I am fifteen years old, attending eighth grade. It’s 1985. My brother Daniel is born. *Back to the Future* will premiere later this year.

I’m still in the Special Education program, although I don’t have any Special Ed classes. My Special Ed handler looks at my grades, and my test results, and then works with me to figure out where I might need help and where I might benefit from more direct instruction. I really like having an adult speak with me and involve me in my education like this, instead of being shoved around the system like a bit of paperwork.

I find myself attracted to the Special Ed classes, because I feel much more relaxed in the smaller groups, and also because the work is so dang easy. I also enjoy having an adult engage me directly. I am content to slack off and remain in Special Ed, perhaps even hoping that I’ll get pulled out of a few regular classes and put into Special Education curriculum.

I’m a bit more socially developed, and it’s easier for adults to judge my intelligence by talking to me. My teacher is also armed with my standardized test scores, and she is too wise to fall for my slacking. She can see clearly that there is a massive disparity between my ability and my performance. That gap might have been muddled in those years when I had a bad home life, intense social dysfunction, and a nervous system full of drugs, but it’s pretty clear now that my scholastic failures have nothing to do with me finding the material to be too difficult.

The disparity is most pronounced in the area of mathematics, where my tests suggest I should be in advanced classes and my grades suggest that I am an imbecile. Part of this is due to the fact that standardized tests often lump “logic” in with math, which greatly elevates my mathematical performance, but most of the problem is due to that fact that math is taught through drills.

Before I got my own computer, I spent about half a year visiting my friend David and learning to program on his Texas Instruments computer. On that machine, you created graphics by using hexadecimal numbers, which represented binary patterns, which mapped directly to patterns of pixels. If you wanted to make a smiley face like this one:

You would do so by looking at the things in groups of four dots. For the first four, I want a zero, followed by three ones, to represent the empty space followed by three colored squares. In hex, that’s represented by a 7. The next four dots is three colored squares followed by an empty one, which is an E. Going down the image, it means this smiley is represented by the sequence: `7E81A581A599817E`

When I was first learning about this, I had to keep consulting a chart in the manual that explained it. With practice, I found myself visiting the chart less often, until I had all of the required patterns memorized. Now I can construct these graphics in my head, a skill I will retain for the rest of my life. This means I can convert between the binary and hexadecimal number systems at will. I also understand binary numbers and binary counting. I didn’t set out to learn any of this. It all happened naturally, as I learned larger things. It’s simply a tool, like any other.

If I’d learned these graphics the way math is taught, then I would have spent three weeks doing worksheets and taking tests to establish and confirm my hexadecimal skills before I was allowed to put them to use or even know what the skill was for. It would have been endless drills with no discernible goal. It would be like learning to be a carpenter by spending six weeks driving nails into a lone piece of wood before anyone showed you that the nails could be used to assemble something.

As far as I can tell, math is boring, tedious, repetitive, and useless. It’s endless sheets of busywork with no goal or purpose.

A few people encourage me to seek the harder math courses, and to my ruin I ignore their advice. To me, math is “hard” because of how boring and time-consuming it is. Homework usually consists of doing the same problem *forty times in a row*! Then tomorrow, we will do forty more of the exact same problem, except with one extra digit of complexity thrown in. The pages march by, an endless procession of mind-numbing paperwork, a treadmill of uninteresting problems. I assume, incorrectly, that if a class is “harder” it will simply be the exact same lessons, except there will be even more homework and additional digits of complexity. (Which never makes any sense to me. Once I can multiply a pair of two-digit numbers I can also multiply twenty-digit numbers. Adding more digits just feels like belaboring the point to me.)

What I fail to understand is that the “harder” classes are where math becomes far more interesting. Instead of forty dull problems, they give you five interesting ones. Instead of pointless drills, you can begin to see how to use math as a tool. They finally give you a pile of two-by-fours and let you start nailing things together. I can put part of the blame on my terrible elementary school experience and my lack of trust in the system. I can put part of the blame on the shameful, idiotic way in which lower math is taught. I could try to pin some of the blame on people like Mrs. Grossman, who made the subject such a chore. But the truth is that most of the blame falls on me. I’m about to miss out on some really valuable and interesting learning because I’m afraid of a little work.

So despite the suggestions of the adults, I stick to the easy math classes, thus dooming myself to a slow purgatory of non-learning. I take “Basic Math” instead of “Algebra I”. Basic Math is just a repetition of what we learned in elementary school: Addition, subtraction, multiplication, and long division. Next year I’ll take “Elementary Algebra I” and “Elementary Algebra II”, which will dilute the already slow-paced introduction of “Algebra I” into a full year of tedium. This mistake will haunt me for the rest of my school career, and it won’t be until I’m close to graduation that I’ll even be aware of just how badly I screwed up. It won’t be my senior year that I will discover the extreme utility of trigonometry and curse myself for passing up the chance to learn it instead of simply sleepwalking my way through another algebra class.

There were a **lot** of blunders in my school career. A lot of people wronged me, mistreated me, neglected me, or hurt me with their incompetence. But this particular screwup was mine.

## Programming Vexations

Here is a 13 part series where I talk about programming games, programming languages, and programming problems.

## The Loot Lottery

What makes the gameplay of Borderlands so addictive for some, and what does that have to do with slot machines?

## Raytracing

Raytracing is coming. Slowly. Eventually. What is it and what will it mean for game development?

## Stolen Pixels

A screencap comic that poked fun at videogames and the industry. The comic has ended, but there's plenty of archives for you to binge on.

