After not posting something for long, I’ll post something a little bit underwhelming. The inactivity wasn’t because I had something really good right now (the only thing I have on the back burner is satire), but it’s because I’ve been busy with school work. With winter break, I’ve gotten more time to work on the things I care about (i.e. NOT school).  I hope you find this interesting, despite this post having no substance.

Remembering that all your students exist

I have 6 wonderful students and one not so wonderful student (screw you, Steven). When I need to list them all or take mental attendance, I have to get out the roster. I realize that I have 5 or 6 people listed and blankly wonder who I forgot, despite all 7 of them being in front of me. I pull up the roster and look for 10 minutes before I realize who is missing, and it seems very obvious to me after I find it.

Then we have teachers whose classes have 30 people a period, and have around 90 to 150 people in total. They can remember who exists without batting an eye; often attendance is done without looking at the seating chart and just by memory of seating arrangement. It truly amazes me how teachers can do that, when I can’t remember 7 people who I converse with often outside of class.

And we don’t understand why seating changes aren’t more frequent.

(I am very sorry, class, but it really is hard to list all of you guys. This probably speaks volumes about my teaching method, which is to make the lecture not tailored to anyone at all, so that the kids will think I am tailoring it to everyone.)

Trying to make problems

Boy, this is going to piss my class off. As if I didn’t already last time.

Whenever I make a conscious effort to make problems (i.e. flip through pages of study guides and textbooks to find an idea I can use), they usually turn out to be crap. (Around 5-10% of my problems are going to make it on, say, the final version of our entrance exam.) In contrast, my shower problems (usually brought on because of a combination of fascination for some idea, stupid flavortext ideas, and guilt that nothing I made in the last hour was remotely salvageable), I have a success rate of around 30-40%, and that is a very stingy estimate. At worst this is an improvement of x3, which I have no idea why.

Obvious Observations

Recently I was given the trivial line $$\angle HBC=90^{\circ}-\angle C.$$ The reasoning took me 10 minutes to realize. For those of you as lazy as me, this is because extending HB makes a right triangle. Oops.

I’m sure I have other idiocies, like $$\angle AOB=2\angle ACB,$$ but I don’t remember any of them as of the moment.



Disclaimer: I usually claim to be knowledgeable in what I blog about, but this time I do not claim to be. If you’re an expert, feel free to correct me, since I’ll probably be wrong most of the time.

Generally, when I write a handout on something, I’ll have two things: theorems, and problems. Theorems used were usually proved very long ago, and problems can easily be sourced as “2018/AMC 10A/25,” though (unfortunately) people don’t do the best job at citing and leave it as “2018 AMC 10,” which makes it take a while to find the problem.

Let’s take a look at what MLA has to say about citing your sources.

So, MLA, there’s this very helpful book for aspiring mathematicians. It is called, “the Art of Problem Solving: Volume 2.” Those of you who don’t know this are probably going on google.com and searching it up, in which case it would be a good citation, since I made it easy to find.

Take for example, this imaginary quote from an imaginary chapter of my imaginary book.

A History of Logarithms

Chapter 1 – What is a Logarithm?

To understand the history of logarithms and their uses, we must first understand what exactly a logarithm is. For this task, I turn to Chapter 1 of “the Art of Problem Solving: Volume 2” for the definition of the logarithm and the six most important properties.

[insert definition]

[insert properties]

Now let’s let the MLA do this for us!

A History of Logarithms

Chapter 1 – What is a Logarithm?

To understand the history of logarithms and their uses, we must first understand what exactly a logarithm is.

[insert definition]

[insert properties]

Then, you get to flip to the end of the book, find the bibliography (this is much more annoying the further in you get), and it will say this following:

Works Cited

Rusczyk, Richard, and Sandor Lehoczky. The Art of Problem Solving. AoPS Inc., 2013.

Insert source here.

Hanging indents suck.

Here’s my initial reaction to this:

When did you use this source? Which AoPS book is this? What counts as a citation? What section did you use? What is wrong with you?

After I calm down, my thought-out and reasonable response would be this: “You can go screw yourself.”

(Note: The original draft of this post had an endnote, and a rant on why footnotes are far superior. Then I remembered that many people will simply put “Bibliography” and have no reasonable way aside from guessing to know where each reference fits in, making it even more annoying.)

How to Fix MLA

I’m not an English/History teacher or professor. If my peers did this, I would be extremely annoyed, but they don’t. Ideally, English teachers would have other English teachers to tell them that they need to stop making their citations so lengthy, effort-requiring, yet worthless. This should mean that I don’t care about MLA citations, since it’s not my place and they don’t affect me.

