Posts Tagged ‘Calculus’

Quiz-Video Combination Instead of Lecture

November 14, 2014

Please help me understand if how much I am rationalizing here.

Here is a reminder of how I have been organizing my classes: I create learning goals for the course, and spend roughly two-thirds of the semester teaching them the content. The grading system is set up so that students have to demonstrate proficiency of each learning goal n times, where n \approx 4. The last third of the semester is spend 50/50 on quizzes and review.

I have felt a tiny bit guilty about this format for two reasons. First, I was concerned that I was depriving the students of 1/3 of the traditional instruction time. Second, I felt like a slacker because I don’t usually have to prep much for classes in the last third of the semester (also during the quizzes: I am writing this post during one of their quizzes, and I am slightly uncomfortable that they are working so hard on the class and I am not).

But I don’t feel all that bad about things now, because I realized a couple of things.

First, taking quizzes is about as active as learning gets (and maybe there are Testing Effect-type effects, especially since I purposefully spread out the learning goals on the quizzes). So students are very actively thinking about the material during the quizzes. So I am definitely giving them learning experiences, which goes a long way to alleviate my first source of guilt.

Also, I spent a lot of time creating solutions for every quiz problem. These are posted right after the quizzes so that students can get immediate feedback. This makes me feel better about my current lack of prep time—especially since I am still spending a decent amount of time writing the quizzes.

This also feels a bit better about my students’ learning experience in the last third of the semester. One of the ways I compress the material down to two-thirds of the semester is that I go lighter on the number of examples I give in the first part of the semester. However, my students probably have at least as many examples from the videos by this point in the semester than they would have gotten under a more usual course structure, and they have the added benefit of having had to attempt the problem first before viewing the solution (I am thinking about trying to make this the norm as much as possible. Ideally, things would go: try a problem on your own, try the problem with your team, see me do the problem, then try a similar problem on your own. This is a different blog post, though).

Finally, my overall impression is that the course is going well. I think that students are learning, and they are probably learning more than previous times I have taught the course.

So how much am I simply rationalizing here, and how much of my reasoning is sound?

Three Benefits of “Accumulation Grading with Tagging”

October 15, 2014

So I decided to give my grading system a name: Accumulation Grading (or Accumulation Grading with Tagging). I just sick of writing “this grading system” or “how I am grading” all of the time.

Here are three benefits that I am seeing from this system. One has been mentioned before here (at least in the comments), one I anticipated, and one I only realized this week.

First, I suspect that there may be some sort of a metacognitive boost with this grading system. Students are forced to reflect on what they have done, and this may be helpful.

Second, grading is much easier when students use different approaches. In a very real way, I am just grading whether their “tags” are legitimate (the are correct, relevant to the problem, and point to a specific part of the solution where it is relevant). This means that students can have wildly different solutions with completely different tags, and they will both get appropriate credit. This hasn’t happened a lot yet, although I imagine it could.

Finally, my new realization is that this grading system may do away with a lot of fighting over grades. For example, a colleague recently complained that when students are asked to “graph functions” in Calculus I, many students were doing so simply by plotting points. My colleague did not want to give them credit, since he intended for them to find intervals of increasing/decreasing/concavity/etc. The students were not happy that they did not receive credit.

This is not an issue in Accumulation Grading with Tagging. Students are welcome to simply plot points to graph a question, but they run into an issue when they start to tag their work with the relevant learning goals (there are none). But nothing is marked wrong (because it isn’t wrong), so there is no real disagree to be had between student and teacher.

Assessment Idea for Calculus I: Near Final Draft

August 18, 2014

Sorry about the two month hiatus—Dana Ernst sucked me into a great research project about games with finite groups.

I previously wrote about my plan for calculus I. Basically, it is this:

  1. 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.
  2. I give students quizzes in class.
  3. For each quiz question, the student solves the problem as best as she can.
  4. Here is the important part: after solving the problem, the student reviews her work and determines which learning goals she has met.
  5. 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.

This basic idea has not changed; I have decided to go for this to see how it works. I have made a couple of changes since last time, though:

  1. I change my learning goals (see below for a list).
  2. I am only requiring that they demonstrate mastery of each learning goal four times, rather than the six that I previously had. There just is not enough time to assess that much, considering that I try to give my students at least twice as many attempts as is required. I am able to cut from six to four by scaling down homework: I previously required at least three demonstrations on a quiz and up to three demonstrations on homework, but I have changed this to requiring at least three demonstrations on a quiz and up to one demonstration on homework.
  3. I change my quiz template to include a margin on the left side. This is where students will write their code for each achieved learning goal. They then need to circle exactly where the learning goal is met, and connect that circle to the code. This should make the quizzes easier to grade and easier to read (less messy). I think that I am not going to require that this be done in a different colored pen, either.

