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Attila SzaboAffiliated researcher

About me

My research focuses on mathematical giftedness, on problem solving, on aspects of prospective teachers´ education and on the use of dynamic geometry software in mathematics education. I am a senior lecturer at the Stockholm Education Administration and author of a textbook series for secondary school mathematics in Sweden.

Also, I am a board member of the Swedish Institute of Educational Research, member of the International Committee at the International Group for Mathematical Creativity and Giftedness (MCG), of the ICMI-Sweden (SKM) and of the Scientific Advisory Board at the Global Center for Gifted and Talented Children (GCGTC).

Currently, I am assistant supervisor for Diana von Börtzell-Szuch and Hannah Holmqvist Mohammed, PhD students within a gifted education doctoral programme for teacher educators.

Research

My research focuses on mathematical giftedness, on problem solving, on aspects of prospective mathematics teachers´ education and on the use of dynamic geometry software in mathematics education.

Also, I am a board member of the Swedish Institute of Educational Research and member of the International Committee at the International Group for Mathematical Creativity and Giftedness (MCG).

Publications

A selection from Stockholm University publication database

  • Displaying gifted students’ mathematical reasoning during problem solving: Challenges and possibilities

    2024. Attila Szabo, Ann-Sophie Tillnert, John Mattsson. The Montana Mathematics Enthusiast 21 (1-2), 179-202

    Article

    When solving problems, mathematically gifted individuals tend to internalize intuitive ideas and approaches, and to shorten their reasoning. Consequently, for teachers it is difficult to observe gifted students’ mathematical reasoning in the context of problem solving. In this paper we investigate nine gifted Swedish 9th grade students’ mathematical reasoning during problem solving in small groups at vertical whiteboards. The data consists of 5 filmed group-activities, that were analysed according to a framework of collaborative problem-solving (Roschelle & Teasley, 1995). The analysis shows that every group solved proposed problems successfully within different socially negotiated Joint Problem Spaces (JPS) and, importantly, that students were able to verbalize and display their mathematical reasoning. Additionally, it is indicated that using vertical whiteboards facilitated considerably the exhibition of students’ mathematical reasoning.

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  • Swedish students’ exploration of trigonometrical relationships: GeoGebra and protractors yield qualitatively different insights

    2022. Ella Kai-Larsen (et al.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)

    Conference

    Trigonometry, an important pre-requisite for many advanced topics of school mathematics, links geometric, algebraic and graphical reasoning, but remains a difficult topic to teach and learn. The dynamic nature of many trigonometric functions is amenable to dynamic geometry software, which, in the form of GeoGebra, is the focus of this paper. However, both generally and in respect of trigonometry, research on GeoGebra’s efficacy seems ambivalent. In this paper, we offer a case study of two groups of Swedish upper secondary students’ solutions to the same tasks. One group was instructed to use GeoGebra and the other a protractor to investigate the sine and cosine functions in in the interval 0° ≤ v ≤ 180°. Analyses yielded qualitatively different outcomes; students using the protractor typically identified a geometrical relationship based on symmetry around the protractor’s 90° line, while those using GeoGebra tended to identify only numerical relationships.

    Read more about Swedish students’ exploration of trigonometrical relationships

  • Prospective teachers constructing dynamic geometry activities for gifted pupils

    2021. Mirela Vinerean (et al.). Gifted Education International

    Article

    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.

    Read more about Prospective teachers constructing dynamic geometry activities for gifted pupils

  • Surveying teachers’ conception of programming as a mathematics topic following the implementation of a new mathematics curriculumSurveying teachers’ conception of programming as a mathematics topic following the implementation of a new mathematics curriculum

    2019. Morten Misfeldt, Szabo Attila, Ola Helenius. Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education, 2713-2720

    Conference
    Read more about Surveying teachers’ conception of programming as a mathematics topic following the implementation of a new mathematics curriculumSurveying teachers’ conception of programming as a mathematics topic following the implementation of a new mathematics curriculum

  • Overexcitability, iconoclasm and mathematical creativity & giftedness

    2019. Matthias Brandl, Szabo Attila. Proceedings of the 11th International Conference on Mathematical Creativity and Giftedness, 53-58

    Conference

    There are several theoretical psychological concepts in the realm of research on (mathematical) creativity and giftedness, e.g. originality, non-conformism, iconoclasm, overexcitability and high sensitivity. By connecting these aspects to one another we show some concept-immanent interdependencies and congruities. Applying those to the specific area of mathematics we identify a natural relation of the mentioned concepts to the character of performing and dealing with mathematics. Additionally, we derive some consequences for classroom teaching.

