Collaborative Research: Applying and Refining a Model for Dynamic, Discussion-Based Professional Development for Middle School Teachers about Fractions, Ratios and Proportions

This project explores the effectiveness of two different versions of professional development (PD) designed to enhance middle school mathematics teachers’ understanding of fractions and proportions, and their teaching of these mathematical concepts to students. The PD uses an approach that engages teachers with web-based apps that allow them to test and experiment with their mathematical ideas. The apps, combined with guiding questions that challenge teachers’ thinking about fractions and proportions, serve both to promote critical thinking about the concepts and to further developing their understandings of the concepts. The researchers will use an innovative approach, topic modeling, to examine the effectiveness of each of version of the PD. Topic modeling will allow the researchers to identify patterns in the language teachers use as they participate in the PD, and subsequently, to better understand the development of the understanding teachers develop. The project has promise to not only enhance teachers’ instruction on topics with which students have traditionally struggled, but also to demonstrate the viability of Topic Models as a means to measure learning using natural language—an approach that could potentially replace large-scale, multiple-choice tests as a measure of student learning with learning activities in the classroom. The project uses a design-based research approach to focus on three main goals: expansion of a pilot PD model to include fractions and proportions; testing of a conjecture about the PD model focused on supporting teachers in making connections between learning content in novel ways to developing pedagogical content knowledge (PCK) from their experiences; and implementing topic modeling as an assessment model for measuring changes in teachers’ participation in the PD. Topic models will be used as the primary assessment, rather than pencil and paper assessments, because of their alignment to the content and the PD approach, which is highly interactive and focused on conjecture testing. The use of topic modeling opens an opportunity for qualitative data to be used as an assessment tool rather than relying on assessment instruments that may not be aligned to the instruction. Proposed outcomes of this work include: a pool of mathematical tasks for teachers that support playful engagement with important mathematical ideas; a guide outlining a coherent 30-hour experience for teachers that engages in developing both content knowledge and PCK related to fractions, ratios, and proportions; evidence of the PD program’s effectiveness that relies on topic modeling to measure change in teachers’ participation and learning in the workshops; data on two different approaches to supporting teachers in linking content knowledge development to PCK development; and a coding framework that defines “robust” understanding of fractions related to referent units and invariance. All aspects of the PD will be grounded in the use of dynamic, web-based “toys” (apps) that have been designed to support the development of robust understandings of proportion and fraction concepts. Contributions to the field include the PD model, the robust understandings framework, and findings specific to the use of topic models. One such contribution will be further insight into the sample size necessary to use topic models for assessment, which will help the field better understand how to use this quantitative approach with relatively small qualitative data sets. The Discovery Research preK-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.