I think that is mainly it. I have included drafts of my learning goals and syllabus (sorry for being three weeks late on this, Robert) below. Please see my previous post to get an idea of what students will do with their quizzes.

As always: feedback is welcome.

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View this document on Scribd

Assessment Idea for Calculus I: Feedback desperately wanted!

June 25, 2014

I am planning an overhaul of Calculus I for the fall. I used a combination of Peer Instruction and student presentations in Fall 2012, and I was not completely happy with it.

So I am starting from scratch. I am following the backwards design approach, and I feel like I am close to being done with my list of goals for the students. Here is my draft of learning goals, sorted by the letter grades they are associated with:

View this document on Scribd

I previously had lists of “topics” (essentially “Problem Types”). These lists had 10–20 items, and tended to be broad (e.g. “Limits,” “Symbolic derivatives,” “Finding and classifying extrema”). This list will give me (and, I hope, the students) more detailed feedback on what they know.

This differs from how I did things in the past, in that I used to list “learning goals” as very broad topics (so they weren’t learning goals at all, but rather “topics” or “types of problem”). Students would then need to demonstrate their ability to do these goals on label-less quizzes.

The process would be this:

  1. A student does a homework problem or quiz problem.
  2. The student then “tags” every instance of where she provided evidence of a learning goal.
  3. The student hands in the problem.
  4. The grader grades it in the following way: the grader scans for the tags. If the tags correspond to correct, relevant work AND if the tag points to the specific relevant part of the solution, the students gets credit for demonstrating that she understands that learning goal. Otherwise, no.
  5. Repeat for each tag.
  6. Students need to demonstrate understanding/mastery/whatever for every learning goal n times throughout the semester.

Below are three examples of how this might be done on a quiz. The first example is work by an exemplary student: the student would get credit for every tag here (In all three of the examples, the blue ink represents the student work and the red ink indicates the tag).

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The second example has the same work and the same tags, but the student would not get credit due to lack of specificity; the student should have pointed out exactly where each learning goal was demonstrated.

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The third example (like the first) was tagged correctly. However, there are mistakes and omissions. In the third example, the student failed to claim credit for the “FToCI” and the “Sum/Difference Rule for Integrals.” Because of this, the student would not get credit for these two goals (even though the student did them; the point is to get students reflecting on what they did).

Additionally, the student incorrectly took the “antiderivative of the polynomial,” which caused the entire solution to the “problem of motion” to be wrong. Again, the student would not get credit for these two goals.

However, the student does correctly indicate that they know “when to use an integral,” could apply the “Constant Multiple Rule for integrals,” and “wrote in complete sentences.” The student would get credit for these three.

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I like this method over my previous method because (1) I can have finer grained standards and (2) students will not only “do,” but also reflect on what they did. I do not like this method because it is more cumbersome than other grading schemes.

My current idea (after talking a lot to my wife and Robert Campbell, and then stealing an idea from David Clark) is to require that each student show that he/she can do each learning goal six times, but up to three of them can be done on homework (so at least three have to be done on quizzes). I usually have not assigned any homework, save for the practice that students need to do to do well on the quizzes. This is a change in policy that (1) frees up some class time, (2) helps train the students on how to think about what the learning goals mean, (3) force some extra review of the material, (4) provide an additional opportunity to collaborate with other students, and (5) provide an opportunity for students to practice quiz-type problems.

My basic idea is that I will ask harder questions on the homework, but grade it more leniently (which implies that I will ask easier questions on the quizzes, but grade it more strictly).

I have been relying solely on quizzes for the past several years, so grading homework will be something that I haven’t done for a while. I initially planned on only allowing quizzes for this system, too, but it seemed like things would be overwhelming for everyone: we would likely have daily quizzes (rather than maybe twice per week); I would likely not give class time to “tag” quizzes, so students would do this at home (creating a logical nightmare); I would probably have to spend a lot more time coaching students on how to tag (whereas they now get to practice it on the homework with other people).

Let’s end this post, Rundquist-style, with some starters for you.

  1. This is an awesome idea because …
  2. This is a terrible idea because …
  3. This is a good idea, but not worth the effort because …
  4. This is not workable as it is, but it would be if you changed …
  5. Homework is a terrible idea because …
  6. You are missing this learning goal …
  7. My name is TJ, and you are missing this process goal …