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  • Bergwall, Andreas, 1972- (författare)
  • On a generality framework for proving tasks
  • 2015
  • Ingår i: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education. - Prague : Charles University in Prague, Faculty of Education and ERME. - 9788072908448 ; , s. 86-92
  • Konferensbidrag (refereegranskat)abstract
    • In this paper I present an analytic framework for generality in textbook proving tasks that involve functions. The framework is discussed in relation to results obtained when analysing tasks in integral calculus. The results show that the frameworks’ categories are easily distinguishable if the functions are explicitly described. The results are also promising regarding the possibility to clarify differences between textbooks. The analysed sections exemplify that there is not necessarily a correlation between the number of general proving tasks and the opportunities for students to engage in reasoning about arbitrary functions. Limitations and possible refinements of the framework are also discussed.
  • Liljekvist, Yvonne, 1967-, et al. (författare)
  • Multi-theoretical approach when researching mathematics teachers’ professional development in self-organized online groups
  • 2019
  • Ingår i: Fortbildning på Facebook, SMEER, ROSE.
  • Konferensbidrag (refereegranskat)abstract
    • Teachers worldwide are using social media as a professional development resource. In studying social media as ‘a place’ for teachers’ professional development, we investigated large Facebook groups with themes connected to teaching and learning in compulsory schools. The interaction in these groups was analysed within the framework of systemic functional grammar. In order to reveal knowledge known and shared by teachers as a community, we have also used Shulman’s (1987) framework. Most posts received responses and this response is in line with the expected response pattern. The speech functions ‘Questions’ and ‘Offers’ were most common. Further, most posts addressed subject specific knowledge. The multi-theoretical approach used when researching mathematics teachers’ professional development in self-organized online groups showed that these large Facebook groups facilitated professional learning.
  • Bergqvist, Tomas, 1962-, et al. (författare)
  • Upper secondary students’ task reasoning
  • 2008
  • Ingår i: International Journal of Mathematical Education in Science and Technology. - 0020-739X .- 1464-5211. ; 39:1
  • Tidskriftsartikel (refereegranskat)abstract
    • Upper secondary students’ task solving reasoning was analysed, with a focus on grounds for different strategy choices and implementations. The results indicate that mathematically well-founded considerations were rare. The dominating reasoning types were algorithmic reasoning, where students tried to remember a suitable algorithm, sometimes in a random way, and guided reasoning, where progress was possible only when essentially all important strategy choices were made by the interviewer.
  • Johnsson, Helena, et al. (författare)
  • En pedagogisk idé för ingenjörsutbildningarna vid Luleå tekniska universitet
  • 2009
  • Konferensbidrag (refereegranskat)abstract
    • Utmärkande för Luleå tekniska universitet (LTU) har länge varit närheten mellan studenterna och lärarna vilket har manifesterats genom klassrumsundervisning, lärartillgänglighet, mindre studiegrupper, koncentrerade campus etc. Undervisningsformerna har dock ändrats till att idag omfatta dels klassiska föreläsningar i stora studentgrupper, men också projektarbete i team där totalt sett 1/3 av all undervisning vid Luleå tekniska universitet sker i projektform. En fråga har ställts: Har Luleå tekniska universitet idag en gemensam pedagogisk idé för ingenjörsutbildningarna? I så fall är ytterligare en fråga hur denna pedagogiska idé tar sig uttryck i organisationen?Intervjuer med 40 aktiva lärare vid Luleå tekniska universitet har genomförts av projektgruppen (tillika författarna) varpå svaren har grupperats och analyserats i fjorton olika teman. Från dessa teman har sedan fyra hörnstenar i en definition av en pedagogisk idé aggregerats. Formuleringen av den pedagogiska idén lyder: Ett aktivt lärande för yrkeslivet – i branschnära projekt och med god vetenskaplig grund tränas förmågan att arbeta som ingenjör genom coachning från lärare i ett nära och öppet klimat. Idén har antagits av den tekniska fakultetsnämnden vid Luleå tekniska universitet och verifierats på institutionerna. Exempel på implementering och hur den pedagogiska idén aktivt verkar presenteras i artikeln.
