene: matematikhistorie som værktøj og matematikhistoriesom mål. Tilgangene inddeles i tre kategorier: illustrationstilgange, modultilgange og historie-baseredetilgange. Hertil kommer en diskussion af hvorvidt inddragelsen af historie i matematikundervisningener motiveret af at ville bringe enten de i-matematiske, de om-matematiske eller eventuelt de medmatematiske aspekter af faget matematik frem i lyset

Den matematikhistoriske dimension i undervisning – gymnasialt set

Nærværende artikel omhandler inddragelsen af matematikhistorie i gymnasiet (stx) medudgangspunkt i bekendtgørelsen af 2007. Det diskuteres (1) hvad formålet i bekendtgørelsen er med atinvolvere matematikhistorie, (2) hvilke tilgange der er til involvering af matematikhistorie i gymnasiet,samt (3) hvad underviserens rolle er i forhold til bekendtgørelsens krav om involvering af matematikhistorie. Første spørgsmål besvares gennem en analyse af den nye bekendtgørelse for matematik i gymnasiet samt en relatering af denne til KOM-rapporten. Andet spørgsmål omhandlende tilgangene belyses gennem en analyse af behandlingen af matematikhistorie i tre af de nye lærebogssystemer til gymnasiet. I besvarelsen af tredje spørgsmål diskuteres i forhold til den danske situation de i nogen grad lignende situationer i så forskellige lande som Norge og Hong Kong. Det konkluderes at bekendtgørelsens formål med at inddrage matematikhistorie kan beskrives som “matematikhistorie som mål”, men at de tre analyserede lærebogssystemer oftest ikke lever op til dette hvorfor opfyldelsen heraf bliver op til de enkelte undervisere. Der diskuteres i artiklen mulige løsninger på dette problem

Counteracting Destructive Student Misconceptions of Mathematics

In this article, we ask the question of what it takes for targeted efforts to be reasonably successful in altering students’ misconceptions and unproductive beliefs and ensuing myths about mathematics as a discipline and a school subject and about themselves in relation to mathematics, so as to pave the way for satisfactory learning. We attempt to answer this question through the analysis of three cases of upper secondary school students, who all struggled with mathematics-related difficulties due to myths resulting from misguided beliefs, erroneous proof schemes, or mistaken interpretations of the didactical contract, the three theoretical constructs we employ in the study. We describe how specially educated teachers, so-called “mathematics counsellors”, taking part in a professional development program conducted by the authors, were able, firstly, to identity these students, then to diagnose more precisely the nature of their difficulties, and finally to design targeted interventions in order to assist the students in actually overcoming (parts of) their difficulties and eventually dispelling some of the myths they were influenced by. We further offer an analysis of the elements responsible for the success of these interventions. More precisely, we identify five such elements. Finally, we zoom in on the role and intricate connectedness of the three theoretical constructs mentioned above

An Interdisciplinary Rendezvous Between Mathematics and Literature: Reflections on Beauty as a Perspective in Comparative Disciplinary Didactics and a Thematic Approach to Interdisciplinary Work in Upper Secondary School

In this paper we propose a thematic focus on aesthetics in the context of an interdisciplinary collaboration between mathematics and literature (Language Arts) as a way to further students’ reflections on and deeper understanding of what characterizes the two subjects. Furthermore, we argue that approaching aesthetics through the perspective of literacy can potentially strengthen students’ understanding of ways of thinking particular to specific (academic) disciplines; ways of thinking that are otherwise often hidden when teaching focuses on more pragmatic aspects. G. H. Hardy’s A Mathematician’s Apology from 1940 serves as the recurring illustrative example in our discussions of the pedagogical potentials of an interdisciplinary rendezvous between mathematics and literature

Preservice teachers’ beliefs about mathematical digital competency – a “hidden variable” in teaching mathematics with digital technology?

Recently the construct of mathematical digital competency (MDC) was put forward in which mathematical competency and digital competency are seen as a connected whole. This entails that student understanding of mathematical concepts may be almost inseparable from digital tools. We report on a quantitative study with n=238 preservice teachers (PSTs) from Germany that investigates PSTs’ beliefs about such a “connected position” of MDC. Results show that a large group of PSTs believe in the potential of digital technology but at the same time opposes the notion of MDC and rather believe that mathematical and digital competency should be separated. Furthermore, PSTs’ beliefs about MDC are largely independent from epistemological beliefs. We hypothesize, that beliefs about MDC may be an overlooked variable which may influence how teacher think about and use digital technology in the mathematics classroom

CAS Assisted Proofs in Upper Secondary School Mathematics Textbooks

This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are identified in ten different textbooks. The CAS based proofs in these textbooks are of three types: complete outsourcing of the proof to CAS; partial outsourcing of the proof to CAS; and additional verification of the proof’ correctness by CAS. Analyses of examples of each of these types are provided. The analyses draw on theoretical constructs related to both proofs and proving (e.g. proof schemes) and to use of digital technologies in mathematics education (lever potential, blackboxing, instrumental genesis). In particular, the analyses make use of a distinction between epistemic, pragmatic and justificational mediations. Results suggest both potential problems with using CAS as an integrated part of deductive mathematical proofs in textbooks, since it appears to promote undesired proof schemes with the students, and difficulties with understanding these problems using the constructs of epistemic and pragmatic mediations that are often adopted in the literature regarding CAS use in mathematics teaching and learning