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In the U.S., state adopted or developed college- and career-ready mathematics standards, including the Common Core State Standards for Mathematics, not only impact districts, students, and their teachers, but also university teacher preparation programs. In order to attain and sustain Common Core’s vision of developing mathematically competent citizens, teacher preparation programs must support pre-service teachers’ development of practical conceptions of the Standards for Mathematical Practice. In this article, we examine the mathematical practices middle grades pre-service teachers (grades 4-9 licensure) and mathematics teacher educators identified as playing a role in attempts to make sense of and work toward solutions to mathematics problems. In addition, we compare the mathematical practices indicated both within and across pre-service teachers and mathematics teacher educators. Results identify pre-service teachers’ potential difficulties operationalizing six specific mathematical habits of mind. Finally, we describe how such comparisons can guide the design of future teacher education and professional learning by describing a process for identifying problems and tasks with the greatest potential to support pre-service teachers’ development of practical conceptions of mathematics or other content-specific habits of mind.

Comparing the Mathematical Practices Pre-Service Teachers and Mathematics Teacher Educators Identified as Relevant to Problems and Tasks