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Lithner, Johan
Publications (10 of 48) Show all publications
diva2:1339947
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)
Funder
Marcus and Amalia Wallenberg Foundation, MAW 2014.0034
Available from: 2019-08-01 Created: 2019-08-01 Last updated: 2019-08-06Bibliographically 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
Jäder, J., Lithner, J. & Sidenvall, J. (2019). Mathematical problem solving in textbooks from twelve countries. International Journal of Mathematical Education in Science and Technology
Open this publication in new window or tab >>Mathematical problem solving in textbooks from twelve countries
2019 (English)In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211Article in journal (Refereed) Epub ahead of print
Abstract [en]

A selection of secondary school mathematics textbooks from twelve countries on five continents was analysed to better understand the support they might be in teaching and learning mathematical problem solving. Over 5700 tasks were compared to the information provided earlier in each textbook to determine whether each task could be solved by mimicking available templates or whether a solution had to be constructed without guidance from the textbook. There were similarities between the twelve textbooks in the sense that most tasks could be solved using a template as guidance. A significantly lower proportion of the tasks required a solution to be constructed. This was especially striking in the initial sets of tasks. Textbook descriptions indicating problem solving did not guarantee that a task solution had to be constructed without the support of an available template.

Place, publisher, year, edition, pages
TAYLOR & FRANCIS LTD, 2019
Keywords
Mathematics textbooks, mathematics tasks, mathematical problem solving, secondary school
National Category
Didactics
Identifiers
urn:nbn:se:umu:diva-164527 (URN)10.1080/0020739X.2019.1656826 (DOI)000484213400001 ()
Available from: 2019-11-15 Created: 2019-11-15 Last updated: 2019-11-15
diva2:1085723
Open this publication in new window or tab >>Assessing mathematical competencies: an analysis of Swedish national mathematics tests
2018 (English)In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 62, no 1, p. 109-124Article in journal (Refereed) Published
Abstract [en]

Internationally, education reform has been directed towards describing educational goals that go beyond topic and content descriptions. The idea of mathematical competencies describes such goals. National tests have been seen as one way of communicating these goals and influence teaching. The present study analyses Swedish national tests in mathematics, and seeks evidence about the extent to which they represent these competencies and may play a role in reforming teaching. The results show that the national tests assess all competencies. However, the study also shows a limited focus on the competencies’ interpretation and evaluation aspects. Thus, the tests do not fully capture the complex nature of the competencies. This may cloud the reform message and restrict the possibilities for the tests to function as levers for reform.

Keywords
assessment, Mathematical competency, national tests, reform
National Category
Educational Sciences
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-133055 (URN)10.1080/00313831.2016.1212256 (DOI)000417602100007 ()2-s2.0-84983339210 (Scopus ID)
Available from: 2017-03-30 Created: 2017-03-30 Last updated: 2018-06-09Bibliographically approved
Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM - the International Journal on Mathematics Education, 49(6), 937-949
Open this publication in new window or tab >>Principles for designing mathematical tasks that enhance imitative and creative reasoning
2017 (English)In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 49, no 6, p. 937-949Article in journal (Refereed) Published
Abstract [en]

The design research programme Learning by Imitative and Creative Reasoning (LICR) studies whether, how and why tasks and teaching that enhance creative reasoning lead to a more productive struggle and more efficient learning than the common but inefficient task designs based on imitating given solution procedures. The purpose of this paper is to synthesise the research outcomes determined to date by providing the following: a conceptual framework for key concepts and relationships among teaching, tasks, student activities and learning; a theoretical basis for analyses of causal effects between task/teaching design and learning outcomes; a design research methodology for transforming initial design ideas, through cycles of evaluation and revision, into firmer design principles; and an application of this theory and methodology to empirical studies carried out to date, in order to propose task-design principles related to imitative and creative reasoning.

Place, publisher, year, edition, pages
Springer, 2017
Keywords
Task design, Rote Learning, Problem solving, Creative reasoning
National Category
Other Mathematics Learning
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-135183 (URN)10.1007/s11858-017-0867-3 (DOI)000412893600010 ()
Projects
Att lära matematik genom imitativa och kreativa resonemang
Funder
Swedish Research CouncilThe Kempe Foundations
Available from: 2017-05-22 Created: 2017-05-22 Last updated: 2018-06-09Bibliographically approved
Jonsson, B., Kulaksiz, Y. C. & Lithner, J. (2016). Creative and algorithmic mathematical reasoning: effects of transfer-appropriate processing and effortful struggle. International journal of mathematical education in science and technology, 47(8), 1206-1225
Open this publication in new window or tab >>Creative and algorithmic mathematical reasoning: effects of transfer-appropriate processing and effortful struggle
2016 (English)In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 47, no 8, p. 1206-1225Article in journal (Refereed) Published
Abstract [en]

