Abstract:

This study intends to understand the knowledge held by the teacher and its influence on the implementation of investigation tasks using graphing calculators. The theoretical framework focuses on the professional knowledge and on the graphing calculator, and emphasises the Knowledge for Teaching Mathematics with Technology (KTMT), a model of teacher’s knowledge developed during this study. This model seeks to articulate previously existing models on professional knowledge and the conclusions that the investigation around the integration of technology has achieved. KTMT is a dynamic knowledge, informed by the practice, that develops from the knowledge on the base domains (Mathematics, Teaching and Learning, Technology and Curriculum), evolving as knowledge in the base domains interacts and as this promotes the development of two sets of inter-domain knowledge (Mathematics and Technology, and Teaching and Learning and Technology), which continue to interact, strengthening relations and leading to the development of an integrated knowledge, where knowledge on the base domains and on the two sets of inter-domains appears deeply integrated into a global knowledge.

The study adopts a qualitative and interpretative methodological approach, undertaking one teacher case study. Data were collected during two school years by semi-structured interviews, class observation, and documental data gathering. All interviews and classes observed were audio taped and transcribed. Data analysis was conducted combining the theoretical framework and data interpretation, considering the problem studied.

The results of the study suggest that the teacher is aware of the potential of investigation tasks, having knowledge of Teaching and Learning, but also knowledge of Curriculum. The characteristics of this type of tasks, including the freedom they give students and the consequent variety of approaches allowed, presuppose that the teacher has the knowledge of Mathematics needed not to fear its implementation. Her familiarity with the graphing calculator, that is her knowledge of Technology, turns this device into a good resource for this type of work proposals. The knowledge of the new emphasis that graphing calculator puts on mathematical content, and of the different representations available and of how to relate and move between them, suggest that the teacher is able of integrating her knowledge of Mathematics and of Technology. In the same way, when the teacher takes into account the new issues that technology requires students to deal with, including the usual difficulties they face, without forgetting the potential of this technology to the teaching and learning, it seems that the teacher is integrating her knowledge of Teaching and Learning and of Technology. And is the integration between all these knowledge into an Integrated Knowledge that seems to be reflected in the teacher’s practice and specifically in the diversity of investigation tasks proposed where the graphing calculator is an important resource. Thus, the KTMT model seems to be directly related to the practice of the teacher, seeming to include the potential to, through the analysis of teacher practice, identify possible areas for future professional development.

Keywords:

Knowledge for Teaching Mathematics with Technology, graphing calculator, investigation tasks.