However, due to the dreadful government institution that serves barely-edible food, has people stand in an orderly grid-ish fashion to take rollcall, has iron gates as a security feature, has officers that patrol the campus, is filled with zero-tolerance policies, and has a schedule strictly to the minute, this becomes my business. (And for those of you wondering whether this is school or prison, this is school. Prison inmates don’t have to write English essays, which may be the only difference.)

The true fault does not lie with the MLA. The fault lies with English and History teachers around the country. If they’d let me write my papers the way I write them, while actually demanding a satisfactory result (i.e. don’t give me 100% for sucking up in the entire essay), I wouldn’t complain about the actions of a far-off organization. When they make me adhere to the standards of a far-off organization, I expose the sheer stupidity of said standards.

TL;DR: Stop making kids do MLA citations!

Training with the Right Perspective

There’s someone who has been bugging me to post something for a while (you know who you are!), so I’ll actually post something substantial. I hope this will be worth the wait.

Studying for a Test

It’s very common in math class that the people who perform consistently well on math tests never study for those math tests specifically. Of course, they still do math often, and truly enjoy the subject. There are a couple exceptions, but in the end everyone knows that’s all there is; they’re just good at tests.

But this first class of people have a name, though this is a very uncommon description. We are known as the competition math kids, though we usually just get called “math kids.” It’s very well known that math is unique in the fact that competition math has nothing to do with school math; competition physics and school physics correlate, as does chemistry, computing, etc.

So why do the kids who do competition math perform so well on school tests, without those performing relatively well on school tests excelling at competition? What makes the difference? And why do people who study for tests for hours each day the week before usually fail, or barely “pass?”

While this is the natural order to ask the questions in for most people, the natural order to answer them in is the opposite. The way you ask your questions, in addition to the actual questions themselves, influence your answer. The reason people have been asking these questions in the wrong order while feeling that it is the right order is because they’ve been conditioned to think about it in the wrong way. The question I’m asked most often is, “How are you smart?” as opposed to “Why am I not?” which reflects the order these type of questions are asked in. (Some survivorship bias is also present when asking just the people who succeed. Often more than not, quite a couple strokes of luck are involved.)

You’ll notice that the lines of thinking for math tests go differently. Some people think, “I’ll study to get a good grade. It’d be nice to get smarter, but that’s not a priority.” Other people think, “I study to get smarter. It’s good to do well on tests, but that’s not a priority.” Surprisingly, it is often the latter type of person who ends up doing better on tests. However, most people think the former, which demonstrates a backwards thinking and a lack of understanding of math.

Most of us know people who study a week or so before every math test. Some end up only studying the night before, and others end up getting respectable grades. But even for those who believe grades are all that matter, people who study not for grades but to get smarter usually are the ones with the best grades.

But having the right mindset is not alone to succeed. I personally know some people who don’t study for grades but are still failing a particular subject. This doesn’t make their efforts worthless; this work ethic is arguably much more valuable than the specific success itself. (While I think some parents overstate the “genius” of competitive math kids, part of the reason they say this is because of the work ethic. After all, nobody gets a job doing high school math olympiads…)

The kids who do math for the sake of math become good at math, which is why they generally crush school tests, if they aren’t exceedingly stupid. (By “exceedingly stupid” I mean “show your work” or something of that sort.) The kids who do math for the sake of a grade become good at getting grades if they are really lucky, but they don’t get much better at math, meaning they have to do it again the next time there’s a test.


In general I think people understate how much they have done and overstate how much they can do. This makes sense from a motivational standpoint; the more you think you can do, the more you will try to do, and the less you feel you have gotten done, the more you feel you need to get something done.

But sometimes I feel this backfires. The feeling of “I’ve never done anything, and anything I try to do ends up sucking” can be very detrimental all the same. When no noticeable improvement occurs during the first few weeks/months of whatever you’re practicing, it can be very disconcerting. It’s very easy to beat yourself up over this, but we often forget how much we have accomplished. I’m certainly very guilty of this. Having your handouts written down somewhere though does help to give perspective, so I have it easy there.

Everything has to come with moderation, though; spending too much time thinking about what you’ve already done leads to a false sense of satisfaction and not doing anything else. Spending too much time thinking about how little you’ve done also leads to getting nothing done. I’m not sure how to quite accomplish this balance, but I’m vaguely aware it’s important.

Grades should be abolished.

Disclaimer: Much of this post doesn’t talk about grades and the reasoning only ties in to reflect grades near the end. The reason the title of this post talks about grades is because the abolition of grades will signify that some major problems plaguing the public school system have been addressed.

