Precalculus Test • Jim Doherty

Introduction

The second assessment in the spotlight is a Precalculus Honors test on conic sections and parametric equations from Jim Doherty (a.k.a. mrdardy). Questions to consider:

  • What do you like (and why)?
  • What would you do differently (and why)?
  • What questions do you have for Jim?

Submission Type

“Share an assessment you don’t hate…”

Assessment

https://www.dropbox.com/sh/geof1hp8yab8gdt/efJg4O0OX1/PCH%20Test%2011.pdf

Author’s Commentary

“Here is a link to my most recent Precalc Honors test. We just finished our long slog through trig and have emerged on the other end with a conics/parametric unit. I stole some ideas from Sam Shah in class and we kept referring back to polars but I chickened out about including them on this test. I’d love to hear any opinions/questions/advice here!”

(More commentary may follow soon is included below.)

Additional Author’s Commentary

“I have long used this structure for tests in this course where there are some quick fact/skill questions at the beginning worth 5 points each while there are longer, multi-step questions worth 10 points each. Based on some reading I’ve done lately (especially from the mathymcmasterson blog) I am thinking of inverting this model so that the majority of points earned are at the skill/recall level while the multi-step problems take a smaller portion of the points on the test. I’m interested in feedback on this balance.

Our text has the conics unit after a long trig unit. My students know that all of my tests are cumulative in nature with some general ground rules in place about what might appear. The central focus will be on the most recent material discussed with one or two questions directly representing material from the most recent test. Often, these will be questions that caused some problems and were the focus of our post-test briefing when I return papers. For some reason this year we had repeated questions about circles and it became a bit of a running gag during the year. I was happy about tying together questions 2, 3, and 8 but on reflecting about this, I’d make them closer to each other in the formatting. I try to write questions like #7 as often as possible. I think it gives me some insight into the kids ability to process some of this algorithmic information in a non-standard way. I started including the editorial note about multiple solutions in reaction to NUMEROUS questions along those lines. I kind of wish I had not done that. For questions 10 I fully expected students to simply solve for t in terms of y and then come up with a non-function parabola. A number of them solve for t in terms of x then had a function square root curve as their answer. Both approaches earned credit with clear support. I typically make the last problem a bit of a giveaway when I am concerned with time. We had a 40 minute class that day and I was worried about time on this one, but the kids did just fine as far as time was concerned. Looking back, I wish it was less driven by straightforward algebraic manipulation of the con is material, but I know I had seen some struggles with the types of word problems where the kids are given clues about a conic and they are to find its equation.

By this point of the year, my class was starting to really stretch out along the grade continuum with scores on this assessment ranging from 50 to 98 in a 10 student class. The mean was 83 with a median of 87.”

On Deck

A sweet-looking Precalculus quiz on the Law of Sines and the Law of Cosines from Luke Hodge.

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6 thoughts on “Precalculus Test • Jim Doherty

  1. Jim, thanks so much for sharing your assessment!

    I’ll come back to share more thoughts later, but I wanted to get the conversation started with a quick comment on my favorite question (#7).

    I love that there are multiple equations that fit the bill. I teach conics (though poorly) and, had I been taking your assessment, I might have missed the fact that there are (MANY) more than two solutions possible. (I expect I would have gone with one of these: https://www.desmos.com/calculator/w9eyww4lxp).

    So once I started down that line of thinking, I began wondering… What if the question asked: “There are MANY hyperbolas with center (1,2) and whose asymptotes have slopes of 2/3 and -2/3. Write equations for THREE of them.”

    I don’t know if that’s the clearest way to ask it (maybe, “Write equations for THREE distinct hyperbolas with these characteristics”) but it would be interesting to see how solid (and flexible) they are in their thinking about hyperbolas, and whether they see this (https://www.desmos.com/calculator/xfk2b7rlan) which just strikes me as cool (and is something I’ve never wondered about or seen in quite that way before).

    Thanks again for sharing your assessment!

    (Note to self: Never say—in an email or a blog post or blog post comment—that what follows will be “quick.” It will almost certainly be a lie.)

  2. Michael

    Thanks for kicking off the conversation here. I was surprised that almost all of my students (a) got a correct solution for this and (b) had a hyperbola with a horizontal transverse axis here. Interesting bias and I am pleased that by this point of the year they were comfortable with these open questions. I like your idea of rephrasing it and I might instead steer them by asking for one of with a horizontal axis and with a vertical axis.

  3. I really like several of your questions! #7 is my favorite, I think.
    One thing I don’t particularly care for is the random order of the problems – I think I would prefer all the review questions grouped together, all the trig questions grouped together, and all the conics questions grouped together. I plan on implementing a version of Dan Meyer’s SBG grading next year, so I would probably put the first group of questions on my first assessment of a standard (when I’m mainly checking to see if they get the basics) and the second group (the more challenging questions) on my second assessment of a standard (when I’m trying to assess whether they understand on a deeper level). But that’s just brainstorming how I would use your questions in my own classroom. Thanks so much for sharing!

  4. Jennifer

    Thanks for joining in on the conversation. One of the things I think about when writing tests is that I want to encourage my students to be more flexible in their thinking. It may be a distraction to my students, as it was to you, when I switch the focus of the questions. I need to reflect on this, I have always consciously switched gears thinking that I was helping my students be more adaptable, but it may be that I am working against them here.

  5. Nice test. I like the fact that you mix in some review questions without any sort of tip-off that they are review questions. I also like the conic questions, but I would maybe add a question that provides a graph and is a little open ended. For example, ask for the possible equation of an ellipse that is mostly in the 2nd quadrant but extends a bit into the first quadrant with no scale shown.

  6. Thanks for the comments. I really value the idea of having review be part of all of my major assessments. I was proud of the open ended question #7. I am going to steal your idea about the ellipse. I may modify it by giving them a center for the ellipse as well as requiring that the graph be contained in one quadrant of possibly in two of them.

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