Online Collaboration to Understand Pre-Service Teachersﾒ Developing MKT
Mathematical knowledge for teaching (MKT), or professionally oriented subject knowledge of mathematics, refers to both the mathematical content knowledge and the pedagogical content knowledge that teachers bring to teaching. To date, research on MKT has been concerned with identifying needed MKT for teachers and posed the challenge to better understand how it can be supported to develop. This project has focused on preservice teachers’ (PTs’) learning to mentor elementary-aged pupils’ work with rich nonroutine mathematics problems, and how MKT might be supported to develop through that process. Prior study has also indicated the need to figure out productive ways to orient and support instructors using the modules.
In this TUES-1 project we (a) studied how the context of an online laboratory (the Math Forum’s Virtual Fieldwork Sequence [VFS]) contributes to PTs’ mentoring of mathematics and whether MKT predicts how PTs work with the VFS modules, and (b) developed a prototype for professional development for instructors to accompany the VFS, or modules like the VFS, that is both collaborative and situated in the experiences and skills of the PTs using the modules.
We focused on the period when MKT is just beginning to develop. Our findings indicate that all participating PTs develop their understanding of the concepts in math problems through their mentoring and that their entering level of MKT predicts the extent to which they develop their abilities to engage instructional conversation and to use content-informed feedback in their work with pupils. The VFS enhances opportunities for mathematical discourse in the classroom as well as online. It provides PTs with language for facilitating mathematical thinking (e.g., grounded observations that use the Math Forum’s “I notice, I wonder” approach), as opposed to generic feedback (e.g., “good job”, “try it a different way”). It also focuses discussion on pupils’ mathematical needs and reasoning. For some PTs, the process of giving feedback on the problems also leads them to work with mathematical concepts (e.g., rates) in ways that are new and challenging for them.
Participating faculty members in this project have worked alongside Math Forum staff members to understand their PTs' MKT by reading research on MKT and studying the PTs' complete field experience, which includes the VFS and then student teaching. The participating faculty members have helped the Math Forum staff members to interpret project findings in light of their experiences as instructors and related research in this field. The collaborating faculty members have been involved in documenting and describing their experiences as project participants in the pilot of collaborative online professional development. They have been supported to collaborate on research projects, using the VFS context to further their individual research programs and professional advancement. In turn, the emergent process and projects become resources for future iterations of the community of practice that supports instructor orientation, investment, and success.
The innovative, integrated design of this project improves the teaching of pre- service teachers and their instructors, while furthering our understanding of PTs' MKT. The collaborative and situated approach enhances the likelihood of adoption at other sites, and involves instructors from institutions that represent diversity in both student population (including nontraditional students, underrepresented minorities, and first-generation students) and in the type of higher education institution (liberal arts college; state university; university regional campus, distance education program; and converted community college). The resulting teacher education community and corresponding professional development program will be broadly available through the Math Forum, with a wide online reach of close to 4 million visits each month. This project provides quality virtual content and methods for online professional development of undergraduate faculty members, content and methods made necessary by the increasing number of online mathematics teacher education courses.
One challenge for us in this project was that preservice teachers who are not interested in mathematics are not inclined to voluntarily complete surveys related to mathematics. We provided explanation of study purpose and used follow up reminders. However, we found that when instructors considered the survey content to be classroom work, surveys were more likely to be completed. This was possible because the surveys did contain module-like tasks.
Two papers describing study findings are in preparation for publication.