Year of grant:
Náttúra og náttúrutilfeingi
Kanning og menning av vitanini hjá støddfrøðilærarum um nýtsluna av CAS í algebrafrálæruni í skúlunum.
Louise Meier Carlsen
Námsvísindadeildin, Fróðskaparsetur Føroya
Grant from the FRC in DKK:
Outline of research project Teachers today have access to a wide span of technological tools as aids and support in their teaching, both in the form of electronic books, resources on the Internet, and also advanced software (Bueno-Ravel & Gueudet, 2007). What is less abundant is knowledge about how - and under what conditions - such technological objects can be used to improve the teaching of specific subjects, in ways that enhance student learning; and most importantly, such knowledge can only become efficient if integrated into the teaching profession. Research on “spontaneous” technology use has demonstrated that teachers orchestrate student work with technologies in very different ways, even within the same subject and teaching environment, with similarly varied results (Doerr and Zangor, 2000; Lagrange and Degleodu, 2009; Lagrange and Ozdemir Erdogan, 2009; Monaghan, 2004; Sensevy, Schubauer-Leoni, Mercier, Ligozat, & Perrot, 2005). An examination of CAS in lower secondary school was made by Drijvers (2013), however the survey raised more questions than it answered, even if we are at present far beyond the naïve belief that technology in itself can solve any didactic challenge.
In this project, the three main aims are:
a) A more refined examination of different types of spontaneous orchestrations of CAS by teachers in lower secondary school, with a special focus on school algebra (abstracted arithmetics, equation solving, functions and function modelling);
b) Investigate new formats to enhance teachers’ autonomous work with such orchestrations, including tools to assess the impact of specific CAS use on student learning;
c) To identify potentials and obstacles for the idea that CAS-use might serve to introduce students to more advanced mathematical topics and working modes (such as modelling, and simple theoretical reasoning).
Based on the anthropological theory of the didactic, in particular the notion of instrumented technique, I will investigate these questions in the setting of mathematics teacher education practice at the University of the Faroe Islands. In part a) and b) I will examine different types of orchestration both arising spontaneously among novice and experienced teachers, and resulting from research and study courses done in the setting of teacher education, with mathematics student teachers. Based on b), the student teachers will implement different types of orchestration in carefully designed teaching situations while in practice. I will be recording and monitoring the student teachers and the lower secondary school pupils’ interaction and progress, with a specific focus on instrumented techniques developed among pupils and their contribution to overall praxeologies within school algebra. Some generic types of orchestration are: Technical-demo orchestration, Explain-the-screen orchestration, Link-screen-board orchestration, Discuss-the-screen orchestration, Spot-and-show orchestration, Sherpa-at-work orchestration (Trouche, 2004); when combined with a teaching design, they can generate examples of didactic techniques for teachers. In part c) the student teachers will write up practice based reports on the potentials and obstacles of introducing more advance mathematical praxeologies among lower secondary school pupils, involving (CAS) instrumented techniques. These reports will not only be part of my data but, hopefully, also serve to demonstrate the potential of “action based research on CAS orchestrations”, done with student teachers and based on the study and research course format for ATD. With my research I hope to gain more refined knowledge about orchestration of CAS in lower secondary school, as well as strategies to develop professional knowledge on this topic together with novice and experienced teachers. In particular, a main focus will be the development of shared, validated knowledge among the teachers on what is “good” and “bad” use of CAS in the sense of furthering pupil learning, and in particular for enabling more advanced mathematical work among the pupils. The findings will both be implemented in my own teaching at The University of The Faroe Island, shared with mathematics teachers trough formats like “open lessons” and video presentations of lesson design, and - of course - disseminated to the international research community through journal publications and conference publications.