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Uncovering the Relationship Between Mathematical Ability and Problem Solving Performance of Swedish Upper Secondary School Students
Stockholm University, Faculty of Science, Department of Mathematics and Science Education. Stockholm City Education Department, Sweden.ORCID iD: 0000-0002-5423-5580
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.ORCID iD: 0000-0003-3679-9187
2018 (English)In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 62, no 4, p. 555-569Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2018. Vol. 62, no 4, p. 555-569
Keywords [en]
high achieving students, mathematical abilities, mathematical problem solving, Swedish upper secondary school
National Category
Didactics
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:su:diva-146532DOI: 10.1080/00313831.2016.1258671ISI: 000435015900005OAI: oai:DiVA.org:su-146532DiVA, id: diva2:1137576
Available from: 2017-08-31 Created: 2017-08-31 Last updated: 2018-07-23Bibliographically approved
In thesis
1. Mathematical abilities and mathematical memory during problem solving and some aspects of mathematics education for gifted pupils
Open this publication in new window or tab >>Mathematical abilities and mathematical memory during problem solving and some aspects of mathematics education for gifted pupils
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics and Science Education, Stockholm University, 2017. p. 139
Series
Doctoral thesis from the department of mathematics and science education ; 17
Keywords
mathematical abilities, mathematical memory, high-achieving students, problem solving, mathematics education for gifted pupils
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-146542 (URN)978-91-7649-948-1 (ISBN)978-91-7649-949-8 (ISBN)
Public defence
2017-11-10, Högbomsalen, Geovetenskapens hus, Svante Arrhenius väg 12, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: In press.

Available from: 2017-10-18 Created: 2017-09-24 Last updated: 2017-10-04Bibliographically approved

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