Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Mathematical abilities and mathematical memory during problem solving and some aspects of mathematics education for gifted pupils
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.ORCID iD: 0000-0002-5423-5580
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
Keyword [en]
mathematical abilities, mathematical memory, high-achieving students, problem solving, mathematics education for gifted pupils
National Category
Didactics
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:su:diva-146542ISBN: 978-91-7649-948-1 (print)ISBN: 978-91-7649-949-8 (electronic)OAI: oai:DiVA.org:su-146542DiVA, id: diva2:1143981
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
List of papers
1. Matematikundervisning för begåvade elever – en forskningsöversikt
Open this publication in new window or tab >>Matematikundervisning för begåvade elever – en forskningsöversikt
2017 (Swedish)In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 22, no 1, p. 21-44Article, review/survey (Refereed) Published
Abstract [sv]

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.

Abstract [en]

The present article offers an overview of those main methodological and pedagogical approaches associated with gifted pupils’ education in mathematics which are focused in the research literature. Furthermore, the article discusses gender differences, motivation and some central aspects of mathematically gifted pupils’ social situation in the classroom. The analysis shows that there are some pedagogical and organizational approaches, e.g. voluntary acceleration where the teaching is adapted to the knowledge and the capacity of the participants or working with challenging mathematical problems in performance-homogenous groups, which may have good effects on gifted pupils’ mathematical achievement. The overview also indicates that mathematically gifted adolescents are facing difficulties in their social interaction and that gifted female and male pupils are experiencing certain aspects of their mathematics education differently.

Keyword
begåvade elever, matematik, undervisning
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-146529 (URN)
Note

Access to the two most recent volumes are password protected.

Available from: 2017-08-31 Created: 2017-08-31 Last updated: 2017-09-24Bibliographically approved
2. Examining the interaction of mathematical abilities and mathematical memory: A study of problem-solving activity of high-achieving Swedish upper secondary students
Open this publication in new window or tab >>Examining the interaction of mathematical abilities and mathematical memory: A study of problem-solving activity of high-achieving Swedish upper secondary students
2017 (English)In: The Mathematics Enthusiast, ISSN 1551-3440, Vol. 14, no 1-3, p. 141-159Article in journal (Refereed) Published
Abstract [en]

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.

Keyword
mathematical ability, non-routine problem solving, Krutetskii, mathematical memory, abstraction, generalization, high achieving students, Swedish upper secondary
National Category
Other Mathematics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-139538 (URN)000396454000009 ()
Available from: 2017-02-08 Created: 2017-02-08 Last updated: 2017-09-24Bibliographically approved
3. Uncovering the Relationship Between Mathematical Ability and Problem Solving Performance of Swedish Upper Secondary School Students
Open this publication in new window or tab >>Uncovering the Relationship Between Mathematical Ability and Problem Solving Performance of Swedish Upper Secondary School Students
2017 (English)In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170Article in journal (Refereed) Epub ahead of print
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.

Keyword
high achieving students, mathematical abilities, mathematical problem solving, Swedish upper secondary school
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-146532 (URN)10.1080/00313831.2016.1258671 (DOI)
Available from: 2017-08-31 Created: 2017-08-31 Last updated: 2018-04-23
4. Mathematical memory revisited: mathematical problem solving by high achieving students
Open this publication in new window or tab >>Mathematical memory revisited: mathematical problem solving by high achieving students
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
Keyword
high-achievers, mathematical memory, mathematical abilities, problem solving
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-146536 (URN)978-1-873769-73-7 (ISBN)
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

Open Access in DiVA

Mathematical abilities and mathematical memory during problem solving and some aspects of mathematics education for gifted pupils(1012 kB)296 downloads
File information
File name FULLTEXT01.pdfFile size 1012 kBChecksum SHA-512
90dd7edebfab9bfe6adeb3ec54593a04e015300f7ca892bea59e85a111f1a79839e3a8254212e2494803f1f853c82a4a0b0b55a2eb42bebef09d845c79fa6278
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Szabo, Attila
By organisation
Department of Mathematics and Science Education
Didactics

Search outside of DiVA

GoogleGoogle Scholar
Total: 296 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 3809 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf