This paper examines what teacher educators, policymakers, and teachers think they know about the current mathematics reforms and what it takes to help teachers engage with these reforms. The analysis is organized around three issues: (1) the "it" envisioned by the reforms; (2) what teachers (and others) bring to learning "it"; (3) what is known and believed about teacher learning. The second part of the paper deals with what is not known about the reforms and how to help a larger number of teachers engage productively with the reforms. This section of the paper confronts the current pressures to "scale up" reform efforts to "reach" more teachers. Arguing that what is known is not sufficient to meet the demand for scaling up, three potential hypotheses about teacher learning and professional development are proposed that might serve to meet the demand to offer more teachers opportunities for learning. (Contains 81 references.) (Author/ND)