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Does the introduction of the graphics calculator into system-wide examinations lead to change in the types of mathematical skills tested?

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Abstract

The paper reports on the introduction of the graphics calculator into three centralised examination systems, which were located in Denmark, Victoria (Australia) and the International Baccalaureate. The introduction of the graphics calculator required those responsible for writing examination questions to consider how to assess mathematical skills within this new environment. This paper illustrates the types of mathematics skills that have been assessed within the graphics-calculator-assumed environment. The analysis of the examination questions indicated that only two out of the six mathematics examinations considered demonstrated any significant change in the types of skills assessed in conjunction with the introduction of the graphics calculator. The results suggest that it is possible to reduce the use of questions assessing routine procedures (mechanical skills) with a graphics calculator, but it is also evident that there have not been major changes in the way that examination questions are written nor the mathematics skills which the questions are intended to assess.

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Notes

  1. Other terms used in the literature include graphic, graphing and graphical.

  2. ‘High-stakes’ assessment is defined as system-wide assessment for certification purposes at the end of secondary school (which can include, for instance, examinations, coursework, oral examinations and practical examinations), which is often used for university course selection.

  3. Many questions in examinations from year to year are similar in style; however, these questions are unusual in that they are uncommon or non-existent in previous examinations.

References

  • Abu-Naja, M. (2008). The effect of graphics calculator on Negev Arab pupils’ learning of the concept of families of functions. Research in Mathematics Education, 10(2), 183–202.

    Article  Google Scholar 

  • Anderson, M., Bloom, L., Mueller, U., & Pedler, P. (1999). The impact of graphics calculator on the assessment of calculus and modelling. International Journal of Mathematics Education Science and Technology, 30(4), 489–498.

    Article  Google Scholar 

  • Ball, G., Stephenson, B., Smith, G. H., Wood, L., Coupland, M., & Crawford, K. (1998). Creating diversity of mathematical experiences for tertiary students. International Journal of Mathematics Education Science and Technology, 29(6), 827–841.

    Article  Google Scholar 

  • Berry, J., Graham, E., & Smith, A. (2006). Observing student working styles when using graphic calculators to solve mathematics problems. International Journal of Mathematical Education in Science and Technology, 37(3), 291–308.

    Article  Google Scholar 

  • Berry, J., Johnson, P., Maull, W., & Monaghan, J. (1999). Routine questions and examination performance. In O. Zaslavsky (Ed.), Proceedings 23rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 105–112). Haifa: Israel Institute of Technology.

    Google Scholar 

  • Bibby, N. (1991). Wherefore “plug and chug”?: Computer algebra versus A level mathematics. The Mathematical Gazette, 75, 40–48.

    Article  Google Scholar 

  • Bloom, B. S., Engelhart, M. D., Furst, E. J., Hill, W. H., & Krathwohl, D. R. (1956). Taxonomy of educational objectives, handbook I: The cognitive domain. New York: McKay.

    Google Scholar 

  • Boers, M. & Jones, P. (1994). Students’ use of graphics calculator under examination conditions. International Journal of Mathematics Education Science and Technology, 25(4), 491–516.

    Article  Google Scholar 

  • Brown, R. (2001). Computer algebra systems and the challenge of assessment. International Journal of Computer Algebra in Mathematics Education, 8(4), 295–308.

    Google Scholar 

  • Brown, R. (2005). The impact of introduction of the graphics calculator into “high stakes” mathematics examinations at the system wide level. Hawthorn: Swinburne University of Technology.

    Google Scholar 

  • Brown, R. (2007). Policy change, graphing calculators and ‘high stakes examinations’: A view across three examination systems. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the fifth Congress of the European Society for Research in Mathematics Education (pp. 2413–2422). Larnaca: Department of Education, University of Cyprus.

    Google Scholar 

  • Cresswell, M. J. (1998). What are examination standards? The role of values in large scale assessment. Paper presented at the 22nd International Association Evaluation Assessment Conference, Beijing

  • DME. (1994). Højt Niveau Matematik, Onsdag den 11 maj 1994; Matematisk Linje Og Sproglig Linje, 2-Årigt Forløb Til B-Niveau (p. 4). Copenhagen: DME.

    Google Scholar 

  • DME. (1995). Bekendtgørelse om ændring af bekendtgørelse om studentereksamen og om højere forberedelseseksamen nr 608. http://www.retsinfo.dk/_GETDOC_/ACCN/B19950060805-REGL Accessed 8 September 2009.

  • DME. (1997, 26. maj 1997). Bekendtgørelse om ændring af bekendtgørelse om gymnasiet, studenterkursus og enkeltfagsstudentereksamen nr 354. http://www.retsinfo.dk/_GETDOC_/ACCN/B19970035405-REGL. Accessed 8 September 2009.

  • DME. (2000). Matematisk Linje 3-Årigt Førlob Til A-Niveau, Matematik Proven Med Hjælpemidler, Torsdag den 11. maj 2000; Matematisk Linje Og Sproglig Linje, 2-Årigt Forløb Til B-Niveau, Matematik Delprøven Med Hjælpemidler, Delprøven Med Hjælpemidler. Copenhagen: DME.

