Today was an assessment day for Mr Dardy

Two sections of BC Calculus taking quizzes. Two sections of AP Stats taking tests. One big question for me in each situation. I’m interested in hearing your opinions.

My first class is a Calculus section. We’ve been working with parametric equations and dipping our toes into the relationship between polar and cartesian equations. We spent a day with Desmos and we spent a day on regular old lecture. They had a five-question quiz and four of the questions were very standard. On one of the questions, I asked them to convert an ellipse in rectangular form (factored already so they could see the center and lengths of the axes) into a parametric equation. Now, they had already had homework converting parametric equations into non-parametric forms. We had also looked at polar forms and I reminded them of the polar equations that would result in a unit circle. My hope was that they would piece those two skills together. It is an AP class and I feel that I owe it to them to ask them to react on the fly to situations that are at least slightly novel. Much grumbling ensued. I haven’t graded them yet to see how they responded, but I did not walk away with a positive feeling. 

My next class was an AP Stats class and we were (finally) taking a test on probability distributions. Between the Christmas break and our snow day this week, this unit has felt very choppy to me. I had two girls finish the test in about twenty minutes and they are two of my stronger students, so I don’t think it was due to just folding up their tents. Some students stayed the whole 45 minutes, but I am sort of convinced that some students will stay sitting and pondering any test as long as they are allowed to. 


So – my two questions are 

  1. What is your feeling about questions on assessments that don’t match up with a practiced skill?
  2. Should I feel any sense of concern that some students finished a 45 minute test in less than half the time I allotted? It somehow feels like I must have aimed too low with them. Again, I haven’t graded yet, so my opinion may change by the end of the night.

Dorm duty calls and I am bound to stay in my apt near my desk all night – so I suspect I’ll get a good amount of work accomplished.


7 thoughts on “Curious”

  1. Jim,
    I’ve definitely run into the issue of tests finishing early, although usually I have the opposite problem! On some level, if your test reached the topics you were trying to assess, I wouldn’t worry too much; maybe there really only was 20 minutes or so worth of knowledge to test.

    As to your first question (I’m doing this backwards), I think it is totally reasonable to give unusual or novel questions -especially at the AP level. Students need to understand that not everything that will be tested will look exactly like the previous 10000 they have practiced.

    Just my 2 cents. And it’s been a long week!


    1. Mike
      Thanks for the comments. Looking at the stats test now, I think that I might chalk this up to the perennial discomfort that some have with probability. When you see – as those two girls clearly did, then it is pretty quick work.

  2. I agree with Mike that (a) it’s been a RIDICULOUSLY long week and (b) especially at the AP level students should be learning how to apply their learning in new situations, but I also think that if you are going to do this, it should be a regular expectation that you have (which it may very well be). That said, my Algebra 2 students have a hard enough time with straightforward problems that they have seen before; if I gave them something new on an assessment they would flip out. And I also have the opposite issue time-wise; today, in fact, I gave a 6-question quiz for which I allotted 25 minutes. A whole crew of them worked over time and had to be chased from the room (another entering class taking a test). I struggle to find the right balance.

    1. Wendy
      Thanks for popping in! My BC kids are used to me asking what we call ‘interesting’ questions. I think the fact that we only had two days this week together on Calculus is why they were more sensitive than usual. We missed school on Tuesday and I stuck to my New Year’s Resolution to have a problem day each week, so we only talked together on Monday and Wednesday. My quiz was 25 minutes and 5 questions. Should have been very manageable but they may not see it that way. Don’t you feel terrible chasing them out? I have to do this and I am filled with a combination of frustration that they aren’t being efficient enough and frustration that I am not allowing them to really ponder and work their way through their difficulties. The struggle for balance is happening here as well.

  3. I hate timed tests. My policy is that I don’t time them; if students need more tie, I let them come back later to finish. I know that’s different from AP rules.

    My other feeling is that if you’re giving an assessment, it’s to evaluate a particular skill. For most summative assessments, this means determining how well a student knows past material. For your quiz, it sounds like you were asking them how well they could piece things together rather than the two (until now) distinct topics.

  4. I would like to give my students more time, but I don’t have my own classroom. In fact, the teacher who uses the Algebra 2 room after me usually comes barreling in the minute the bell rings, especially when she is giving a test.

    I agree with you, @wwndtd, in that a summative assessment should test specific skills. But the results of giving students a challenging problem to work through can be very informative for the teacher.

  5. Hi. Thanks for sharing. I recently finished a contract at a school where I had to use tests I didn’t create and ended up feeling like I had to argue on the “math shouldn’t be about working FAST” and “students should have time on a test to think” camp. I often had no students finishing early and some of the students I thought were stronger, but slower and more careful with their work, didn’t finish.

    As to whether you should put novel/interesting questions on tests for grade, that’s going to depend on a lot, including the policy documents you are working under. But I think it also depends a lot on the grade level and how those questions are created – there are times when 5 + 7 seems much different from 5 + 5 and 5 + 2 examples. At some levels, and for some topics, changing the numbers is enough to find out if students are proficient at the skill or understand the idea and in other cases the scenario needs to change, the process needs to be reordered, or the students have to decide how to put multiple skills or concepts together in a way that is reasonable and works.

    I think it’s important that students have access to all the information they need to solve a problem. I have seen tests with obscure vocabulary or formulas that were not the crux of topic being required to fully answer a test question and I don’t like them; even as bonus questions. (Fun bonus questions or in jokes for the class are different, but I think makes the assessments less accurate to students abilities).

    This is where students creating their own questions, either in class, or as practice can be extremely valuable for them and maybe this is a good check of whether a question is reasonable on a test or not – could the students have feasible come up with the question themselves with at most a little bit of prodding or research (google/wikipedia)?

    The policy documents I work under (Ontario) at the later levels of high school require students not only to solve, answer, explain, describe, etc. but also to show problem solving skills, test ideas, discover concepts, and investigate stuff. Teachers here have some freedom towards what of this stuff gets counted towards the grade but it’s all got to be done at some point. I’m brand new so I’m still learning where and when to do what, but appreciate hearing about your class and reading your thoughts on this! Thanks again!

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