Magnus Österholm

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Title:Learning mathematics by reading - a study of students interacting with a text
Type:Research report, number 03-29 in report series from the Department of Mathematics, Linköping University
Also for the conference PICME-10, Nordic Preconference to ICME 10, Växjö, Sweden, 9-11 May, 2003
Fulltext: pdf-document (116 kB)
Other: Information from Libris (Swedish university libraries)

This study investigates the situation when students on their own read a new mathematical text, and solve problems relevant to the text. The students, who volunteered to take part in this study, worked together in pairs on a given text with a video camera recording their activity. The text given to the students was an excerpt from a text used in an introductory course at the university level, about the absolute value of real numbers. First, the students were instructed to read and discuss the text without any given tasks. Thereafter, the students were given exercises relevant to the text, and they were allowed to keep the text and use it when working with these exercises. Two pairs of students participated, all of them from the same mathematics class, and at this time they were in their last year on the natural science programme at the Swedish upper secondary school, and they had all high grades from all previous mathematics courses (A, B and C).

In many aspects the two pairs of students acted quite differently. Although the students in the first pair were aware of parts of the text they did not seem to understand, they did not try to make sense of it with the help of a discussion. The students in the second pair did discuss all parts of the text, but sometimes they were satisfied with asking each other whether they had understood a certain part of the text without dealing with how they had understood this part. The first pair often focused on small parts or fragments of the text, without considering its role in a larger context. This includes cases when focusing on and analyzing a fragment of a statement, without considering the whole statement. The second pair often ignored details in the text, and instead focused on the meaning of the text.

In the text, both pairs focused on the worked example, both in their free discussions about the text and also when solving the tasks. But the example, and the text in general, was used in very different ways by the two pairs, where the first pair tried to find clues in the text on how to deal with the exercises, a search that was carried out in a non-systematical way, while the second pair used the text mainly to check that their ways of solving the tasks agreed with what was said in the text.

The observations in this study show that the two pairs seem to have fundamentally different goals with their activities, where the first pair focused on details in the text and on doing something with the text without any thorough reflections on their activities, while the second pair tried to reach an understanding of the content of the text and of the solutions of the tasks.

From the study some issues arise that would be interesting to examine in more detail. It is unclear why the students in the first pair do not discuss parts of the text that are not fully understood. Is it because they focus on problem solving, and not (necessarily) on understanding all of the text, or could it be caused by some properties of the text itself? What relationship exists between more general aspects of mathematics and the more specific about reading mathematical texts, and how could you ‘isolate’ the interesting aspects of the specific about the situation when reading mathematical texts?

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Magnus Österholm
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Umeå University
Umeå School of Education
Faculty of Science and

Department of Science
and Mathematics Education

Umeå Mathematics
Education Research Centre

Mid Sweden University
Faculty of Science,
Technology and Media

Department of Engineering,
Mathematics and Science

Monash University
Faculty of Education

Linköping University
The Institute of Technology
Department of Mathematics


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