More resources of all types—money, time, leadership, attention—need to be invested in professional development for teachers of mathematics, and those resources already available could be used more wisely and productively. Each year a substantial amount of money is invested in professional development programs for teachers. Individual schools and districts fund some programs locally. Others are sponsored and funded by state agencies, federal agencies, or professional organizations. Much of the time and money invested in such programs, however, is not used effectively. Sponsors generally fund short-term, even one-shot, activities such as daylong workshops or two-day institutes that collectively do not form a cohesive and cumulative program of professional development. Furthermore, these activities are often conducted by an array of professional developers with minimal qualifications in mathematics and mathematics teaching. Professional development in mathematics needs to be sustained over time that is measured in years, not weeks or months, and it needs to involve a substantial amount of time each year. Our recommendations to raise the level of professional development are as follows:

• Local education authorities should give teachers support, including stipends and released time, for sustained professional development.

• Providers of professional development should know mathematics and should know about students’ mathematical thinking, how mathematics is taught, and teachers’ thinking about mathematics and their own practice.

• Organizations and agencies that fund professional development in mathematics should focus resources on multi-year, coherent programs. Resources of agencies at every level should be marshaled to support substan tial and sustained professional development.

In this report we have set forth a variety of observations, conclusions, and recommendations that are designed to bring greater coherence and balance to the learning and teaching of mathematics. In particular, we have described five strands of mathematical proficiency that should frame all efforts to improve school mathematics.

Over the past decades, various visions have been put forward for improving curriculum, instruction, and assessment in mathematics, and many of those ideas have been tried in schools. Unfortunately, new programs are tried but