# Our teachers need a deeper knowledge of the mathematics they are teaching

#### Summary

The visions of mathematics teaching portrayed in Principles and Standards of School Mathematics (NCTM, 2000) and Professional Teaching Standards (NCTM, 1991) are premised on teachers having a deep understanding of the mathematics they teach. Yet many of our teachers in the elementary and middle grades have not had the kinds of learning experiences that could help them develop this knowledge. How can we help teachers broaden and deepen their knowledge of mathematics for teaching?

#### Strategies

*Developing content knowledge through professional development grounded in the practice of teaching*This strategy employs (a) rich tasks selected in an area that teachers recognize as a weakness in their preparation to teach, that they can try in their own classroom, that contain extensions beyond what students would be expected to do, and (b) occasions where teachers can work independently and with others to discuss ways of reasoning about problems, justifying approaches and solutions, and analyzing carefully selected pieces of student work that have the potential to push at teachers' own knowledge.

#### Diagnosis

These tools helped probe teachers understanding of mathematics.

*Learning from mistakes and misconceptions: PD materials*include tools that help teachers diagnose their own misconceptions by asking them to analyze those in examples of student work.