## Are Lootboxes Gambling?

Obviously they are. Right? Actually, is this another one of those sneaky hard-to-define things?

MATH IS EVIL!!!!!

well at least the boring parts.

It’s good to know the education system wasn’t THAT bad.

P.S first and where did the editing go?

So we’re going to start doing this “first” crap here?

You should go and look at the comments for “DM of the Rings” which was around when the whole ‘first!’ thing started on youtube. Shamus, actually got so annoyed he started putting in the first comment before the blog post was even up for public view. Just to deny people the opportunity.

I still have a standing policy of forward-dating any blatant first posts, moving the “first” person down the page by an hour. I think this should be standard practivce. I’ve never had to punish, delete or warn anyone, and there has never been a repeat offender.

The real skill is in going “last!”, then being and remaining correct.

I wanted to Like this comment and started looking around the screen for the button.

Then I remembered that this isn’t Facebook.

Scary, isn’t it?

DM of the Rings was my introduction to this fine site. I loved Shamus’s response.

God I was such a loser back then

1. It’s maths for short as the whole word is mathematics. Just a nitpick.

2. I never understood the US system of slow learning until University, often encouraging a post-grad course. Other school systems will push you through most of it (although IMHO they shouldn’t ‘offer’ advanced courses, I too turned them down to my regret but I ended up taking a music career anyway) and let the slackers stay until they drop out from failing year 11/12.

Although a lot of the blame is to be put on the teachers for not explaining things properly for you or me Shamus, you’re dealing with people who should be trained to deal with ‘special ed’ kids. I went from the best student in my school at English in yr 7 to an average mark for my ATAR.

I find that this is an issue which many education systems have. For me, it happened at university. I got taught Algebra (Matrices, Vectors, Eigenvalues, and so on) without ever seeing any example that interested me. So I ignored everything, and just scrambled by somehow. Half a year later, I start to take a look at this 3D-graphics thing. Boy, was I in for a surprise.

And that’s not the only thing, really. People wonder what they will ever use differential equations for, but if you want to make a career in any engineering discipline, you will come across differential equations at some point. Some disciplines use it less (e.g. writing software*), but others use them a lot more, and might not be too far off to begin with (e.g. designing Hardware). Someone has created all these tools we use daily (cars, computers, phones, microwaves, buildings), and they all got Engineering degrees and must know Math. “I will never use this knowledge” is only true if you want to spend the rest of your life packing someone’s groceries into paper bags.

*And then you see a paper on how to compute a distance between two points on a 3D-surface, and Lagrange gets thrown around on page 1.

This. Math is one of the few subjects where everyone will use it in some way the rest of their lives. Not necessarily advanced calculus or anything, but basic arithmatic and logic.

While there is value in learning history and art and chemistry, people may never actually NEED to know these things. It is enjoyable and being able to talk about something that’s happened in the past or why a painting or a film is beautiful will make that person more tolerable to be around, it’s not something they really need to be able to do in order to complete basic life function.

tl;dr: it’s not repetition that is bad, it’s forcing the same amount and speed onto everyone.

I am not going to defend the public education system, neither in the USA nor here, but one thing about repetition is true, i.e. that many people learn a lot of things only really well by repetition. Do it once or twice – forgotten after a week.

Even the most basic calculation, up to 10×10, is learnt by repetition only. The human brain is not capable of computing numbers like a computer’s ALU, it works more like a lookup-table, storing the results of each basic calculation for quick retrieval, and more complicated calculations are broken down into parts until the individual parts match a lookup-table.

However, this does not apply to everyone to the same degree, and to make matters more complicated, it usually also depends on their specific interest in the topic at hand. Generally, many students loathe math, not just for the way it is taught, but by itself. Some just don’t like numbers and logic and will always struggle with anything but the simplest mathematical formulas.

Shamus gave a good example how to do it right, the way he learnt hex and binary – it was also through repetition, but in a way that interested him, made a lot of sense, he could directly put to use, and – very importantly – at the speed that he is comfortable with.

Now, what does not work is shoving the same thing down everyone’s throats in a “eat or die” manner (actually, that doesn’t work well in any area, not just education).

You drove the nail home, Mephane. Shamus learned binary and hex not by mindless repetition, but by

practicingthe skill he was learning. You know, with a useful goal in sight. Seymour Papert and others spent decades proving just that: people learn best by doing.Of course, once you start teaching kids that way, it becomes almost impossible to keep track of what they’re all up to, let alone grade them. And for various reasons, that’s considered inconceivable.

Nope, that’s not the case. That’s WHY New Math was so different that parents couldn’t help their kids with it. You didn’t memorize multiplication tables “up to 10×10”, you SAW what it was therefore you knew WHY the answer was what it was, and you could express it in any numeric base you happened to be using. Base-7 6×6 becomes 52. You knew that not because you memorized it but because that’s how the numbers behaved. Shamus talks about memorizing a hex chart, but for the kids who got a REALLY good grounding in New Math (who’d have to have gone to schools that had teachers that ALSO understood it and would be about 50-55 today), they’d not have had to memorize it because they’d already KNOW that as easily as most people “know” today that “3 times 4 is 12”.

