## Using Math to Teach Math: Mathematicians and educators investigate the mathematics needed for teaching

### Abstract

The Mathematical Sciences Research Institute (MSRI) hosted a workshop in May 2005 to provide an opportunity for mathematicians to cooperate with experts from other communities on the improvement of mathematics teaching and learning. The organization of the workshop and of this booklet draws significantly from research conducted at the University of Michigan by Deborah Ball, Hyman Bass, Heather Hill, Mark Hoover Thames, and others."The goal of the present document...is to draw more mathematicians' attention to the problem of the mathematical preparation of teachers and to assist those who want to get involved. It is my hope that by providing a coherent synthesis of the many ideas assembled at the workshop, this document will support mathematicians, mathematics educators, and others in their efforts to improve mathematics courses and programs for K-8 teachers. ... The work seeks to understand the nature of teacher mathematical knowledge as it arises out of, and is used in, teaching. Emerging from this research is a characterization of mathematical knowledge for teaching as, just that, mathematical knowledge for teaching. In other words, the mathematics teachers need to know is connected to the distinctive work teachers do. This characterization of mathematical knowledge for teaching focuses attention on what matters most -- that the mathematics taught to teachers be useful to them and help to improve teaching and learning. It also provides a framework for viewing and connecting a variety of efforts across the country that work on the problem of teacher content knowledge in different ways. For both reasons, this characterization of teachers' mathematical knowledge served well as the basic structure for the workshop and for this document."