The Standards for Mathematical Practice are eight simple descriptions of active learners in the mathematics classroom. Essentially, they are the habits of student mathematicians.
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning 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.
My favorite, and the most important in my mind, is number one on the list. Getting students to make sense of a problem and persevere is half the battle. If a teacher can get students to approach a problem with an open mind and a commitment to solving it, the other practices will fall in place. The biggest challenge and maybe the biggest strength of the Common Core is the push to get students to persevere in problem solving.
So often, students want to know the procedure or list of steps in solving a problem. Their one and only goal is to get the right answer. They don’t appreciate that there is not always one way to get to the correct answer.
What would it be like if students didn’t view math as a list of steps? What if mathematics was not viewed as a one way street that you follow from point A to B? How would students discuss problems if they viewed math as a box of tools that they can use in multiple ways to solve a variety of problems? I already try to foster these ideas in my classroom, but it can be difficult when students have been through years of “this is how you get the right answer.”
My daughter is in kindergarten this year. I am hopeful that by the time she is old enough to be a student in my algebra class, she and her classmates will be those “student mathematicians” that the Common Core promises. Hopefully, they will thrive from solving problems in creative ways.