Through my first years of teaching so far I have come to realize that a math classroom needs a specific culture built into it. I want students not only to "get" the things they are taught (what does this mean anyway?), but to actually engage in the act of practicing mathematics. There shouldn't be such a disparity between the work of actual mathematicians and how students experience mathematics in school. And on top of this success in today's workplace does nothing short of requiring students coming in to be creative thinkers with strong collaboration skills. Students need real chances to build these skills to the point where they become habits before they get to college or the workplace.
It is pretty well known that we remember very little of what we only see or hear but much of what we actually experience. And it takes failing and struggling. And it takes time. So I think that it is unreasonable to only give a student one chance to show what he or she has learned. The brain has remarkable plasticity to grow and learn, and it is even designed for making mistakes and needing multiple tries to achieve mastery of something. This means that grading should be designed around this learning process. This is why I use an adaptation of Standards-Based Grading (SBG). Here are the particulars:
- The year is broken down into core content skills. We learn them together.
- Students take a test after we have covered a few skills.
- Students are given a score for each skill on a scale of 0-4 based on their level of understanding.
- Students are given feedback to help them take their learning and move it forward.
- Any skill that isn't mastered can be retaken once a student feels they have a better understanding.
- Students fill out a reflection at the end of each quarter to get them thinking about their learning and habits of mind.
Here is the scoring rubric for content skills as well as a sample copy of a test, which contains a section for feedback and a section for the student to make corrections to the original test.
Just as important as the content standards are the mathematician and scholar standards. I call these the TARMADs and the TARSADs. These are essential habits that excellent mathematicians and scholars should consistently display.