That does not contradict what I said. There is a lot of things you can approach from those two sides – learning to do them automatically, without ever thinking about it (simple calculation, driving, handwriting, even speaking) while still, of course, there is a theoretical, scientific approach to understand what is actually going on. I was talking about the former, while you are talking about the latter. :)

But the only reason we KNOW that “3 times 4 is 12” is because we’ve memorized it. When we were seven years old, “3 times 4” was something we actually had to COMPUTE, perhaps by drawing a little three-by-four grid of squares and then counting them. Once we had a little more knowledge in our brains, we could compute “3 times 4” more quickly, perhaps by counting “3, 6, 9, 12”. Eventually, through repetition, we just memorized the answer. Now we know it so well that we often forget the process we went through to learn it.

Those who study such things call this progression

encapsulation: as our brains become more familiar with any given process, we no longer think of that process as a complicated collection of steps, but as a single primitive step–which we can then incorporate into a larger process. Iterate as desired.For example, in order to do algebra, you need to know your basic arithmetic facts. It’ll be very hard to solve an equation if, every time you want to add 6 to both sides, you have to stop and count on your fingers to accomplish the act of adding 6. By the time you get that done, you’ll have lost your place in the algebra problem. Arithmetic needs to be “encapsulated” before you can build algebra on top of it. Likewise algebra for calculus; likewise calculus for differential equations, ….

But as Shamus learned, sometimes we have to come face-to-face with that need for encapsulation in order to get it to happen. Myself, I was awful at remembering my multiplication facts in grade school; I never really learned them well until I found myself in algebra classes where I was greatly inconvenienced by not knowing them. Fortunately, nobody tried to prevent me from taking algebra classes just because I hadn’t yet memorized the whole multiplication table.

The part about breaking things into parts is EXACTLY how I do math. I just tend to do it so much faster than anyone else.

I always heard the expression that high school students would make the best spies. They can memorize large quantities of information for a short period of time, and then completely forget it.

Howdy,

Ever since late high school – when I took calculus at the neighboring university – it has struck me that higher math is taught in a manner that is completely artificial, overly abstracted, and counterproductive.

Very little math was developed on its own, as a thought exercise; it was almost all developed in concert with the (engineering, scientific, logical, etc.) problems it was used to analyze, quantify, solve, etc. It doesn’t really make sense to teach math as its own separate subject; it should be taught in the context of the problems it is used to solve.

This is done to a degree in some places and disciplines – I never had a class in complex analysis, but learned it in concert with DSP, and you can take ‘Physics with Calculus’ or ‘Physics w/o Calculus’ (Physics Lite) most places – but not to anywhere near the degree that I think would be helpful. It’s much easier to learn math when you know what it is for, and much easier to understand science when you use the proper tools, instead of having both presented to you as received wisdom.

Alex

Speaking as a current maths undergrad I have to strongly disagree with both the idea that maths was largely thought up in order to solve problems in other fields and that it can’t hold up as its own subject.

It is true that a lot of what is learnt during school years, at least in the UK, is almost exclusively things with applications. Also the fact that many of the basic concepts of calculus were developed by Newton in order to solve physics problems may lead one to believe that the majority of maths is developed for application.

The reality is more that maths is developed for its own sake. To take the example you cited of linear algebra being useful for programming; linear algebra has been around for a couple of hundred years, it was most certainly not created purely for computer science, that just happens to be somewhere where it can be used.

Also there is quite a lot of maths which is entirely ‘useless’ for anything other than developing more maths. It /might/ turn out that someone can find a use for, say, high dimension topology (or indeed high dimension anything) but that doesn’t stop the theory being developed and being interesting in its own right.

This reminds me of this xkcd comic.

Yeah. As far as I remember Fourier and Laplace transforms, two key transforms for electrical engineering, werent invented as far as I know for that purpose, but when need arose for more complex electrical models, and people were getting tired of diferential equations, somebody dug up those works and realized they had an application.

Oh, and the way to quickly compute Fourier transform (which wasn’t really necesary untill late XX century) was invented by Gauss all the way in 1800s (allthough then he did develop it for a practical problem, but the solution was forgotten until 1970s),

I’m pursuing a 5 year degree in engineering cybernetics, and I completely disagree. Though this is probably just the horrible way things are done at NTNU (Norwegian University of Science and Technology):

The mathematics is taught separately to & in tandem with the “applied” subjects (such as circuit analysis, programming, control engineering, physics etc). The problem is that the people who teach the math have little to no experience with the “applied” subjects, and the people who teach us what to use the math for have no time for teaching the intricacies of the mathematics. The problem is that both parties try to teach something they aren’t equipped for: The math courses have a lot of nonsensically oversimplified engineering examples, and the applied courses endlessly repeat things that are thoroughly taught in the math courses. I’ve had 2nd degree linear differential equations in 5 subjects now!

It’s much better to teach math with total disregard for its applications, then let the people who teach the “applied” courses teach their own thing, knowing that the pupils have a thorough understanding of the underlying mathematical concepts and techniques. Everybody saves time, and the students learn more & with less paperwork.

There is a pitfall even there. If those that teach math forget it actually will have an application, they WILL go to far.

@klasbo – That sounds like a terrible approach and is not at all what I was advocating. ‘Parallel’ teaching by different instructors in different classes seems to me to be unlikely to work for any number of reasons and in any number of fields. Teaching the math required for understanding the scienctific or engineering subject under study simultaneously with that subject (same class and teacher) is what I was advocating, and what seemed to work well in some of my classes.

@Demo & 4th Dimension – I’m afraid I probably overstated my case, as I’ve never had any ‘history of science’ or ‘history of math’ courses. (And I did have Newton particularly in mind.) Still, for most math that can be applied, and particularly for most science that requires specialized math, it makes perfect sense (to me) to combine the two, rather that teaching the math in abstraction, which I think makes it much harder for most people to grasp, both in terms of subject matter, and, just as importantly, relevance. (As a physics TA, I got really tired of students who couldn’t understand why they would need to know this stuff for their careers – which were ostensibly going to be in medicine. Of course, math was the least of their problems, in general.)

