I am halfway through the semester where I am using a new grading scheme for Calculus I. Here is a rough summary of the scheme:

- I give the students a list of learning goals. These are much finer than I have done in the past, which means that there are many more of them.
- I give students quizzes in class.
- For each quiz question, the student solves the problem as best as she can.
- Here is the important part: after solving the problem, the student reviews her work and
*determines which learning goals she has met*. *She indicates exactly where she met each learning goal*. If she does not claim a learning goal, she does not get credit for the learning goal.

Basically, the students are forced to reflect on what they did in order to get credit for their work.

I just completed my midterm grades, and I would like to report on them. But I will first summarize where we are and describe my assessment of the course prior to seeing the grades.

We just finished off differential calculus. We will cover all of integral calculus in the next 2.5 weeks (I accelerate the schedule), and then we will move on to the review-and-quiz portion of the semester (we have quizzes for the entire class on Tuesdays and Fridays, and we review for the quizzes on Mondays and Wednesdays).

I have been simply thrilled with both sections of Calculus I. They discuss ideas, ask questions, and generally are willing to try whatever I throw at them. This has been a really fun semester. In contrast, I have heard that the other Calculus I classes have been struggling.

The good news is that my midterm grades reflect this. There are only three students who are presently in danger of getting below a C, assuming students continue on their current paces (one drawback to this grading system is that literally every student technically has an F right now, due to the fact that none of them have demonstrated any ability to work with integrals. But this is simply because they haven’t had a chance yet. But my original point for this parenthetical statement is that any student who starts slacking off is in danger of failing).

I am pleased and relieved about this. I certainly had considered that having the students claim credit for relevant learning goals could have been a disaster, but this not the case; the students have had minimal trouble with this.

One reason why they may not have had trouble is that I have been specifically referencing learning goals when they come up in class and then posting the slides to the CMS so that students can find where each learning goal is introduced. I also have been highlighting the relevant learning goals in the daily assignments (Example: “For Wednesday: We will discuss Learning Goals C4 and B9. Read 2.4 and 2.8. You should be able to do Preliminary Exercises 1 and 2 of 2.4, Exercises 63 and 65 of 2.4, and Preliminary Exercise 1 of 2.8.”).

So I am very happy and relieved at how the first half of the semester has gone. I really think that the focus on the learning goals has helped students learn how to talk about calculus. I will keep you all posted.

Tags: Grading, Learning Goals, SBG, Tagging

October 9, 2014 at 12:52 am |

This sounds so cool, I’m glad it’s going so well. I’m curious, do your math tutors struggle with how the various sections of calc are doing such different things?

October 9, 2014 at 2:37 am |

Not that I have heard. I have talked to some of the tutors, and they say that they are working with my students. But they didn’t say anything about things being weird.

I think this might be because the content of the different sections is pretty constant. I think that the main difference between what I do and a “standard” calculus class is that I ask a lot more conceptual questions (e.g. here is the graph of f, sketch f’ or here is a table of values for f: does f look like it is concave up or down?). But the students are doing really well with the conceptual questions, so I am guessing that most of the time spent with tutors would be on the more algebraic stuff (i.e. what every other section is doing).

October 9, 2014 at 4:54 am |

Very cool. Identifying the appropriate learning goal is fairly challenging task so you must have figured out a really nice level of granularity, specificity in the statement of your learning goals, and support across the course if you have managed to have so many of your students be successful. Other than than this aspect of your quizzes, are you doing anything new with this section?

October 9, 2014 at 1:09 pm |

Hi Joss,

My learning goals are very granular (in my opinion), and I worked hard to get specific. I was initially planning on having some broad category like “Students will be able to answer conceptual questions about derivatives,” but then I decided to split that into five separate categories such that I would be convinced that they could “answer conceptual questions about derivatives” if they could do each of the five separate categories. I am glad I did that—it took some work, but it was a better product and it helped me be a better teacher to clarify this.

This might turn into another blog post, but there are a couple of other differences:

1. As I mentioned above, I constantly refer to learning goals in assignments and in class.

2. I am primarily organizing my class around the learning goals, rather than the textbook (although they line up reasonably well).

3. I had students present problems in the second half of the semester in 2012, and I will not be doing that this time around. Instead, I will be doing ad-hoc review sessions on learning goals that students need extra help on (and a lot of quizzes). The presentations were no good.

4. Our school changed its schedule from a weird 6-day cycle to the standard MWF-TTh schedule. So now I teach 55 minute class on MWF and one 80 minute class on Tuesday. I have my TA use Monday’s class for quizzes. Previously, we would average slightly more than four classes per week, with each class being 70 minutes long. I would teach 2.5 of those classes, and the TA would teach the remaining 1.5ish.

I also changed some of my Peer Instruction/Clicker questions, although I don’t think that this would make a huge difference.

So, really, the two main changes so far are the learning goals (and a new focus on them) and the cycle structure of the college.

Bret

October 15, 2014 at 7:21 pm |

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