Every week, I try to come up with a poem for my TA sections to provide another fun way to learn material. My favorite poem so far would have to be the Saturday, September 13th entry titled "Oh, the limits you'll do!" My next two favorites would probably be the October 13th entry titled "String cheese, the dentist, and transformers", and then the September 24th entry titled "Oh, the derivatives you'll do!" Below is my work thus far:
Thursday, September 4th:
I came up with a haiku about trigonometry. I call it a πku:
Cosine is like x,
remember sine is like y,
on the unit ring.
Extra πku:
"One-to-one" is weird,
Two inputs, different outputs.
More like "two-to-two"?
Tuesday, September 9th:
I came up with another πku:
Hard identities?
Just draw the unit circle,
x is cos, y sin.
Thursday, September 11th:
I came up with a couple of limericks (I'm aware that my syllable count is a bit off):
If you're trying to find a tangent line,
and you find yourself caught in a bind,
just pick two points on your graph,
use point-slope with a laugh,
taking the limit of the secants, you'll find.
To find the value of the function,
you would like to just plug in.
Limits are your hero,
when it's "zero over zero",
just rewrite and try again.
Saturday, September 13th:
I came up with a rather long poem which took about an hour and 45 minutes to think of. To be fair though, I thought of it all in my head while I was at the gym, so it's not like I was really procrastinating. Every two lines are supposed to rhyme, so when you're reading, you might have to adjust your speed to make it right and stretch a little (e.g. read minus as "my-nuss"). I will be presenting it in class on Tuesday.
Oh, The Limits You'll Do!
You might be thinking that limits are tough,
when really in math, we can't get enough.
When the graph of your function looks like it merges,
we say the limit exists and the function converges.
And if the function doesn't converge and all hope has died,
we can still do something and take a limit from one side.
From the right is with plus,
and the left minus.
You might be thinking those last lines were a bit of a stretch,
well, to find a limit, make a table, plot points, or sketch.
Limits can be fun if you have a little patience,
For example, limits work quite nicely with the four operations.
Sum is sum, product is product, what's the difference, you mill.
It's the difference, even the quotient's the quotient when the bottom's not nil.
When factors cancel you might get a hole,
and when they don't, you might get an asymptote that looks more like a pole.
Soon we'll be at derivatives which might make you mope,
But really it's the limit of difference quotients that gets you the slope.
And then we'll be at integrals in a couple or few,
But you might be expecting earrings because that's limited too!
So, limits might be hard with epsilons, deltas, and such,
but they let us work with functions that we couldn't even touch.
You'll soon be reflecting on how much you grew,
I'm so excited, oh, the limits you'll do!
Wednesday, September 17th:
In lecture, we introduced the derivative as the limit of difference quotients. I came up with a couple new πku's to describe what the derivative tells us and how to find it:
f prime is the change,
positive means f's increasing,
negative dropping.
Looking for f prime?
Just find the difference quotient,
then take the limit.
Sunday, September 21st:
The first midterm is on Wednesday, so I decided to write a limerick to wrap things up. If you're in one of my sections, reading this limerick, you'll see you're in for a treat for Tuesday!
Until this current junction,
we've been studying functions.
Point-slope for a line,
limits and sine,
Almost as sweet as munchkins!
Wednesday, September 24th:
The first midterm was today, and I wanted to think of a cute way to transition in the next part of the course: finding derivatives without using limits. It doesn't quite have the same high quality of flow, but I came up a mini-version of my Saturday, September 13th entry:
Oh, the derivatives you'll do!
Limits, trig, and logs, it's all been quite fun,
but you'll see the story's not even close to done!
I know derivatives have been rather grim,
just a tedious application of taking the lim,
but you'll soon be learning shortcuts which you should treat as tools,
for example, there are the power, sum, quotient, and product rules.
Remember the derivative is the slope of the tangent line,
so, it can help us learn about functions like secant and sine.
Think about the tangent line at a min or max,
it'll be flat like a ball that's been dropped on tacks.
So, if we are in search of a valley or a hill,
it's often enough to find where the derivative is nil.
So, our next topic is a page turner, up there with Nancy Drew,
welcome to Chapter 3, oh, the derivatives, you'll do!
Saturday, September 27:
I decided to switch it up from standard poetry this week. This week, we are learning derivative rules, or rather memorizing. This got me to thinking that Leibniz could teach us a bit about how we should go about our lives.
Leibniz's Life Lessons
1. (πku)
If you're a fire,
C in front is a minus.
Ditto if student.
