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'Ordinary' teachers using technology: concerns, theoretical approaches, case studies
Location and Schedule
Time slot: 
RL-5 on Sunday 13, 10:30 – 11:30
Auditorium: 
S04-Genaro Salinas Quiroga Auditorium – Leyes
Metadata information
Author(s): 
Jean-Baptiste Lagrange, IUFM University of Reims and Didirem, University Paris 7, France. jean-baptiste.lagrange@univ-reims.fr, Web Site: http://jb.lagrange.free.fr/site/
Language: 
English
Keywords: 
'Ordinary' teachers, Technology, Curricular pressure, Dynamic geometry, Spreadsheet, Instrumented techniques, Emergent goals, Instrumental genesis, Teachers' aspirations
Abstract: 

My initial concern is the small number of teachers really using computer applications with their students in the classroom, contrasting with the emphasis put by authorities in many countries on this new dimension of Education. A related concern is the gap between potentialities of technology highlighted by research and innovation, and the motivations of teachers that seem related to rather general and more or less realistic aspirations, rather than to an analysis of didactical potentialities.

In my interpretation, teachers’ reservation towards classroom use of technology and the discrepancy between potentialities and actual uses do not denote simply a resistance to change. As Hennessy et al. (2005) say, although cautious, teachers initiate changes, tackling constraints arising in their workplace and beyond. Furthermore, a persistent observation is that unexpected phenomena frequently occur, producing discrepancies between what was expected and what really happens, contrasting with the usual stability of teachers’ practices. My assumption is, then, that for a teacher in 'ordinary' conditions, technology use brings more complexity, constraints and uncertainty.

To understand these complexity, uncertainty and constraints, there are advantages in gathering data in settings where curricular pressure fosters classroom use of a technological tool. It is then more likely that ‘ordinary’ teachers can be found implementing technology in the classroom. For the same reasons, it is better to consider tools widely recognized as potentially contributing to mathematics teaching and learning rather than innovative applications. That is why the case studies reported here consider dynamic geometry software (DG) and the spreadsheet.

Rather than a single overarching framework, I advocate the use of a plurality of theoretical approaches chosen for their capacity to address specific concerns (Lagrange et al. 2002). The first concern is how technology impacts teaching systems and how new systems build up. Chevallard’s idea of praxeology, linking types of tasks, techniques to perform these tasks and theorisations, is designed to address this concern. In this approach, techniques play a key role as a bridge between tasks and theorisations, and thus the impact of technology can be seen as resulting from the introduction of new "instrumented" techniques (Lagrange 2000).

Another concern is the complexity and uncertainty of teachers’ activity involving classroom use of technology. Among frameworks developed to analyse human activity, Saxe’s cultural perspective is particularly well suited to the purpose of analysing teachers’ activity in technology-based lessons. It includes the four parameters model whose interest Monaghan (2005) pointed out as means to analyse teachers’ activity ‘as a whole’. Another feature is the notion of ‘emergent goals’, suitable for interpreting unexpected phenomena.

Because teachers’ activity is not an end in itself, students’ cognitive activity has to be taken into account. A crucial question is how teachers deal with computer feedback as a way to trigger students’ reflection. This concern points towards Brousseau’s notions of milieu and adidactic situation. In ordinary teaching, that we consider here, Perrin-Glorian and Hersant (2005) note that there can be a milieu, which provides some feedback on the actions of the students, but most often, "the feedback alone may be insufficient for the students to produce new knowledge on their own."

Teachers’ aspirations with regard to technology is another concern. Ruthven and Hennessy (2002) offered “a practitioner model of the use of (technology) to support mathematics teaching and learning” built from a statistical analysis of themes occurring in interviews with teachers. This is a frame to analyse how teachers’ aspirations intervene in their classroom activity. Finally the notion of “instrumental genesis” (Trouche 2000), that is to say the process by which a user appropriates a computer artefact to become a functional mathematical tool, is helpful at two levels: how teachers take charge of students’ instrumental genesis, and how their own instrumental genesis takes place.

Two case studies are considered. The first one deals with the use of dynamic geometry (DG) at middle school. Successive gaps are observed between research conceptualisation of DG, the official instructions of the French curriculum, and textbooks. Two typical uses of DG appear in the textbooks and I illustrate each by an observation of a teacher. These observations are interpreted using principally Ruthven and Hennessy’s model, showing the central role played by teachers’ aspirations in the way they deal with emergent goals. The second case study considers two teachers with very different parameters, teaching a new curriculum for upper secondary non-scientific classes that makes spreadsheet use compulsory. In addition to a study of this curriculum, I contrast the two teachers’ parameters, and analyse their activity in two similar lessons. Goals emerging in these lessons show that instrumented techniques, milieu, and cultural representations and values are linked issues in this activity. They show also that favourable setting and parameters do not guarantee an easy integration although they do provide a basis for an evolution.

References
Hennessy, S., Ruthven, K., Brindley, S.: 2005, Teacher perspectives on integrating ICT into subject teaching: commitment, constraints, caution and change. Journal of Curriculum Studies 37(2), 155–192
Hersant, M., Perrin-Glorian, M.J. : 2005, Characterization of an ordinary teaching practice with the help of the theory of didactic situations, Educational Studies in Mathematics 59, 113–151.
Lagrange, J.-B.: 2001, L’intégration d’instruments informatiques dans l’enseignement: une approche par les techniques, Educational Studies in Mathematics 43, 1–30.
Lagrange, J.B., Artigue M., Laborde C., Trouche L.: 2003, Technology and Math education: a multidimensional overview of recent research and innovation. In Bishop, Clements, Keitel, Kilpatrick, Leung (eds.) Second International Handbook of Mathematics Education, (Kluwer)
Monaghan, J.: 2004,Teachers’ Activities in Technology-based Mathematics Lessons, International Journal of Computers for Mathematical Learning 9(3), 327-357.
Ruthven, K. , Hennessy, S.: 2002, A practitioner model of the use of computer-based tools and resources to support mathematics teaching and learning, Educational Studies in Mathematics 49, 47–88.
Trouche, L. : 2000, La parabole du gaucher et de la casserole à bec verseur: Étude des processus d’apprentissage dans un environnement de calculatrices symboliques, Educational Studies in Mathematics 41:239–264.