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Norqvist, M., Jonsson, B. & Lithner, J. (2019). Eye-tracking data and mathematical tasks with focus on mathematical reasoning. Data in Brief, 25, Article ID 104216.
Open this publication in new window or tab >>Eye-tracking data and mathematical tasks with focus on mathematical reasoning
2019 (English)In: Data in Brief, E-ISSN 2352-3409, Vol. 25, article id 104216Article in journal (Refereed) Published
Abstract [en]

This data article contains eye-tracking data (i.e., dwell time and fixations), Z-transformed cognitive data (i.e., Raven's Advanced Progressive Matrices and Operation span), and practice and test scores from a study in mathematics education. This data is provided in a supplementary file. The method section describes the mathematics tasks used in the study. These mathematics tasks are of two kinds, with and without solution templates, to induce different types of mathematical reasoning.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Eye tracking, Mathematics education, Mathematical reasoning, Problem solving
National Category
Didactics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-161778 (URN)10.1016/j.dib.2019.104216 (DOI)000495104500242 ()31372482 (PubMedID)
Funder
Marcus and Amalia Wallenberg Foundation, MAW 2014.0034
Available from: 2019-08-01 Created: 2019-08-01 Last updated: 2020-01-16Bibliographically approved
Norqvist, M., Jonsson, B., Lithner, J., Qwillbard, T. & Holm, L. (2019). Investigating algorithmic and creative reasoning strategies by eye tracking. Journal of Mathematical Behavior, 55, Article ID 100701.
Open this publication in new window or tab >>Investigating algorithmic and creative reasoning strategies by eye tracking
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2019 (English)In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, Vol. 55, article id 100701Article in journal (Refereed) Published
Abstract [en]

Imitative teaching and learning approaches have been dominating in mathematics education. Although more creative approaches (e.g. problem-based learning) have been proposed and implemented, a main challenge of mathematics education research is to document robust links between teaching, tasks, student activities and learning. This study investigates one aspect of such links, by contrasting tasks providing algorithmic solution templates with tasks requiring students’ constructions of solutions and relating this to students’ learning processes and outcomes. Information about students’ task solving strategies are gathered by corneal eye-tracking, which is related to subsequent post-test performances and individual variation in cognitive proficiency. Results show that students practicing by creative tasks outperform students practicing by imitative algorithmic tasks in the post-test, but also that students that perform less well on creative tasks tend to try ineffective imitative strategies.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Mathematical reasoning, Cognitive proficiency, Eye tracking, Productive struggle, Solution strategies
National Category
Didactics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-158187 (URN)10.1016/j.jmathb.2019.03.008 (DOI)000484789500012 ()2-s2.0-85063910258 (Scopus ID)
Funder
Marcus and Amalia Wallenberg Foundation, MAW 2014.0034
Available from: 2019-04-17 Created: 2019-04-17 Last updated: 2019-11-14Bibliographically approved
Norqvist, M. (2018). Cognitive Abilities and Mathematical Reasoning in Practice and Test Situations. In: Bergqvist, E., Österholm, M., Granberg, C., & Sumpter, L. (Ed.), Proceedings of the 42ndConference of the International Group for the Psychology of Mathematics Education: . Paper presented at 42nd Annual Meeting of the International Group for the Psychology of Mathematics Education, Umeå, Sweden, July 3–8, 2018. (pp. 419-426). Umeå, Sweden: PME, 3
Open this publication in new window or tab >>Cognitive Abilities and Mathematical Reasoning in Practice and Test Situations
2018 (English)In: Proceedings of the 42ndConference of the International Group for the Psychology of Mathematics Education / [ed] Bergqvist, E., Österholm, M., Granberg, C., & Sumpter, L., Umeå, Sweden: PME , 2018, Vol. 3, p. 419-426Conference paper, Published paper (Refereed)
Abstract [en]

Research studies have shown that to develope conceptual understanding of mathematics, practice needs to that focus this skill. In this study, the aim is to examine how different practice tasks, which promotes either imitative or creative mathematical reasoning, can influence which variables (i.e., cognitive abilities, mathematics grade, and gender) that are important for task completion. Two earlier studies show that cognitive abilities are more important in the test situation when students have practiced with imitative tasks. The result from this study indicate that although cognitive abilities are important when practicing with creative tasks, the influence of cognition is only implicit during the test. Since students often practice imitatively with given solution methods, this study suggests that a substantial part of what we test in school could be cognitive abilities rather than mathematics.

