Research Tutorial Group 2009, Dr. Marek Rychlik
The professional development of teachers has been a major strand in educational research for many years now. In mathematics education, it has been generally believed that student learning was linked to the teacher's knowledge of mathematics, but the nature of that relationship has eluded researchers, making professional development a rich vein for research. In 1986, Lee Shulman introduced the idea of pedagogical content knowledge (PCK), which led to the a better understanding of the types of knowledge teachers need in order to teach mathematics.
However, it has been well documented that professional development (that is, the continuing education of inservice teachers) is not as effective as educators would like. My research focuses on the ways in which teachers bring knowledge gained in content-based professional development courses into their own classrooms. These connections may not be as direct or as explicit as previous measures have hoped, but there is strong evidence that sustained, content-based professional development influences teachers' understandings and attitudes toward mathematics (Sowder, Philipp, Armstrong, & Schapelle, 1998).
A fascinating opportunity I had in graduate school was researching collaborations between mathematicians and mathematics educators as they co-taught courses for pre-service secondary mathematics teachers (Prasad, McGraw & Blackburn, 2010). As a result, I developed an interest in how members of each discipline communicate within and across their disciplines. Since mathematics and math education are so closely tied together, practitioners of each use very similar language and forms of communication, but often the phrases mean very different things. Moreover, the process of collaboration forces instructors to make explicit thoughts or rationales they usually took for granted. In many cases, collaborators would spend time explaining their previously established methods of teaching.
An informal research interest of mine has been pre-service teacher preparation. Having taught the pre-service elementary education math course and supervised a student teacher in the Secondary Mathematics Education Program, I have become very interested in the ways in which colleges prepare undergraduates for a career in teaching. In courses and workshops I teach, I include research-based perspectives on elementary mathematics, such as Cognitively Guided Instruction (Carpenter, Fennema, Franke, Levi & Empson, 1999). This has formed in me a deeply-held belief in grounding pre-service teacher preparation in actual examples of student work and thinking. My teaching always links mathematics content to student thinking.