Archive for the ‘Calculus’ Category

First week of school

One week (a partial week) is in the books, and this school year looks to be an interesting one.   I introduced SBG to my Calculus class.  We haven’t yet taken a standards assessment (it will be next Tuesday), so they haven’t made any real judgments on the system.  They seem skeptical, but we’ll see how things go.   I’m not used to giving assessments as often as it will be needed with SBG, so it will be different for me as well.

The Math of Sports and Games class has been pretty fun so far.  On the first day of class, I presented them the classic Monty Hall problem. I asked them what they would do, and I then showed them this video clip from the movie 21 (by the way, that’s the best website for math video clips anywhere, so check it).

They were skeptical even after watching it.  The guy sounded smart, but they weren’t sure what to make of it.  I made no comments on anything at this point in time.

At this point, I WANTED to have the kids use their iPads to perform a simulation of the Monty Hall question (I like to program).  However, they decided not to give iPads to the iPad-centered class, so we couldn’t do it.  Instead, I gave them 3 post-its and a little piece of paper and had them simulate it in a “hands-on” method with another classmate.

They recorded their answers and we pooled the results to discuss.

It went pretty well, but the fact that a fellow classmate was choosing where to put it gave us some skewed results (since it wasn’t truly random).


Standards Based Grading – Calculus

I’ve read about SBG for a few years now.   My first exposure to the idea coming from Dan Meyer.  I liked some aspects of it, but had some misgivings.   This next year, I’ll be giving it a trial run in my Calculus class.

The problems that I have now with my current grading system are as follows:

  • Rampant cheating on homework due to the 30% chunk of the grade
  • Pursuit of grades/points more than knowledge of the topics
  • Gradebook doesn’t let me identify quickly what kids have trouble with
  • Students can’t identify what they have trouble with
  • No clear path of remediation for kids (can’t search on youtube for p. 154: #’s 3, 8, 12, and 16)

In my previous system, all homework was graded for correctness and could be fixed.   There was a process that went on (with lots of work on my time) where kids did and re-did problems over and over again (with my feedback) until they could figure things out.  The cheating that occurred with the homework and the other things I listed lead me to think a change is necessary.

I believe that SBG can rectify many of these problems.  I’ll be borrowing some things from Sam Shah at Continous Everywhere but Differentiable, John at Quantum Progress, Shawn at Think Thank Thunk, and Bowman Dickson.

I haven’t quite worked through the nitty gritty details of it all, but I’ve thought about a few obstacles.

Obstacle #1:  Discretizing the Subject

I do lots and lots of work to get students to see the big picture of the subject.  Learning is not the mastering of 85 discrete standards (as SBG might make it look), but rather the understanding of the overarching themes of the subject.  A true understanding of the overarching themes will manifest itself as the mastering of the 85 discrete topics.  However, it is possible (and done in many math classrooms across the country including my own at times) for students to never understand the overarching themes but still show mastery of the procedural aspects of the many different topics.  I believe SBG, if not done carefully, can turn a course into the mastery of discrete skills instead of the overarching themes.  Though of course there are probably large chunks of math teachers that don’t use SBG and still turn the subject into the mastery of skills.  I further think that an extremely valuable tool for students to have at their disposable is the ability to decide when to use which tool at their disposal. I think carefully written questions (and perhaps standards) can help avoid this obstacle.

Obstacle #2:  Grade breakdown

How do I breakdown the student’s grades?   Some people use a 100% standard-based model.  I’m wary to place such a huge emphasis on standards.   I don’t want to reward slackers.   There should be some penalty for students who aren’t ready for assessments (due to their own neglect) when they are given.  I believe that SBG doesn’t intrinsically reward slackers, but I moreso am afraid that students will think when they system is presented to them that they can put forth less than a stellar effort and it won’t harm them in the long run.    I’m also afraid that students won’t do homework if there is no credit for it.  For that reason, I believe that a hybrid system is something more up my ally.

Bowman has this breakdown in his hybrid SBG system:

  • 35% – Standards – How much I understand right now
  • 10% – Quizzes – I am keeping up with the pace of the class
  • 30% – Tests – Connecting topics and converting short term knowledge into long-term knowledge
  • 5% – Homework – I am doing my part in learning by practicing on my own
  • 20% – Final – Retained knowledge and have the big picture of Calculus.

I think the small percentage of homework would negate most of the cheating, but still allow me to track who is doing their part.  I think that I can ditch the quiz part of Bowman’s system.  Tests will determine that, and I don’t want to over-assess them.   I want to add  in some space for projects.  These projects would allow me to test for the bigger connections and, more importantly, give them some space for problem solving.   Here is my tentative grading system:

  • 50% – Standards
  • 20% – Final
  • 5% – Homework
  • 25% – Projects/Tests
Categories: Calculus