Microworlds: Influencing Children's Approaches to Linear Equations

Microworlds: Influencing Children's Approaches to Linear Equations

Stuart Cork (University of Cambridge, UK)
DOI: 10.4018/978-1-4666-8714-1.ch012
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This chapter combines the well-researched area of mathematics education, linear equations, with the field of mathematical microworlds. Insights into the current knowledge of both areas are presented before focusing the discussion on a new study in which pre-secondary school learners, with no prior formal teaching on the topic, explore linear equations through an algebra-based microworld called DragonBox. DragonBox is a touch-enabled mobile application available on all major platforms and to which the author has no affiliation. Touch-enabled mobile devices have great potential as vessels for mathematical microworlds and this chapter draws conclusions regarding the influence such microworlds have on a learner's understanding. Although learners in this study demonstrated procedural fluency when working with DragonBox, it was only through encouraged reflection that a relational understanding seemed to take effect and without it the children developed inconsistent notions about the structure of the microworld.
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This chapter is based upon a research project I conducted in 2013. My aim for the project was initially to understand how iPads could be employed successfully in mathematics education and the learning opportunities they might afford in a ubiquitous classroom. This was an ambitious task, particularly given that much of the research in this area was a year or more away from publication. A chance encounter during a teacher conference changed and focused my direction; the compere mentioned DragonBox as an app in which I might be interested. I downloaded the app during the break and found myself, in the final talk, exploring the levels of DragonBox rather than paying full attention. This final talk was incidentally led by professors Celia Hoyles and Richard Noss who would later be known to me as key researchers in my field of study.

I am thankful I played DragonBox that day in 2013. Through immersing myself in the surrounding literature I came to learn about Seymour Papert, whose constructionist perspective on learning led to the conceptualisation of the microworld. Up until this point, much of the technology I had experienced as a mathematics teacher replicates traditional teaching. Expositional elements have become video tutorials; drill and practice has moved from the textbook to online quizzes. Although these technologies may provide self-paced learning and instant feedback, perhaps they are just a more efficient version of antiquated pedagogy. In comparison, Papert’s ideas, which led to his creation of LOGO in the 1960s, represent something that I feel is exciting and innovative in the area of learning technology. Yet microworlds still remain a relatively niche area of research. This is perhaps due to barriers, such as funding and the skill-set required to create a rich microworld. Now that many schools are beginning to incorporate 1:1 computing schemes, whether hand-held mobile devices or otherwise, with so much technological power in the hand of the learner it seems to me that we have the potential to incorporate mathematical microworlds into contemporary mathematics education. This is, of course, easier said than done and, as with any pedagogical change, there must be some associated caution. My own journey suggests that a teacher figure is a key element in the learning afforded by a microworld. A teacher who encourages a learner to reflect may facilitate a deeper understanding of the mathematical domain embodied by the microworld. Without encouraged reflection, inconsistent notions may be constructed by the learner, which can be left unresolved. Microworlds then, are not ‘teacher-proof’, as is often seemingly desirable with contemporary mathematics educational technology (Perrotta & Evanst, 2013).

In the first section of this chapter, I give an overview of the literature relating to linear equations and microworlds. This literature review facilitates an analytical framework that is later applied to two case studies of young learners working with DragonBox. Through discussion and analysis of the evidence, recommendations and conclusions about future design and incorporation of microworlds in mathematics education are tentatively drawn.

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