College Math Teaching

March 30, 2014

Common meme one: having fun with it…

Filed under: calculus, pedagogy — Tags: , — collegemathteaching @ 8:09 pm

Quiz (NOT for professors or teachers!)

1. For the $sin(x)$ figure: IF you assume that this figure is correct, what is different about this figure and those on its row and the row beneath it? If the figure is assumed to be wrong, how might you fix the formula to make this right?

2. For the $a^x$ figure, what assumption is made about $a$?

3. For the $log_a(x)$ figure, what assumption is made about $a$?

1. Okay, I’m procrastinating on grading, so I’ll bite. I’m a professor, but not of any field involving math–is that what you had in mind, or are you looking for people who work with numbers professionally but don’t teach? I have to say, I find these questions pretty baffling and all of my answers would have a question mark at the end of them if I were saying them aloud.

1. the arms go both up and down. If the figure is wrong? I have no idea (of the many, many things I hated about math, graphing was the WORST), but I’m guessing the formula needs to be one that makes both arms look like the arm on the right?

2. that a is a positive number.

3. I give up. Seriously–no idea whatsoever. Something that makes the left arm go up at a steeper angle than the right arm–but since I’m not sure what a log is, I’m baffled.

Comment by good enough professor — March 31, 2014 @ 2:11 am

• I won’t answer just yet; this is something a math major or a really good calculus student (or advanced calculus student) should get. These are all functions that are seen in such a course. The average calculus student might get the “sin(x)” one and perhaps the a^x one (maybe) but probably not the log_a(x) one.

Comment by blueollie — March 31, 2014 @ 2:17 am

• Oh, that’s a relief! I thought this was supposed to be locking onto some basic mathematical intuitions. Glad to know it’s not! I’ll just back away slowly and leave you all to it… 🙂

Comment by good enough professor — March 31, 2014 @ 3:05 am

2. I’m a math teacher, but I think the log one is wrong no matter what a is. (Unless, … I won’t say it in case I’m right, but that would be ugly.)

Comment by suevanhattum — March 31, 2014 @ 3:45 am

3. Nah, I tried a log base i on Wolfram, and that doesn’t look like this. I don’t think any log does.

Comment by suevanhattum — March 31, 2014 @ 3:46 am