  • Scheja, Max, et al. (författare)
  • Transformation and contextualisation : conceptualising students' conceptual understandings of threshold concepts in calculus
  • 2010
  • Ingår i: Higher Education. - : Springer Netherlands. - 0018-1560 .- 1573-174X. ; 59:2, s. 221-241
  • Tidskriftsartikel (refereegranskat)abstract
    • Research on student learning in higher education suggests that threshold concepts within various disciplines have the capacity to transform students' understanding. The present study explores students' understanding in relation to particular threshold concepts in mathematics-integral and limit-and tries to clarify in what sense developing an understanding of those threshold concepts involves a transformation of understanding in relation to ways of thinking in mathematics. Drawing on data collected in interviews with students taking a basic course on calculus the analysis offers an initial characterisation of students' understandings as algorithmic. It then proceeds to construct a more fine-grained theoretical account for how these understandings develop in the course of the interview, suggesting that the transformative aspects of threshold concepts may be conceptualised in terms of shifts in students' contextualisations allowing the development of conceptions at different levels of abstraction simultaneously interacting to shape students' awareness of the ways of thinking and practising in the subject.
  • Sjögren, Jörgen, et al. (författare)
  • Concept Formation and Concept Grounding
  • 2014
  • Ingår i: Philosophia. - : Springer Science+Business Media B.V.. - 0048-3893 .- 1574-9274. ; 42:3, s. 827-839
  • Tidskriftsartikel (refereegranskat)abstract
    • Recently Carrie S. Jenkins formulated an epistemology of mathematics, or rather arithmetic, respecting apriorism, empiricism, and realism. Central is an idea of concept grounding. The adequacy of this idea has been questioned e.g. concerning the grounding of the mathematically central concept of set (or class), and of composite concepts. In this paper we present a view of concept formation in mathematics, based on ideas from Carnap, leading to modifications of Jenkins’s epistemology that may solve some problematic issues with her ideas. But we also present some further problems with her view, concerning the role of proof for mathematical knowledge.
  • Jansson, Fredrik (författare)
  • What Games Support the Evolution of an Ingroup Bias?
  • 2015
  • Ingår i: ; 373, s. 100-110
  • Tidskriftsartikel (refereegranskat)abstract
    • There is an increasing wealth of models trying to explain the evolution of group discrimination and an ingroup bias. This paper sets out to systematically investigate the most fundamental assumption in these models: in what kind of situations do the interactions take place? What strategic structures – games – support the evolution of an ingroup bias? More specifically, the aim here is to find the prerequisites for when a bias also with respect to minimal groups – arbitrarily defined groups void of group-specific qualities – is selected for, and which cannot be ascribed to kin selection.Through analyses and simulations of minimal models of two-person games, this paper indicates that only some games are conducive to the evolution of ingroup favouritism. In particular, this class does not contain the prisoners' dilemma, but it does contain anti-co-ordination and co-ordination games. Contrasting to the prisoners' dilemma, these are games where it is not a matter of whether to behave altruistically, but rather one of predicting what the other person will be doing, and where I would benefit from you knowing my intentions.In anti-co-ordination games, on average, not only will agents discriminate between groups, but also in such a way that their choices maximise the sum of the available payoffs towards the ingroup more often than towards the outgroup. And in co-ordination games, even if agents do manage to co-ordinate with the whole population, they are more likely to co-ordinate on the socially optimal equilibrium within their group. Simulations show that this occurs most often in games where there is a component of risk-taking, and thus trust, involved. A typical such game is the stag hunt or assurance game.
