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Neglected critical issues of effective CAS utilization. (English) Zbl 1284.97033
Summary: This paper examines two neglected critical issues of the effective utilization of computer algebra system (CAS). Using a number of examples from an upper secondary mathematics education, these issues deal with the instrumentalization of CAS, and support to students when solving tasks by CAS (i.e. CAS-based task design). Regarding this instrumentalization, the paper considers the extent to which it can be done with CAS tools at present, and discusses several critical issues in doing so with respect to tool, task and designer (learner). Concerning this support, the paper calls for a detailed task design that also includes the issues of acceptable solutions and scaffolding offered, which should be, in some detail, clarified and given in examination materials. Several challenges relating to the two critical issues are considered.
MSC:
97U70 Technological tools, calculators (aspects of mathematics education)
97D50 Teaching mathematical problem solving and heuristic strategies
68W30 Symbolic computation and algebraic computation
Software:
DERIVE
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[1] Aguilera-Venegas, G.; Galán-García, J. L.; Galán-García, M. A.; Padilla-Domínguez, Y.; Rodríguez-Cielos, P., Teaching differential equations and its applications using derive 6 as a pecas, (Galán-García, J. L.; Aguilera-Venegas, G.; Rodríguez-Cielos, P., Proceedings of TIME 2010, (2010), University of Malaga Malaga, Spain)
[2] Amrhein, B.; Gloor, O.; Maeder, R. E., Visualizations for mathematics courses based on a computer algebra system, J. Symb. Comput., 23, 5-6, 447-462, (1997)
[3] Artigue, M., The teaching and learning mathematics at the university level - critical questions for contemporary research in education, Not. Am. Math. Soc., 46, 11, 1377-1385, (1999) · Zbl 0974.00010
[4] Beaudin, M., 2007. Using \(\ln(| x |)\) as an antiderivative for \(1 / x\) is a bad choice!. Paper presented at the AAC 2007 Conference, 19-22 July, 2007, Rochester, Michigan, USA. Retrieved September 12, 2013, from https://cours.etsmtl.ca/SEG/mbeaudin/Paper_Beaudin_PDF.pdf.
[5] Berger, M., A framework for examining characteristics of computer-based mathematical tasks, Afr. J. Res. Math. Sci. Technol. Educ., 15, 2, 111-123, (2011)
[6] Böhm, J., Improving CAS: critical areas and issues, (Kadijevich, Dj.; Zbiek, R. M., Proceedings of the 6th CAME Symposium, (2009), Megatrend University Belgrade, Serbia), 11-14, Retrieved September 12, 2013, from
[7] Brown, R.; Davies, E. W., The introduction of graphic calculators into assessment in mathematics at the international baccalaureate organization: opportunities and challenges, Teach. Math. Appl., 21, 4, 173-187, (2002)
[8] Drijvers, P., Learning algebra in a computer algebra environment, Int. J. Comp. Algebra Math. Educ., 11, 3, 77-89, (2004)
[9] Drijvers, P.; Kieran, C.; Mariotti, M.-A., Integrating technology into mathematics education: theoretical perspectives, (Hoyles, C.; Lagrange, J.-B., Mathematics Education and Technology - Rethinking the Terrain, (2010), Springer Heidelberg), 89-132
[10] Figueiredo, N.; van Galen, F.; Gravemeijer, K., The actorʼs and observerʼs point of view: a geometry applet as an example, Educ. Designer, 1, 3, (2009), Retrieved September 12, 2013, from
[11] Fuglestad, A. B.; Healy, L.; Kynigos, C.; Monaghan, J., Working with teachers: context and culture, (Hoyles, C.; Lagrange, J.-B., Mathematics Education and Technology - Rethinking the Terrain, (2010), Springer Heidelberg), 293-310
[12] Gjone, G., The use of CAS in school mathematics: possibilities and limitations, (Kadijevich, Dj.; Zbiek, R. M., Proceedings of the 6th CAME Symposium, (2009), Megatrend University Belgrade, Serbia), 19-23
[13] Heid, K. M., How theories about the learning and knowing of mathematics can inform the use of CAS in school mathematics: one perspective, Int. J. Comp. Algebra Math. Educ., 8, 2, 95-112, (2002)
[14] (Hoyles, C.; Lagrange, J.-B., Mathematics Education and Technology - Rethinking the Terrain, (2010), Springer Heidelberg) · Zbl 1176.00007
[15] Joubert, M., Using computers in classroom mathematical tasks: revisiting theory to develop recommendations for design of tasks, (Margolinas, C., Task Design in Mathematics Education: Proceedings of ICMI Study 22 (vol. 1), Oxford, UK, (2013)), 71-79
[16] Kadijevich, Dj., Coordinating the process and object features of mathematical knowledge by CAS, (Böhm, J., Tagungsband: DES-TIME-2006 (on a CD). bk teachware, Linz, Austria, (2006)), Retrieved September 12, 2013, from
[17] Kadijevich, Dj., Towards relating procedural and conceptual knowledge by CAS, (2007), (presentation given at CAME 5). Retrieved September 12, 2013, from
