## Perspectives on Deepening Teachers' Mathematics Content Knowledge: The Case of the Arizona Teachers Institute

### Abstract

"The Arizona Teaching Institute (ATI) is a partnership between the University of Arizona and Tucson Unified School District. ATI has developed and implemented a Master's degree in Middle School Mathematics Leadership for middle school teachers, a Certificate in Mathematics Teacher Mentoring for secondary-certified teachers, and a postdoctoral fellowship in Teacher Preparation for recent mathematics Ph.D. graduates. The Master's degree in Middle School Mathematics Leadership is designed as a three-year, part-time degree consisting of two years of mathematics and education coursework, followed by a year of fieldwork. Courses are offered during the summer and part-time during the academic year. For example, the Numbers and Number Sense course described here addressed algorithms for operations; properties of arithmetic operations; and meanings for integers, rational numbers, and real numbers with a special emphasis on fractions. Instructors deliberately incorporated review of elementary and middle-school level mathematics concepts into explorations of more advanced topics. The course attended to pedagogical content knowledge through discussions about common misconceptions and strategies for presenting difficult material, interwoven with discussions of the mathematics disciplinary content. Although anticipated and encouraged by facilitators, these discussions were often participant-initiated, rather than planned. The sequence of mathematics courses addresses logic and proof as mathematical ways of knowing, and those learning goals are primarily dealt with in the Geometry and Algebra courses. In addition, the Numbers and Number Sense course modeled the process of making distinctions among related mathematical constructs as a way of knowing and understanding mathematics."

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