The last element that makes a “modern classrooms” approach to math instruction work is mastery-based grading. I typically set mastery at 80% accuracy. There are numerous benefits to a mastery model:
I am more able to understand what each student has and has not mastered
I can use that knowledge to provide more targeted instructional support to students when they need it
Students are more likely to retain the information long-term instead of simply “getting through” until the end of a unit
Students feel more confident and productive – they feel like they really understand what they’re learning and are more able to identify specific areas where they need more support
The first step is for students to develop mastery. In my math classroom, students engage in a mix of collaborative and independent work. Our math curriculum is problem-based – students mainly learn by trying a real-world problem and then discussing it with peers – and each activity and lesson builds on to the last narrative. There are various ways in which students develop mastery, including times when students work independently and then share their thinking with others, times when students dialog with partners, and times in which small groups work together to design something and organize their shared thinking or solve a problem. Students learn how to critique the work of fictional students and then how to transfer those skills to identifying mistakes and correcting their own work. Students are always given opportunities to revise their work and understand that revision is a necessary part of working towards mastery – no one is expected to get everything right the first time they try it.
The next step is to assess student mastery of the lesson, section, or unit. Students complete “Mastery Checks” individually to determine whether they’ve shown an appropriate understanding of the topic. When students don’t show mastery on a Mastery Check, I can work with students on the particular area of difficulty. Students also can identify which lesson was challenging for them and review that lesson specifically, as well as related resources – a skill that will help students greatly in their further education. Then, students can reassess. This term, I’ve experimented with providing students with Mastery Checks every few lessons instead of every lesson with mixed feedback from students. Some students have said that they prefer this because it takes up less time to check in bulk at the end of a section instead of individually at the end of each unit. Other students have said that they would like to go back to lesson checks because they want more immediate feedback on whether they understand something or not.
I look forward to continuing to refine this model to meet the needs of my individual students. I’ve been delighted with how students have responded to it for the most part – mastery-based grading definitely helps students develop a growth mindset. “I can’t do this” becomes “I can’t do this yet,” and “math is hard, and I’ll never get this” becomes “this lesson is hard, but I can ask for help.”