## Researching Mathematical Meanings For Teaching

### Abstract

"Teachers' mathematical knowledge for teaching is a central focus of recent research on teaching mathematics. At the same time, research on mathematical knowledge for teaching has focused largely on teachers' declarative knowledge, which is difficult to link to teachers' decisions and actions in the context of teaching or planning to teach. Much of current research on assessing mathematical knowledge for teaching seeks correlates between declarative knowledge and successful teaching instead of looking for reasons for teachers' decisions and actions. This distinction is important when the goal is to use assessments diagnostically, to design interventions meant to affect teachers' instructional decisions and actions. In this chapter I argue in principle and by example that a focus on teachers' mathematical meanings for teaching mathematics is both important and potentially productive regarding the improvement of teachers' teaching, which I take as necessary for the improvement of students' mathematical learning. I also outline a method for developing items and instruments that focus on teachers' mathematical meanings for teaching mathematics. I then examine how we can link research and assessment more intimately than simply using the results of each in the activities of the other."