Digital Tools for Algebra Education: Criteria and Evaluation
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Digital Tools for Algebra Education: Criteria and Evaluation Christian Bokhove • Paul Drijvers
Published online: 30 April 2010 The Author(s) 2010. This article is published with open access at Springerlink.com
Abstract In the Netherlands, as in many other countries, the algebraic expertise of students graduating from secondary education is an issue. The use of digital tools for algebra education is expected to change epistemologies, activity structures and student achievement. Therefore, a study was set up to investigate in what way the use of ICT in upper secondary education might enhance the algebraic expertise of students. One of the first decisions to be made concerned the choice of appropriate digital tools. This paper describes the process of designing and using an instrument for evaluating digital tools. The conceptual framework guiding this process includes notions on symbol sense, instrumental genesis and formative assessment. The evaluation instrument is designed through a Delphi method and provides a blueprint of tool features that are relevant for the purpose of this study. The results show that such an evaluation instrument is valuable both for choosing appropriate digital tools and for making concrete the aims and expectations that researchers have on the issue of integrating technology in algebra education. The final instrument is presented and illustrated through examples implemented in different digital algebra tools. Keywords ICT tools Algebraic skills Evaluation instrument Tool use Assessment
1 Introduction Currently, algebra education is the subject of worldwide discussions. Different opinions on goals, approaches, and achievements are at the heart of ‘math war’ debates (Klein 2007; Schoenfeld 2004). Crucial in these debates is the relationship between procedural skills and conceptual understanding in the teaching and learning of algebra. On the one hand,
C. Bokhove (&) P. Drijvers Freudenthal Institute for Science and Mathematics Education, Utrecht University, Aı¨dadreef 12, 3561 GE Utrecht, The Netherlands e-mail: [email protected]
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computational skills are seen as a prerequisite for conceptual understanding (National Mathematics Advisory Panel 2007). Complaints from tertiary education focus on the lack of such procedural skills, and in several countries higher education makes a plea for entrance tests on basic algebraic skills (Engineering Council 2000). On the other hand, some see the core of algebra education to be the development of strategic problem-solving and reasoning skills, symbol sense and flexibility, rather than procedural fluency (National Mathematics Advisory Panel 2007). Future societal and professional needs lie in flexible analytical reasoning skills rather than in procedural skills, according to this point of view. As a consequence, algebra education should change its goals, focusing on new epistemologies and aiming at new types of understanding. This position is expressed in the Discussion Document of the 12th icmi study on
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