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On Aspects of Mathematical Reasoning: Affect and Gender
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics. (Matematikdidaktik)
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis explores two aspects of mathematical reasoning: affect and gender. I started by looking at the reasoning of upper secondary students when solving tasks. This work revealed that when not guided by an interviewer, algorithmic reasoning, based on memorising algorithms which may or may not be appropriate for the task, was predominant in the students reasoning. Given this lack of mathematical grounding in students reasoning I looked in a second study at what grounds they had for different strategy choices and conclusions. This qualitative study suggested that beliefs about safety, expectation and motivation were important in the central decisions made during task solving.  But are reasoning and beliefs gendered? The third study explored upper secondary school teachers conceptions about gender and students mathematical reasoning. In this study I found that upper secondary school teachers attributed gender symbols including insecurity, use of standard methods and imitative reasoning to girls and symbols such as multiple strategies especially on the calculator, guessing and chance-taking were assigned to boys. In the fourth and final study I found that students, both male and female, shared their teachers view of rather traditional feminities and masculinities. Remarkably however, this result did not repeat itself when students were asked to reflect on their own behaviour: there were some discrepancies between the traits the students ascribed as gender different and the traits they ascribed to themselves. Taken together the thesis suggests that, contrary to conceptions, girls and boys share many of the same core beliefs about mathematics, but much work is still needed if we should create learning environments that provide better opportunities for students to develop beliefs that guide them towards well-grounded mathematical reasoning. 

Place, publisher, year, edition, pages
Umeå: Print & Media, Umeå University , 2009. , 39 p.
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 41
Keyword [en]
affect, beliefs, gender, mathematical reasoning, problem solving, upper secondary school
National Category
Other Mathematics
Research subject
didactics of mathematics
Identifiers
URN: urn:nbn:se:umu:diva-22437ISBN: 978-91-7264-791-6 (print)OAI: oai:DiVA.org:umu-22437DiVA: diva2:216376
Public defence
2009-06-01, MA 121, MIT-huset, Umeå universitet, Umeå, 13:15 (English)
Opponent
Supervisors
Available from: 2009-05-11 Created: 2009-05-08 Last updated: 2009-05-11Bibliographically approved
List of papers
1. Upper secondary students’ task reasoning
Open this publication in new window or tab >>Upper secondary students’ task reasoning
2008 (English)In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, Vol. 39, no 1Article in journal (Refereed) Published
Abstract [en]

Upper secondary students’ task solving reasoning was analysed, with a focus on grounds for different strategy choices and implementations. The results indicate that mathematically well-founded considerations were rare. The dominating reasoning types were algorithmic reasoning, where students tried to remember a suitable algorithm, sometimes in a random way, and guided reasoning, where progress was possible only when essentially all important strategy choices were made by the interviewer.

National Category
Didactics Mathematics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-6853 (URN)10.1080/00207390701464675 (DOI)
Available from: 2007-12-19 Created: 2007-12-19 Last updated: 2011-03-16Bibliographically approved
2. A reason to believe: beliefs as an influence on students task solving
Open this publication in new window or tab >>A reason to believe: beliefs as an influence on students task solving
2008 (English)Report (Other academic)
Abstract [en]

Upper secondary students’ task solving reasoning was analysed, with a focus on what grounds they had for different strategy choices and conclusions. Beliefs were identified and connected with the reasoning that took place. The results indicate that beliefs have an impact on the central decisions made during task solving. Three themes stand out: safety, expectation and motivation.

Place, publisher, year, edition, pages
Umeå: Department of Mathematics and Mathematical Statistics, Umeå University, 2008. 45 p.
Series
Research report in mathematics education, ISSN 1401-6796 ; 2
National Category
Other Mathematics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-22424 (URN)
Available from: 2009-05-08 Created: 2009-05-08 Last updated: 2009-05-08Bibliographically approved
3. Teachers' conceptions about students' mathematical reasoning: Gendered or not?
Open this publication in new window or tab >>Teachers' conceptions about students' mathematical reasoning: Gendered or not?
2009 (English)Report (Other academic)
Abstract [en]

This study looks at how upper secondary school teachers gender stereotype aspects of students' mathematical reasoning. Girls were attributed gender symbols including insecurity, use of standard methods and imitative reasoning. Boys were assigned the symbols such as multiple strategies especially on the calculator, guessing and chance-taking. 

Place, publisher, year, edition, pages
Umeå: Department of Mathematics and Mathematical Statistics, Umeå University, 2009. 30 p.
Series
Research report in mathematics education, ISSN 1401-6796 ; 2
Keyword
teachers' conceptions, gender, mathematical reasoning, upper secondary school
National Category
Other Mathematics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-22425 (URN)
Available from: 2009-05-08 Created: 2009-05-08 Last updated: 2012-08-14Bibliographically approved
4. Upper secondary school students' gendered conceptions about mathematics
Open this publication in new window or tab >>Upper secondary school students' gendered conceptions about mathematics
2009 (English)Report (Other academic)
Abstract [en]

This study explores Swedish Natural Science students' conceptions about gender and mathematics. I conducted and compared the results from two questionnaires. The first questionnaire revealed a view of rather traditional feminities and masulinities, a result that did not repeat itself in the second questionnaire. There was a discrepancy between the traits the students ascribed as gender different and the traits they ascribed to themselves.

Place, publisher, year, edition, pages
Umeå: Department of Mathematics and Mathematical Statistics, Umeå University, 2009. 25 p.
Series
Research report in mathematics education, ISSN 1401-6796 ; 3
Keyword
gender, students' conceptions, upper secondary school
National Category
Other Mathematics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-22426 (URN)
Available from: 2009-05-08 Created: 2009-05-08 Last updated: 2012-08-14Bibliographically approved

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