For an upcoming post, could you please answer the following multiple choice question?
Which graph best represents the importance of teacher knowledge of mathematical content as a function of grade level taught?¹
You may answer in the comments section or complete the online fill-in-the-bubble test.
The first 100 respondents will be the lucky recipients of Reflections in the Why merchandise. If in six to eight weeks you have not yet received your package, wait longer.
¹The horizontal axis should be labelled K, 3, 6, 9, 12, not 0, 3, 6, 9, 12. Blame GeoGebra, not me.
Update (February 3, 2013): Thank-you to all who have taken my quiz. If you haven’t, there’s still time before ‘marks cut-off.’ In a week or so, I hope to find time to summarize and interpret the results as well as provide my answer key. I did realize that, without a scale labelled on the vertical axis, B & C are indistinguishable. I tried to slip that by an audience of math educators. No such luck. But tell me this is the first time you’ve had to read the mind of a teacher when answering a quiz question. Also, the wording of the question is ambiguous. I’m cool with that. I can’t help you. It’s a quiz. Choose the best answer.
Chris Hunter 
Hey Chris,
Some quick feedback. The link to the online survey is missing a : (colon) which makes it broken. I’m going to fill out your survey now.
David
Missed a colon in the URL. Here’s the address:
http://www.surveymonkey.com/s/8K7Q5CL
Interesting question and I’m looking forward to what comes of it. FWIW, here was my response in the optional comments box of the survey:
The more I learn about high school math (second year teacher, now teaching Alg I, Alg II, Pre-Calc), the more I realize how nuanced upper level topics are. I sat in on a Calculus class and was blown away at the difficulty of it (coming from a math major!) – we’re not just cranking out derivatives here.
While TEACHING each grade level requires specific knowledge of HOW students learn each topic, I think the complexity of the math itself increases. Probably not exponentially, but faster than linearly.
That’s interesting. Hard to pick just one, and I notice there’s no linear option going down. In an ideal world, I think we’d like C, but in the absence of that, the best option might be A. If you can lay down a good foundation, then as the work gets harder, ideally the students would become the experts, and the teacher can simply verify if and when they’re on the right track. (That said, if the students get stuck, and the teacher doesn’t know enough to assist… well, problem.)
I think part of the issue too is that it’s totally different teaching Grade 3 from Grade 9. I have no idea how I’d teach addition. You just, you know, do it. Suspect I’d be bored to tears after a couple days and tempted to bring in integers. At the same time, it’s probably really important that I know, to give me insight into why students start (incorrectly) adding bases when we get to exponential models…
B