Place, publisher, year, edition, pages
Umeå, Sweden: PME, 2018
Series
Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education, ISSN 0771-100X
Keywords
Cognition, Mathematical reasoning
National Category
Didactics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-146866 (URN)
Conference
42nd Annual Meeting of the International Group for the Psychology of Mathematics Education, Umeå, Sweden, July 3–8, 2018.
Available from: 2018-06-15 Created: 2018-06-15 Last updated: 2019-07-19Bibliographically approved
Vennberg, H. & Norqvist, M. (2018). Counting on: Long Term Effects of an Early Intervention Programme. In: Bergqvist, E., Österholm, M., Granberg, C., & Sumpter, L. (Ed.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: . Paper presented at 42nd Conference of the International Group for the Psychology of Mathematics Education, Umeå, Sweden, July 3-7, 2018 (pp. 355-362). Umeå: PME, 4
Open this publication in new window or tab >>Counting on: Long Term Effects of an Early Intervention Programme
2018 (English)In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] Bergqvist, E., Österholm, M., Granberg, C., & Sumpter, L., Umeå: PME , 2018, Vol. 4, p. 355-362Conference paper, Published paper (Refereed)
Abstract [en]

This paper reports the long-term results of an intervention study with 134 six-year-old students from seven preschool-classes in northern Sweden to evaluate whether the Think, Reason and Count in Preschool-class programme (TRC) could prevent at-risk students from becoming low-performing students in mathematics. Whereas the pre-test score revealed that the intervention and the control group preformed equally, scores on the delayed follow-up-test in Grade 3 showed that the intervention group performed better than the control group and that at-risk students had closed the performance gap between themselves and their not-at-risk peers.

Place, publisher, year, edition, pages
Umeå: PME, 2018
Series
Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education, ISSN 0771-100X
National Category
Didactics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-148101 (URN)
Conference
42nd Conference of the International Group for the Psychology of Mathematics Education, Umeå, Sweden, July 3-7, 2018
Available from: 2018-06-15 Created: 2018-06-15 Last updated: 2020-03-09Bibliographically approved
Van Steenbrugge, H. & Norqvist, M. (2018). Students' Reasoning in the Classroom: An Approach for Analysis. In: Bergqvist, E., Österholm, M., Granberg, C., & Sumpter, L. (Ed.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education: . Paper presented at 42nd Conference of the International Group for the Psychology of Mathematics Education (pp. 305-305). Umeå: PME, 5
Open this publication in new window or tab >>Students' Reasoning in the Classroom: An Approach for Analysis
2018 (English)In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] Bergqvist, E., Österholm, M., Granberg, C., & Sumpter, L., Umeå: PME , 2018, Vol. 5, p. 305-305Conference paper, Poster (with or without abstract) (Refereed)
Place, publisher, year, edition, pages
Umeå: PME, 2018
Series
Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education, ISSN 0771-100X
Keywords
Mathematical Reasoning, Analytical approach
National Category
Didactics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-147060 (URN)
Conference
42nd Conference of the International Group for the Psychology of Mathematics Education
Available from: 2018-06-15 Created: 2018-06-15 Last updated: 2018-06-21Bibliographically approved
Norqvist, M. (2018). The effect of explanations on mathematical reasoning tasks. International journal of mathematical education in science and technology, 49(1), 15-30
Open this publication in new window or tab >>The effect of explanations on mathematical reasoning tasks
2018 (English)In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 49, no 1, p. 15-30Article in journal (Refereed) Published
Abstract [en]

Studies in mathematics education often point to the necessity for students to engage in more cognitively demanding activities than just solving tasks by applying given solution methods. Previous studies have shown that students that engage in creative mathematically founded reasoning to construct a solution method, perform significantly better in follow up tests than students that are given a solution method and engage in algorithmic reasoning. However, teachers and textbooks, at least occasionally, provide explanations together with an algorithmic method, and this could possibly be more efficient than creative reasoning. In this study, three matched groups practiced with either creative, algorithmic, or explained algorithmic tasks. The main finding was that students that practiced with creative tasks did, outperform the students that practiced with explained algorithmic tasks in a post-test, despite a much lower practice score. The two groups that got a solution method presented, performed similarly in both practice and post-test, even though one group got an explanation to the given solution method. Additionally, there were some differences between the groups in which variables predicted the post-test score.

