Record Details

An instrumental approach to modelling the derivative in Sketchpad

Pythagoras


 
 
Field Value
 
Title An instrumental approach to modelling the derivative in Sketchpad
 
Creator Ndlovu, Mdutshekelwa; University of Stellenbosch Wessels, Dirk; University of Stellenbosch de Villiers, Michael; University of KwaZulu-Natal
 
Subject Mathematics Education; Mathematics; Education Geometer’s Sketchpad; derivative; calculus; instrumental genesis
Description Encouragement to integrate information and communication technologies into mathematics education curricula is an increasingly universal phenomenon. As a contribution to the discourse, this article discusses the potential use in the classroom of The Geometer’s Sketchpad® (Key Curriculum Press, Emeryville, CA, United States) mathematics software in modelling the derivative and related concepts in introductory calculus. In an empirical study involving first-year non-mathematics major undergraduate science students, a hypothetical learning trajectory (HLT) was conjectured and implemented for students to experience the visualisation and multiple representations of calculus concepts on the Cartesian plane with a computer graphic interface. The utilisation scheme is interpreted through the lens of the instrumental1 approach proposed by Trouche. The HLT was partly informed by the historical development of the derivative as synthesised from the literature on the history of calculus and partly by the affordances, enablements, constraints and potentialities of Sketchpad itself. The findings of the study suggest that when exposed to the capabilities of this software, learners can experience Geometer’s Sketchpad® as an effective visualisation tool or instrument for the representation and learning of the derivative and related concepts in introductory calculus. However, the effectiveness of this tool is not a given or a foregone conclusion − it is a product of the teacher’s instrumental orchestration, gradual learner mastery of the software syntax and careful resolution of theoretical-computational conflicts that can arise during early use of the instrument.
 
Publisher AOSIS Publishing
 
Contributor
Date 2011-11-23
 
Type — Qualitative
Format text/html application/epub+zip text/xml application/pdf
Identifier 10.4102/pythagoras.v32i2.52
 
Source Pythagoras; Vol 32, No 2 (2011); 15 pages
 
Language en
 
Relation http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/754 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/755 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/756 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/757 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/758 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/759 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/760 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/761 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/762 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/763 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/764 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/765 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/767 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/768 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/769 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/770 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/771 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/773 http://www.pythagoras.org.za/index.php/pythagoras/article/download/52/774
 
Coverage — — undergraduate students
Rights Copyright information Ownership of copyright in terms of the Work remains with the authors.The authors retain the non-exclusive right to do anything they wish with the Work, provided attribution is given to the place and detail of original publication, as set out in the official citation of the Work published in the journal. The retained right specifically includes the right to post the Work on the authors’ or their institutions’ websites or institutional repository.Publication and user license The authors grant the title owner and the publisher an irrevocable license and first right and perpetual subsequent right to (a) publish, reproduce, distribute, display and store the Work in  any form/medium, (b) to translate the Work into other languages, create adaptations, summaries or extracts of the Work or other derivative works based on the Work and exercise all of the rights set forth in (a) above in such translations, adaptations, summaries, extracts and derivative works, (c) to license others to do any or all of the above, and (d) to register the Digital Object Identifier (DOI) for the Definitive Work.The authors acknowledge and accept the user licence under which the Work will  be published as set out in http://creativecommons.org/licenses/by/2.5/za/legalcode (Creative Commons Attribution License South Africa)The undersigned warrant that they have the authority to license these publication rights and that no portion of the copyright to the Work has been assigned or licensed previously to any other party.Disclaimer: The publisher, editors and title owner accept no responsibility for any statement made or opinion expressed by any other person in this Work. Consequently, they will not be liable for any loss or damage sustained by any reader as a result of his or her action upon any statement or opinion in this Work. In cases where a manuscript is NOT accepted for publication by the editorial board, the portions of this agreement regarding the publishing licensing shall be null and void and the authors will be free to submit this manuscript to any other publication for first publication.Our copyright policies are author-friendly and protect the rights of our authors and publishing partners.