[(cos x)' = -sin x, (csc x)' = -csc x cot x, (cot x)' = -csc^2 x]
2. An ex will always be an ex.
(e to the x)' = e to the x
3. It's a sin to cos. (pronounced coss like cuss)
(sin x)' = cos x
4. It's sec z to tan sec z.
(sec z)' = tan z sec z <---- my personal favorite
Wednesday, October 1st, 2014:
We are studying the wonderful tool that is the Chain Rule. I wrote a limerick to celebrate it and help remember it.
To differentiate a function P
you can write as f composed with g,
first find g prime,
then f one time,
plugging in g and doing the product, you'll see.
Saturday, October 4th, 2014:
We are adding more to our repertoire of tools for calculating derivatives. Two of our last weapons: implicit differentiation and differentiation by logarithms. I wrote two πku's about them:
For crazy quotients,
or when you've f to the g,
find y prime by log.
When you've f of y,
take normal derivative
with y prime after.
Thursday, October 9, 2014:
I was rather busy with my midterms, so I didn't come up with any poems for this section. Instead, I shared two of my original jokes:
What do cars use to listen...? Engine-ears!!
Did you hear about this new craze of physicists posting videos of themselves calculating forces and radii and multiplying them together...? I think they call it... torqueing?
Monday, October 13, 2014:
We are beginning Chapter 4, which describes how we can use derivatives to learn about the graphs of functions. More specifically, we learned about ideas such as the Extreme Value Theorem, the First Derivative Test, and the Second Derivative Test. Note that the writing in blue are things you should read aloud, and writing in orange represent gesticulations and should not be read aloud. Below is a poem I've written about the topic:
String cheese, the dentist, and transformers
From calculating derivatives to analyzing graphs is where our focus caroms,
We'll start by looking at a few tests and exciting new theorems.
Will a continuous function attain a min and max is a question you posed,
the Extreme Value Theorem says yes when our domain's an interval that's closed.
First evaluate where the derivative doesn't exist or equals nil,
then compare with the endpoints to find a valley and hill.
What happens when our domain isn't so, surely all hope is lost,
well, the First Derivative Test can help us with little extra cost.
I think the name "critical point" is perfect for when y prime doesn't exist or is zero,
for it's essential to us like string cheese and bone marrow.
So, at these points, put your hands up in the air like you're hanging a poster, (put hands up)
at a max, your graph will go up and then down like at the top of a coaster.
(motion one of your hands going up and then down in the shape of a ^)
But if you asked me which method to use, which I thought was best,
I wouldn't stutter at all before saying the second derivative test.
For instance, when your graph goes down and makes a cup,
(motion one of your hands going down and then up in the shape of a U)
the second derivative will be positive and y prime will be going up.
This is really important, I hope you see the gravity,
You don't even need to go to the dentist when you get concavity!
These tests are so useful, it should be a crime,
If you asked which is my favorite transformer, I'd have to say f double prime.
This stuff might seem hard, it might make you cry,
But it's so helpful for us, there's really more than meets the eye.
This stuff's so incredible, better fasten your buckle!
Well, maybe not that great, but I hope you at least had a chuckle.
Saturday, October 18th, 2014:
We have the second midterm on Wednesday, so I decided to write a limerick about how I at least like to deal with test anxiety since it appears that a lot of students suffer from it. I will present it during Tuesday's discussion section:
If you're feeling anxious and stressed,
when taking tomorrow's test,
"the studying's done,
now let's have some fun,"
then go out there and try your best.
Thursday, October 23, 2014:
I gave back exams today, and I expected some students to be a little bummed. So, I began discussion by passing back exams and then leading some discussion about some things I thought of. I thought this was a valid use of time because two of my major goals of discussion are: 1. to TA as I would like to be TA'd, and 2. to promote academic success: both in calculus and overall. I thought that discussion would be a light way to get their mind off their tests and make them feel better, while also promoting their academic and personal success. These are the things that we discussed:
Things I wish I knew before college
1. Any workout is good as long as you try to make exercising a lifelong hobby.
2. Gravitate towards those people who treat you well.
3. Treat others as you would like to be treated... while understanding others are possibly from you.
4. Try to have a college experience that you can be happy about 10 years from now.
5. Reflect about your feelings, actions, and thoughts.
Saturday, October 25th, 2014:
We are introducing integrals as a way to find areas under curves. To help understand the method by which we calculate integrals using the definition, I wrote a limerick:
To solve "find the area" capers,
the idea is to use skyscrapers;
split [a,b] into bites,
find f at the rights,
you'll get a view that's like Don Draper's.
