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Changing assessment methods: new rules, new roles. (English) Zbl 1284.97032
Summary: Over the past 20 years, the use of computer algebra systems (CAS) has helped with the teaching of mathematics in engineering schools. However the traditional use of CAS only in math labs has led to a narrow view by the student: the CAS is an additional work, not included in the learning process. The didactic guidelines of the European Higher Education Area (EHEA) propose a new teaching-learning model based on competencies. We suggest the use of the CAS be adapted to the new rules. In this paper, we present a model for the integrated use of the CAS, and we describe and analyze two experiments carried out in the academic year 2011–2012. Our analysis suggests that the use of CAS in all learning and assessment activities has the potential to positively influence the development of competencies.
MSC:
97U70 Technological tools, calculators (aspects of mathematics education)
97M50 Physics, astronomy, technology, engineering (aspects of mathematics education)
68W30 Symbolic computation and algebraic computation
Software:
DERIVE; MACSYMA; Maple
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References:
[1] Aguilera, G.; Galán, J. L.; Gálvez, J.; Jiménez, A.; Padilla, Y.; Rodríguez, P., Cas + programming = mathematical creativity, (First Central and Eastern European Conference on Computer Algebra and Dynamic Geometry Systems in Mathematics Education, CADGAME, (2007))
[2] Amrhein, B.; Gloor, O.; Maeder, R. E., Visualizations for mathematics courses based on a computer algebra system, J. Symb. Comput., 23, 5-6, 447-452, (1997)
[3] Artigue, M., Learning mathematics in a CAS environment: the genesis of a reflection about instrumentation and the dialectics between technical and conceptual work, Int. J. Comput. Math. Learn., 7, 245-274, (2002)
[4] Baartman, L. K.J.; Bastiaens, T. J.; Kirschner, P. A.; Van der Vleuten, C. P.M., The wheel of competency assessment: presenting quality criteria for competency assessment programs, Stud. Educ. Eval., 32, 153-170, (2006)
[5] Brown, R., Computer algebra systems and the challenge of assessment, Int. J. Comp. Algebra Math. Educ., 8, 4, 295-308, (2001)
[6] Brown, R. G., Does the introduction of the graphics calculator onto system-wide examinations lead to change in the types of mathematical skills tested?, Educ. Stud. Math., 73, 181-203, (2010)
[7] Davenport, J.; Siret, Y.; Tournier, E., Computer algebra. systems and algorithms for algebraic computation, (1988), Academic Press · Zbl 0679.68058
[8] Drijvers, P.; Doorman, M.; Boon, P.; van Gisbergen, S., Instrumental orchestation theory and practice, (Proceedings of CERME 6, 2009, Lyon, France, (2009)), 26-09-2012
[9] Drijvers, P.; Trouche, L., Handheld technology for mathematics education: flashback into the future, ZDM Math. Educ., 42, 667-681, (2010)
[10] European Commission, Directorate-General for Education and Cultures, 2009. ECTS usersʼ guide. 26-09-2012, http://ec.europa.eu/dgs/education_culture/publ/.
[11] García, A.; García, F.; Rodríguez, G.; de la Villa, A., A toolbox with derive, Derive Newsl., 76, 5-13, (2009)
[12] García, A.; Díaz, A.; de la Villa, A., An example of learning based on competences: use of maxima in linear algebra for engineers, Int. J. Tech. Math. Educ., 18, 4, 177-181, (2011)
[13] García, A.; García, F.; Rodríguez, G.; de la Villa, A., Small projects: a method for improving learning, (3rd International Research Symposium on Problem-Based Learning, Coventry, (2011))
[14] Joyner, D., Open source computer algebra systems: axiom, ACM Commun. Comput. Algebra, 42, 2, 39-47, (2008) · Zbl 1322.68285
[15] Hsiung, C. M., An experimental investigation into the efficiency of cooperative learning with consideration of multiple grouping criteria, Eur. J. Eng. Educ., 35, 6, 679-692, (2010)
[16] Lagrange, J. B.; Artigue, M.; Laborde, C.; Trouche, L., Technology and mathematics education: a multidimensional overview of recent research and innovation, (Leung, F. K.S., Second International Handbook of Mathematics Education, vol. 1, (2003), Kluwer Academic Publishers Dordrecht), 237-270
[17] Limniou, M., Smith, M., 2012. The role of feedback in e-assessments for engineering education. Educ. Inf. Technol., http://dx.doi.org/10.1007/s10639-012-9200-5, in press.
[18] MacAogáin, E., A CAS-index, Int. J. Comp. Algebra Math. Educ., 9, 4, 305-313, (2002)
[19] Marshall, N.; Buteau, C.; Jarvis, D.; Lavicza, Z., Do mathematicians integrate computer algebra systems in university teaching?. comparing a literature review to an international survey study, Comput. Educ., 58, 423-434, (2012)
[20] Meagher, M., 2000. Curriculum and assessment in an age of computer algebra systems. ERIC Digest.
[21] Moses, J., Macsyma: a personal history, J. Symb. Comput., 47, 2, 123-130, (2012) · Zbl 1231.68291
[22] (Niss, M.; Højgaard, T., Competencies and Mathematical Learning. Ideas and Inspiration for the Development of Mathematics Teaching and Learning in Denmark, IMFUFA 485-2011, (2011), Roskilde University)
[23] 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, 59-93, (2004)
[24] Sangwin, C., Assessing mathematics automatically using computer algebra and the Internet, Teach. Math. Appl., 23, 1, 1-14, (2004)
[25] Stallman, R. M., The GNU operating system and the free software movement, (DiBona, C.; Ockman, S.; Stone, M., Open Sources: Voices from the Open Source Revolution, (1999), O‘Reilly & Associates Inc. Sebastopol, CA)
[26] Thomson, R.; Santaella, A.; Boulat, M., Maple and other CAS (computer algebra systems) applied to teaching and assessing mathematics, School of Doctoral Studies (European Union) Journal, 1, 136-170, (2009)
[27] de la Villa, A., Problemas de álgebra, (2011), CLAG Madrid
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