USinG dYnaMic GeoMetRY SoFtWaRe in MatHeMaticS teacHinG: Keith Jones offers a revised research bibliography updating that written for Micromath in 2002

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ynamic geometry software (dGS) provides an environment in which to create and then manipulate geometric constructions thereby providing learners with opportunities to interact with geometrical theorems and see the results. Well-known examples of dGS include Cabri, GeoGebra, Sketchpad, plus many others; a useful comparative review is provided by Mackrell (2011). in an earlier survey of research on the use of dGS in mathematics teaching (Jones, 2002), i identified three main threads in research up to that time. the first was the ways in which learners interact with the software, especially how they learn to use the capability of the software to drag objects, such as points, when constructing geometrical figures. an example of such research is Hölzl (1996) who provide insights into how students use the drag-mode in dGS. a second thread concerned the design of teaching activities so that learners come to understand geometrical ideas and concepts; laborde (2001) provides an example, which illustrates the time it can take to utilise the full potential of dGS, in the classroom. the third thread was the impact of using dGS on learning proof, especially whether the opportunities offered by dGS environments to ‘see’ mathematical properties on-screen might reduce, or even replace, any motivation for proof, or, on the contrary, whether dGS might open up new meaningful approaches to learning to prove. an example of research on these issues is provided by Jones (2000), showing how, over time, students’ mathematical explanations can evolve to ones that should help provide a foundation on which to build further notions of deductive reasoning. Since that earlier survey of research, dynamic geometry software has evolved; so much so that such software might now be called dynamic mathematics software, or perhaps mathematics visualisation software, as increasingly algebraic and other capabilities are being added. at the same time, research has both continued to delve into the issues identified above, while also expanding to cover newly surfacing matters. the aim of this revised research bibliography is to update the main themes and findings of research into the use of dGS in mathematics teaching and to illustrate newly emerging themes. other useful reviews are those by laborde et al (2006) and Hollebrands et al (2007).

the issue of how learners interact with the software, and learn to use the tools that are provided, continues to be the focus of research. examples of such studies include Hollebrands (2007), Maymon-erez and Yerushalmy (2007) and olivero and Robutti (2007). likewise, the impact of using dGS on learning to prove continues, an example being Baccaglini-Frank and Mariotti (2010). a newly emerging theme in the research is the use with learners of pre-constructed dGS files; see, for example, leung (2011), Sinclair (2003) and trgalová et al (2011). another theme, given the challenges faced by teachers when using dGS for the first time (erfjord, 2011), is how collaboration between teachers and education researchers can help teachers learn about using dGS from other teachers (lavicza et al, 2010). a third newlyemerging theme concerns new developments with the software, such as the facility to import digital pictures, and the development of software for 3-d geometry; examples include accascina and Rogora (2006), Jackiw and Sinclair (2009) and pierce and Stacey (2011). it continues to be the case that research on using dGS to teach transformation geometry is relatively limited, as is the use of dGS to teach ideas of loci. Research into the impact of linking the geometry capabilities of dGS with the increasingly incorporated algebraic capabilities is only just beginning. research Bibliography - publications i