The research and educational activities of this project focus on advancing the field in the area of fraction operation algorithm development. The goal of the research is to identify core mathematical teaching practices that engage and support students in algorithmic thinking associated with fraction operations. The project has four objectives: (1) understand and document local instructional theories and routines of practice exemplary teachers use as they engage students in algorithmic thinking for fraction operations; (2) develop a prototypical model of core routines of practice generated from exemplary teachers that support students as they engage in algorithmic thinking for fraction operations; (3) design, pilot and study the usability of the prototypical model as a professional development tool with typical teachers as they engage students in algorithmic thinking for fraction operations; and (4) identify specific core routines of practice that are shown to be productive for use with typical teachers and explore ways of disseminating them at a larger scale.
Phase One involves collaborative work with and intensive observational study of the practice of four exemplary teachers while they teach a common unit on fraction operations. Individual teacher case and cross-case examination will focus on mathematical development, use of representational modes, aspects of purposefulness in the teachers' practice, and discursive considerations and positioning of the learner. The identified local instructional theories and routines of practice that emerge will lead to the development of a prototypical model of teaching practice that engages students in algorithmic thinking for fraction operations. The prototypical model will frame the development of activities and tools to be piloted and studied with 15 typical middle grade teachers from urban and suburban districts in Phase Two. A study group focused professional development setting will be used to implement, study, and refine frameworks, activities and tools.
The product of this work will be written educational materials that can be used by other teacher educators to support the general population of teachers in this domain. These materials will identify core routines of practice associated with algorithmic thinking for fraction operations and offer activities and tools to support their development in practice. The domain of rational number has been identified as the most challenging and the most essential topic in elementary and middle school mathematics needed to succeed in higher mathematics and science. Moving forward in this area is critical in the successful preparation of students for STEM careers.