    Google Scholar 

  • DME. (2003). Matematisk Linje 3-Årigt Førlob Til A-Niveau, Matematik Proven Med Hjælpmidler; Matematisk Linje Og Sproglig Linje, 2-Årigt Forløb Til B-Niveau, Delprøven Med Hjælpemidler. Copenhagen: DME.

    Google Scholar 

  • DME. (2005). Matematisk Linje 3-Årigt Førlob Til A-Niveau, Matematik Proven Med Hjælpmidler; Matematisk Linje Og Sproglig Linje, 2-Årigt Forløb Til B-Niveau, Delprøven Med Hjælpemidler. Copenhagen: DME.

    Google Scholar 

  • Drijvers, P. (1998). Assessment and new technologies. The International Journal of Computer Algebra in Mathematics Education, 5(2), 81–93.

    Google Scholar 

  • Drijvers, P. & Doorman, M. (1996). The graphics calculator in mathematics education. Journal of Mathematical Behavior, 15, 425–440.

    Article  Google Scholar 

  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103–131.

    Article  Google Scholar 

  • Elia, I. & Spyrou, P. (2006). How students conceive function: A triarchic conceptual-semiotic model of the understanding of a complex concept. The Montana Mathematics Enthusiast, 3(2), 256–272.

    Google Scholar 

  • Forster, P., Flynn, P., Frid, S., & Sparrow, L. (2004). Calculators and computer algebra systems. In B. Perry, G. Anthony & C. Diezmann (Eds.), Research in mathematics education 2000–2003 (pp. 313–336). Flaxton: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Forster, P. A. & Mueller, U. (2001). Outcomes and implications of students’ use of graphics calculators in the public examination of calculus. International Journal of Mathematics Education Science and Technology, 32(1), 37–52.

    Article  Google Scholar 

  • French, D. (1995). Computer algebra systems and A level examinations some thoughts prompted by Martin Taylor’s article. The Mathematical Gazette, 79, 545–548.

    Article  Google Scholar 

  • Gagatsis, A. & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational Psychology, 24(5), 645–657.

    Article  Google Scholar 

  • Galbraith, P. & Haines, C. (2000). Conceptual (mis)understandings of beginning undergraduates. International Journal of Mathematics Education Science and Technology, 31(5), 651–678.

    Article  Google Scholar 

  • Gardiner, T. (1995). Wrong way, go back! Mathematical Gazette, 79, 335–346.

    Article  Google Scholar 

  • Graham, T., Headlam, C., Honey, S., Sharp, J., & Smith, A. (2003). The use of graphics calculators by students in an examination: what do they really do? International Journal of Mathematics Education Science and Technology, 34(3), 319–334.

    Article  Google Scholar 

  • Guin, D. & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3, 195–227.

    Article  Google Scholar 

  • Harvey, J. G. (1992). Mathematics testing with calculators: Ransoming the hostages. In T. A. Romberg (Ed.), Mathematics assessment and evaluation (pp. 139–168). Albany: State University of New York Press.

    Google Scholar 

  • Heid, M. K. (1988). Resequencing skills and concepts in applied calculus using the computer as a tool. Journal for Research in Mathematics Education, 19(1), 3–25.

    Article  Google Scholar 

  • Hong, Y. Y., Thomas, M., & Kiernan, C. (2000). Supercalculators and university entrance calculus examinations. Mathematics Education Research Journal, 12(3), 321–336.

    Google Scholar 

  • IBO. (1992). Groups 3–6: Use of calculators in examinations. Examination sessions: May 1994 onwards. IB Coordinator Notes (December 1992).

  • IBO. (1993). Mathematics subsidiary level: Paper 1, paper 1: Mathematics subsidiary level: Paper 2, paper 2: Mathematics with further mathematics. Higher level: Paper 1, May paper 1: Mathematics with further mathematics. Higher level: Paper 2, May paper 2. Geneva: IBO.

    Google Scholar 

  • IBO. (2000). Mathematical methods SL paper 1, May 2000; Mathematical methods SL paper 2, May 2000; mathematics HL paper 1, May 2000; Mathematics HL paper 2, May 2000. Geneva: IBO.

    Google Scholar 

  • IBO. (2003). Mathematical methods SL paper 1, May 2003; Mathematical methods SL paper 2, May 2003; mathematics HL paper 1, May 2003; Mathematics HL paper 2, May 2003. Geneva: IBO.

    Google Scholar 

  • IBO. (2005). Mathematical methods SL paper 1, May 2005; Mathematical methods SL paper 2, May 2005; mathematics HL paper 1, May 2005; Mathematics HL paper 2, May 2005. Geneva: IBO.

    Google Scholar 

  • Kendal, M. & Stacey, K. (2001). The impact of teacher privileging on learning differentiation with technology. International Journal of Computers in Mathematics Learning, 6(2), 143–165.

