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- Juter, Kristina, 1971-
(författare)
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Development of students' concept images in analysis
- 2009
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Ingår i: Nordisk matematikkdidaktikk. - Göteborg : NCM, Göteborgs universitet. - 1104-2176. ; 1:4, s. 65-87
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Tidskriftsartikel (refereegranskat)abstract
- Students’ pre-knowledge and conceptual development in analysis were investigated at a teacher education program to reveal what pre-knowledge endured and how the students perceived the concepts a year after the course had ended. Questionnaires and interviews were used to collect data. Two students’ results are presented in more detail in the article. The study was cognitively framed with the influence of situated theories to take as many aspects of concept development into account as possible. The students showed numerous connections between concepts, but they were often unable to discern valid links from invalid links. The perceived richness from many connections causes unjustifiably strong self-confidence which prevents further work with the concept. A tool for classification of the students’ connections between concepts resulted from the analysis.
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| 2. |
- Juter, Kristina, 1971-
(författare)
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High achieving students’ conceptions of limits
- 2006
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Ingår i: Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (30th, Prague, Czech Republic, July 16-21, 2006). Volume 1. - Prague : Charles university. ; , s. 1:265-
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Konferensbidrag (refereegranskat)abstract
- Students learning limits of functions perceive and treat limits differently. A study on students’ conceptual development of limits of functions was conducted at a Swedish university (Juter, 2006). The results imply differences in high achieving and low achieving students’ work with limits, but also a lack of differences at some points. The students’ developments and abilities were studied in terms of concept images (Tall & Vinner, 1981) in the sense that their actions, such as problem solving and reasoning, were considered traces of their mental representations of concepts. A concept image of a concept comprises all mental representations of that concept and is linked to related concepts in a web. As could be expected, high achieving students’ abstraction abilities were more developed than other students’. The former group were to a much higher degree than the latter able to link theory to problem solving and explain the meaning of, for example, the limit definition. The students were studied during a semester and there were similarities of the high achieving students’ developments with the historical development of limits that the other students did not reveal. Several similarities were linked to abstraction and formality. Students with positive attitudes to mathematics in general were better limit problem solvers. Most of the high achieving students thought that they had control over the concept of limits, but many of the low achieving students also claimed to have control even if that was not the case. An unjustifiably strong self confidence can prevent students from further work on erroneous or incomplete parts of their concept images. There were no clear patterns of students’ mental representations of limits as exact values or approximations, limits as objects or processes, and limits as attainable or unattainable for functions. Of the 15 students interviewed, only two showed a coherent trace of their concept images. Both students were high achievers. The lack of patterns in all students’ concept images, particularly in the high achievers’, points to the complex nature of limits and the challenge to teach and learn limits.
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| 3. |
- Juter, Kristina, 1971-
(författare)
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Learning analysis : students' starting point
- 2009
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Ingår i: Nordic research in mathematics education. - Rotterdam : Sense. - 9789087907815 ; , s. 127-134
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Konferensbidrag (populärvet., debatt m.m.)abstract
- Most concepts taught in a basic analysis course at university are somewhat familiar to the students. They use their representations from prior experiences to form new knowledge about the concepts. Fifteen students’ were examined at the beginning of a basic university course in analysis. Their pre-knowledge was sometimes vague and even wrong, often due to intuitive perceptions
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| 4. |
- Juter, Kristina, 1971-
(författare)
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Learning analysis: Students’ starting point.
- 2009. - 1
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Ingår i: <em>Nordic Research in Mathematics Education </em>. - Rotterdam, the Netherlands : Sense Publishers. ; , s. 127-134
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 7. |
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| 8. |
- Juter, Kristina, 1971-
(författare)
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Limits of functions : students solving tasks
- 2006
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Ingår i: Australian senior mathematics journal. - 0819-4564. ; 20:1, s. 15-31
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Tidskriftsartikel (refereegranskat)abstract
- This study was conducted to reveal how students at university level justify their solutions to tasks with various degrees of difficulty. The study is part of a larger study of students' concept formation of limits. The mathematical area is limits of functions. The study was carried out at a Swedish university at the first level of mathematics. The results are, however, applicable to other countries as well since students meet similar challenges in their learning of limits. I have, in discussions with some Australian mathematics teachers at university level, found out that the topics taught in basic mathematics courses in Australia are similar to Swedish courses. Two groups of students taking the same course in successive semesters have been solving tasks. Their solutions are categorised here and analysed to create a picture of how students reason about limits.
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| 9. |
- Juter, Kristina, 1971-
(författare)
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Limits of functions : traces of students' concept images
- 2005
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Ingår i: Nordisk matematikkdidaktikk. - 1104-2176. ; 10:3-4, s. 65-82
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Tidskriftsartikel (refereegranskat)abstract
- Students at a Swedish university were subjects in a study about learning limits of functions. The students' perceptions were investigated in terms of traces of concept images through interviews and problem solving. The results imply that most students' foundations were not sufficiently strong for them to understand the concept of limit well enough to be able to form coherent concept images. The traces of the students' concept images reveal confusion about different features of the limit concept.
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