Calculus Standards 2011-2012: Feedback Requested

I’ve been toying around with my learning objectives for Standards Based Grading in Calculus for three years now, and I want to get some other people to weigh in on what I have. Please, take a look, tell me what you think!

Some notes:

1. I love the first person language, which is an idea I think I stole from @kellyoshea.
2. The physics modelers all have crazy acronyms for their standards like CVPM and UBFPM and ERMAHGERD. These seemed confusing to me at first, but then I thought that students might really benefit from this. The standards aren’t organized around chapter numbers, or something else arbitrary, but rather BIG DEEP IDEAS (models!). I wanted to do something similar for Calculus, so I organized mine around Local Linearity, Slope Functions, Proportional Rates and Accumulating Change (with short, simply worded descriptions in the document below). I don’t know how well this worked last year, but one goal for me is to try to always relate the standards back to their big ideas.
3. I didn’t do the standards like this fully in order, and this year I am totally changing the order. But just to give you an idea of how I did things, I did all the IP and LL (limits) standards, then SF.a through SF.g (basic derivatives), then PR.a (optimization), then SF.h through SF.n (graph sketching), then PR.b-PR.h (exponential functions), then SF.o/PR.i (implicit and related rated), then all the AC standards. It was a bit confusing to go back and forth, but organizing the standards like that made it make so much more sense to me. Tell me what you think about that…
4. I struggle with how general/specific to make the standards, and how to include both calculation and interpretation into the standards. Sometimes I split the two, sometimes I kept them together. This is the hardest thing for me!

Anyway, any thoughts are necessary! These are my standards from last year, the second time I taught Calculus.

Calculus Standards 2011-2012

Posted on September 23, 2012, in Calculus, Standards Based Grading and tagged , , , , . Bookmark the permalink. 8 Comments.

1. suevanhattum

Are you locked into starting with functions and limits? This semester I started with the basic idea of the slope for a curve, and so far have only done a small bit of the limit work with my students. I won’t know until afterwards whether it works well or not. (Maybe I still won’t know then.) But it feels more sensible to me. I think I like your level of detail, but I’ll keep thinking. Thanks for sharing this. I may use it to help my students see what they’re working on overall.

• no, not at all – im actually experimenting with that this year! i kept my ap calc class with the traditional route, but in non ap we are going basic derivatives-limit definition-limits and continuity-more complicated derivatives-derivative applications…. etc. sounds similar to what you are doing. agree that it’s too early to tell, but i’m totally loving it – they keep connecting stuff that we are doing to local linearity, so everything feels way more motivated. thanks for your great planning document by the way! it’s been a good resource.

• suevanhattum

Thanks for letting me know. I didn’t think anyone else was using it. I’m glad it’s been of use.

2. Thanks, for sharing these. I definitely want to check these over and think about them. I have to go to sleep, but I’ll come back and look again. I got a set of standards from Mr. Kern at Jenks HS. Found them online and I emailed him and he said to have at it. I think I only changed a couple.

3. I haven’t read through the entire document closely (and haven’t had the chance to teach Calculus, so I’m not the best critical eye there anyway), but here’s the first thought (other than that they look pretty good) that I had:

I wonder whether there’s some higher-level of structure that would make sense for some of these (for example: product rule, quotient rule, chain rule) that would group them as one big objective (maybe even with separate feedback for each, still, but only one overall score). That would both shorten the total list and also let you check whether students know when to use each one (since to test on that objective, they would need to be working problems that involved each of those).

Not sure whether or not it makes sense to go in that direction with the list, but looking at it prompted some wondering. 🙂

• hey, i think that’s a really nice idea. one of my struggles with SBG has been how to include synthesis. my method so far has been sort of the default of not being able to go full SBG in my department (standards=40% now, so I still include points-based tests). so they have to figure out which derivative rule to use on something like that. but when i head to another school, where i probably will go all sbg, this is a way to make that work. i tried a little bit of the big structure with the modeling type categories, but there are only 4 for the whole year, so that might be a little too much! i am grouping some in my head as i type this… this is something to ponder. thanks Kelly.

4. Farah Khan

Thanks for sharing these – I’m just developing my own standards for Calculus this year so this is immensely helpful. I especially like your choice of big ideas – and the language that you have used. You’ve managed to step away from the embedded language of calculus to something the average person can understand. One area that I struggled with when writing my unit plans was local linearity because tied into the concept of limits is the idea of infinity, and the infinitesimally small, getting closer and closer but never quite there, yet close enough to say that we can measure the slope. I was trying to find a way to incorporate that along with the idea of local linearity that you mention..

Will have more feedback as I teach this year. Another issue I’m struggling with, with regards to SBG – what happens if they re-take a standard and do worse than they did originally? Perhaps they understood but then forgot, or perhaps they made a different kind of error in their second attempt – how do you deal with that situation?

Feel free to e-mail me your response.

• Hey Farah, The best activity that I have done to connect Local Linearity with limits is one that Shawn Cornally originally wrote up where students are given two stopwatches, a rolly chair, and are asked to find its instantaneous rate of change at a point. Another blogger @wp202 wrote up his description of this: http://wp202.wordpress.com/2012/08/21/calculus-introduction-to-derivatives/ –> I did it BEFORE doing limits to introduce and motivate the whole need for limits and I think it actually worked pretty well.

If they do worse on a reassessment, then their grade goes down. The strength of SBG is that grades reflect current understanding, not how you did on a quiz 2 months ago (because that has nothing to do with what you know NOW, what you have actually learned). Putting the lower grade in instead of the higher one is an indication to them that they need to work on this topic (an indication that they wouldn’t get by leaving their grade the same). It also prevents kids from just trying again for the heck of it (my students self schedule all reassessments). I think it forces them to be a bit more deliberate.