Recently I’ve had quite a lot of homework. This mostly is my fault due to procrastination; things I had weeks to work on, I chose to save for the last minute. But I’m not the only person I know who doesn’t procrastinate; nearly every kid who goes to school tends to procrastinate their homework, and this is the first time I really mean all schools when I say school, not just public schools. This is mostly because people don’t view homework as something worth doing.

When I see something worth doing, I will usually start on it pretty soon and worry about the nitty-gritty later. This is because the things I want to do are usually worth doing; I would not be so eager to start doing something I didn’t want to. Conversely, I worry more about the details for things I don’t want to do (see homework). I will usually postpone it and get ideas for it (if it requires and usage of brain cells) without putting them into action. So what does this mean for homework? It’s one of the things we’d like to have done, but that we never do until we absolutely have to. Usually, the reason we do homework is because we have to; and for those who say “You can choose not to do your homework,” that’s akin to saying “You can choose to abandon your future by pushing your car off a cliff.” That’s not a choice. Wrecking your car would make your wallet unhappy, and wrecking your grades would make your future unhappy.

But school should be a time to experiment with what matters to you; children don’t know what they want to do in the future (usually), so they have a place that is supposed to be convenient to experiment. Instead we get the opposite; experimentation is discouraged, and conformity is a must. There are many problems with school, including the extremely short periods we have to work with, stupid spirit days, “core” classes being mandatory, and this comes together to penalize motivation.

However, examples of schools that are starting at better situations and have fewer problems exist; the example I use is the CACC of Pleasanton. Nothing’s perfect, but doing something like that – or doing anything, really, is a long shot better than what we have now.

What’s Your Time Worth?


We often hear people say something to the effect of “I just spent 3 hours of my life reading Quora/Facebook/Instagram.”  These statements seem innocuous enough; we all have our guilty pleasures which we waste asinine amounts of time on. And it seems fine to us! Instagram is a free social media service, and we aren’t paying by the minute to read what our friends posted. But this isn’t true in the slightest; we are paying a minute by the minute.


Why do I value time so much? Some people argue time is money; and this is certainly a good analogy for not wasting time, especially if you are frugal. I argue that time is potential for change. Time, in its purest, is potential. You cannot do anything meaningful without spending time, and it’s probably difficult as well to do something meaningless without spending much time as well.

But the analogy with money is the best to conceptualize time with. If you approximate how much each hour of your time is worth with money (in my case, it’d probably be around $20 dollars), we can make some surprising changes.

“I spent 3 hours on Quora” becomes “I paid $60 to read a couple of posts to mildly entertain myself.”

“I slept in for an hour” becomes “I paid $20 because I didn’t want to deal with life.”

“I decided to binge 10 episodes of Rick and Morty” becomes “I paid $65 to watch a show about an old grandpa and a dimwitted kid explore the galaxy in a sci-fi comedy.”

If we up the scale, even more surprising/outrageous statements can be made.

“I hate going to school” becomes “I’m being forced to spend $36000 on something and I hate it.”

“I went to prison and served a year of time” becomes “I was fined $175200 for something I didn’t do.”

Of course, money and time aren’t this similar. Time is something that cannot be invested, saved (most of the time), etc, but the most important difference is you can’t take back spent time.


The value of your time is not constant. I’d imagine the time Bob has as a researcher is more valuable than the time he was a baby. Conversely, the time Bob was a baby is probably more valuable than the time he spends in school. So spending time to make your time more valuable is one of the best uses of your time.

This is why it’s so important to spend time learning. (I really hope school doesn’t use this quote; as a disclaimer, school is awful because you feel like you learned, but you really didn’t.) This, I also suspect, is why kids and parents (mostly parents) think doing math makes you smart; survivorship bias plays a role, and they see how valuable the time of the “smart kids” is.

Also, this is why writing is important; the easier you see things, the faster your time becomes worth more. Writing isn’t about explaining to someone else, it’s about clarifying your own thoughts to yourself.


What I find awfully annoying is people deciding to split my time into pieces. This is the biggest reason why I really despise school, if you don’t count the administration. I think my first post goes over this in a little more detail.

When your parents give you a chore to do in a 3-hour study session that takes 10 minutes, you aren’t left with 2 hours and 50 minutes. You are left with two chunks of 1 hour and 25 minutes. There really is a difference! I’d like to present the following example: Let’s say you play video games for 1 minute, then you do math for 1 minute, and so on for around an hour. I think you’d have a much better time playing Smash for 1 hour and doing math for 1 hour, don’t you think?

And this isn’t some extreme work of fiction; this is called multitasking. This dilution of your time makes it less valuable, just like diluting gold/silver/etc makes it less valuable. People are prone to multitasking, so the best way is probably to reduce the amount of things you need to do. This is why I do as little homework as I can get away with for some classes; I’m still in middle school, so most grades don’t count for HS.