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Learning mathematics without a suggested solution method: durable effects on performance and brain activity
Umeå University, Faculty of Social Sciences, Department of Psychology. Umeå University, Faculty of Medicine, Department of Integrative Medical Biology (IMB). Umeå University, Faculty of Medicine, Umeå Centre for Functional Brain Imaging (UFBI).
Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
Umeå University, Faculty of Social Sciences, Department of Psychology.
Karlstad, Sweden.
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2015 (English)In: Trends in Neuroscience and Education, ISSN 2211-9493, Vol. 4, no 1-2, 6-14 p.Article in journal (Refereed) Published
Abstract [en]

A dominant mathematics teaching method is to present a solution method and let pupils repeatedly practice it. An alternative method is to let pupils create a solution method themselves. The current study compared these two approaches in terms of lasting effects on performance and brain activity. Seventythree participants practiced mathematics according to one of the two approaches. One week later, participants underwent fMRI while being tested on the practice tasks. Participants who had created the solution method themselves performed better at the test questions. In both conditions, participants engaged a fronto-parietal network more when solving test questions compared to a baseline task. Importantly, participants who had created the solution method themselves showed relatively lower brain activity in angular gyrus, possibly reflecting reduced demands on verbal memory. These results indicate that there might be advantages to creating the solution method oneself, and thus have implications for the design of teaching methods.

Place, publisher, year, edition, pages
Elsevier, 2015. Vol. 4, no 1-2, 6-14 p.
Keyword [en]
Mathematics, Learning, fMRI, Parietal cortex, Angular gyrus, Education
National Category
Psychology (excluding Applied Psychology)
URN: urn:nbn:se:umu:diva-109088DOI: 10.1016/j.tine.2015.03.002ISI: 000363545300002OAI: diva2:854762
Available from: 2015-09-17 Created: 2015-09-17 Last updated: 2016-08-25Bibliographically approved
In thesis
1. On Mathematical Reasoning: being told or finding out
Open this publication in new window or tab >>On Mathematical Reasoning: being told or finding out
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Om Matematiska resonemang : att få veta eller att få upptäcka
Abstract [en]

School-mathematics has been shown to mainly comprise rote-learning of procedures where the considerations of intrinsic mathematical properties are scarce. At the same time theories and syllabi emphasize competencies like problem solving and reasoning. This thesis will therefore concern how task design can influence the reasoning that students apply when solving tasks, and how the reasoning during practice is associated to students’ results, cognitive capacity, and brain activity. In studies 1-3, we examine the efficiency of different types of reasoning (i.e., algorithmic reasoning (AR) or creative mathematically founded reasoning (CMR)) in between-groups designs. We use mathematics grade, gender, and cognitive capacity as matching variables to get similar groups. We let the groups practice 14 different solution methods with tasks designed to promote either AR or CMR, and after one week the students are tested on the practiced solution methods. In study 3 the students did the test in and fMRI-scanner to study if the differing practice would yield any lasting differences in brain activation. Study 4 had a different approach and focused details in students’ reasoning when working on teacher constructed tasks in an ordinary classroom environment. Here we utilized audio-recordings of students’ solving tasks, together with interviews with teachers and students to unravel the reasoning sequences that students embark on. The turning points where the students switch subtask and the reasoning between these points were characterized and visualized. The behavioral results suggest that CMR is more efficient than AR, and also less dependent on cognitive capacity during the test. The latter is confirmed by fMRI, which showed that AR had higher activation than CMR in areas connected to memory retrieval and working memory. The behavioral result also suggested that CMR is more beneficial for cognitively less proficient students than for the high achievers. Also, task design is essential for both students’ choice of reasoning and task progression. The findings suggest that: 1) since CMR is more efficient than AR, students need to encounter more CMR, both during task solving and in teacher presentation, 2) cognitive capacity is important but depending on task design, cognitive strain will be more or less high during test situations, 3) although AR-tasks does not prohibit the use of CMR they make it less likely to occur. Since CMR-tasks can emphasize important mathematical properties, are more efficient than AR- tasks, and more beneficial for less cognitively proficient students, promoting CMR can be essential if we want students to become mathematically literate. 

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2016. 55 p.
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300
mathematics education, creative reasoning, reasoning, cognitive proficiency, fMRI
National Category
Educational Sciences Mathematics Didactics Learning
Research subject
didactics of mathematics
urn:nbn:se:umu:diva-124677 (URN)978-91-7601-525-4 (ISBN)
External cooperation:
Public defence
2016-09-16, MA121, MIT-huset, Umeå, 13:00 (Swedish)
Available from: 2016-08-25 Created: 2016-08-22 Last updated: 2016-09-02Bibliographically approved

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Karlsson Wirebring, LinneaLithner, JohanJonsson, BertNorqvist, MathiasNyberg, Lars
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Department of PsychologyDepartment of Integrative Medical Biology (IMB)Umeå Centre for Functional Brain Imaging (UFBI)Department of Science and Mathematics EducationUmeå Mathematics Education Research Centre (UMERC)Department of Mathematics and Mathematical StatisticsDiagnostic Radiology
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