Is that first picture you? Your hair looks almost… Black.

Pictures are weird like that sometimes. My cousin has white-blond hair, and I’ve seen a few pictures where he looks like a very dark-haired redhead.

I occasionally appear to have reddish hair in pictures, but outside of them it’s really just light brown (or dark blond, depending on your point of view). I suspect it’s due in part to colors that actually are in your hair (my grandmother had red hair, for example), they just are normally drowned out by your “real” hair color. Like bright colors in leaves drowned out by chlorophyll or something.

Yes, yes a thousand times yes. This is a massive problem in (American) high school math. The students in the slower classes need application the most. In my experience it depended on the teacher. I was in the advanced math course. One teacher taught us matrices. I raised my hand and asked what practical application came out of matrices. I was curious about why they existed. The teacher looked me dead in the eye, then turned her back on me and continued teaching. If she couldn’t be bothered to tell me why they are important, I can’t see why I should remember them, so I forgot them. I am now a software developer and curse her daily, because I had to relearn them later on.

I then had an AP Calculus class where the teacher made ALL homework optional. We had books with problems in them. If we wanted practice, we could do the problems. I didn’t want to, so I didn’t. I got a 5 (out of 5) on the AP Calculus test. Just because some people learn by boring repetetive chores, doesn’t mean everyone has to.

Oh, and that second teacher explained how calculus was used to derive many of the physics formulas that we were learning in physics. Holy Crap, Math has practical application beyond figuring out how much change I should get back when I buy something?

Physics is currently my favorite part of math, although my high school physics class was unfortunately lacking and didn’t really get beyond basic algebra. (Which made it so boring in comparison to my Calculus class that I slacked off and almost failed…) Physics is now among the subjects I’m trying to teach myself, although I probably need a refresher on calculus.

Homework in my Calculus class wasn’t optional, but I also never found it boring. The problems were almost always explained in real-world terms, and regardless, as Shamus suggested, we didn’t get all that many homework problems in the first place (since even just five or ten could take most people an hour or more). I also made it a bit more exciting by doing my Calc homework in the cafeteria after I ate my lunch. (Calculus was my first class in the afternoon.)

how the heck do you do proper physics without trigonometry? (Thinks for a second) Okay, it’s mostly just motion and forces that really requires trig. I think.

I actually rather like the way my AP Calc teacher does HW. We have a notebook, and every night we do our problems and the next day he gives a minus, check, or plus, depending on how much we did. These add together to give 1 point extra credit each on the test. There’s also a separate notebook check due the day of the test, where he grades it more thoroughly, so you do have to do it eventually. (I have 3 assignments to do tonight, actually :D)

Well don’t you look silly? Ok if any teacher had done that to me I would have put my hand straight back into the air and made really annoying noises until I was answered. Then again maybe she didn’t know… in which case why is she teaching it?

In fact I had a maths teacher who was completely useless at the subject and I spent most of the lessons trying to copy her really strong Irish accent and odd word choices. Went back eventually to a competent teacher that must have had some trouble at his last job because he was way too good to work at my school.

My Algebra II teacher had a poster in her room that had the topics that we covered and what careers used them.

She’s also the head of the Math Department at that school and the Mu Alpha Theta sponsor (Mu Alpha Theta – high school and 2-year college math association)

I didn’t take physics in high school or my first year of college because I figured it’d be too hard–although I did well in Calc I in high school (or at least my AP score was good), I kind of slacked off in Calc II, and figured physics would just be more of the same.

But I finally took physics this year and I am loving it! I’m loving it so much it has made me seriously consider changing my major from computer science to something more related to the physical world. Calculus was fun and interesting because it’s about practical applications, but physics is even more so! (and I have to say, it’s not nearly as hard as I thought it’d be, considering I’ve already taken calculus and the basic physics class I’m in doesn’t actually use any calculus. So I understand the underlying principles behind some of the stuff we do, like the relationship between position/velocity/acceleration, a lot better than some other people in the class who didn’t have calculus.)

I do wonder why they don’t start teaching physics earlier, though. I know it’s related to calculus and it’s hard, but… couldn’t you come up with some way to teach the basic principles to at least younger high school students? That’s really where math becomes practical. I think if you got people to realize just how important math is, that it literally determines how the universe runs, a whole lot more people would be interested in it.

EDIT: Of course I would be the one to carefully reread my comment to make sure everything was spelled correctly, only to realize the instant I submitted it that I put “people would be interesting in it” instead of “interested”… makes for a slightly different spin on the sentence!

At my school there’s an on-level physical science course and a pre-AP physics class available at 10th grade. *shrug*

In Math 20IB (IB is the International Baccalaureate, an alternative to AP that focuses on much the same advanced work but with a more international flavour to things), our teacher started us on matrices halfway through the semester.

The regular Math 20 kids learned how to use matrices within their graphing calculators to solve 3-variable 3-line sets of functions. All that they learned, essentially, was how to input numbers into a calculator.

We learned how to do them manually, and only learned the calculator method as an aside on the last day of the unit. When asked, the teacher said “Well, they’re useful for (these) functions, and if you’re going into programming, Math 35IB, or any university mathematics course, you’re going to need to know how to do these manually and in large sizes.”

