Characteristics of teacher knowledge produced by pre-service mathematics teachers: the case of open-ended problem-based learning

One major issue in mathematics teacher education regards the role of university-level mathematics in teacher knowledge. In the context of a design-based research project, an advanced mathematics teacher education course aimed at strengthening the connections between university-level mathematics and school mathematics was developed. In this paper, I present a case study, conducted within the education course, in which I analyse the characteristics of teacher knowledge produced by five small groups of pre-service teachers in an open-ended problem-based learning task. The results indicate the problem-based learning approach has the potential for enhancing specialised content knowledge such as knowledge of different representations of and applications of mathematical concepts. The results also highlight the challenges in using this approach for enhancing horizon content knowledge such as knowledge about the relationships between mathematical concepts. The findings in this case study suggest that problem-based learning can be used to develop mathematics teacher education, although further research is needed to design instructional practices that enhance pre-service teachers’ horizon content knowledge.