Deepening research on the mathematics teacher
There now is a large body of research on the mathematics teacher that covers a broad range of topics, directly or indirectly related to prospective and practising teachers’ learning or education. Specific areas of the field of mathematics education addressed by these topics include mathematics teachers’ knowledge, beliefs, identity, learning, teaching and professional development. Given that we now know a lot about these areas, the challenge for researchers is to not merely validate what we know, but, in some way, to transcend what already exists to broaden or deepen our understanding of the mathematics teacher and effective teacher education.
The articles in this issue of the Journal of Mathematics Teacher Education provide a basis of interpreting how some researchers are trying to deal with this challenge. The four articles address topics for which there is clear evidence to support their nature and importance to mathematics teachers’ learning and teaching. Liang Soon Tan and Keng Cheng Ang’s article highlights a school-based professional development; Dawn Teuscher, Kevin Moore and Marilyn Carlson’s article highlights teacher use of student thinking; Sarah Roller’s article highlights noticing; and Vince Geiger, Tracey Muir, and Janeen Lamb’s article highlights video-based professional learning. However, while the studies involved validate to various degrees what is known about these areas, they also contribute to our understanding of these areas based on the frameworks, constructs, and/or contexts they employed as indicated in the following summaries of them.
Tan and Ang investigated a school-based professional development (SBPD) program that was devised and implemented in three secondary schools in Singapore to help teachers develop the necessary competencies for teaching mathematical modeling. They adopted a framework for mathematical modeling instruction as a resource for teachers to plan and design modeling learning experiences in the SBPD. The framework consists of a set of decision procedures that aim at helping novice teachers to plan developmentally appropriate modeling lessons. Based on two of the participants, the authors show how this SBPD has potential to positively influence teachers’ knowledge and enacting modeling learning experiences.
Teuscher et al. investigated the ability of a United States teacher to effectively focus on and leverage student thinking in the moment of teaching. They adopted the construct of decentering to interpret the teacher’s actions and thinking in making in-the-moment instructional decisions based on student thinking. They applied decentering in a way that was sensitive to the teacher reflecting on and building an in-the-moment model of student thinking. They share specific instances of a secondary mathematics teacher attempting to make sense of and act on student thinking while teaching that illustrate the effect of decentering on student–teacher interactions and a teacher’s ability to effectively understand and draw on student thinking to inform her instruction.
Roller investigated what a sample of secondary mathematics prospective teachers (PTs) in the United States were able to notice when viewing videos of their own co-teaching in a microteaching setting with peers. She adopted a developmental model of teacher concerns and a noticing framework to gain insight about PTs’ abilities to notice in their own videos. The PTs successfully used lenses that had been modeled and developed in the methods class to make a variety of observations. They demonstrated the ability to notice good and problematic moments and to look beyond themselves in the video and focus on students and student learning that went beyond the level that past research had expressed for novice teachers.
Finally, Geiger et al. investigated the potential of video-stimulated recall teacher professional learning for supporting teacher reflection on the teaching of numeracy in Australia. They adopted a two-dimensional framework (levels of reflection and objects of the reflective process) related to the utilization of teacher reflective practice as a means of enhancing instruction. They considered two situations with teachers who participated in “relatively short programs” that focused on improving the teaching of numeracy: (1) One teacher viewed videos of his own classroom while interacting with one researcher. (2) A pair of teachers worked with videos of each others’ classrooms with a pair of researchers. They found that video-stimulated recall was an effective medium for promoting teacher professional learning in both cases.
The combination of framework or construct and context used in each study was central to making insightful contributions to the field. This implies one way of deepening research on the mathematics teacher, that is, considering unique combinations of framework and contexts.
Two of the articles involve “intervention studies” to impact change in the teaching of modeling and numeracy, respectively. The other two articles involve studies of teacher thinking and noticing. The limitations, both explicit and implicit, of these studies also suggest examples of ways or specific areas in which deeper research is needed regarding mathematics teachers’ learning, thinking, and teaching.