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'Calculators can make you think.'
How can calculators be used to promote understanding in mathematics? New technology is constantly changing the mathematical demands made by society. This has wide-ranging implications for the school curriculum. Whether or not the curriculum changes radically, research suggests that calculators have potential as a tool to enhance learners' understanding of mathematics
CAS project
This project reports on the impact that dedicated access to hand-held CAS had on the 'algebraic skills' of students following a year-12 mathematics course in Scottish schools. Teachers and students used the TI-92 (pre flash) in their studies but not in assessment. Student performance in an algebraic test was compared with that of students in control schools who did not have access to the same technology. The results show that the students using CAS improved on their performance compared to the control. The discussion explores underlying reasons for these differences, considering: teaching approaches promoted by staff; impact of mathematical rigour demanded by the technologies; motivational effect of dedicated access to CAS; and how assessment influences the uptake of CAS. Many opportunities are acknowledged, but difficulties are noted in trying to separate 'learning' from 'assessment', the latter being seen as the biggest barrier to further use of CAS.
Calculators in Mathematics Education
This project involved teachers of 5 to 14 -year-olds in the Edinburgh area in an investigation of the role of the calculator in teaching and learning mathematics. Participants were able to develop a wide variety of resources, which make use of calculators, and try them out in their own classrooms. Findings highlight the potential value of hand-held technology in increasing motivation, investigating pattern, improving mental skills, developing number sense and estimation skills, building number concepts (particularly place value) and tackling 'real life' mathematics.
Graphics Calculators 10-14
While most teachers appreciate the usefulness of graphics calculators in upper secondary, the time required for learning to operate them means they may not be fully exploited. An investigation of the possibilities of introducing graphics calculators much earlier in the system therefore seemed appropriate. We have been able to collect, adapt or develop activities involving a natural use of
graphics calculators for P6-S2. The calculators have been found to be of value for the 10-14 age group. Used with care, the technology can allow exploratory learning leading to deeper understanding of the mathematics involved.
Articles to download:
Macintyre, Tom. 'Cross-Curricular Mathematics with Autograph or TI 83plus', Scottish Mathematical Council Journal 31, 2002.
Searl, J.W. 'Of Babies and Bath Water', The Fifth International Conference on Technology in Mathematics Teaching, University of Klagenfurt August 2001 Strand 7: Global Perspective of Information Technology.
CAS Project
Macintyre, Tom & Forbes, Ian 'Algebraic Skills and CAS - Could Assessment Sabotage the potential?' + Figures & Tables, International Journal of Computer Algebra in Mathematics education Vol9.1 (29-56).
Macintyre, Tom. 'Improving maths skills with CAS technology- A CAS project carried out in Scotland with 16-17 year olds using TI-92s', in Manfred Borovcnik, Hermann Kautschitsch (eds): Technology in Mathematics Teaching. Proceedings of the ICTMT 5 in Klagenfurt 2001, Schriftenreihe Didaktik der Mathematik v. 25. bv&hpt, Vienna 2002.
Calculators in Mathematics Education
Forrester, Ruth. 'Calculators and Numeracy', Mathematics Teaching 2001 Conference Report.
Forrester, Ruth. 'It is not calculators but how they are used...', Chapter 1 in Way, J. and Beardon, T.(eds) ICT and Primary Mathematics (Open University Press) (to be published).
Forrester, Ruth. 'Approaches to Practitioner Research', presented at the European Conference on Educational Research (ECER), University of Edinburgh, and published on the Education line http://www.leeds.ac.uk/educol September 2000.
Graphic Calculators 10-14
Forrester, Ruth and Searl, John. 'Uncle BODMAS and Old Friends', Mathematics Teaching MT173, p34-35, Dec 2000.
Forrester, R. 'Graphic Calculators (pdf)', report of presentation at IMECT2 conference, University of Cambridge, published on the NRICH website http://nrich.maths.org/conference/reports/forrester.html, July 2000.
Forrester, R. 'Using a TI73 from S1 to S3', Scottish Mathematical Council Journal 30, p37-38, 2001.
Forrester, Ruth, 'It is not calculators but how they are used...', Chapter 1 in Way, J. and Beardon, T.(eds) ICT and Primary Mathematics (Open University Press) (to be published).
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