  • Viirman, Olov (författare)
  • The functions of function discourse : University mathematics teaching from a commognitive standpoint
  • 2014
  • Ingår i: International journal of mathematical education in science and technology. - : Taylor & Francis Group. - 0020-739X .- 1464-5211. ; 45:4, s. 512-527
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper addresses a topic within university mathematics education which has been somewhat underexplored: the teaching practices actually used by university mathematics teachers when giving lectures. The study investigates the teaching practices of seven Swedish university teachers on the topic of functions using a discursive approach, the commognitive framework of Sfard. In the paper a categorization of the construction and substantiation routines used by the teachers is presented, for instance various routines for constructing definitions and examples, and for verifying whether an example satisfies a given definition. The findings show that although the overall form of the lectures is similar, with teachers using ‘chalk talk’, and overt student participation limited to asking and answering questions, there are in fact significant differences in the way the teachers present and do mathematics in their lectures. These differences present themselves both on the level of discursive routines and on a more general level in how the process of doing mathematics is made visible in the teachers’ teaching practices. Moreover, I believe that many of the results of the study could be relevant for investigating the teaching of other mathematical topics.
  • Player-Koro, Catarina (författare)
  • Hype, Hope and Reality, the paradox of ICT in education
  • 2010
  • Konferensbidrag (refereegranskat)abstract
    • For 30 years there has been ongoing argument that developments of information and communication technology (ICT) will inevitably change education systems and practices. This innovation of education by using ICT-tools is often described as more or less self-evident with a naïve faith in the promises of new technology to enable teachers to make improvement in the content, the methods and the organisation of teaching and learning, with far-reaching influence on students’ skills and knowledge (Westera 2005; Nivala 2009). One example is ICT literacy defined as an important component in a set of generic skills that all citizens in the neo-liberal market society must possess (Kozma and Voogt 2003; Krumsvik 2009; Robertson 2003; De Castell, Bryson, and Jenson 2002). However, educational practices seem to have failed to live up to these utopian expectations and the process of integration of ICT has often been described as slow. Reasons for this lethargy has by many researchers been identified in various aspects of educational practice ranging from technical factors such as lack of technology and software in schools and the limited personal expertise of teachers in the use of ICT, to other factors, such as for example teachers’ beliefs, and knowledge about how to integrate ICT in teaching (Robertson 2003; UNESCO Launches ICT Standards Effort 2008; De Castell, Bryson, and Jenson 2002; Goktas, Yildirim, and Yildirim 2009; Govender and Govender 2009). The aim with this paper is to discuss how ethnographic methods can be used to make visible what educational technologies might offer for teaching and learning of mathematics. The paper offers critical considerations of the official discourse (described above), stemming from economic interests, exhorting the field of education to adopt and integrate information and communication technology (ICT), in teaching and learning. It calls for an alternative, reflexive and critical approach where questions about technology uses in education are emphasised. But the question is, what educationally, does ICT really offer for education? In the present study a group of student teachers were followed during 20 weeks of a mathematics course as part of a three and a half to four yearlong education. The course was followed in its entirely but the material discussed here represents participants observation together with conversional interviews with students from lab work where student teachers work with computers . One way of understanding the attractiveness of ICT for educational policy makers, is the way new technology is formulated in official discourse, by the society and its selected agents, where digital technology in many way defines society, and the position education has as a driving force of economic competiveness (Ball 2006). The argument for ICT use in education formulated in this discourse is rooted in economistic theorizing rather than in an educational theory (De Castell, Bryson, and Jenson 2002). The present study try to redress this imbalances. It uses Basil Bernstein conceptual framework about the construction of pedagogic discourse as a grammar underlying fields of production, recontextualisation and pedagogical practice. These theoretical concepts could be used to understand the process where dominant groups in society ideologically create unrealistic expectations about the effects of ICT use on teaching and learning. It does this through its concern with the intrinsic feature of pedagogic discourse, with the distinctive form and structure of what actually goes on the process of education (Bernstein 2000).
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