Saturday, November 1st, 2014:
We have just been introduced to the Fundamental Theorem of Calculus, a 2-part weapon of epic power and functionality. I wrote a limerick to talk about how to use the second part:
To find the integral of f on [a,b],
when you know an antiderivative of f is g,
in g you'll play
first b then a,
the integral's the difference by FTC.
Saturday, November 8th, 2014:
We have transitioned from viewing integrals purely as computations to viewing it as a tool to compute areas and volumes. Note how this is analogous to how we transitioned from viewing derivatives purely as computations to being a tool to learn about the graphs of functions. I wrote a limerick about how we can use integrals to find the area between curves. This limerick is quite a bit off in terms of syllables, but to be fair I had a lot of trouble trying to find words that rhyme with "meet" or "touch":
For the area cinched by f and g,
first draw a picture to help you see.
The points where they touch,
your limits are such.
Integral of bigger minus smaller your answer'll be.
Thursday, December 4th, 2014:
Today, I showed my Study Guide to the GRE (which you can find on my website). One might be thinking I'm hawking my stuff during discussion, but the study guide is freely available on my website and I gain no profit from its future use, other than warm feelings inside. Showing this served two purposes: 1. to introduce them to the GRE which they may be taking later, 2. and more importantly, for me to bring up that I believe that they are all intelligent people and that I believe in that they are all able to achieve academic success. I know I have been always grateful and appreciative when a superior of mine has voiced their confidence in me.
I also shared with them "Derek's Key to Good Health". It is rather simple. It states "Always have something soon to look forward to." From my experiences in undergraduate and this semester, there are rough times for everyone when they're not sure if they spending their time at college well or they're doubtful whether they belong to be here. I think this key is incredibly important to here because having something to look forward to, in my opinion, creates enthusiasm to wake up in the morning and to work for hours. I also stated that they if they ever don't have something to look forward, then they should work hard to find that something in their life. It could be something innocuous like going to the gym or going to Calc 1 discussion section, and "soon" might mean the weekend, but they should try to find that something. I also had the students fill out their ICES form today.
Tuesday, December 9th, 2014:
Today was the last discussion section tragically. I gave them my compilation of poems (which you can find at the link https://drive.google.com/folderview?id=0B-P0Cy9_Gp-ldl9SSjN0d0ZIdG8&usp=sharing as a PDF under the title "Poem Compilation"). At the beginning of class, I put up the rather depressing quote "You could have learned everything here at community college." Note that I put quotations around the quote on the board to emphasize that these weren't my actual feelings. Then, at the beginning of class, I asked if they ever heard this before. I knew that some students were struggling in the class, and had been doubting their decision to take the class for some weeks now. Some students nodded with recognition after I asked. Then, I said I thought that this was an appropriate quote to conclude the class by. Because yes they probably could have learned the same material with a higher grade elsewhere, but there was really much more to the class than just the material. Elsewhere, they wouldn't have had such a passionate professor and enthusiastic TA, trying their best to create interest in calculus. They wouldn't have had such intelligent peers and classmates to learn and discuss the material with. They wouldn't have heard extra study tips and probably wouldn't have been treated with such care if they had learned under other people. So, in the future, I hope they reflect upon the semester and the course and feel they received more from the course than their grade, much like how I hope they receive more from college than a degree and a job.
I felt that I did a solid job over the semester. I improved quite a bit with my worksheets and the layout of my discussion sections. A few people asked me why I stopped writing poems all of a sudden. The truth is that as the semester became more difficult, the students began having more trouble with the material. Initially, I thought that hearing poems would offer a nice introduction to the material because they should had heard the content of the poems in the lecture before, but I found that they had they effect of reassuring some students that they didn't have a good grasp of the material. So, my ingenuity (or so I think) in my poems rather than being viewed as creative, I felt was seen as somewhat demeaning. I will try to come up with poems next semester and see how it goes. It takes an average of 45 minutes to an hour and a half, so it takes up quite a bit of my free time with having to think. Otherwise, I am very proud of my performance this semester as a TA and I feel I accomplished my goals of: 1. being enthusiastic; 2. making students feel comfortable in contacting me when they need assistance; 3. being flexible in changing in order to meet the students' needs; 4. making students feel very open to give me feedback; 5. returning work on time; 6. being seen as reliable to my students; and 7. ending the semester with students feeling comfortable to reaching out with me when they need help in the future. Overall, my overarching purpose was to provide students with the discussion section experience I would want if I was a student who wanted to do well and gain something more from the class other than L'Hopital's rule and implicit differentiation; I think I succeeded. In conclusion, DONE!
I compiled all of my poems in a single word document titled "Poems Compilation." This document can be found at the Google Drive folder I made for the course, which can found at the left tab "Fall '14: Math 220."
