The learning of mathematical practices, that is, the specific processes that successful mathematics learners engage in when doing mathematics, such as the use of justifications and various representations, is as important in achieving high performance in mathematics as it is to know the theory of mathematics. Yet, the role of these practices in school mathematics has been peripheral. Many students’ experience with mathematics is limited to the memorization and practice of facts and procedures and little emphasis is placed on the development of these practices. This is particularly true in diverse, urban environments where students have been traditionally under-performing in mathematics. However, recent reform efforts are calling for a shift of mathematics instruction to foster the development of such practices in all students. If these practices are to become a meaningful part of school mathematics programs, we must advance our understanding of students' development of these practices and the conditions that promote that development. While research has provided us with valuable insights on several of these practices, there has been little understanding of how these practices develop as a whole and over time especially in challenging instructional settings.
The Urban Math project is aiming to address this topic. Over the next five years this study will trace the development of middle school students' competencies in the mathematical practices of representation and justification and will identify conditions that influence that development. We first begin with a broad analysis of a large number of urban students’ conceptions of mathematical practices. This will be followed by a focused and detailed analysis of the development of 6th to 8th grade students, using a variety of instruments and classroom observations. The goal is to go beyond documentation of the current conditions, and to trace and understand changes in students’ competencies over time. Furthermore, the study will analyze classroom teaching practices that influence these changes. To achieve this, the students' teachers will participate in concurrent professional development activities designed to enhance their understandings of middle school students' development of mathematical reasoning and classroom practices that promote that development, and will also be studied in parallel with their students |
