The Common Core State Standards in Mathematics require us to no longer teach surface-level concepts to students using procedures they don’t understand. I refer to this as going a “mile long” with concepts, by covering all the “things” we are “supposed” to cover regardless whether or not the student truly understands and can apply the content we are teaching. Instead we need to make a paradigm shift and start teaching math concepts a “mile deep.” If students only understand the procedures with which to solve a problem by showing them with pencil and paper, do they truly understand it? Many students can show they “understand” the concept but their application skills for how to solve the problem and how to communicate their reasoning are often much weaker than we think. How far do you take your students in the concepts you teach in math?
Performance Tasks or Rich Math Tasks are the outcome or execution of the the CCSS and 8 Mathematical Practice Standards being taught solidly, which will require students and teachers to go beyond the basics in their math thoughts. They provide the opportunity for students to grow in their understanding, strategies, and reasoning skills. Teachers are able to use performance tasks to formatively assess how deeply students are understanding the concepts being taught. Performance Tasks give you guidance, as a teacher, to decide where you need to put more emphasis in your instruction and where misconception may lie. I challenge you to give your class a grade-appropriate Performance Task (from the website below) and comment about your thoughts on how well your students did. Or if you have already embedded Performance Tasks as a part of your math instruction, tell me how it has changed the way you teach math. You will discover you can rate your students as Novice, Apprentice, Practitioner, or Expert (NAPE) across three arenas of learning math.