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GeoGebra, Enhancing Creative Matematical Reasoning
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.ORCID iD: 0000-0002-8152-1638
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [sv]

Det övergripande syftet med avhandlingen har varit att nå insikter i hur man kan designa en didaktisk situation inklusive en dynamisk programvara (GeoGebra) för att stödja elevernas lärande genom matematisk problemlösning och kreativt resonemang. En bärande idé har varit att elever som själva konstruerar lösningsmetoder till problembaserade uppgifter lär sig matematik bättre än elever som får en metod att följa. Resultaten visar att GeoGebra är ett stöd vid konstruerandet av lösningsmetoder och att elever då också resonerar kreativt. Det vill säga, de skapar en för dem en ny resonemangssekvens som innehåller en lösningsmetod som stöds av argument förankrade i matematik. Idén med att elever på egen hand konstruerar lösningen på uppgifter har även belysts genom att jämföra med elever som löser uppgifter där de får vägledning till lösningsmetoden. Resultaten visar att elever som får en lösningsmetod inte resonerar kreativt, de utnyttjar inte GeoGebras potential att stödja ett undersökande arbetssätt, och de lär sig mindre av den matematik som ingår i uppgifterna. Denna avhandling består av 4 artiklar och en kappa. De fyra artiklarna är:

I. Granberg, C., & Olsson, J. (2015). ICT-supported problem solving and collaborative creative reasoning: Exploring linear functions using dynamic mathematics software. The Journal of Mathematical Behavior, 37, 48-62.

II. Olsson, J. (2017). The Contribution of Reasoning to the Utilization of Feedback from Software When Solving Mathematical Problems. International Journal of Science and Mathematics Education, 1-21.

III. Olsson, J. Relations between task design and students’ utilization of GeoGebra. Mathematical Thinking and Learning. (Under review)

IV. Olsson, J., & Granberg, C. Dynamic software, problem solving with or without guidelines, and learning outcome. Technology, Knowledge and Learning. (Under review)

Artikel 2 och 3 är jag ensam författare till. Det innebär att jag designat studien, planerat och genomfört datainsamling, analyserat data och formulerat slutsatser, samt skrivit texten och korresponderat med tidskrifter. Artikel 1 och 4 har jag skrivit i samarbete med Carina Granberg. Vi bedömer att arbetet med artikel 1 fördelats lika. Allt skrivarbete har fortgått genom åtskilliga granskningar av varandras utkast och diskussioner om slutgiltiga formuleringar. I arbetet med artikel 4 har jag haft huvudansvaret för designen av studien och planering för datainsamlingen. Skrivarbetet har genomförts på samma sätt som i arbetet med artikel 1.

Place, publisher, year, edition, pages
Umeå: Umeå Universitet , 2017.
National Category
Pedagogical Work
Identifiers
URN: urn:nbn:se:mdh:diva-40990ISBN: 978-91-7601-697-8 (print)OAI: oai:DiVA.org:mdh-40990DiVA, id: diva2:1250252
Public defence
(Swedish)
Opponent
Supervisors
Available from: 2018-09-24 Created: 2018-09-22 Last updated: 2018-09-24Bibliographically approved
List of papers
1. ICT-supported problem solving and collaborative creative reasoning: Exploring linear functions using dynamic mathematics software
Open this publication in new window or tab >>ICT-supported problem solving and collaborative creative reasoning: Exploring linear functions using dynamic mathematics software
2015 (English)In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, ISSN 0732-3123, Vol. 37, p. 48-62Article in journal (Refereed) Published
Abstract [en]

The present study investigates how a dynamic software program, GeoGebra, may support students' collaboration and creative reasoning during mathematical problem solving. Thirty-six students between the ages of 16 and 17 worked in pairs to solve a linear function using GeoGebra. Data in the form of recorded conversations, and computer activities were analyzed using Lithner's (2008) framework of imitative and creative reasoning in conjunction with the collaborative model of joint problem space (Roschelle & Teasley, 1994). The results indicated that GeoGebra supported collaboration and creative reasoning by providing students with a shared working space and feedback that became the subject for students' creative reasoning. Furthermore, the students' collaborative activities aimed toward sharing their reasoning with one another enhanced their creative reasoning. There were also examples of students using GeoGebra for trial-and-error strategies and students engaging in superficial argumentation.

National Category
Didactics
Identifiers
urn:nbn:se:mdh:diva-40988 (URN)10.1016/j.jmathb.2014.11.001 (DOI)
Available from: 2018-09-22 Created: 2018-09-22 Last updated: 2018-10-01Bibliographically approved
2. The Contribution of Reasoning to the Utilization of Feedback from Software When Solving Mathematical Problems
Open this publication in new window or tab >>The Contribution of Reasoning to the Utilization of Feedback from Software When Solving Mathematical Problems
2018 (English)In: International Journal of Science and Mathematics Education, ISSN 1571-0068, E-ISSN 1573-1774, Vol. 16, no 4, p. 715-735Article in journal (Refereed) Published
Abstract [en]

This study investigates how students’ reasoning contributes to their utilization of computer-generated feedback. Sixteen 16-year-old students solved a linear function task designed to present a challenge to them using dynamic software, GeoGebra, for assistance. The data were analysed with respect both to character of reasoning and to the use of feedback generated through activities in GeoGebra. The results showed that students who successfully solved the task were engaged in creative reasoning and used feedback extensively.

National Category
Didactics
Identifiers
urn:nbn:se:mdh:diva-40987 (URN)10.1007/s10763-016-9795-x (DOI)000427491000007 ()2-s2.0-85009935536 (Scopus ID)
Available from: 2018-09-22 Created: 2018-09-22 Last updated: 2018-09-24Bibliographically approved
3. Dynamic Software, Task Solving With or Without Guidelines, and Learning Outcomes
Open this publication in new window or tab >>Dynamic Software, Task Solving With or Without Guidelines, and Learning Outcomes
(English)In: Technology, Knowledge and Learning, ISSN 2211-1662, E-ISSN 2211-1670, ISSN 2211-1662Article in journal (Refereed) Epub ahead of print
Abstract [en]

The present study contributes to knowledge about how to design tasks that benefit from dynamic software in math education, comparing practice performance and learning outcomes among 129 students practicing on two different task designs using GeoGebra. The task designs differed with respect to the presence or absence of guidelines on how to solve the task. One student group practiced on the guided task while the other student group practiced on the unguided task, and 1 week later a posttest was conducted. Data were statistically analyzed and showed significant differences with regard to success during practice for students solving the guided task. Among the students who succeeded in solving the task (guided or unguided) during practice, however, the analysis showed significant differences in the posttest performance in favor of the unguided students.

National Category
Didactics
Identifiers
urn:nbn:se:mdh:diva-40986 (URN)10.1007/s10758-018-9352-5 (DOI)
Available from: 2018-09-22 Created: 2018-09-22 Last updated: 2018-10-01Bibliographically approved

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http://umu.diva-portal.org/smash/get/diva2:1085687/FULLTEXT01.pdf

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