What algebraic knowledge may not be learned with CAS-a praxeological analysis of Faroese exam exercises
Tipo de documento
Autores
Lista de autores
Carlsen, Louise M.
Resumen
We are interested in the potentials and pitfalls of introducing computer algebra systems in lower secondary school, investigating the case of the Faroese Islands. In order to identify what algebraic knowledge is tested in the final written exam in mathematics after the ninth grade, and how this would change if computer algebra systems were allowed at that exam, we analyse all exam exercises from the past 10 years in terms of the techniques required to solve the exercises both with and without symbolic tools. The comparison suggests that fundamental algebraic structures may not be learned if students consistently use computer algebra systems for the tasks given in the exam.
Fecha
2019
Tipo de fecha
Estado publicación
Términos clave
Estrategias de solución | Instrumentos | Otro (álgebra) | Tipos de evaluación
Enfoque
Nivel educativo
Idioma
Revisado por pares
Formato del archivo
Referencias
Bosch, M. (2012). Doing research within the anthropological theory of the didactic: the case of school algebra. Paper presented at the Proceedings du 12ème International Congress on Mathematical Education. Bosch, M., & Gascón, J. (2014). Introduction to the Anthropological Theory of the Didactic (ATD) Networking of theories as a research practice in mathematics education (pp. 67-83): Springer. Chaachoua H. (2011) La praxéologie comme modèle didactique pour la problématique EIAH. Etude de cas : la modélisation des connaissances des élèves. In Abboud-Blanchard M., Flückiger A. (eds). Séminaire national de didactique des mathématiques. 81-102. Paris. http://www.irem.univ-paris-diderot.fr/up/publications/AAR12001.pdf Chevallard, Y. (1999). L'analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en didactique des mathématiques, 19(2), 221-265. Flynn, P., & McCrae, B. (2001). Issues in assessing the impact of CAS on mathematics examinations. Paper presented at the Numeracy and Beyond. Proceedings of the 24th Annual Conference of the Mathematics Education Research Group of Australasia. Hitt, F., & Kieran, C. (2009). Constructing Knowledge Via a Peer Interaction in a CAS Environment with Tasks Designed from a Task–Technique–Theory Perspective. International Journal of Computers for Mathematical Learning, 14(2), 121-152. doi:10.1007/s10758-009-9151-0 Kaput, J., & Blanton, M. (2001). Algebrafying the Elementary Mathematics Experience: Part 1: Transforming Task Structures, part II Transforming practice on a district-wide scale. Proc. 12th ICMI Study ‘The future of the teaching and learning of Algebra, 344-353. Kokol-Voljc, V. (1999). Exam Questions When Using CAS for School Mathematics Teaching. Lagrange, J.-B. (2005). Using symbolic calculators to study mathematics. In S. US (Ed.), The didactical challenge of symbolic calculators (pp. 113-135). Måsøval, H. S. (2011). Factors Constraining Students’ Establishment of Algebraic Generality in Shape Patterns : A Case Study of Didactical Situations in Mathematics at a University College. Faculty of Engineering and Science, Univeristy of Agder. Pierce, R. U. (2001). An exploration of algebraic insight and effective use of computer algebra systems. theage (https://math.stackexchange.com/users/140931/theage), Is there a law that you can add or multiply to both sides of an equation?, URL (version: 2015-01-13): https://math.stackexchange.com/q/1102501 Trouche, L. (2005). An instrumental approach to mathematics learning in symbolic calculator environments. The didactical challenge of symbolic calculators (pp. 137-162): Springer.