Facilitating Growth in Prospective Teachers’ Knowledge: Teaching Geometry in Primary Schools

Jun. 10, 2012

Source: Journal of Mathematics Teacher Education, Vol. 15, Iss. 3, June 2012, p. 227-249.
(Reviewed by the Portal Team)

The current study focused on growth of understanding about teaching geometry by a group of prospective teachers engaged in lesson plan study within a computer-supported collaborative learning (CSCL) environment.

Specifically, the authors were interested to investigate how a lesson plan study (LPS) activity conducted within the context of a learning environment based on the adoption of both socio-cognitive and technological determinants of knowledge building (Scardamalia 2002) would impact on prospective teachers’ repertoires of pedagogical-content knowledge (PCK) about teaching primary school mathematics.

The research study was guided by the following two research questions:
1. What changes occurred to the participants’ repertoires of PCK about the teaching and learning of primary school mathematics?
2. What factors influenced those changes?

Design and method
This study used a teaching experiment methodology.
Lesson plan study was the vehicle chosen to frame the teaching experiment.
This methodology was extended by having the prospective teachers collaboratively design lesson plans for the teaching of geometry within the context of a CSCL community.
The participants in this study were a tutorial group of twenty-one prospective primary school teachers enrolled in a one-semester third-year Bachelor of Education (Primary) mathematics education subject at a university in eastern Australia.

The 21 prospective teachers were formed into seven planning teams of three.
Each team was allocated a particular primary school geometry topic (e.g., symmetry, transformations, or 3d shapes) and grade levels (lower or upper primary) and asked to generate a lesson plan for the topic appropriate for the designated grade levels.


By the end of this study, it was found that the prospective teachers had made considerable advances to their repertoires of PCK.
The authors found several factors that influenced growth in PCK.
One of these factors was the provision of spaces for both private and public discourse.
Within this study, within-team private discourse occurred during team face-to-face meetings and within their online Private Team Spaces.
The private discourse enabled the teams to better process ideas implicit in the cognitive scaffolds.

A second factor was provided by the asynchronous nature of the between-teams public discourse that occurred in the Knowledge Forum virtual space.
The opportunity and time to process information when generating or reacting to comments provided by the asynchronous public discourse enabled the teams to better engage in the advancement of the epistemic artifacts.

A third factor was the meta-language scaffolds provided to the participants.
The analysis of the data showed that Knowledge Forum discourse played important roles in facilitating the knowledge building of PCK epistemic artifacts.
Two of the Knowledge Forum scaffolds did much to enhance knowledge-building discourse: ‘‘What we like about your plan’’ and ‘‘How your plan can be improved’’.
The three other scaffolds, ‘‘How our plans are similar’’, ‘‘How our plans are different’’ and ‘‘Asking for help/advice’’, had limited roles in facilitating knowledge-building discourse.

Finally, the analysis of data revealed that meta-language facilitated knowledge-building discourse and the growth of the prospective teachers’ pedagogical-content knowledge about the teaching of geometry in the primary school.


The evidence from this study suggests that having prospective teachers engage in LPS within the context of a CSCL environment that provides appropriate cognitive scaffolding and both private and public spaces for knowledge-building discourse is a most efficacious means for facilitating the construction of mathematical PCK.

It also indicates that the efficacy of the prospective teacher activity utilized in this study could be further enhanced in three ways.
First is the scaffolding of longer threads of online discourse.
Second is the expansion of meta-language from Pirie and Kieren’s (1994) theory to include both growth of understanding and teacher intervention meta-language notions.
Third is enhancing the knowledge-building efficacy of the private discourse spaces.

Pirie, S., & Kieren, T. (1994). Growth of mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics, 26, 165–190.

Scardamalia, M. (2002). Collective cognitive responsibility for the advancement of knowledge. In B. Smith (Ed.), Liberal education in a knowledge society (pp. 67–98). Chicago: Open Court.

Updated: Apr. 30, 2014