Recycle Your Math is an idea I adapted from a wonderful professor in graduate school. In fact, all of the professors in our department used this technique to further our understanding and facilitate Mastery Learning.
Here’s how it works:
When you return assessments or other assignments, ask students to “recycle” their work by completing this form. The goal is for students to closely examine the concept, the processes involved within the concept, how and why it works, and their own understanding.
Explain that they can earn back half of the points (or some other amount you deem fit) lost on each question if, and only if….
• all of the steps are accurately shown
• the answer is completely accurate (no partial credit on recycling!)
• the process and reasoning involved in completing the problem are explained in detail
Examples of these requirements are included on the recycle form (I’ve provided 3 versions of the form: one with an elementary example, another with a secondary example, and one blank.), but I tell them to write as if they are explaining their work to a younger student and to go beyond the typical standards of “show all work”. In other words, prove that they see and get the entire picture, not just the outline. I find it helpful to have students complete the “recycle” in class at least once before assigning it for homework. See the preview for an annotated visual representation of this explanation.
Common Core Standards: in MATH PRACTICE
MP1 Make sense of problems and persevere in solving them.
MP6 Attend to precision.