When you were describing the idea of having A quizzes vs B quizzes (with A quizzes being more valuable), I was thinking about how to make students think of points more in the way that they think of objectives. Here’s the first idea I have (this is centered around using a system that mirrors my conjunctive-style grading, so please imagine it with other tweaks that make it the way you’d want it to be):
- Figure out how many A objectives are in the first quarter. Divide 70 by the number of A objectives for that quarter. That is the number of points that each A objective is worth during that quarter (may vary by quarter). Each A-level quiz is worth a number of points equal to (the number of A objectives in that bundle) * (the value of each A objective for that quarter).
- Do the same thing with B objectives in the first quarter, but this time divide 20 by the number of Bs for the quarter. That is the number of points each B objective is worth that quarter.
- Create a tree structure where each bundle is dependent on bundles beneath it. So the B-level quiz for that model would be above the A-level quiz for the same model. The B-quiz for projectile motion would be above the B-quizzes for CVPM and CAPM. The central force quizzes would be above the UBFPM quizzes (both A- and B-level). Etc etc. Actually, even cooler might be to have your students decide on how to construct the tree as it goes along, so that you are building a concept-mapping activity right into the assessment structure and giving the students more control and ownership in the process. It would probably be helpful to give them an example tree of skills at the start of the year from some other arena that they would be able to understand by analogy (even if they don’t create the physics tree themselves).
This wasn’t included in my original comment, but I drew up the quick beginnings of an example physics tree to make the rest of this post a bit more visual. Here you go—
- You need a way of keeping track of each student’s score specifically in each part of the tree structure (I think this could be accomplished without too much trouble in either AG or BH). So. Here’s the conjunctive-SBG part snuck into points clothing (bear with me, this will take a few bullet points of setting up): In order to be eligible for any particular quiz, they must have mastered all of the bundles on which it depends (per the tree). So to take a CVPM B-level quiz, they must have current mastery on the CVPM A-level quiz. To take a PMPM quiz, they must have current mastery on the CAPM B-level quiz (and the CAPM/CVPM A-levels, and maybe others, depending on the specifics of your tree).
- B quizzes would necessarily involve A objectives. It might be possible to show some holes in A-level understandings on a B quiz. That should affect the score for the A bundle, since having the score go up and down throughout the process of gaining deep mastery is a pretty essential part of SBG. With the point system, that can be a little rough (especially if parents are seeing grades constantly reported). Here’s the idea, though—if a student later regresses on a previously mastered A objective, it changes the score for that A-level bundle, but it just freezes the scores for all of the bundles dependent on that A-level one (that is, the other bundle scores still count as part of the grade, but cannot be improved yet). In order to test at any higher level in the tree in the future, the student must go back and regain a mastery-level score on that older A-bundle. Once they have, the other bundles are now unfrozen and can be tested on again. So more than just because of a higher point-worth (something that is sometimes too abstract or far-off-feeling to teenagers), the A-objectives (and even the earlier B-objectives, like solving kinematics problems) are very clearly essential. And lacking mastery on a core skill requires immediate attention and remediation.
- It might be necessary to be a little more forgiving about what triggers tree-freezing when it comes to B-level bundles. It might be a certain number of Bs in the bundle that must be mastered to test at a higher level, or it might be that particular ones in the bundle must be mastered in order to advance. Solving problems with UBFPM should be a B-level, not an A-level objective (since it is about problem solving and not a conceptual skill or diagram). It still must be mastered in order to have a chance at solving problems with the central force model.
- I’m leaving the final 10 points of the grade (how to get above a 90) up to what you do already (or would like to do for that piece). Capstone project? Goal-less problems? Etc. Or, if those don’t make sense for a particular class, maybe the Bs can get you all the way to 100?
- Throughout the quarter, the grade could be constantly reported since the total number of points available that quarter is 100. It will take quite a while for the students to get a grade that doesn’t sound ridiculous (“I have a 13 in Physics right now!”), so it would keep a bit of the feel of the your-grade-does-not-exist (until I have to turn it in at the end of the semester) aspect that I really like in my own system.
- Which maybe leads to another piece to consider—whether the grade should start at 0/100 or 50/100 at the start of a quarter. If it makes more sense to start at 50, then each A would be worth 20/(number of As) points each quarter.
- The old objectives (from a previous quarter) would still be relevant in future quarters, so they may continue to be tested (and may required being tested if they result in freezing the higher parts of the tree). At the end of a new quarter, it might make sense to update the grade for a previous quarter. Same after the exam.
- Even if you ultimately have to do some averaging of an exam and quarters, the day-to-day business of learning physics would probably be rather SBG-like with this type of system. Also, they’d be really, really ready to crush an exam since they’ve been required to keep testing on old skills until they internalize them.
Anyway, that’s just the first draft of an idea that I’ve had so far about how to make SBG live within such a constrained points system.
One other thing—I really like your requirement of getting help from someone before being allowed to take a new test. How do you check for that? I’m imagining that they must have another person (a classmate, someone from another section, an older student who has taken the class before, their teacher, another physics teacher, etc) sign off on their practice. That could be really neat.
So what do you all think? Other ideas? Let’s hear it.