This post is about Standards Based Grading (SBG). Refer to this post if you want to know more about what I’m doing next year or can’t follow along what’s going on below.
Having read Mathy McMatherson recently, he convinced me to organize my standards into categories by types, not just units. If you want more info on these categories, read here and here. He breaks standards in to 3 categories: Foundational (I think he calls them Procedural), Conceptual, and Synthesis.
Brief Outline: Foundational, Conceptual, and Synthesis Standards
I’m going to briefly explain my understanding/adoption of these categories, and if you want a much better analysis, go read the two posts I liked above.
Foundational standards are ones that are essential for students to have before moving on. For example: before doing just about anything in Algebra I, a student must be able to do basic operations on integers: add, subtract, multiply, and divide. (That would probably be 4 different standards, at least, but moving on.)
I pictures Conceptual standards as ones that make up the majority of a course: being able to graph a line and understanding what that means, for example.
Synthesis standards are ones that combine two or more other standards, usually conceptual, but not necessarily, and are much more difficult for the average student. For example, two standards might be “S1: Basic operations (+, -, ×, ÷) with fractions” and “S2: Solving simple equations for a variable” and a sample synthesis standard might be “S3: Solving equations for a variable with fractions”.
(Whether or not S1 and S2 are conceptual or foundational might depend on the course. I would consider those foundational for a Pre-Calculus course.)
I really like this distinction because it helps the teacher to know what to look for. I decided that as I am assessing this upcoming year, I might not allow students to assess a synthesis standard unless they show at least “Proficient” in the standards that make up the synthesis standard.
Furthermore, getting a “proficient” or “mastery” level (my highest two levels) in a Synthesis standard would be cause for me to add a “proficient” or “mastery” level to the standards that are combined to form that Synthesis standard. This does a few things: (1) it adds to the amount of evidence that a student knows a standard, which is good for me and for them; (2) it could help their grade (right now I’m planning on averaging the latest 2 assessments).
However, doing poorly on a synthesis standard is not necessarily grounds for lowering a standard, and there are a few reasons for this: (1) I cannot necessarily identify which standard they did not understand or apply correctly in the context of a combined problem, unless they showed their work very carefully; (2) it may be that they are perfectly fine at each individual standard, but they have trouble combining the standards in some way because it relies on some other knowledge/standard that I did not identify.
All this figuring out “where/why does a student get a problem wrong” reminds me of an excellent website, which is Michael Persham’s project: mathmistakes.org. This website was only of cursory interest before I moved to SBG, but now this kind of understanding is essential for students’ grades. Which is excellent because it should have been essential even before the move to SBG. One of the things SBG requires (if implemented property) is that it forces teachers (and students) to focus on what a student does and does not understand, which is essential for effective teaching & learning. I hope to contribute (and get feedback) much more this upcoming year using that excellent website.
So understanding mistakes are important, and if ambiguous, I can “mark down” in a Synthesis standard easily from a Synthesis assessment, but not so easily from a non-Synthesis assessment. That’s just one more step to helping me use SBG better. The more of that I do now before the year starts, the better for me (and for my students!).