Understanding the Core Standards for Mathematics
For Mathematics, the Core Standards describe a progression of learning for students in grades Kindergarten through 12th that leads to college and career readiness. The Standards are different from previous academic standards in that they not only define what students should understand, they define what students should be able to do with the mathematics. In other words, "What does mathematical understanding look like?
As stated on the Common Core State Standards website, "One hallmark of mathematical understanding is the ability to justify... why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from."
The Standards begin with eight Standards for Mathematical Practice. They define what mathematical understanding looks like and the expertise that mathematics educators should seek to develop in students. The Standards for Mathematical Practice are then followed by grade level learning expectations.
Standards for Mathematical Practice
MP1 Make sense of problems and persevere in solving them.
MP2 Reason abstractly and quantitatively.
MP3 Construct viable arguments and critique the reasoning of others.
MP4 Model with mathematics.
MP5 Use appropriate tools strategically.
MP6 Attend to precision.
MP7 Look for and make use of structure.
MP8 Look for and express regularity in repeated reasoning.