Workshop by André
Boileau and Denis Tanguay
from the Université du Québec à
15th International Conference ACA 2009 (Montréal, june 2009)
At the secondary level, this third idea prevails, and graphing
calculators in math classes are used mainly in algebra courses, as a
tool to go back and forth between algebraic expressions of a given
function, its table of values and its graph. The aim of the APTE team
is to extend this usage by employing CAS calculators in order to help
students in their construction of meaning and conceptualization, within
the more literal-symbolic segment of secondary level algebra, apart
from any functional consideration. The team has thus designed classroom
activities (i. e. consistent and connected sequences of tasks)
targeting an apprenticeship of techniques in algebra (at the 3rd and
4th secondary level), such as factorization and expansion, equation
solving, substitution, while fostering the conceptual (theoretical)
thinking for such notions as :
In this communication, we will present one of these activities, with the relevant work and productions from the students with which it has been experimented. We will discuss some aspects of its design which we evaluate as important, in particular regarding the co-emergence of technique and theory and their mutual interactions (Kieran & Drijvers, 2006): going back and forth from paper-and-pencil work to CAS work, comparison between standard algebraic syntax and CAS syntax, triggering use of the unexpected/startling CAS-output, conjectures, justifications of the conjectured formulae, large group discussions, role of the teacher...
Duval, R. (1993). Registres de représentation sémiotique et fonctionnement cognitif de la pensée. Annales de Didactique et de Sciences Cognitives, n°5, pp. 37-65. IREM de Strasbourg.
Kieran, C. & Drijvers, P., in coll. with A. Boileau, F. Hitt, D. Tanguay, L. Saldanha, J. Guzmán (2006). Learning about equivalence, equality, and equation in a CAS environment: The interaction of machine techniques, paper-and-pencil techniques, and theorizing. Proceedings of the 17th ICMI Study ‘Technology Revisited’. C. Hoyles & J.-B. Lagrange, eds. Program Committee, Hanoï, Viet-Nam.