Note to Self

My students probably struggled with the last few topics covered in the semester as my coverage on those topics was not as thorough as my coverage on the rest of the topics covered in the semester.

On a related note, I occasionally ponder the possibility of covering less, but in greater detail.

On a different note, I think it's strange how many students ask for review sessions, but when I bring up the idea of extending class time or a separate hour (temporarily ignoring the issue of increasing credit) to my peers, there is the idea that students wouldn't agree to it. The problem with office hours is that students either have other classes schedule during that time or are afraid to come. Office hours by appointment is fine, as long as it isn't abused.

Maybe there should be a game. Played by a professor. Every time the professor says something that might be on the exam, students should say some key phrase like "That's magic!" Perhaps every once in a while, and especially the first week, this should be aided with a pause or a hand signal or a sign (much like an "Applause" sign).

Next TA Meeting

This general idea of removing bias crossed my mind. How should we, if at all, deal with section to section discrepancies? I like the idea of mixing up the exams and having the person's name on the very back page of the last problem. That way, you can keep the scoring page on the front, and when you hand back the exams, you just turn the pile over and they can look for their names without seeing each other's scores. It also reduces section bias. But undoubtedly there is differences for the homework portion and emphasis of material from section to section. Maybe one of the TA emphasizes a certain type of problem and grades with respect to that emphasis. So even unbiased grading on midterm and final exams will be lopsided. I definitely would either scale each section so that all sections are comparable, or assign grades based on individual sections. TAs might expect a certain student to do well or do poorly.

See also next post.

Other Ideas to Focus On

$\lim a_n=0$ does not imply convergence.

Students use the ratio/root test on the endpoints of a power series. It's hard for them to grasp that those are exactly the points where the ratio/root test gives 1, and hence inconclusive. Apply the ratio/root test is a waste of time. Just as bad is when they apply the ratio/root test to the endpoints and get a value other than 1.

$\lim\left(1+\frac{x}{n}\right)^n=e^x$

Mistakes

THE FOLLOWING IS FALSE:
$$\frac{c}{a+b}=\frac{c}{a}+\frac{c}{b}$$

FAKE EXAMPLE OF THIS ERROR BEING MADE:
Student writes:
$$\frac{x^2}{1+x^2}=\frac{x^2}{1\vphantom{x^2}}+\frac{x^2}{x^2}$$

TRY IT WITH NUMBERS:
$$\frac{2}{1+1}=1$$
$$\frac{2}{1}+\frac{2}{1}=4$$