[18] Kadijevich, Dj., Critical issues of improving computer algebra systems, (Kadijevich, Dj.; Zbiek, R. M., Proceedings of the 6th CAME Symposium, (2009), Megatrend University Belgrade, Serbia), 25-29
[19] Kadijevich, Dj. M., Examining errors in simple spreadsheet modeling from different research perspectives, J. Educ. Comput. Res., 47, 2, 137-153, (2012)
[20] Kadijevich, Dj. M., Learning about spreadsheets, (Kadijevich, Dj. M.; Angeli, C.; Schulte, C., Improving Computer Science Education, (2013), Routledge New York), 19-33
[21] Kieran, C.; Saldanha, L., Computer algebra systems (CAS) as a tool for coaxing the emergence of reasoning about equivalence of algebraic expressions, (Chick, H. L.; Vincent, J. L., Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (vol. 3), (2005), PME Melbourne), 193-200
[22] Kieran, C.; Saldanha, L., Designing tasks for the codevelopment of conceptual and technical knowledge in CAS activity: an example from factoring, (Heid, M. K.; Blume, G. W., Research on Technology and the Teaching and Learning of Mathematics: Cases and Perspectives (vol. 2), (2008), Information Age Charlotte, NC), 393-414
[23] Kokol-Voljc, V.; Kadijevich, Dj.; Haapasalo, L., CAS-based task requirements and critical activities in completing them, (Kadijevich, Dj.; Zbiek, R. M., Proceedings of the 6th CAME Symposium, (2009), Megatrend University Belgrade, Serbia), 31-34
[24] Kutzler, B., The algebraic calculator as a pedagogical tool for teaching mathematics, (Gagatsis, A.; Makrides, G., Proceedings of the Second Mediterranean Conference on Mathematics Education, (2000), Cyprus Mathematical Society Nicosia), 142-160
[25] Kutzler, B.; Kokol-Voljc, V., A plead for PECAS (= pedagogical CAS), (Gagatsis, A.; Papastavridis, S., 3rd Mediterranean Conference on Mathematical Education: Mathematics in the Modern World, Mathematics and Didactics, Mathematics and Life, Mathematics and Society, (2003), Hellenic Mathematical Society, Cyprus Mathematical Society, Athens, Nicosia), 331-334
[26] Leigh-Lancaster, D., The case of technology in senior secondary mathematics: curriculum and assessment congruence, (Glascodine, C.; Hoad, K. A., Make It Count: What Research Tells us About Effective Mathematics Teaching and Learning, (2010), Australian Council for Educational Research Camberwell, Australia), 21-26
[27] Monaghan, J., 14-19 mathematics and ICT: curriculum and assessment issues (report to qualifications and curriculum authority), (2006), Retrieved September 12, 2013, from
[28] National Council of Teachers of Mathematics, NCTM, 2000. Principles and standards for school mathematics. NCTM, Reston, VA. Retrieved September 12, 2013, from http://www.nctm.org/standards.
[29] Parnas, D. L., Precise documentation: the key to better software, (Nanz, S., The Future of Software Engineering, (2011), Springer Berlin), 125-148
[30] Pierce, R.; Stacey, K., A framework for monitoring progress and planning teaching towards the effective use of computer algebra systems, Int. J. Comput. Math. Learn., 9, 1, 59-93, (2004)
[31] Richardson, D., Some undecidable problems involving elementary functions of a real variable, J. Symb. Log., 33, 4, 514-520, (1968) · Zbl 0175.27404
[32] Sangwin, C. J.; Ramsden, P., Linear syntax for communicating elementary mathematics, J. Symb. Comput., 42, 9, 920-934, (2007) · Zbl 1261.00007
[33] Stacey, K., Using computer algebra systems in secondary school mathematics: issues of curriculum, assessment and teaching, (Chu, S.-C.; Yang, W.-C.; de Alwis, T.; Lee, M.-G., Technology Connecting Mathematics, Proceedings of the 8th Asian Technology Conference in Mathematics. Asian Technology Conference in Mathematics, Taiwan R.O.C., (2003)), 40-54, Retrieved September 12, 2013, from
[34] Stanic, G.; Kilpatrick, J., Mathematics curriculum reform in the united states: A historical perspective, Int. J. Educ. Res., 17, 5, 407-417, (1992)
[35] Stoutemyer, D. R., Ten commandments for good default expression simplification, J. Symb. Comput., 46, 7, 859-887, (2011) · Zbl 1216.68348
[36] Tort, F., Bruillard, E., 2010. Informatics education: beyond the opposition between information technology and computer science. Paper was presented at the IFIP Workshop “New Developments in ICT and Education”. Amiens, France, 28-30 June, 2010. Retrieved September 12, 2013, from http://www.stef.ens-cachan.fr/annur/tort/tb_ifip_2010.pdf.
[37] Trouche, L., An instrumental approach to mathematics learning in symbolic calculator environments, (Guin, D.; Ruthven, K.; Trouche, L., The Didactical Challenge of Symbolic Calculators: Turning a Computational Device Into a Mathematical Instrument, (2005), Springer New York), 137-162
[38] Zehavi, N., Symbol sense with a symbolic-graphical system: a story in three rounds, J. Math. Behav., 23, 2, 183-203, (2004)
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