Abstract:

The key person for the successful integration of technology in the classroom is the teacher, due to the fact that he/she is in charge of the designing, and the application of teaching and the coordination of learning outcomes. In order to successfully integrate technology in mathematics teaching, three types of knowledge are needed: (a) technological knowledge, that is to know how technological tools are work, (b) content knowledge, in other words to know the concepts, the processes and the philosophy of the cognitive domain teachers are suppose to teach and (c) pedagogical knowledge, that is to know contemporary methods of teaching and the philosophy of education (e.g., Koehler & Mishra, 2008).The theoretical framework of Technological Pedagogical Content Knowledge (TPACK) provides a strong foundation about the interconnection and intersection of content, pedagogy and technology. The purpose of this study is to examine how the involvement of prospective teachers in authentic exploration activities that integrate contemporary technological tools can enhance the TPACK in 3D shapes’ nets.

Fifteen prospective teachers participated in two exploration activities. The first activity asked the participants to construct all the best possible nets of a cube and then write a set of instructions for constructing all the possible nets of a cube. The second activity required students to construct different nets of hexagonal pyramid and provide a check-list of criteria that a pyramid net should meet. The participants were asked to make their constructions by using the dynamic software Origrami Nets (developed under the DALEST Project). Origami Nets allows the users to build nets by selecting 2D figures and then fold them. The data for this study were collected through videotape of students’ work during the activities, students’ constructions in the software, students’ answer sheets and researchers’ field notes. Data were analyzed using interpretative techniques for evidence of students’ interactions with the software and for evidence of enhancing aspects of their technological pedagogical content knowledge.

The results of the study provided evidence to suggest that students’ interaction with the dynamic application could enable students to overcome their difficulties, misconceptions and insufficient knowledge regarding 3D shapes’ nets. In the first task, students managed to construct the eleven nets of a cube and most importantly they reflected on their building procedures to write a set of instructions for building cube nets, by providing the least possible information. In the second task, students constructed a great variety of pyramid nets and provided sustainable criteria for constructing pyramid nets. Their description showed that their interaction with the software could have enhanced not only their technological knowledge, but aspects of the interaction of their technological knowledge with (a) their content knowledge, by providing a classification of cube nets, and (b) their pedagogical knowledge, by self-reflecting on the critical dimensions of 3D shapes’ nets teaching, such as the effective coordination and interaction of visualization processes and the apprehension of 3D shapes properties.

References:
Koehler, M. J., & Mishra, P. (2008). Introducing TPCK. In AACTE Committee on Innovation and Technology (Ed.), Handbook of Technological Pedagogical Content Knowledge for Educators (pp. 3 – 29). New York and London: Routledge.

Keywords:

Technological pedagogical content knowledge, nets.