We design our assessments so problems are centered around a specific standard. A problem may incorporate aspects from several related standards, but the central standard is the one that receives a grade. 

As we walk students through the problem, we discuss the solutions and potential errors. Students are asked to designate each part of a problem as essentially correct, partially correct, or incorrect. Some teachers use symbols instead, such as checks, x's, and circles. This allows us to discuss the nuance of different solution methods and how they reflect student understanding. Students then combine the parts of the problem into an overall level of understanding.

To further address your wondering, this process would allow us to discuss a part of the problem that comes from a related standard, but not include it in the grading aspect of the discussion. 

Thanks for your kind comments. One thing we love about students self-assessing that didn't make it into the video is its effect on our conversations with students. The students are asking questions that focus in understanding the concepts instead of asking questions regarding points or extra credit. 

We go over the answers as a class, so students are able to ask the teacher for clarification when needed. There is not a lot of peer interactions during the self-assessment. 

It was a long process! At first, a couple of brave teachers adopted the standards-referenced grading, proficiency scales, and self-assessment. The discussion surrounding the successes and challenges they faced encouraged other teachers to try it. Even our most skeptical teachers were happy with how the students responded, but it was a bumpy road. Even after 5+ years of pursuing this, our approach to grading and self-assessment is still evolving.

If you are moving in that direction, then I would encourage you and a colleague to pilot it.

For our AP courses, we rely on the rubrics provided for the AP exam. However, in non-AP courses, the students can be involved in building rubrics. 

One benefit of self-assessment that we did not anticipate was the impact it had on student discussions. The conversations have become more nuanced about the concept being assessed and less about arguing for points. 

Thanks for your comment. We have largely relied on AP scores to measure student understanding since it is the only outside measurement that students put their full effort into. The pandemic threw a bit of a wrench in analyzing this data, but overall we have been seeing an increase in passing student scores (by proportion) over the past 5 years.