Advocates of problem-based instruction argue that the approach can help students develop a deeper understanding of mathematics, acquire more positive attitudes toward mathematics, and gain experience with more authentic applications of mathematics. Engaging students in problem-based instruction, however, increases challenges to teachers who must attend to the influence of student prior knowledge and adjust instruction accordingly. The proposed project will develop and study a professional development framework that is designed to help high school geometry teachers attend more carefully to student prior knowledge, interpret the learning implications of student prior knowledge, and adjust teaching practices accordingly. Participating teachers will learn to perform these complex tasks by participating in study groups to analyze animations of productive teaching practices; to collaborate in planning, implementing, and analyzing geometry lessons; and to critique videos of their own classroom instruction. Prior research has shown that collective examination of videos can help teachers increase attention on student thinking, a key to noticing and accommodating student prior knowledge.
A key, innovative feature of the professional development framework for this study is the use of animated vignettes of classroom instruction to prepare teachers to examine videos of their own practice. The advantage of using cartoon-based animations of classroom practices is that they can be designed to depict specific teaching actions while excluding the usual distractions in videos, such as physical features, clothing, or individual mannerisms. Also, teachers can develop a critical eye for relevant interactions without feeling the need to be overly polite when discussing fictional scenarios portrayed by cartoon characters. This preliminary practice will also enable teachers to develop a common language about noticing and responding to student prior knowledge before critiquing videos of their own classroom practices.
This project advances knowledge of professional development experiences that help teachers notice and take into account the prior knowledge that students bring to the classroom. Results from studying the effects of coupling analysis of animated vignettes of classroom practices with critiquing videos on one's own classroom practices have the potential to significantly enhance professional development practices among mathematics teachers, as well as teachers in general. Results from the project will be broadly disseminated via conference presentations, articles in diverse media outlets, and a project website that will make project products available, be a location for information about the project for the press and the public, and be a tool to foster teacher-to-teacher communication. The results of this study, as well as the protocols and instruments developed during the research project, will inform and support the researcher's own efforts to better understand and improve teacher learning. The education plan of the researcher focuses on translating the outcomes of this study to the practices of preservice teacher education by connecting instructional decision-making more explicitly to research on student learning, thereby promoting learning trajectory based instruction.