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Mathematical memory revisited: mathematical problem solving by high achieving students
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.ORCID iD: 0000-0002-5423-5580
2017 (English)In: Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1-5, 2017) / [ed] Thérèse Doole, Ghislaine Gueudet, Dublin: DCU Institute of Education, ERME , 2017, p. 1202-1209Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Dublin: DCU Institute of Education, ERME , 2017. p. 1202-1209
Keywords [en]
high-achievers, mathematical memory, mathematical abilities, problem solving
National Category
Didactics
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:su:diva-146536ISBN: 978-1-873769-73-7 (electronic)OAI: oai:DiVA.org:su-146536DiVA, id: diva2:1137591
Conference
Tenth Congress of the European Society for Research in Mathematics Education, Dublin Ireland, 1 – 5 February, 2017
Available from: 2017-08-31 Created: 2017-08-31 Last updated: 2018-03-23Bibliographically 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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