CCSSM Standards for Mathematical Practice - #1 & 2

Standard #1: Make sense of problems and persevere in solving them.
Important Points:

• Problem solving is notoriously a difficult task for students of all grades levels. Teachers have been known to create more basic or simplified problems for their students to solve, in hopes of eliminating confusion. However, this is not the goal of the CCSS Mathematical Practices. In fact, this simplification of problems does not allow students to be challenged or take away any meaning from problem solving.
• It is crucial for teachers to create effective problems for students to solve. The CCSSM recommends that problems are interesting to students, utilize meaningful mathematical situations that are attainable for students to solve, allow students the opportunity to apply the concepts that they are currently learning or have previously learned, are challenging enough, allow for multiple solving strategies to be used, and have the ability to gauge a student's understanding of the problem. 
• Problem solving involves many comprehension strategies that students learn in reading. These strategies can greatly assist students while problem solving. Encouraging students to break a problem up into smaller, more understandable pieces may help them to identify the most important information, decide useful strategies to solve, and reflect on problems they have previously solved that may be similar to the one at hand.
• Some students get so caught up in finding the right answer to a problem, that they do not think about anything else while problem solving. It is important for a teacher and students to remember that getting a correct answer is great, but just going through the process of problem solving can be very useful and students can take a lot of learning away from it to apply to future problems.

Standard #2: Reason abstractly and quantitatively.
Important Points:

• Reasoning in mathematics can help students to better comprehend and find effective ways to use concepts and procedures. In addition, reasoning can help students to look back on past information that they have learned, and apply it to their current learning.
• Helping students to build a strong number sense can lead them to have better reasoning abilities in mathematics. Some things that can assist with this are helping students to apply relationships to numbers, realizing the largeness and complexity of certain numbers, and learning different ways to compute numbers.
• Promoting the discussion of reasoning as a whole class or in small groups can also benefit students in building their reasoning skills during problem solving.
• Students who can reason effectively look at mathematics as more than just solving number problems and getting a correct answer; they see it as a way to understand their own lives and the world that they live in.

References:

Briars, D. J., Austurias, H., Foster, D., and Gale, M. A. (2013). Common core mathematics in a PLC at work: Grades 6-8. Bloomington IN: Solution Tree Press.

Larson, M. R., Fennell, F., Adams, T. L., Dixon, J. K., Kobett, B. M. & Wray, J. A. (2012). Common core mathematics in a PLC at work: Grades 3-5. Bloomington IN: Solution Tree Press.

Larson, M. R., Fennell, F., Adams, T. L., Dixon, J. K., Kobett, B. M. & Wray, J. A. (2012). Common core mathematics in a PLC at work: Grades K-2. Bloomington IN: Solution Tree Press.

National Governors Association (2010). Common Core State Standards Initiative - Mathematics Standards. Retrieved from http://www.corestandards.org/