Review of the use of technology in Mathematics education Prepared for the School Curriculum and Standards Authority, Western Australia Barry Kissane | Andrew McConney | Kai Fai Ho School of Education Murdoch University Perth, Western Australia December 2015 Please cite this document as: Kissane, B., McConney, A., & Ho, K.F. (2015, December). Review of the use of technology in Mathematics education and the related use of CAS calculators in external examinations and in post school tertiary education settings. Perth, WA: School Curriculum and Standards Authority. ISBN 978 0 7307 2843 6 © School Curriculum and Standards Authority, 2015 This document—apart from any third party copyright material contained in it—may be freely copied, or communicated on an intranet, for non-commercial purposes in the educational institutions, provided that the School Curriculum and Standards Authority is acknowledged as the copyright owner, and that the Authority’s moral rights are not infringed. 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School Curriculum and Standards Authority 303 Sevenoaks Street CANNINGTON WA 6107 For further information please contact: Telephone: +61 8 9273 6300 Email: [email protected] Web: www.scsa.wa.edu.au Review of the use of technology in Mathematics education and the related use of CAS calculators in external examinations and in post school tertiary education settings Executive Summary This research is intended to inform the Mathematics Course Advisory Committee (CAC) of the Western Australian School Curriculum and Standards Authority (SCSA) about appropriate and effective use of digital technologies in Mathematics courses for upper secondary school students and in examinations that contribute to students’ Australian Tertiary Admissions Rank (ATAR). Various sources of information were used to produce an integrated report, drawing on the results from literature review and interviews/discussions with officials and Mathematics education personnel, locally, nationally and internationally, analysis of relevant technologies and surveys of local senior secondary school Mathematics teachers and some Year 12 students. It was agreed that the project would deliver to SCSA: A summary of key research related to the use of technology for secondary school Mathematics, particularly related to the use of computer algebra system (CAS) and graphics calculators, and highlighting the role of teachers; Results of survey research, canvassing opinions and attitudes of teachers and students regarding the use of technology in senior secondary school Mathematics courses; Information gathered from other educational jurisdictions nationally and internationally and universities with respect to the use of technology in examinations; Description and analysis of the latest technologies for school Mathematics and how best to integrate these into teaching, learning and assessment; Comment on the professional developmental needs of Mathematics teachers to enhance their own and their students’ personal confidence and competence in the use of technologies; and Advice regarding the use of technology in Mathematics secondary courses and exams. CAS calculators are described as an extension of graphics calculators, which are in turn an extension of scientific calculators. These technologies have been developed specifically for school mathematics education. Scientific calculators have been used in WA Mathematics courses and external examinations for around 40 years, graphics calculators for around 20 years and CAS calculators for about 8 years. Research has clearly indicated the pivotal role of teachers in the successful integration of technology into the school Mathematics curriculum. While teachers need support to develop the necessary technological and pedagogical content knowledge that is uniquely associated with the effective use of technology, adequate support has frequently not been provided, so that unrealistic expectations have been made of teachers. Empirical research summaries have consistently suggested that the use of graphics calculators and CAS calculators by secondary school students can result in improvements in conceptual i understanding in mathematics, although the improvements are modest and depend on the extent to which teachers and students make effective classroom use of them. Definitive large- scale studies on the effectiveness of sound use of CAS in secondary schools are not yet available. In practice, CAS calculators have often been used to replace traditional procedures more than they have been used to enhance students’ conceptual understanding. Consistently, research has demonstrated that students do not suffer a decline in by-hand mathematical skills as a result of using technologies of these kinds. Research and careful analysis have highlighted some of the challenges of effective use of CAS in particular, requiring careful consideration of the nature of algebra and calculus especially in both CAS and non-CAS environments, and developing suitable expertise by both students and teachers to integrate the tools appropriately. Since it has become a common practice for students to be assessed both with and without access to technology when CAS is used, the use of CAS has been recognised as creating special difficulties for the assessment of student learning, especially in timed examinations. In order to provide opportunities to assess discretionary use of technology, test items for which CAS is not helpful are necessary; similarly, to assess effective technological and mathematical competence, test items for which CAS is helpful are also necessary. Finding a suitable balance in practice is recognised by researchers as challenging. There is a range of practices and no clear professional consensus regarding the use of technologies in senior secondary school mathematics internationally. CAS calculator use is prominent in some European countries and in the USA; graphics calculator use has been common in OECD countries for some years and is integrated into International Baccalaureate courses; some countries, notably some Asian countries, do not permit any use of calculators in high-stakes examinations. There are some developments to use laptop computers as school mathematics tools, to supplement or replace calculator use; these typically provide students with access to computer algebra capabilities at least as powerful as those on CAS calculators. There is similarly a range of practices within Australia regarding the use of technology for Mathematics. School practices are regarded as closely aligned to examination rules in each state. Some states permit the use of CAS calculators, others expect students to use graphics calculators and one state (NSW) permits students to use only scientific calculators. One state (Victoria) has a small pilot program for a computer-based alternative to calculators, using sophisticated software, including computer algebra. There are also variations among states and internationally on the use of a separate technology-free examination component, on the opportunity for students to take some personal notes to examinations, and on requirements to clear calculator memories for examination purposes. Again, no clear consensus of examination practice is currently observed. University use of technology for teaching, learning and assessment in mathematics in the early undergraduate years varies internationally. In some countries, use of hand-held technologies typical in schools such as CAS calculators and graphics calculators is common, while in other cases (such as Australia), learning technologies such as calculators are rarely used beyond secondary school. In the case of the five Western Australian universities, neither CAS calculators nor graphics calculators are systematically used for instruction in first year mathematics classes, and technology use in assessment is mostly confined to scientific calculators. This situation is well-known to many local teachers, who often interpret it as an ii argument against the use of these technologies in school mathematics. Mathematics teachers in local universities are generally unfamiliar with the use of CAS calculators or graphics calculators as learning tools, do not use them for teaching purposes and regard them only as computational devices. In some first year statistics teaching, students with graphics calculators are permitted to use them, including for assessment. Beyond first year, mathematics students are likely to encounter more sophisticated technologies, such as professional computer software. University mathematics teachers do not report substantial unease from students about the lack of use of CAS or graphics calculators. Both the existing Mathematics syllabuses (concluding with Year 12 in 2015) and the new syllabuses (starting with Year 11 in 2015) explicitly recognise roles for technology. In each case, however, there is very little specific advice and guidance offered to readers to clarify in any detail how that technology might be used for teaching, for learning