NCTM's Quest for a Coherent Curriculum
In response to reports from an international study of assessments noting that the U.S. curriculum is unfocused and covers too many topics (IEA 2001), NCTM released the Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (2006). Focal Points identified the most important mathematical topics for each grade level PreK-8 and specified the mathematical content that a student needs not just to know but also to understand deeply, guided by the principles and processes described in Principles and Standards. At each grade level for PreK-8, Focal Points clusters the most important concepts and skills and adds a focus on reasoning and skill to arithmetic, geometry, and algebra, which are foundations for the further study of math and science. To clarify that a balance between skill and concept is necessary, the need for a solid understanding of basic facts is stated explicitly
Focus in High School Mathematics
For high schools, NCTM published the book, Focus in High School Mathematics: Reasoning and Sense Making (2009), which described and provided models of the type of reasoning processes that cut across the high school curriculum and that should be expected of high school students. The following broad list of reasoning habits illustrates the types of thinking that should become routine: analyzing a problem, implementing a strategy, seeking and using connections, and reflecting on a solution (9-10).