A trajectory of teacher knowledge in designing a problem
There is international concern that the standard of mathematics education requires improvement. In order to facilitate this improvement, preservice teacher education needs to meet the demands of our technological age. As well, an international trend in mathematics curriculum development should focus on problem solving and modeling. This trend is evident in Australia, where the first national curriculum is currently being implemented. The need for attention to changing curriculum and introduction of reform-oriented pedagogies has ramifications for programs that provide preservice teacher education. New ways of thinking about mathematics and the teaching of mathematics is an important theme in such reforms. One offshoot of this development is focusing on teacher knowledge and its potential impact on students' performance. Our research is set against this background and the aim of this exploratory study is to identify teacher knowledge that is activated in the context of designing mathematical problems. The methodological approach is qualitative and quantitative. The participants of the study are twenty-six preservice teachers at an Australian university. Findings show that having preservice teachers design rich learning activities which incorporate modeling of problems provides opportunities for them to demonstrate a rich repertoire of mathematical knowledge for teaching. This mathematical knowledge is complex and its development can be captured by mapping the trajectory of their learning. A key finding is that our approach provided opportunities for participants to construct subject-matter and pedagogicalcontent knowledge in a blended manner. An implication for preservice teacher education is that program coursework needs to support the development and activation of different types of knowledge for teaching.