Abstract:

Developments in digital technology allow teachers to improve their teaching by presenting their students with better learning opportunities. Implementing digital technology in mathematics education demands changes in the approach to teaching such as favoring student-centered teaching, where the learning approach is exploratory and inquiry-based, and learners use the technology to discover and build their mathematical knowledge. Hence, it is crucial that teachers develop their TPACK – Technological, Pedagogical, and Content Knowledge. In essence, TPACK is an amalgamation of technological knowledge (TK), pedagogical knowledge (PK), and content knowledge (CK) (Koehler & Mishra, 2009, based on Shulman, 1986). The TPACK model has become a useful framework to describe and understand the knowledge teachers require to effectively integrate technology into their teaching. The model’s complexity is reflected in the common components of basic knowledge. For example, TCK – technological content knowledge – is knowing how technology can create different representations for a specific concept; it demands that the teacher understands how specific technologies can affect learners' skills and understanding of the relevant concepts and content. TPK− technological pedagogical knowledge – is familiarity with the range of technologies that can be integrated into teaching and understanding how their use can affect teaching methods.

Teachers with strong TPACK can use technology to expose their students to various representations of mathematical and scientific concepts during various inquiry and problem-solving, and problem-posing activities. Problem posing often requires the teacher to carefully analyze the structure and underlying concepts of existing problems, meaning that they require enhanced skills to effectively deconstruct and reconstruct problems (Kaur & Rosli, 2021). Dynamic geometry environments (DGEs) provide powerful tools to engage in problem-posing activities related to geometric concepts and relationships. In fact, several studies have explored how DGEs can facilitate and enhance teachers' abilities to pose effective geometric problems (Author et al., 2018, 2021).

The research question guiding this current research was: Does mathematical problem-posing in a DGE (GeoGebra) promote teachers' TPACK and, if so, how?

The research was conducted during the course "Integrating Technology into Geometry Instruction" which was given by the author as part of an M.Ed. mathematics education in primary school program.

The task that the in-service teachers were given was the following:
(1) choose a geometry problem from the textbook and "translate" it into the DGE, and
(2) identify what more can be asked as a result of its dynamic form and pose new geometry problems accordingly.

This process exposed the teachers to the inherent potential in the textbook problem, options for expanding the problem, and additional features and characteristics that could be pointed out and discussed in class.

In my presentation, I will describe the processes of two groups of mathematics teachers who worked on this task and the profoundly surprising way that their TPACK knowledge developed.

Keywords:

Primary school mathematics teachers, Technological Pedagogical and Content Knowledge (TPACK), problem-posing, dynamic geometry environments.