The 8 Standards for Mathematical Practices are what I feel is the biggest shift in history in how we teach math. We are not simply putting a new name on the old way of doing business in math education, but instead we are actually changing to a new method of educating students in mathematics.
We can’t expect to give students the same input we’ve been giving them for years and receive a different output. Math lessons that are 100% teacher directed, utilize “ping-pong” math (teacher asks a question, gets an answer from the student, and fires off another question), or emphasize students memorizing procedures and concepts they don’t understand must become a thing of the past. Traditionally, we teach math “a mile long” by covering concepts “an inch deep” just to make it to the finish line. The result: students lacking a solid foundation of number sense in the elementary years, which causes problems when they move to algebra and other higher-order math.
The 8 Standards of Mathematical Practice (SMPs) represent a different input. As educators, we know differently about how students learn and understand math concepts, and thus we have a responsibility to act differently based on that knowledge. In order to be effective, today’s math instruction should involve a focus on inquiry-based teaching and student-directed lessons based on a correct implementation of the 8 SMPs blended with grade-level math standards. This will allow for students’ understanding of math concepts to extend “a mile deep,” even into the realm of real life application.
However, when reading the 8 SMPs, teachers often struggle to understand how they fully relate to their students in their grade level. I always recommend examining these 8 practices vertically, across the grade levels, to see how they build on each other and change from one level to the next. Check out these great resources from K-12 dissecting each practice