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To explore and verify in mathematics
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Teacher Education, Department of Interactive Media and Learning. (Matematikdidaktik)
2001 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

This dissertation consists of four articles and a summary. The main focus of the studies is students' explorations in upper secondary school mathematics.

In the first study the central research question was to find out if the students could learn something difficult by using the graphing calculator. The students were working with questions connected to factorisation of quadratic polynomials, and the factor theorem. The results indicate that the students got a better understanding for the factor theorem, and for the connection between graphical and algebraical representations.

The second study focused on a the last part of an investigation, the verification of an idea or a conjecture. Students were given three conjectures and asked to decide if they were true or false, and also to explain why the conjectures were true or false. In this study I found that the students wanted to use rather abstract mathematics in order to verify the conjectures.

Since the results from the second study disagreed with other research in similar situations, I wanted to see what Swedish teachers had to say of the students' ways to verify the conjectures.

The third study is an interview study where some teachers were asked what expectations they had on students who were supposed to verify the three conjectures from the second study. The teachers were also confronted with examples from my second study, and asked to comment on how the students performed. The results indicate that teachers tend to underestimate students' mathematical reasoning.

A central focus to all my three studies is explorations in mathematics. My fourth study, a revised version of a pilot study performed 1998, concerns exactly that: how students in upper secondary school explore a mathematical concept. The results indicate that the students are able to perform explorations in mathematics, and that the graphing calculator has a potential as a pedagogical aid, it can be a support for the students' mathematical reasoning.

Place, publisher, year, edition, pages
Umeå: Institutionen för matematik och matematisk statistik, Umeå universitet , 2001. , 159 p.
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 21
Keyword [en]
Explorations, mathematical reasoning, empirical investigations, graphing calculators, conjectures.
National Category
Didactics Mathematics
Research subject
didactics of mathematics
URN: urn:nbn:se:umu:diva-9345ISBN: 91-7305-116-0OAI: diva2:149016
Public defence
2001-11-01, MIT-huset, Ma 121, Umeå universitet, Umeå, 10:15 (Swedish)
Available from: 2008-03-25 Created: 2008-03-25 Last updated: 2011-03-01Bibliographically approved

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Bergqvist, Tomas
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