The entire class being composed of keeners, we all gladly learned matrices. I particularly enjoyed them, and I used Cramer’s Rule in whatever I could. I was the only one to know what it was since I had taught myself back in grade 9. Of course, until the teacher found out that I used Cramer’s Rule, and made all of her example and exam matrices have a general determinant of zero.

I dropped down to regular Math 30 and 31 after that. 30 was a slog, but 31 was Calculus. Fun times, since the teacher was nice and told us to do practical problems from the get-go. I really enjoyed Calculus, and I used it to solve stupid problems in my spare time, as well as analyze and come up with a few interesting aviation equations when I got my Private Pilot’s License in grade 12. I wasn’t particularly good at calculus, but I enjoyed it.

Kind of like history and social studies classes. I’m a fan of history, not so much a student of it. I love learning about historical events and the causality of pretty much everything and how every single act in history affects everything else. However, I am absolutely terrible at typing out and sourcing all the dry essays that history classes entail. I can tell you a whole mess of information and events concerning just about any point in time, but if you ask me to source the information on the spot, I just kind of shrug. I just read books and browse Wikipedia in my spare time. Not the most professional thing to do, but it makes for interesting conversations.

Quel coincidence, my brother’s name is Daniel, andIwas born in 1985! Well, it’s a stretch, but still sort of a coincidence.Quite frankly, I liked my math classes in very early school (possibly because we mostly did word problems that kind of made sense, and whenever I’d learned something I was allowed to learn something else to build on top of it), but after I moved (as I keep blaming all of my school problems on), math turned into the kind of boring repetition you speak of, complete with flash card drills on the multiplication tables. (The rest of the class wasn’t allowed to learn long division until they could get a certain speed on the flash cards, I think 20 in a minute. I’d learned long division the previous year, but have never been a fast person in any way, and so was stuck on the damn cards anyway for the entire year.)

In higher math (after my second move, a better school even than the first), I did enjoy Algebra, Geometry, Precalculus, and Calculus (I did take the advice to join Algebra in eighth grade), but it was all almost ruined by the horrendous boringness that was Algebra II. (My school did Algebra -> Geometry -> Algebra II -> Precalculus (a. k. a. Trigonometry with some other bits thrown in) -> Calculus). I generally got As in my math classes, but Algebra II I barely scraped by with a C. It seemed to me like, instead of giving you tools and letting you see how well you could do the job with them, seemed to be nothing but lists of rules. In retrospect, I understand that the rules themselves were tools as well, but at the time it seemed more like a bad history class than a good math class. I think slogging through that class may be my best frame of reference for your experience in math classes, with perhaps Precalculus and Calculus as my equivalents to your fun in hex-based programming. (When you learn trigonometry by going on a scavenger hunt, outside, with nothing but a compass (north-finding, not circle-drawing) and some notes on sine, cosine, and tangent, something somewhere went very right.)

Grammar Nazi to the rescue : don’t you mean

QuelLEcoà¯ncidence ?On an unrelated note, we don’t seem to call the subdivisions of math (calculus, algebra…) by their name that often. I’m ok in math but I don’t think I could tell you which rules/problem belong in which category…

Is this an American thing ?

Huh. People don’t classify it like that? At least in the US, yes, we definitely do. Basic math is addition, subtraction, multiplication, exponents, that sort of thing. Algebra is problems with variables of varying complexity. Trig is sine, cosine, tangent, all the triangle/unit circle stuff. Calculus is… well, calculus. Integration and derivation and all that.

There’s really places where math doesn’t get split up like that? I honestly had no idea. What part of the world do you hail from?

Up until I went to university all my courses in mathematics had simply been called “Mathematics”. Sure, I knew what in the courses were trigonometry and what was calculus but the courses were not divided by these divisions.

For example the course Mathematics B covers linear equations, systems of equations, geometry, some algebra and statistics and probability. I don’t know if this is better or worse but a lot of these areas are connected to each others in many ways. You’ll differentiate and integrate trigonometric and logarithmic functions, you can use calculus to derive formulas you use in geometry, and algebra is needed for pretty much everything. I don’t think mixing them together is a bad idea.

Yup. Here I studied electrical engineering – computer specialization at University, and my Math was allways simply Math.

Ah, those moments you wish you could reload and put skill points elsewhere.

Also the quest rewards are botched. The amount of gold you get after finishing the PhD guest is just ridiculous – when the “Become a plumber” quest takes only third of the time and makes you twice as much gold.

Yes, you get more XP from getting a PhD, but the skill tree you can use your hard-earned skill points isn’t very practical.

Yeah but then you get stuck grinding repetitive dailies of ‘Fix pipe’ and ‘Unclog sink.’ It’s just not worth it unless you’re looking for wealth for side quests

This is my favorite comment thread to date.

Personally i think having to do repetitive dailies of “Fix Pipe” and “Unclog Sing” are probably better than if you end up taking the “Become A Convenience Store Manager” quest when your dailies are “Shoo the teenagers out of the store” and “Refill the slurpee machine”

Im rather dissapointed that i ended up putting most of my points into my Reading skill and every single English class iv had has been pretty much the same as Shamus’ math classes.

Yeah, everyone always overlooks the fact that the gold drops actually only come from the completion of the dailies. The PhD dailies involve thinking and reasoning all day, while the plumbing dailies largely involve squatting and mucking around in other people’s filth. I think the rewards are commiserate.

My problem is that I didn’t know I had to take the “vector analysis” and the “ODE solving” feats at level 3 in order to make actual use of my character class skills at level 10 … wasn’t in the description.

