
As I am currently teaching a 4graduate course mathematics series at UMF for math leaders, I zeroed in on the statement on p. 60:
"In other words, a coherent program supports effective teaching as well as higher
levels of student learning."
In codeveloping these graduate courses, I have been reading about mathematical content knowledge. Below I have included a few articles by two names in the field, Heather Hill and Deborah Ball:
 · Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development initiative. Journal for Research in Mathematics Education, 35 (5), 330351.
 · Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371406.
 · Hill, H. C., & Ball, D. L. & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topicspecific knowledge of students. Journal for Research in Mathematics Education, 39, (4), 372400.
This work listed above mirrors the readings this week that discuss the NCTM Professional Standards: communication, reasoning & proof, representations, connections/integration and problem solving in real situations.
What math content knowledge does a teacher need to teach math effectively.
This is my favorite section of the book so far, probably because I am currently so steeped in the content Leinwald presents here. In so few pages he has hit so many high points:
 exercises vs problems; characteristics of tasks: rich opportunities for student to be active and to perform as they STRUGGLE to grasp important mathematical ideas.
 coherence: learning progressions, logical structures, focus on connections & making sense of...