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  • Uncovering the Relationship Between Mathematical Ability and Problem Solving Performance of Swedish Upper Secondary School Students

    2018. Attila Szabo, Paul Andrews. Scandinavian Journal of Educational Research 62 (4), 555-569

    Article

    In this paper, we examine the interactions of mathematical abilities when 6 high achieving Swedish upper-secondary students attempt unfamiliar non-routine mathematical problems. Analyses indicated a repeating cycle in which students typically exploited abilities relating to the ways they orientated themselves with respect to a problem, recalled mathematical facts, executed mathematical procedures, and regulated their activity. Also, while the nature of this cyclic sequence varied little across problems and students, the proportions of time afforded the different components varied across both, indicating that problem solving approaches are informed by previous experiences of the mathematics underlying the problem. Finally, students’ whose initial problem formulations were numerical typically failed to complete the problem, while those whose initial formulations were algebraic always succeeded.

    Read more about Uncovering the Relationship Between Mathematical Ability and Problem Solving Performance of Swedish Upper Secondary School Students

  • Examining the interaction of mathematical abilities and mathematical memory

    2017. Attila Szabo, Paul Andrews. The Mathematics Enthusiast 14 (1-3), 141-159

    Article

    In this paper we investigate the abilities that six high-achieving Swedish upper secondary students demonstrate when solving challenging, non-routine mathematical problems. Data, which were derived from clinical interviews, were analysed against an adaptation of the framework developed by the Soviet psychologist Vadim Krutetskii (1976). Analyses showed that when solving problems students pass through three phases, here called orientation, processing and checking, during which students exhibited particular forms of ability. In particular, the mathematical memory was principally observed in the orientation phase, playing a crucial role in the ways in which students' selected their problem-solving methods; where these methods failed to lead to the desired outcome students were unable to modify them. Furthermore, the ability to generalise, a key component of Krutetskii's framework, was absent throughout students' attempts. These findings indicate a lack of flexibility likely to be a consequence of their experiences as learners of mathematics.

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  • Matematikundervisning för begåvade elever – en forskningsöversikt

    2017. Attila Szabo. Nordisk matematikkdidaktikk 22 (1), 21-44

    Article

    Artikeln redovisar de huvudsakliga pedagogiska och organisatoriska metoder relaterade till begåvade elevers matematikundervisning som fokuseras i forskningslitteraturen – även könsskillnader, motivation och matematiskt begåvade elevers sociala situation i klassrummet diskuteras. Översikten visar att det finns åtgärder – t.ex. frivillig acceleration i ämnet där undervisningen är anpassad till elevens förkunskaper och kapacitet eller arbete med utmanande uppgifter i prestationshomogena grupper – som antas ha goda effekter på begåvade elevers kunskapsutveckling i matematik. Analysen visar också att det kan uppfattas som problematiskt att vara begåvad i matematik samt att begåvade flickor upplever vissa aspekter av matematikundervisningen annorlunda jämfört med motsvarande grupp pojkar.

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  • Mathematical memory revisited

    2017. Attila Szabo. Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1-5, 2017), 1202-1209

    Conference

    The present study deals with the role of the mathematical memory in problem solving. To examine that, two problem-solving activities of high achieving students from secondary school were observed one year apart - the proposed tasks were non-routine for the students, but could be solved with similar methods. The study shows that even if not recalling the previously solved task, the participants’ individual ways of approaching both tasks were identical. Moreover, the study displays that the participants used their mathematical memory mainly at the initial phase and during a small fragment of the problem-solving process, and indicates that students who apply algebraic methods are more successful than those who use numerical approaches.

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  • Mathematical abilities and mathematical memory during problem solving and some aspects of mathematics education for gifted pupils

    2017. Attila Szabo.

    Thesis (Doc)

    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.

    Read more about Mathematical abilities and mathematical memory during problem solving and some aspects of mathematics education for gifted pupils

  • Matematiska förmågors interaktion och det matematiska minnets roll vid lösning av matematiska problem

    2013. Attila Szabo.

    Thesis (Lic)

    The thesis deals with the interaction of mathematical abilities and the mathematical memory's role in problem-solving. To examine those phenomena, I analyzed the expression of mathematical abilities for high achieving students from upper secondary school. The study shows that the mathematical memory accounts for a relatively small proportion of time of the problem-solving process and that the mathematical memory emerges mainly during the initial phase of the process. Although the mathematical memory accounts for a small percentage of the time of the problem-solving process, the mathematical memory has a decisive role for the choice of problem-solving methods, because the students choose their solution methods in the initial phase of their problem-solving activity. The study shows that the choice of problem-solving method has significant consequences for the students' problem-solving activity; if the chosen methods did not lead to the desired outcome, so the students found it very difficult to change their initially chosen problem-solving methods. The study also shows that students who use general problem-solving methods perform better than students who use numerical methods.

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  • Prospective teachers designing tasks for dynamic geometry environments

    2022. Maria Fahlgren, Szabo Attila, Mirela Vinerean. Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)

    Conference

    The paper examines the quality of digitized tasks designed by 10 (small) groups of prospective upper secondary school teachers as part of a geometry course assignment. The results indicate that a small instructional intervention, addressing the planning and implementation of tasks in digitized task environments as well as how to stimulate students to make mathematical generalizations, led to a relatively high proportion (8 out of 10) of high-quality tasks designed by the prospective teachers.

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