The main design principles in the New York State Common Core Learning Standards (CCLS) for Mathematics standards are focus, coherence and rigor. These principles require that, at each grade level, students and teachers focus their time and energy on fewer topics, in order to form deeper understandings, gain greater skill and fluency and more robustly apply what is learned. Focus in the curriculum is meant to give students an opportunity to understand concepts and practice with them in order to reach a deep and fluent understanding. Coherence in the curriculum means progressions that span grade levels to build students’ understanding of ever more sophisticated mathematical concepts and applications. Rigor means a combination of fluency exercises, chains of reasoning, abstract activities and contextual activities throughout the module.
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the National Council of Teachers of Mathematics (NCTM) process standards of problem solving, reasoning and proof, communication, representation and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately) and productive disposition (habitual inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy).
Instructional Shifts Demanded by the Common Core Learning Standards in Mathematics
| Shift 1|| Focus|
| Shift 2|| Coherence|
| Shift 3|| Fluency|
| Shift 4|| Deep Understanding|
| Shift 5|| Application|
| Shift 6|| Dual Intensity|