Two separate studies, Jonsson et al. (J. Math Behav. 2014;36: 20–32)and KarlssonWirebring et al. (Trends Neurosci Educ. 2015;4(1–2):6–14),showed that learning mathematics using creative mathematical reasoningand constructing their own solution methods can be moreefficient than if students use algorithmic reasoning and are giventhe solution procedures. It was argued that effortful struggle was thekey that explained this difference. It was also argued that the resultscould not be explained by the effects of transfer-appropriate processing,although this was not empirically investigated. This studyevaluated the hypotheses of transfer-appropriate processing andeffortful struggle in relation to the specific characteristics associatedwith algorithmic reasoning task and creativemathematical reasoningtask. In a between-subjects design, upper-secondary students werematched according to their working memory capacity.The main finding was that the superior performance associated withpracticing creative mathematical reasoning was mainly supportedby effortful struggle, however, there was also an effect of transferappropriateprocessing. It is argued that students need to strugglewith important mathematics that in turn facilitates the constructionof knowledge. It is further argued that the way we construct mathematicaltasks have consequences for how much effort students allocateto their task-solving attempt.

Keywords
Creative mathematical founded reasoning, algorithmic reasoning, effortful struggle, transfer-appropriate processing
National Category
Psychology (excluding Applied Psychology) Learning
Research subject
Psychology
Identifiers
urn:nbn:se:umu:diva-122308 (URN)10.1080/0020739X.2016.1192232 (DOI)000387791400004 ()
Available from: 2016-06-16 Created: 2016-06-16 Last updated: 2018-06-07Bibliographically approved
Bergqvist, T. & Lithner, J. (2016). Why is learning via creative reasoning effective?. In: Csíkos, C., Rausch, A., & Szitányi, J. (Ed.), Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education: . Paper presented at PME 40, The 40th Conference of the International Group for the Psychology of Mathematics Education, 3-7 August 2016, Szeged, Hungary. Szeged: PME
Open this publication in new window or tab >>Why is learning via creative reasoning effective?
2016 (English)In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education / [ed] Csíkos, C., Rausch, A., & Szitányi, J., Szeged: PME , 2016Conference paper, Oral presentation with published abstract (Refereed)
Place, publisher, year, edition, pages
Szeged: PME, 2016
Keywords
Mathematical reasoning, Creative reasoning, Algorithmic reasoning
National Category
Didactics Mathematics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-124740 (URN)
External cooperation:
Conference
PME 40, The 40th Conference of the International Group for the Psychology of Mathematics Education, 3-7 August 2016, Szeged, Hungary
Projects
Att lära matematik genom imitativa och kreativa resonemang
Available from: 2016-08-23 Created: 2016-08-23 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)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: 2018-06-07Bibliographically approved
Lithner, J. (2015). Learning mathematics by imitative and creative reasoning: plenary lecture. In: Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education: . Paper presented at Mathematics education: climbing mountains, building bridges (PME39), Hobart, Australia, July 13-18, 2015 (pp. 35-50). Hobart: UniPrint, University of Tasmania, 1
Open this publication in new window or tab >>Learning mathematics by imitative and creative reasoning: plenary lecture
2015 (English)In: Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education, Hobart: UniPrint, University of Tasmania , 2015, Vol. 1, p. 35-50Conference paper, Published paper (Refereed)
Abstract [en]

This paper presents an interdisciplinary research program carried out in collaboration between researchers from mathematics education, psychology and neuroscience. A large body of research has shown that imitative models of mathematics teaching and learning are both common and largely ineffective. The purpose of the program is to explore if and how teaching, including task design, based on students‘ creative task solution reasoning may be more effective. 

Place, publisher, year, edition, pages
Hobart: UniPrint, University of Tasmania, 2015
Series
PME proceedings, ISSN 0771-100X
Keywords
Mathematics education, problem solving, reasoning
National Category
Didactics
Identifiers
urn:nbn:se:umu:diva-111929 (URN)978-1-86295-829-6 (ISBN)
Conference
Mathematics education: climbing mountains, building bridges (PME39), Hobart, Australia, July 13-18, 2015
Available from: 2015-11-26 Created: 2015-11-26 Last updated: 2019-06-26Bibliographically approved
Lithner, J. (2015). Learning mathematics by imitative or creative reasoning. In: Sung Je Cho (Ed.), Selected regular lectures from the 12th international congress on mathematical education: (pp. 487-506). Springer
Open this publication in new window or tab >>Learning mathematics by imitative or creative reasoning
2015 (English)In: Selected regular lectures from the 12th international congress on mathematical education / [ed] Sung Je Cho, Springer, 2015, p. 487-506Chapter in book (Refereed)
Place, publisher, year, edition, pages
Springer, 2015
Keywords
learning difficulties, rote learning, creative reasoning, problem solving, reasoning, creativity
National Category
Educational Sciences
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-110888 (URN)9783319171869 (ISBN)
Available from: 2015-10-29 Created: 2015-10-29 Last updated: 2018-06-07Bibliographically approved
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