Place, publisher, year, edition, pages
Abingdon: Taylor & Francis, 2018
Keywords
Mathematical reasoning, explanations, problem-solving, productive struggle, algorithmic reasoning, creative reasoning
National Category
Didactics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-137297 (URN)10.1080/0020739X.2017.1340679 (DOI)000427408100003 ()
Projects
Att lära matematik genom imitativa och kreativa resonemang
Available from: 2017-06-29 Created: 2017-06-29 Last updated: 2018-06-09Bibliographically approved
Norqvist, M. (2016). Explanations do not improve algorithmic reasoning tasks: Volume 1. In: Csíkos, C., Rausch, A., & Szitányi, J. (Ed.), Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education: Volume 1. Paper presented at 40th Conference of the International Group for the Psychology of Mathematics Education, Szeged, Hungary, August 3-7, 2016 (pp. 110-110). Szeged, Hungary: International Group for the Psychology of Mathematics Education, 1
Open this publication in new window or tab >>Explanations do not improve algorithmic reasoning tasks: Volume 1
2016 (English)In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education: Volume 1 / [ed] Csíkos, C., Rausch, A., & Szitányi, J., Szeged, Hungary: International Group for the Psychology of Mathematics Education , 2016, Vol. 1, p. 110-110Conference paper, Oral presentation with published abstract (Refereed)
Place, publisher, year, edition, pages
Szeged, Hungary: International Group for the Psychology of Mathematics Education, 2016
National Category
Educational Sciences
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-124707 (URN)
Conference
40th Conference of the International Group for the Psychology of Mathematics Education, Szeged, Hungary, August 3-7, 2016
Available from: 2016-08-22 Created: 2016-08-22 Last updated: 2018-06-07Bibliographically approved
Norqvist, M. (2016). On Mathematical Reasoning: being told or finding out. (Doctoral dissertation). Umeå: Umeå universitet
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. p. 55
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300
Keywords
mathematics education, creative reasoning, reasoning, cognitive proficiency, fMRI
National Category
Educational Sciences Mathematics Didactics Learning
Research subject
didactics of mathematics
Identifiers
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)
Opponent
Supervisors
Available from: 2016-08-25 Created: 2016-08-22 Last updated: 2018-06-07Bibliographically approved
Norqvist, M., Lithner, J., Jonsson, B. & Liljekvist, Y. (2015). Creative Reasoning More Beneficial For Cognitively Weaker Students. In: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education: . Paper presented at CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education, Feb 2015, Prague, Czech Republic (pp. 502-503). Prague: Charles University
Open this publication in new window or tab >>Creative Reasoning More Beneficial For Cognitively Weaker Students
2015 (English)In: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education, Prague: Charles University , 2015, p. 502-503Conference paper, Poster (with or without abstract) (Refereed)
Abstract [en]

In a study with 91 upper-secondary students the efficiency of two different types of mathematical practice tasks, procedural based algorithmic tasks and creative reasoning tasks, were studied. It was found that although the algorithmic group outperformed the creative group during practice the latter performed significantly better on a follow-up test. Closer inspection revealed that the difference in test performance was, contrary to common beliefs, driven by the cognitively weaker students.

Place, publisher, year, edition, pages
Prague: Charles University, 2015
Keywords
Mathematical reasoning, creative reasoning, cognitive proficiency
National Category
Didactics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-112211 (URN)000466853900072 ()978-80-7290-844-8 (ISBN)
Conference
CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education, Feb 2015, Prague, Czech Republic
Projects
Learning by imitative and creative reasoning
Available from: 2015-12-03 Created: 2015-12-03 Last updated: 2020-01-14Bibliographically approved
Karlsson Wirebring, L., Lithner, J., Jonsson, B., Liljekvist, Y., Norqvist, M. & Nyberg, L. (2015). Learning mathematics without a suggested solution method: durable effects on performance and brain activity. Trends in Neuroscience and Education, 4(1-2), 6-14
Open this publication in new window or tab >>Learning mathematics without a suggested solution method: durable effects on performance and brain activity
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2015 (English)In: Trends in Neuroscience and Education, ISSN 2211-9493, Vol. 4, no 1-2, p. 6-14Article 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
Keywords
Mathematics, Learning, fMRI, Parietal cortex, Angular gyrus, Education
National Category
Psychology (excluding Applied Psychology)
Identifiers
urn:nbn:se:umu:diva-109088 (URN)10.1016/j.tine.2015.03.002 (DOI)000363545300002 ()
Available from: 2015-09-17 Created: 2015-09-17 Last updated: 2018-06-07Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-7594-5602

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