The Common Core State Standards have introduced new standards for mathematics. The Standards for Mathematical Practice describe varieties of expertise that educators at all levels will seek to develop in their students. These rest on concepts with longstanding importance in mathematics education. Firstly, these standards are based on the National Council of Teachers of Mathematics process standards of problem solving, reasoning and proof, communication, representation, and connections. Secondly, the standards are based on the standards of mathematical proficiency specified in the National Research Council's report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding, procedural fluency, and productive disposition.
The following standards serve for mathematics practice:
1) Make sense of problems and persevere in solving them
2) Reason abstractly and quantitively
3) Construct viable arguments and critique the validity of others
4) Model with mathematics
5) Use appropriate tools strategically
6) Attend to precision
7) Look for and make use of structure
8) Look for and express regularity in repeated reasoning
The new Common Core State Standards embody key shifts in the previously existing standards:
1) Greater focus on fewer topics
2) Coherence: linking topics and thinking across grades
3) Rigor: pursue conceptual understanding, procedural skills, fluency, and application with equal intensity
The Common Core State Standards in Mathematics were adopted by California in 2010. These cover the required levels for the grades from kindergarten to 12th grade in high school.