I fundamentally believe that a key to learning mathematics is to develop habits of mind that, among other things, help you reason about mathematical situations. To be prepared for the future, students need more than just a memory bank of facts and procedures. They need conceptual understanding, strategic competence, adaptive reasoning, and a productive disposition to be able to use mathematics to solve new problems.
My research aims to address the growing need for students to learn mathematics at the middle and high school grade level by engaging in mathematical practices, such as justifying and proving, as part of their everyday experience in the mathematics classroom.
In particular, I have sought to:
- identify and document aspects of students' learning when producing mathematical arguments, focusing on practices that bridge students' intuitive, empirical arguments to more logically sound, deductive arguments ( Bieda & Lepak, 2012)
- investigate the development of students' understanding of how to evaluate arguments (Bieda & Lepak, 2014); and
- unpack how existing curricula support learning about mathematical argumentation (Bieda, Ji, Drwencke & Picard, 2014; Bieda, 2010).
I am also focused on research and development of structures for prospective teacher education that promote novice teachers in developing knowledge and skills to engage students in mathematical practices. Some of this work has examined how incorporating lesson study in secondary mathematics teaching methods courses can promote novice teacher reflection on practice and, perhaps more importantly, catalyze mentoring of novice teachers by experienced mentors when novices and mentors collaborate during the lesson study process. A manuscript on this work is forthcoming in the September 2015 issue of Mathematics Teacher Educator.
My work on using post-secondary, non-credit bearing remedial courses as sites for prospective secondary mathematics teachers to engage in supervised teaching is currently funded with an NSF TUES grant #DUE-1245402 (2013-2015, $194,717). More information about the project can be found here.
Most recently, colleagues Kenneth Frank, Peter Youngs, Serena Salloum and I have received funding from both the W.T. Grant Foundation and the NSF REAL program (#DRL-1420532, $1,499,472) to study the effects of beginning elementary teachers' school-based social networks on their enactment of ambitious mathematics instruction. This funding will provide more opportunities to better understand the effects of mentoring on novice teacher practice.