High achieving students’ conceptions of limits

• 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.

Ämnesord

SOCIAL SCIENCES  -- Educational Sciences -- Didactics (hsv//eng)

SAMHÄLLSVETENSKAP  -- Utbildningsvetenskap -- Didaktik (hsv//swe)

SAMHÄLLSVETENSKAP  -- Utbildningsvetenskap (hsv//swe)

SOCIAL SCIENCES  -- Educational Sciences (hsv//eng)

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Subject didactics

Ämnesdidaktik

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