Instrumental Genesis Stages of Programming for Mathematical Work
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Instrumental Genesis Stages of Programming for Mathematical Work Chantal Buteau 1 Kirstin Dreise 1
& Eric
Muller 1 & Joyce Mgombelo 2 & Ana Isabel Sacristán 3 &
# Springer Nature Switzerland AG 2020
Abstract In this article, we seek to understand how university students learn to use programming as an instrument for ‘authentic’ mathematical investigations. We use the instrumental approach as a framework, focusing on how the transformation of the programming language into an instrument requires that the user develops or mobilizes multiple schemes at different stages of the task development. Moreover, we propose to adapt Assude’s instrumental integration model for teachers and shift its focus to students to describe four instrumental stages of student development (i.e. instrumental genesis) of their schemes. These four stages are illustrated by examining two undergraduates’ engagement at different times during a first-year, programming-based, mathematics course. The proposed approach takes into account not only individual scheme development, but also the development of a complex web of schemes. It incorporates the concept of schemes in the different instrumental stages for students and also unfolds Brennan and Resnick’s three-dimensional computational thinking development framework (for mathematics) as students appropriate programming as an instrument. Keywords Programming . Mathematics . Investigation project . Instrumental genesis .
Instrumental integration . Scheme . Web of schemes . Authentic mathematical investigation There is a growing interest of programming as educational resources in general and in mathematics in particular. Benton et al. (2017) remind us that, back in the 1970s and 1980s (and until the 1990s), research interests focused on the potential for learning mathematics that programming could provide (e.g. Papert 1980). But later, and until the relatively recent re-emergence of interest for integrating coding in schools, Electronic supplementary material The online version of this article (https://doi.org/10.1007/s40751-02000060-w) contains supplementary material, which is available to authorized users.
* Chantal Buteau [email protected] Extended author information available on the last page of the article
Digital Experiences in Mathematics Education
programming environments in mathematics received relatively little attention in research and teaching (DeJarnette 2019). With the renewed interest, there have been new studies linking programming with mathematics, although mostly at the pre-university level. This points to the need for research on programming and mathematics at the university level. When aiming at analyzing the integration in mathematics learning with a digital technology such as programming, the instrumental approach (Rabardel 2002) provides a useful framework (Artigue 2002; Guin and Trouche 1999). It is helpful in gaining insight into how students appropriate a (technological) tool through instrumental genesis: the transformation of an artefact (e.g. mathematics software) into
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