Now here I am and do not know what to make of a negative imaginary part in a complex eigenvalue of a Jacobi matrix… sounds smug, but it has just noo meaning!

Shamus, I feel your pain.

But the nice thing is that these days there are not just wikipedia entries but also books, many of which can explain the thing better and in more interesting terms than most of your teachers did.

Those moments you wish there was a reset button…

I’ve always thought that if I was going to be a super hero, I’d want my super power to be “quicksave” and “quickload”.

Be very careful what you wish for

http://www.youtube.com/watch?v=tAHSPR1iY_0

This is why you always mind your surroundings before quicksaving.

teachers in my country do it only for money. they have no interest in teaching. infact they treat us like competitors. also i like computer programming, but absolutely hate vectors.<— its not real maths…

maybe i hate vectors because because our geometry teacher is the worst person on the planet.

Whatever else is going on, vectors are most definitely real math. Not only this, but most of the really useful applications of math, the stuff that you don’t even know is there are just really fancy vectors (computer graphics, error-correcting codes, MP3 and the likes, computer ANYTHING, almost, except for cryptography).

http://en.wikipedia.org/wiki/Initialization_vector

Would like a word with you. Even crypto has vectors. :P

It sure does, but it has a lot more groups and number theory and all that jazz… On the other hand, any practical algorithm from analysis is ultimately made of vectors.

I remember going into Jr. High and being invited to the Quest program, where we were taught advanced English, Science, and History for three years. I was afraid that I wouldn’t be good enough, that the classes would be too hard, even though I had been in the Gifted and Talented classes in elementary school. But thankfully, I made the leap and joined Quest. I never regretted it. I still remember the day I discovered what the normal classes were like, and I couldn’t believe it. My classes were

easier. Looking back, it’s probably because they were more interesting, and less tedious, and not necessarily because the work was easier. So I feel for you, Shamus. I know what schoolcouldhave been like for me, but I was one of the lucky ones.Ooh, does this mean I should have paid attention to matrices in H. Algebra I last year? ^_^

Oops.

Shamus, I don’t think anything you’ve written so far made me feel more sorry for you. Passing advanced math?

I’ve felt enraged at some of the people you described. Outraged. But this was a very, very depressing entry. I don’t think I could have lasted school without advanced maths and mathematical contests to go into.

To think that somebody with similar potential to mine had to miss it all…. I shatters my mind. I am happy you had programming to keep you afloat.

Shamus let me just say first that it’s not your fault, the teacher should have understood that your brain has logic gates instead of synapses.

All kidding aside, it can’t be your fault since you did not know.

Somewhere someone did not explain what the advanced classes was so you could make an informed decision.

On the general math stuff I agree it’s very boring.

Here in Norway (when I grew up) there where (elementary I believe it’s called?) grades 1-6, and high-school grades 7-9, after that would be the college equivalent I guess where actual work specific classes could be chosen, and beyond that university.

Grades 1-6 went mostly ok although at the end I did start to get school fatigue, this really began kicking me in 7th grade, and not long after I started 8th grade I explained as best as I could. (Boring, tedious, it’s not fun, I didn’t care.)

I agreed to relocate to a dayschool, it was actually called that too, two of them in my town, the second one was the one I ended up at with a II at the end of the name, almost smack in the middle of downtown, good times indeed. Walking around downtown between classes was fun indeed.

Instead of classes of 30+, there was only one class a mixed grades class (7,8,9 grades), and we where only 7 or 8, and that meant basically one teacher per two or three students. The kids where there for various reasons, some probably the same as mine, some with issues at home etc.

The funding was pretty good, we did a lot of trips, once even to Sweden a neighboring country. Went skiing a lot (alpine/skiing hills etc.)

Got free moped driving lessons and traffic law training and moped driving license.

We had pottery room/furnace, wood shop/metal shop, a small computer room (with BBC Micro’s back then if I recall correctly).

We made self-standing shoe-cleaning rig, (metal grating with two metal “sticks” with two shoe brushes attached) we welded it/made it then sold it, the money was used for some event I think that I can’t recall any more.

During the part of the 8th grade I was there and the 9th grade my attendance to the school shot up through the roof compared to the old regular school over the last 3-4 years.

My grades climbed steadily too. There was still some “study” grind of subjects obviously but not that bad, each student either worked on class tasks or individual tasks.

And best of all…NO HOMEWORK. (unless you really really wanted for some odd reason I guess… Which did happen on occasion heh…)

After 9th grade you are basically graduated, from there on it’s either college (aka advanced school) to start the first step in specializing, or start working right away.

I did however get the option to do a “10th” grade, which I took. And that resulted in a bunch of D’s and C’s to become the rare D and a mix of C’s/C+’s and B’s with one A even.

After that I was to have gone to college to start in beginning electronics I/electric I, but it was full and they told me that maybe janitorial line might be worth a shot. A week after I dropped out, so guess not.

I then decided to take a year “off”, but that lasted only around half a year or so as I took the opportunity to take my mandatory year in the military earlier than I was scheduled to do. (those not in school or working must do mandatory service, those in school or work can ask for a extended delay).

After my stint in the Royal Norwegian Airforce, I moped around about a year+, did 1 work training week at a industrial storage/warehouse, and then a couple days per week for half a year work training with a VVS/Plumber company, both funded/arranged by the unemployment/social services office Several months after that I got eventually my first “proper” job. I worked as a Embroidery Designer (those fancy logos and stuff you see on clothes and caps and bags and sports gear, we did embroidery work for Pepsi, Coca-Cola, Siemens and pretty much all the big brands with a presence in Norway), eventually I ended up doing almost the designs exclusively, and I was so good at it that other embroidery companies in Norway had me do their designs. (as it was cheaper than outsourcing to asia at the time, yeah I was that fast and good).

