## Graphing Logarithms using the Ace of Base Formula?

July 10th, 2006Well, no, not really. But I did have “It’s a Beautiful Life” inexplicably stuck in my head in class today; inexplicable, that is, until I realized that the words “Change of Base” were being bandied about all day. (If you want to know what the change of base formula is you can click here, but be careful because following this link may cause blood to shoot out of your eyeballs. Thankfully Wikipedia comes to the rescue with a concise and non-ugly presentation of the change of base formula.) But there are more important things to consider about my Algebra class.

We took a test on Friday and nearly three quarters of the class did not finish the test. We got our tests back and the mean score was somewhere near 50%. How could so many students be struggling to the point of failure? Consider this sample from my test.

I got every part of the answer right. The table is correct. The graph is correct. I failed to show how that (1/3)^{-2} is equivalent to 3^{2}. But the next step was performed properly. Such a simple calculation as taking the reciprocal and squaring it is an autopilot operation to me. I tried my best to meet the draconian “show all work” requirements set by my teacher, but according to her I skipped a step. I guess I skipped it twice, so that’s why I lost two points for a correct answer. Okay, let’s take a look at the next problem.

How? Maybe I followed the directions and used my calculator’s graphing functionality? And insects? I leave off the word “insects” on a math test and I lose 2 points? What the heck!? And these were the questions I got **right**!

With grading like this I shouldn’t be surprised that I need to get 88% on the rest of the quizzes and tests in the class just to pass. I’m tempted to go drop the class, but I switched the grading to credit/no credit a couple weeks ago, so I guess I ought to just finish it up and give it my best shot. At least it will help me when I take the class again. Oh, and there were some people that learned today that no matter what they do they can no longer pass the class. They seemed really happy about their plight as they grabbed their belongings and stormed out of the class. I wonder how many people will end up passing. I’m guessing less than one quarter of those that started.

July 10th, 2006 at 10:16 pm

Wow, that’s really lame grading. She should be exposed.

July 12th, 2006 at 3:51 pm

I think she wanted you to show the proof on the (1/3)^-2 conversion. That way she would now you didn’t use the calculator. man, that’s WEAK!

July 12th, 2006 at 7:04 pm

A big problem in this class is not enough time to finish the test. I’ve taken to racing through as fast as possible to do the problems, then to go back an “fill in” the work

I’m supposed to show. Rushing leads to stupid sign errors

andto incomplete “work” being shown.Oh, and on the “which day” problem with the insects, she wanted me to list the coordinates like this:

Intersection: (7.738,500)

How this shows anything more tha.n what I already put, I have no idea. Don’t tell me that it shows I didn’t copy, because if I

hadcopied I could have just as easily copied the intersection as well! I don’t know. There are only 12-15 people left in the class out of the original 30 or so. One kid dropped the class but is still coming to learn so he can pass when he retakes to course.July 13th, 2006 at 12:23 pm

I love when you get penalized for understanding something well. That always makes me feel good. That intersection answer is bogus, there isn’t enough informaition specified in the question to justify that answer. In fact, I would say it is less clear than what you answered. There needs to be a venue for complaints like this because it happens way too often. So much of your GPA is weighted on the professor that you get. I have had friends who took the same class with different professors and our lives were very different as far as the workload and grading went.

July 13th, 2006 at 12:54 pm

There is at least one resource that I’ve found to be rather helpful: ratemyprofessors.com. I went there and looked up my teacher. She had over 40 different ratings from students and most of them gave her a “low easiness” rating (as they put it) and low ratings for helpfulness and clarity in teaching. Of course, I looked up all the other teachers available to me next semester and found nearly the same ratings for all the teachers I could take the class from.

One surprising thing about that website is that ~65% of the ratings are positive. You’d think it would just be bashing, but it’s not. It seems pretty accurate to me, at least for the teachers I’ve had that I looked up. Look up some of your old profs and see how they score compared to your experience with them. You can also leave your own ratings, of course, to help those that come after.

In conclusion, HOORAY for arbitrary grading and unclear expectations! That problem should have included “Identify the intersection.” I did everything it said!!! Argh!

July 21st, 2006 at 3:42 am

As a graduate maths student who has TAed a few classes, I can tell you that I would have given you full marks for the first question. The fact that (1/3)^(-2) = 9 is obvious to anyone who has ever understood Grade 11 exponents and should not require an explanation, whether in college or in high school. In fact, I would have expected the students to have been able to fill out the table with NO marks on the sheet.

For the second question, part a), I would have given you full marks as well. Unless the teacher demanded of me to lower the mark because a proper conclusion was not given. In that case, I would remove 0.5

For part b), the question is retarded and the answer you have given adequately answers the question, given that there was absolutely no specification for work [though what work you can write, I can only wonder]

Is your professor a mathematician? If so, then I’m deeply shameful for the quality of these questions and for the marking.

July 21st, 2006 at 9:33 am

@Phil

Thanks for your reassurance that I’m not mad and that my teacher can’t grade tests worth jack. Your site, Phil’s Proof, is pretty awesome, by the way. Thanks for coming by here!