    Article  Google Scholar 

  • Kokol-Voljc, V. (1999). Exam questions when using CAS for school mathematics teaching. International Journal of Computer Algebra in Mathematics Education, 7(1), 63–76.

    Google Scholar 

  • Miles, M. & Huberman, A. M. (1994). Qualitative data analysis. Thousand Oaks: Sage.

    Google Scholar 

  • Monaghan, J. (2000). Some issues surrounding the use of algebraic calculators in traditional examinations. International Journal of Mathematics Education Science and Technology, 31(3), 381–392.

    Article  Google Scholar 

  • Oppenheim, A. (2000). Questionnaire design, interviewing and attitude measurement (2nd ed.). London: Cassell.

    Google Scholar 

  • Penglase, M. & Arnold, S. (1996). The graphics calculator in mathematics education: A critical review of recent research. Mathematics Education Research Journal, 8(1), 58–90.

    Google Scholar 

  • Pointon, A. & Sangwin, C. J. (2003). An analysis of undergraduate core material in the light of hand-held computer algebra systems. International Journal of Mathematics Education, Science and Technology, 34(5), 671–686.

    Article  Google Scholar 

  • Ruthven, K. (1990). The influence of graphical calculator use on translation from graphic to symbolic forms. Educational Studies in Mathematics, 21, 431–450.

    Article  Google Scholar 

  • Ruthven, K. (1996). The technology test: New items for a new era. Mathematical Gazette, 80, 360–361.

    Article  Google Scholar 

  • Ruthven, K. (2002). Instrumenting mathematical activity: Reflections on key studies of the educational use of computer algebra systems. International Journal for Computers in Mathematics Learning, 7, 275–291.

    Article  Google Scholar 

  • Smith, G. H. & Wood, L. (2000). Assessment of learning in university mathematics. International Journal of Mathematics Education Science and Technology, 31(1), 125–132.

    Article  Google Scholar 

  • Smith, G. H., Wood, L., Crawford, K., Coupland, M., Ball, G., & Stephenson, B. (1996). Constructing mathematical examinations to assess a range of knowledge and skills. International Journal of Mathematics Education Science and Technology, 27(1), 65–78.

    Article  Google Scholar 

  • Threlfall, J., Pool, P., Homer, M., & Swinnerton, B. (2007). Implicit aspects of paper and pencil mathematics assessment that come to light through the use of the computer. Educational Studies in Mathematics, 66, 335–348.

    Article  Google Scholar 

  • VBOS. (1994). VCE Mathematical methods common assessment task 3: Analysis task; VCE mathematical methods common assessment task2: Facts, skills and applications task; VCE Specialist mathematics common assessment task 2: Facts, skills and applications task; VCE specialist mathematics common assessment Task 3: Analysis task. Melbourne: VBOS.

  • VBOS. (1997a). Approved calculators in VCE examinations. VCE Bulletin, 1997, 3–4.

    Google Scholar 

  • VBOS. (1997b). Use of calculators in examinations. VCE Bulletin, September

  • VCAA. (2000). Mathematical methods: Written examination 1 Part II.; Mathematical methods: Written examination 2 (analysis task); Specialist mathematics: Written examination 1 Part II; Specialist mathematics: Written examination 2 (analysis task). Melbourne: VCAA.

    Google Scholar 

  • VCAA. (2003). Mathematical methods: Written examination 1 Part II.; Mathematical methods: Written examination 2 (analysis task); Specialist mathematics: Written examination 1 Part II; Specialist mathematics: Written examination 2 (analysis task). Melbourne: VCAA.

    Google Scholar 

  • VCAA. (2005). Mathematical methods: Written examination 1 Part I; Mathematical methods: Written examination 2 (analysis task); Specialist mathematics: Written examination 1 Part II; Specialist mathematics: Written examination 2 (analysis task). Melbourne: VCAA.

    Google Scholar 

  • VCAA. (2006). Assessment report: Mathematical methods GA 3: Written examination 2. Melbourne: Victorian Curriculum and Assessment Authority.

    Google Scholar 

  • Waits, B. & Demana, F. (2000). Calculators in mathematics teaching and learning: Past, present, and future. In M. J. Burke & F. R. Curcio (Eds.), Learning mathematics for a new century (pp. 55–66). Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Wu, H. (1996). The mathematician and the mathematics education reform. Notices American Mathematical Society, 43, 1531–1537.

    Google Scholar 

  • Yin, R. K. (1994). Case study research: Design and methods (2nd ed.). Thousand Oaks: Sage.

    Google Scholar 

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Acknowledgements

I would like to thank the three examination authorities and their respective examiners who demonstrated a willingness to support and provide materials for this study. I acknowledge as well the anonymous reviewers and the editor for their comments on earlier versions of this paper.

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  1. University of Leeds, Leeds, UK

    Roger G. Brown

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Brown, R.G. Does the introduction of the graphics calculator into system-wide examinations lead to change in the types of mathematical skills tested?. Educ Stud Math 73, 181–203 (2010). https://doi.org/10.1007/s10649-009-9220-2

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