After almost a decade doing that I eventually got bored, and my interests had moved more and more towards computers ever since I first laid my eyes on one back in elementary school.

And I’ve been freelancing ever since, barely scraping by unfortunately, if I hadn’t been blessed with a great mother helping me through tough times I would have probably been “living on the streets” by now though.

This confuses me a little. Was there no system in place to actually show the students what the different kinds of courses contained? If not, how are they supposed to be able to make a decision?

I had that problem as well. I walked into my high school planning meeting, where they expected me to create a plan for my entire high school career. I was supposed to pick courses. I had no idea what ‘acapella’ even meant. I didn’t know what music theory would be, or why I needed to take algebra I

andII as well as geometry, or what the difference between physical science and physics is, or why I need to takefour classes of English. I had no idea what most of the classes on that 70-80+ list were. SOOOOOO unfair.This was my experience as well. Even better is that once you pick something, you’re locked into it. Are you worried the class is too hard for you. Better change it quick! The longer you wait, the harder it is to get out of it and the further behind you will be in the replacement class – assuming one is available. If you fail, you might not graduate on time, thus delaying your entire career for a full year over a single credit in one subject.

School should be a buffet where you can sample or binge where your skills and passions take you. Instead it creates all these incentives to avoid challenge and stick to what you already know.

Eighth grade (or possibly ninth grade) should just be a big long session of “try stuff out”. Each week is a new subject, next week you move on to the next. You’re not testing kids – you’re just letting them get a feel for a bunch of different subjects, so

next yearyou can ask them to pick a course of study that matches their interest.So, in American high schools you have to pick out all your courses before you even start? Like, in Gr 9 you’ll know what you have for 4th period second semester Gr 11? Am I just wildly misinterpreting this? Cuz if not, that’s pretty crazy.

They want you to have a good idea of what you are going to do. You plan out your whole year, then you make alterations to your plan where necessary, based on your interests and grades. But administrators want you to stick to the plan so their paperwork is easier and students file through the system, even though many teachers feel otherwise.*

*This is the current situation, anyway. I don’t know the specifics of Shamus’s time. I’m a sophomore, so this is pretty recent. Keep in mind that even fundamentals of school policies change based on your district. (District changes in more or less every town/city. There are a lot of them.)

Explicitly, no. But depending on the school you go to, the first class you choose might get you stuck on rails that are very hard to move away from. i.e., if you pick pre-Algebra as a freshman course, you won’t have the prerequisites for Geometry next year, which means you can’t take Pre-Calc Junior year, and you’ll probably graduate without seeing a single page of real Calculus thanks to a choice you made as a freshman.

And if that isn’t enough, some schools (mine included) had an “advanced” track that was also very difficult to cross. In my case, every math class had an “X” version (“Algebra X”, “Pre-calc X”, etc…) each of which required the “X” version before it unless you wanted to jump through 50 hoops getting approvals from professors. So if you want to take advanced calculus four years from now, you have to start off in advanced algebra.

Fortunately, my first math teacher recognized that I was smart in math, I just never did homework, and so helped me move out of the basic track. The difference between “X” and basic was that they actually taught you the applications of what you were doing in “X,” instead of just bombarding you with information without context in the basic courses. I would’ve been sunk otherwise.

When I was nearing the end of 8th grade everyone in my grade was supposed to have a meeting with one of the high school counselors to decide what our “general plan” was for high school. This was where said counselor would look at our grades and decide whether we would be taking the “Advanced” courses, the “regular” courses, or the “Special Ed.” courses. If we had really high grades in some subjects but low grades in others, the counselors could mix and match accordingly. At the beginning of each year we would be given a list of available courses (such a list would be divided up between required curriculum and electives) based on the plan we made in 8th grade. We would then be let loose to choose from the list and to try to make a schedule that worked.

I think that is a very school specific policy. My school did not allow us to choose our own classes in such a manner untill 10th grade, perhaps that is just when they decided to adopt that method. Though we couldn’t choose our main classes we could decided elective courses.

One thing to keep in mind–the US does not have a national system of education. The federal education agency is very small in overall terms, even with NCLB (Bush-era legislation that vastly expanded the federal agency’s mission, size, and influence). Most educational standards and programs are set at the state level (for non-USians, there are 50 of them, and several territories), or even more locally. Due to their sheer population and size, California and Texas’s education agencies probably have more influence than the federals, since publishers tailor textbooks to their curricula and smaller states just have to live with them.

Hence, I’ve never heard of having to plan out your entire high school curricula upfront. but I’m not surprised that some places do it. For me, up to 8th grade there were no choices, high school (years 9-12) had choices which amounted to one of three or four tracks, and for the really advanced math kids, you could take classes at the state (public) university in the same town.

You got to choose your high school courses? I was just handed a schedule every fall. Well, we got to choose one elective course (music or art, etc) each year and which language to study, but everything else was just predetermined based on my grade and that I was in honors classes. At least, that’s how I remember it.

College/University was a bit more like what Shamus describes above. I had time there to pursue various interests as they struck, though I would have loved more. I almost wish I could have just taken a liberal arts degree and not had to choose one subject at all. I always say that if I had any money, I’d still be in school, studying something new every year.

