Didactising: Continuing the work of Leen Streefland |
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| Authors: | Erna Yackel Michelle Stephan Chris Rasmussen Diana Underwood |
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| Institution: | (1) Department of Mathematics, Computer Science, and Statistics, Purdue University Calumet, Hammond, U.S.A |
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| Abstract: | In this paper we present three cases of instructional design that illustrates both horizontal didactising, the activity of
using already established principles to design instruction, and vertical didactising the activity of developing new tools
and principles for instructional design. The first case illustrates horizontal didactising by elaborating how the constructs
chains of signification and models were used to design an instructional sequence involving linear growth. The second and third
cases illustrate vertical didactising by developing argumentation analyses and generative listening, respectively, as instructional
design tools. In the second case, argumentation analyses emerge as a tool that other designers can use to anticipate the quality
of conversations that can occur as students engage in tasks prior to implementing the instructional sequence. The third case
develops the notion of generative listening as a conceptual tool within the context of designing differential equations instruction
to gain insights into what are, for students, experientially-real starting points that are mathematical in nature and to provide
inspirations for revisions to instructional sequences.
This revised version was published online in August 2006 with corrections to the Cover Date. |
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| Keywords: | argumentation chains of significantion differentieal equations generative listering horizontal didactising linear equations vertical didactising |
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