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- Bergman Ärlebäck, Jonas, 1972-
(författare)
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Mathematical modelling in upper secondary mathematics education in Sweden
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The aim of this thesis is to investigate and enhance our understanding of the notions of mathematical models and modelling at the Swedish upper secondary school level. Focus is on how mathematical models and modelling are viewed by the different actors in the school system, and what characterises the collaborative process of a didactician and a group of teachers engaged in designing and developing, implementing and evaluating teaching modules (so called modelling modules) exposing students to mathematical modelling in line with the present mathematics curriculum. The thesis consists of five papers and reports, along with a summary introduction, addressing both theoretical and empirical aspects of mathematical modelling.The thesis uses both qualitative and quantitative methods and draws partly on design-based research methodology and cultural-historical activity theory (CHAT). The results of the thesis are presented using the structure of the three curriculum levels of the intended, potentially implemented, and attained curriculum respectively.The results show that since 1965 and to the present day, gradually more and more explicit emphasis has been put on mathematical models and modelling in the syllabuses at this school level. However, no explicit definitions of these notions are provided but described only implicitly, opening up for a diversity of interpretations.From the collaborative work case study it is concluded that the participating teachers could not express a clear conception of the notions mathematical models or modelling, that the designing process often was restrained by constraints originating from the local school context, and that working with modelling highlights many systemic tensions in the established school practice. In addition, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported.In a questionnaire study with 381 participating students it is concluded that only one out of four students stated that they had heard about or used mathematical models or modelling in their education before, and the expressed overall attitudes towards working with mathematical modelling as represented in the test items were negative. Students’ modelling proficiency was positively affected by the students’ grade, last taken mathematics course, and if they thought the problems in the tests were easy or interesting. In addition empirical findings indicate that so-called realistic Fermi problems given to students working in groups inherently evoke modelling activities.
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- Lindström, Torsten, 1965-, et al.
(författare)
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Mathematics, Science, and Dynamical Systems : An Introduction
- 2021
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Ingår i: Handbook of the Mathematics of the Arts and Sciences. - Cham : Springer. - 9783319706580 ; , s. 1967-1968
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In this short introduction, the section “Mathematics, Science, and DynamicalSystems” of the Handbook of the Mathematics of the Arts and Sciences issummarized.
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Refractions of mathematics education : Festschrift for Eva Jablonka
- 2015
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Samlingsverk (redaktörskap) (övrigt vetenskapligt/konstnärligt)abstract
- The diversity of research in mathematics education has been addressed as both, a problem and a strength. When manifested through adherence to different intellectual roots and theoretical orientations, diversions constitute ‘refractions’ of mathematics education. The collection and analysis of empirical data in a study are by necessity refracted through the specific analytical lens employed, as well as the aim of the study itself. Refractions can also refer to looking at old phenomena through new lenses.The chapters in this book are refracted through philosophical, political, mathematical and personal lenses by distinguished authors in the field, addressing issues about the elusive experience of doing mathematics, purification of texts, refractions, mathematics and ethnomathematics, political messages in textbook tasks, mathematics education policy debate, the political in mathematics education research, philosophy and mathematics, meanings and representations, identity of mathematical modeling, and dilemmas in the teaching of calculus.An ancient Sanskrit adage states that Knowledge is something that grows when shared, but shrinks when hoarded. Academics engaged in the generation of new Knowledge are blessed with both the time and the freedom to engage in pursuits that allow for intellectual pleasure. As a phenomenon of the Zeitgeist many have succumbed to the increased corporatization of academic work, engaging in activities for monetary and self advancement purposes. Are there any real intellectuals left in academia, a là Adorno, Bourdieu, Chomsky, Foucault, among others? This Festschrift is dedicated to academics that don't bother with self promotion or aggrandizement of themselves or their ideas in simplistic terms.
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- Szabo, Attila, 1965-
(författare)
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Mathematical abilities and mathematical memory during problem solving and some aspects of mathematics education for gifted pupils
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis reports on two different investigations.The first is a systematic review of pedagogical and organizational practices associated with gifted pupils’ education in mathematics, and on the empirical basis for those practices. The review shows that certain practices – for example, enrichment programs and differentiated instructions in heterogeneous classrooms or acceleration programs and ability groupings outside those classrooms – may be beneficial for the development of gifted pupils. Also, motivational characteristics of and gender differences between mathematically gifted pupils are discussed. Around 60% of analysed papers report on empirical studies, while remaining articles are based on literature reviews, theoretical discourses and the authors’ personal experiences – acceleration programs and ability groupings are supported by more empirical data than practices aimed for the heterogeneous classroom. Further, the analyses indicate that successful acceleration programs and ability groupings should fulfil some important criteria; pupils’ participation should be voluntary, the teaching should be adapted to the capacity of participants, introduced tasks should be challenging, by offering more depth and less breadth within a certain topic, and teachers engaged in these practices should be prepared for the characteristics of gifted pupils.The second investigation reports on the interaction of mathematical abilities and the role of mathematical memory in the context of non-routine problems. In this respect, six Swedish high-achieving students from upper secondary school were observed individually on two occasions approximately one year apart. For these studies, an analytical framework, based on the mathematical ability defined by Krutetskii (1976), was developed. Concerning the interaction of mathematical abilities, it was found that every problem-solving activity started with an orientation phase, which was followed by a phase of processing mathematical information and every activity ended with a checking phase, when the correctness of obtained results was controlled. Further, mathematical memory was observed in close interaction with the ability to obtain and formalize mathematical information, for relatively small amounts of the total time dedicated to problem solving. Participants selected problem-solving methods at the orientation phase and found it difficult to abandon or modify those methods. In addition, when solving problems one year apart, even when not recalling the previously solved problem, participants approached both problems with methods that were identical at the individual level. The analyses show that participants who applied algebraic methods were more successful than participants who applied particular methods. Thus, by demonstrating that the success of participants’ problem-solving activities is dependent on applied methods, it is suggested that mathematical memory, despite its relatively modest presence, has a pivotal role in participants’ problem-solving activities. Finally, it is indicated that participants who applied particular methods were not able to generalize mathematical relations and operations – a mathematical ability considered an important prerequisite for the development of mathematical memory – at appropriate levels.
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- Szabo, Attila, fil.dr. 1965-, et al.
(författare)
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Prospective teachers constructing dynamic geometry activities in order to challenge gifted pupils
- 2022
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Ingår i: On the Road to Mathematical Expertise and Innovation. - Münster : WTM – Verlag für wissenschaftliche Texte und Medien. - 9783959872263 - 9783959872157 ; , s. 265-271
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Konferensbidrag (refereegranskat)abstract
- Described as fundamentally egalitarian, the Swedish educational system has, until recently, accorded little attention to gifted pupils. We investigated the effects of an instructional intervention for prospective teachers (PTs), i.e., a seminar about mathematical giftedness and problems appealing to gifted pupils. The PTs used dynamic geometry software (DGS) to construct activities for pupils in mixed-ability classrooms. The results indicate that 9 of 10 activities addressed some main characteristics of the gifted, importantly, the ability to generalize mathematical relationships.
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