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- Lingefjärd, Thomas, 1952, et al.
(author)
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Teaching concepts of calculus
- 2017
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In: At Right Angles. ; 6:3, s. 76-80
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Journal article (other academic/artistic)abstract
- The topic of calculus is an integral part of the senior secondary mathematics curriculum. The concepts of limits and derivatives, which form the foundation of Calculus, are often hard to teach. In this article, we suggest a dynamic way of teaching the concept of the derivative through practical examples which may be easily explored through GeoGebra applets available through the Internet.
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- Lingefjärd, Thomas, 1952, et al.
(author)
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The Elusive Slope
- 2018
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In: International Journal of Science and Mathematics Education. - : Springer Science and Business Media LLC. - 1571-0068 .- 1573-1774. ; 16:6, s. 1187-1206
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Journal article (peer-reviewed)abstract
- In understanding upper secondary school students’ interpretations of information in graphical representations of a distance–time graph and an ECG graph, little attention has been paid to the analysis of the condition of the conceptual development related to their utterances. Understanding this better can help improve the teaching of interpretations of information in graphical representations of different situations. This paper integrates results from 2 studies and 3 theoretical perspectives: Tall and Vinner’s theoretical perspectives on learning, Chi’s ontological perspectives on conceptual development and Friel’s theoretical perspectives on interpretation of graphical information. The findings provide evidence to support the conjecture that iconic interpretations could be stimulated and generated as a result of student categorisation of a distance–time graph as an event, when in fact the graph is being used to describe and communicate a process. The outcome further indicates that students found a resemblance between the ECG diagram and the periodic function of f(x) = sin(x).
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| 4. |
- Lingefjärd, Thomas, 1952, et al.
(author)
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The Symbolic world of mathematics
- 2017
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In: Journal of Research in Mathematics Education. - : Hipatia Press. - 2014-3621. ; 6:2, s. 118-135
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Journal article (peer-reviewed)abstract
- In understanding upper secondary school students’ interpretations of information in symbolic representations of a distance-time-relation, little attention has been paid to the analysis of the condition of the conceptual development related to utterances. Understanding this better can help improve the teaching of attribute and information in symbolic representations of different phenomena. Two theoretical perspectives have been used to conduct the analysis: Tall and Vinner's theoretical perspectives on learning and Gray’s & Tall’s theory of three mathematical worlds together with Hähkiöniemi’s interpretation of these three worlds. The findings provide evidence that a detailed analyse of student’s utterances show difference in quality related to student’s interpretations of a distance-time relation. The qualities were related to student’s concept images of functions and derivatives.
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