# Math5 – Precalculus Reflection

Here are my reflections on this precalculus class, recorded to remind me of what I noticed and thought about and learned teaching this class. Note that this isn't well written, and are in no particular order; these are mostly intended as notes for myself that I will read over before teaching my next class.

#### Think about When the Students Will Reach for a Calculator

Calculators aren't bad, but students rely on them as a crutch, and then run to them instead of learning something. Like if I ask what does arcsin(sin(17pi/4)) is equal to, they can just punch that into a calculator without a thought. Again, not bad, but it makes it hard to assess their understanding. I need to remember this when writing questions on assessments.

#### Introduce Basic Set Theory Notation

Like intervals, and $\mathbf{R}$ for the reals, because I want to use it so much anyways. I've never realized how hard it is to talk about math without some basic theory. Especially describing the domain and ranges of functions. And set union and intersection too.

#### The Undergraduates Apologize so Much

Data: by the end of week six, there are 18 emails in my inbox from students in this class that contain the word sorry. Like, there are quite a few "sorry for being late" messages and some "sorry for the inconvenience" and "sorry to bother you". But also a "I'm sorry I'm not doing my best" and some "I'm really sorry for my response on the homework" and "sorry that my responses are short" and "sorry I didn't reach out", all in response to me just reaching out and expressing concern for the midterm check-in. And one "I'm sorry for disappointing you this week!"

I should head this off at the get-go starting a new class. But idk how? Like, this is not just an isolated issue of saying sorry, but it instead either a sign of past trauma (women apologizing to men in power) or generally just an indicator of how the students view me as an authoritative figure whom they need to gain the approval of. I don't want to be this oppressive figure; any respect they give me should come from their acknowledgement of my mathematical prowess, and not from my position of authority as the one who judges them, and assigns them a grade at the end of the term. So the broad question is, how do I head this off? ...

#### Learn to be Conscious of my Speech Tics

This is tough to do without some kind of outside perspective feedback. I have some verbal tics when I'm teaching math, like asking the class "okay?" when I have no intention of hearing a response, or asking if anyone is "unhappy with this" to signal now is a good time to raise questions. Are these the best things to do? Like, the lack of students that actually respond to these things makes me think I should axe them? Or at the very least I need to clarify with the students the level of interaction I expect from them (say I want them to respond) and then design my speech/lecture style to promote that sort of responding from them.

#### I've Struggled to Plan the Whole Course from the Beginning

Once again, I've planned this course week by week. Really this is fine, but I've been dreaming of designing a class from start to finish for awhile now. I've wanted to have a solid over-arching narrative for a class, where I can speak week one knowing exactly where we're going towards the end of the class. I should try to buckle down and do this! It'll save me time in the long run, and I curious to what degree it makes the class flow better.

Experiment idea: give the students an exam on day one as a sort of placement/orientation test, but then give them that same test for the final (or part of the final) to see how they've learned and grown.

#### Make it Clear I'm NOT Going to Respond to Emails on Weekends.

Which is rough since they all put off the homework until the weekend, and I have it due at 8am Monday. But really, instill in the students a respect for their time and labor by demonstrating a respect for my own. Also show them this and this about the strange relationship American's have with work.

#### Don't Underestimate the Value of Quizzes!

For real, I never want to look at all their homework. I need to use ungraded (pop?) quizzes as a way for the students to assess their own understanding and to allow me to check in on them. I screwed up in this class at the beginning, thinking I'd just look at their homework instead.

#### Students don't have to Submit all their Homework

In line with the last point, I can't read all of their homework, but having them submit all of it maintains some impression that I'll read it all. So that's dishonest. Like for real, don't ask them to submit anything (exercises) that I know I'm not going to look at. And make sure the Reflection section reflects this. Like, don't ask them if they want me to look more closely at any exercises if I don't want to. Just ask which exercises they struggled with to get a general impression of the class and give me ideas for stuff me and the TA should revisit.

More broadly, it's important to build the impression in the students that doing the homework, like creating a homework document with all the exercises worked out, isn't the point of homework. The point is to learn! The point is their own transformation! And it's not necessary to do all the homework to learn.

And also, idk if this is related, but none of them emailed me for help during the term. They have no idea how available I am for office hours. I should enforce a vibe that they should email me while they're doing the homework.

#### Precalculus can be Boring

I noticed I had a harder time preparing to teach this class because (1) there's a plague going on and I was mildly depressed, but also (2) I know all this material so well that I'm not too excited by it anymore, so it was harder for me to summon the willpower to plan for this class than for past classes. Idk how to fix this; just an observation. But there were specific lessons, like the day we talked about functions, or the day we started trigonometry, where I honestly didn't know what much there is to say. And I probably didn't say some important things just because they were so plainly evident to me.

#### Students don't Know How to Assess Themselves

I think it's important to specify the “important things” in the class so they have specific guidelines to judge their progress. Like, before a midterm reflection, spend a class outlining the learning goals, and ask questions like, “do you know how to do this?” Similarly, instead of those little summaries I'm putting on the webpage, instead list the goals!

Also, for the writing in general, they should have a idea how much to write. The lack of detail on reflections and some Writing prompts was killing me. Say to them, If you're writing is less than the prompt, this should be a red flag. Establish some standards through examples! They have no examples.

Another point here, they don't understand that all that matters is what they know by the end of the course. Like, when I asked them to assign themselves grades, at least one student assigned himself a B because he messed up the first quiz, despite having learned the material from the first quiz since then.

Another note, I asked them after week 5 what they thought they deserved in the class, and all but one student asked for a B or a high C. With that exception, the students doing excellently couldn't identify themselvs, and the students failing couldn't identify themselves. For real, this effect was exacerbated on the finals. (Remember to look at the spreadsheet I kept) There were about six students who answered the vast majority of questions on the final incorrectly, but still thought they were doing well in the course and deserved to pass. One of these students even asked for an A-. Like, I can't tell if they're delusional and really have no idea how little they know, of if they're playing the game with me as if I wasn't going to look at their finals.

#### These Student Aren't Strong

This killed me on the final, because I ask them six questions that I think are pretty standard questions, and they are bombing them miserably. I should have known better though. Like, I get why Dr Weisbart did the thing where on the exam he's got these "C level questions" that are just bonehead easy and he says the students gotta be able to answer those to pass the class. Like really some of these students in Weisbart's class could only do bonehead-easy questions, and giving them six actual questions makes it hard for me to judge whether they could have done these bonehead questions.

When you leave feedback, it doesn't tell students where the feedback is, so like they might scroll threw pages of nothingness! This is yet another reason not to ask to collect the exercises; only collect things that I really really intend to look at.

More generally, Gradescope has a heavy vibe towards grading. It's built to be navigated and easy to use for graders working on an exam from a large lecture class. It's too much just for collecting work. Like, it's not easy to go through and look at one student's work. Simply using email would have been better.

#### Having Large Classes Makes Ungrading More Difficult

Obviously, but yeah. I don't really know any of the students personally, save a couple. I still had to keep a spreadsheet of notes about all of them, which is still dehumanizing. Teaching in a dehumanizing way was like trying to keep 30 simultaneous conversations going, which is simply not possible.

#### Use more GIFs!

Next time I teach this class, since I've already written homework and set an appropriate schedule for the class, I'll have time to find hella math GIFs to illustrate core concepts.

#### Provide Solutions to Everything

Another thing to do next time since I'll have more time is to make sure there are final answers listed to all the exercises I create, so that students have something to check their work against.