I Don’t Say These Things to Hear Myself Talk…

Weeks ago, I told the seniors that knowing the function values on the unit circle would be helpful when we got to the next section on graphing the trig functions. Too many of them didn’t believe me. Now some of them can’t tell the difference between the graphs of sine and cosine.

I spoke to my mentor about the situation. His suggestion was to give a daily unit circle quiz, all or nothing. Lose a negative sign? Too bad, no credit. This continues every day until the entire class gets it right.

I told them about it on Monday. Our first quiz was yesterday. Yesterday’s results? 46% got it. Today? 82%.

Prior to this we had cut out the special triangles and moved them around the unit circle. We filled out a chart of all six function values from 0° to 360° ( or from 0 to 2π, take your pick). We talked about the patterns. We’ve drawn triangle after triangle in the circle. That didn’t seem to matter for some of them. I’m dismayed that it took such drastic measures for them to learn the function values. I’m not sure if they’re able to apply them to anything yet. We’ve spent the last two days in the lab, working on a Sketchpad investigation of transformations.

Now, if they had only believed me last semester about needing to understand the the affect effect of 2f(x) + 1. “But Mrs. B, we thought you were kidding when you said this stuff would come back…”

Image: I Δ Triangles by xueexueg via flickr

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17 Responses to I Don’t Say These Things to Hear Myself Talk…

  1. Now, if they had only believed me last semester about needing to understand the the affect of 2f(x) + 1

    (nitpick: “effect”)

    As a college-level calculus teacher, thank you for teaching those sorts of effects. I remember learning them myself, and then being far, far ahead of my classmates when it came to curve sketching. My students have (in general) no idea how to turn algebraic manipulations into geometric alterations, and when they start differentiating they have no idea what it means beyond just another algebraic manipulation of the formulas.

    Please make sure your kids know what the shape of a graph and the parts of the formula have to do with each other when you leave. If it helps, relay to them that if they understand it they’ll find calculus a lot easier in college, and their professors will like them more.

  2. Jackie says:


    Thanks for being nitpicky (as I said here in the first footnote I knew I’d goof that up). I’m working on their understanding of transformations. I actually started a nice exploration activity with the freshmen this week that will hopefully help too.

  3. Sarah says:

    I remember taking Unit Circle quizzes, though I haven’t yet gotten the pleasure of giving them. Are you timing them? Do you reduce the time from week to week at all?

  4. Jackie says:

    Timed? Uh, no. I’m not sure if I’m going to. I’m actually okay if they are thinking about it as opposed to just memorizing the pattern. We’ll see. I may, once again, change my mind.

  5. Jackie says:

    Day two results: 83% (I’m rounding and there were a few absent today). Tomorrow’s title, “Now for Something Completely Different: A Unit Circle Quiz”. I’m open to alternate titles. I think I may be doing this for a while.

  6. Jackie says:

    Today: 89% and everyone actually tried it. I think the end may be in sight.

  7. mathmom says:

    Are you retesting the kids who have already gotten 100% on the quiz? If so, why?

  8. Jackie says:

    @mathmom – Well, it has only been three times (we didn’t have one today – shortened schedule due to assembly schedule, reviewing graphing…). Actually, some of the kids who aced the first one have since made some mistakes. Today one student voiced that she finally saw the relationship between the unit circle and the graph. Another in the same class said “I see why you made us do this”.

    I’m not sure where this will go. We’ll see what happens next week.

  9. Ben Chun says:

    Keep it up! I love the idea of continuous retesting — we’re not looking for momentary memorization, but true memory. Of course it has to be kept relevant, but I’m assuming they spend the rest of the class applying these facts in order to solve problems. That’s why we do it.

    I always had the opening question on this unit test as either, “Draw a unit circle and label the important coordinates” or “Fill in the coordinates of each point on this unit circle”. They appreciate having something as simple as fact recall gain them some points, and it shows that we do value their time commitment. I so the same when it comes to the definitions of the limit, and the test for continuity. And we go up Bloom’s taxonomy from there…

    It does seem annoying that you have to do so much as a teacher to get this little list of numbers memorized, but keep in mind that our students probably haven’t had much experience needing to internalize technical information. If you’re lucky they can recall SOH CAH TOA and tell you what it means. Students tend not to take requests for memorization seriously, as well they shouldn’t. But as you continue to show them the utility — the necessity — of having these numbers on call in order to solve more interesting problems, they will appreciate your insistence.

  10. CdnMathTeacher says:

    My students had trouble with this too. I did do one quiz with just the coordinates. But I like the idea of doing it over and over until the whole class gets it. I’m also bookmarking this page with the comment from the professor about transformations! Thanks Jackie!

  11. Jackie says:


    Yep. We’ve been applying it. As for the SOH CAH TOA, one student still keeps asking me how to spell it. Oy.


    Yeah. I’m still (internally) wavering on the “until the whole class gets it”. The vast majority of them have gotten it. And see the relevance. There are a few holdouts that have just shut down. I’m not sure at what point it becomes counterproductive for the rest of the class. I’m asking myself, “what’s my goal?”

  12. mathmom says:

    Is there something else the kids who have gotten it can do with the time? Perhaps a small extra-credit assignment so they feel rewarded rather than punished for mastering the unit circle. You could require two 100%’s in a row to prove mastery, to get around the issue where some kids are getting it then forgetting again. But I’m not big on holding the whole class hostage at the level of the lowest performers.

  13. I’m not sure at what point it becomes counterproductive for the rest of the class. I’m asking myself, “what’s my goal?”

    Oh.. I just figured you were trying for the Private Pyle effect, à la Full Metal Jacket.

  14. Jackie says:


    Well, I don’t think the others are seeing it as punishment. One student was trying to pay people to fail the quiz. He wanted the points. I don’t think they really get the whole weighting thing. I do not want to hold them hostage. I want them to somehow get this in their long-term memory.



  15. mathmom says:

    My point wasn’t that they felt punished by having to keep doing it, but if it was to the point where it was no longer productive for most of the class, and you wanted to have them do something else instead, but not feel “punished” by having to do “extra” work that the others don’t have to do, then you could make it for a small amount of extra credit.

  16. Jackie says:


    Ahhh. Thanks – for both the clarification and the idea.

  17. shana donohue says:

    If I give s simple tri gproblem where one angle (other than the right angle) and one side are known, they obviously have to use trig to find one of the other sides.

    But do you think it’s overkill to use a trig ratio to find the third side or to just use a2 + b2 + c2?

    In any case, I made a silly trig video that I put on YouTube. http://www.youtube.com/watch?v=Q_iFEoffBxg

    I use a2 + b2 = c2 to find the last side but I feel guilty that it’s not a trig video through and through! But is it overkill?

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