Common Core Math Content Standards or any math-specific standards. This could also be called the “traditional” math grade. Typically, content skills and knowledge are not very transferable to other courses, except ones that directly use math content (e.g. physics).
Examples of assessments include exit slips, quizzes, tests, and content-specific tasks. There may be (and often is) more than one content standard per assessment. I typically assess three separate standards in one sitting.
Common Core Standards for Mathematical Practice or other 21st Century Learning Skills. These could be seen by some as an “application” grade, but should could (and should) include all standards for mathematical practice such as justification and precision. Typically, these skills are transferable to other courses and other fields.
Examples of assessments include error analysis, collaborative group activities, modeling projects, and any task intended to measure the mathematical practices. Just like content standards, you could assess multiple practice standards in one assessment. In fact, many of my collaborative tasks include both content standards and practice standards.
Scholarship standards represents a student’s progress towards the transferable qualities of being a productive student. This includes "soft skills" such as executive functioning skills, punctuality and preparedness, working flexibly, self-monitoring, and reflection. Typically, these skills are transferable to all other academic settings. One example of a scholarship standard assessment is a personal reflection using a rubric.
How these Interact with a Traditional Grading SchemeUnfortunately it can be hard to pull these three types of standards apart in the grade book, especially if you're working in a traditional system with an online grade book that averages all the grades together to get one final grade. If that's your reality, I suggest setting up your online grade book with these three buckets as categories. Then, when progress report or report cards get sent out, simply print out a category report. Then, you can:
- Send it home to parents so they can understand their student's specific strengths and areas for improvement
- Conference with the students one-on-one so they understand the connection between the categories (e.g. scholarship standards have an impact on content standards)
- Use it to help write comments on report cards (e.g. students with high practice standard scores often get something like "Works like a mathematician by collaborating with others, attending to precision, and persisting through challenges"
Now, I'm pretty sure this is all stolen. I vaguely remember reading about categorizing standards years ago, but I can't remember the source. So, if anyone can point me in the right direction, I would be happy to give credit where credit is due.