Besides the three major shifts in Common Core’s treatment of standards (focus, coherence, and rigor), the Common Core also sets expectations for the processes and proficiencies that students should demonstrate in every lesson. These eight “Standards of Mathematical Practice” were developed from research that identified the ways in which students must interact with mathematics content in order to develop a complete understanding.
The challenge is for teachers to develop lesson plans that give students the opportunity to demonstrate each of these practices. This will help students to become successful with math.
For example, the first Standard for Mathematical Practice is for students to be able to make sense of problems and persevere in solving them. A teacher needs to present students with problems, allow them the freedom to figure out what the problem is, and ask them to find the answer. In a classroom of students, there may be many ways to solve a problem. Instead of focusing on the single correct answer, this shift has students actively engaged in a manner that develops critical thinking and independence.
For instance, instead of teaching students how to measure and calculate a perimeter by telling the students the formula for perimeter at the onset of a lesson, a teacher may present students with an authentic problem that requires them to determine how to calculate a perimeter. For young students, the problem may be as simple as “How can we find out the length of a border needed to go around our classroom bulletin board?” The students work together to discuss the problem, find possible solutions, share their ideas verbally and ultimately discover how to calculate perimeter. At that point, the teacher begins her direct teaching to solidify their understanding and provide more examples. This type of teaching encourages students to be active learners and develop confidence in their abilities to understand and solve problems independently. Not only is this approach instructionally sound, but it is also much more engaging for students and turns a static math lesson into a quest for a solution.