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Investigating the Potential of Computer Environments for the Teaching and Learning of Functions: A Double Analysis from Two Research Traditions

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Abstract

The general goal of this paper is to explore the potential of computer environments for the teaching and learning of functions. To address this, different theoretical frameworks and corresponding research traditions are available. In this study, we aim to network different frameworks by following a ‘double analysis’ method to analyse two empirical studies based on the use of computational environments offering integrated geometrical and algebraic representations. The studies took place in different national and didactic contexts and constitute cases of Constructionism and Theory of Didactical Situations. The analysis indicates that ‘double analysis’ resulted in a deepened and more balanced understanding about knowledge emerging from empirical studies as regards the nature of learning situations for functions with computers and the process of conceptualisation of functions by students. Main issues around the potential of computer environments for the teaching and learning of functions concern the use of integrated representations of functions linking geometry and algebra, the need to address epistemological and cognitive aspects of the constructed knowledge and the critical role of teachers in the design and evolution of students’ activity. We also reflect on how the networking of theories influences theoretical advancement and the followed research approaches.

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Notes

  1. “ReMath” (Representing Mathematics with Digital Media), 6th Framework Programme, Information Society Technologies, IST-4-26751-STP, 2005–2009 (http://remath.cti.gr).

  2. Actually, \(x_{M}\) was the label of the button allowing choosing a variable, which explains why the students mention this label, while being aware of \(y_{M}\) being the right choice. This label, very confusing, has been changed in further versions of Casyopée. The design decision at the time of this experiment was to implement key actions at Casyopée’s interface by way of buttons like in Dynamic Geometry. The difficulty was to find icons that could accurately represent the nature of the action.

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Authors and Affiliations

  1. University of Reims and LDAR University Paris Diderot, Rue Chevaleret, 75013, Paris, France

    Jean-Baptiste Lagrange

  2. Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, 157 84, Athens, Greece

    Giorgos Psycharis

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  1. Jean-Baptiste Lagrange
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  2. Giorgos Psycharis
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Lagrange, JB., Psycharis, G. Investigating the Potential of Computer Environments for the Teaching and Learning of Functions: A Double Analysis from Two Research Traditions. Tech Know Learn 19, 255–286 (2014). https://doi.org/10.1007/s10758-013-9211-3

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