An instrumental approach to modelling the derivative in Sketchpad
Date
2011-11
Journal Title
Journal ISSN
Volume Title
Publisher
AOSIS Publishing
Abstract
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.
Description
Please cite as follows:
Ndlovu, M., Wessels, D., & De Villiers, M. 2011. An instrumental approach to modelling the derivative in Sketchpad. Pythagoras, 32(2):1-15 (Art. #52), doi:10.4102/pythagoras.v32i2.52.
The original publication is available at http://www.pythagoras.org.za
Ndlovu, M., Wessels, D., & De Villiers, M. 2011. An instrumental approach to modelling the derivative in Sketchpad. Pythagoras, 32(2):1-15 (Art. #52), doi:10.4102/pythagoras.v32i2.52.
The original publication is available at http://www.pythagoras.org.za
Keywords
Sketchpad, Mathematics -- Study and teaching
Citation
Ndlovu, M., Wessels, D., & De Villiers, M. 2011. An instrumental approach to modelling the derivative in Sketchpad. Pythagoras, 32(2):1-15 (Art. #52), doi:10.4102/pythagoras.v32i2.52.