I remember those meetings.

I didn’t have much of a problem with them aside from the terminology that the school used in its descriptors. One particular example was “You can take any math course you want after Math 10, which is the basic introductory math course. Based on your performance, you can go into Math 20IB, Math 20, Applied Math 20, or repeat Math 10.”

I went “Oh! Applied Math! That means you’re actually using math for useful things instead of finding random things constantly and just making busy paperwork!”

Little that I know that Applied Math 20 was the class that people went to when they did better than failing Math 20, but worse than going onto Math 30.

Thankfully, the advisor pointed this out in a gentle manner (“Umm, that’s not what you think it is, trust me. Go into IB instead”) and I happily went into Math 20IB the semester after.

Math. One of superpowers I never gained a enough of a high level. I was actually one of best students at Math in my elementary and middle (or should I translate it as High school?!) school (Grades 1-9 and 10-13, after which there is only Uni, for you westerners), but at the Uni I had loads of problems with it.

I mostly understood WHY we do something, my problem was applying that to solving problems. The problem was I think that instead of giving us a tool, we got bombarded by difficult problems.

So now I’m an engineer, and I can understand how some formula got calculated, but I wouln’t be able to do it myself.

When I saw the title of this post, I immediately thought of a dentist drill, then had the mental picture of a needle of novocaine being stuck into my gums while I read this entire post. So, thanks for that Shamus.

Odd that just reading the word “drill” can trigger such painful mental pictures.

I do constuction stuff with my dad sometimes, even though he’s a programmer, so I thought of that kind of drill. Down here in the south, we do stuff ourselves! (More or less.) (That also made think he did construction in this chapter like I do now, and made me wonder if building something more physical was a precursor to programming for a lot of people.)

Boy, did this bring back memories of high school for me. I was on a roller coaster of good and bad teachers when it came to a variety of subjects, even though I was a fairly good student.

Geometry was just something that seemed to come instinctively to me, and I seemed to grasp many of the concepts really quickly. However, I was cursed with a teacher that would force me to go through all the proofs even though I could “see” the correct answer and put it down. The low point in that class where geometry turned from fun into sullen resentment was when she gave me a “0” on a test where I had all the answers right but didn’t complete any of the full proofs she wanted. she even accused me of cheating on the test, which was pretty ludicrous since none of the people sitting around me scored higher than 80. It wasn’t until my junior year of college that geometry became fun again, when I had an amazing instructor that pretty much turned us loose, providing gentle reins and encouragement to explore and master the skills.

I spent any number of years trying to find a proof to one of the “impossible” geometry problems he tossed into the mix of questions he asked us to solve – Trisection of an angle with only straightedge and compass. We corresponded for a number of years after I graduated until he passed away. Professor Joe Kennedy, you’re still missed!”

I remember when I was being taught multiplication the teacher told us when we brought down a zero to make it a smiley face, she would mark my work wrong if I just used a zero.

Heh, I did the same thing with my Texas Instruments TI-99/4a computer… I drew graphics and consulted that chart, until eventually I didn’t need it anymore. I’m a left-handed/right-brained type, so I’ve found that visualizing mathematical problems has always helped me better understand them and the solution.

I didn’t skip all the hard math in school, though my pre-algebra and algebra courses in junior high school were really difficult… I averaged C’s all year and felt like a moron. To this day, I’m still not certain if it was the teacher, the books, or just me not being fully ready for it…

I re-took algebra in High School because I’d moved and they weren’t doing algebra UNTIL high school in that curriculum. I aced that year, and every subsequent year, math wasn’t a problem. I even used my Trigonometry class in high school to write a Star Trek game.

I do agree, though, that American mathematics teaching needs serious help. I just have to look around my workplace in Seattle… More than half of my co-workers are from other countries that actually value mathematics and engineering.

I learned graphics on the TI that way, too. That happy face brought back a lot of nostalgia. I wrote a Dragon’s Lair type game on it (obviously with worse graphics and it wasn’t as long). My friend wrote a Bingo caller and also a 2 player split-screen Gauntlet type game with procedurally generated mazes (and a lot fewer monsters).

I’m not certain it’s really fair to blame yourself for making a bad choice when you didn’t have all the information. If you knew then what you know now, etc., but I’m not sure how you could have known that the knowledge you based those decisions on was flawed.

Sometimes things aren’t anyone’s fault, though if someone had taken the time to teach you something about math before that point perhaps things would have been different.

Imagine if Neighbour Dave had been as interested in math as he was in history…

Okay, so… I’m 26 and I’ve never had any Calculus.

I mean ANY Calculus.

I don’t really have a good grasp on Algebra yet! Where can I go to learn this advanced stuff? Do I really have to go from the ground up?

Khan Academy, my friend.

Or take a community college course.

Either way, algebra is pretty much required in the real world these days. Calculus not so much.

You’re missing out of something. Calculus is what turned mathematics from adding numbers together on a paper to something that could actually be interesting.

You should probably spend time getting a good handle on the “lower” maths before you attempt Calculus. Algebra and Trig are pretty much required learning before attempting Calculus. I say this from prior experience.

Ok, so yeah, you screwed up.

I made similar screwups at university, and they were mine, and there is noone else to blame for them. But on the other hand, I can’t help but think that if someone had sat down with me and explained how the system worked, I might have made better decisions. And if someone had managed to show you that higher math was the good stuff, you might have too. Given (what sounds like) the paucity of adults whose opinion you would have trusted on the matter at the time, maybe there was nothing to be done. But it still seems like a bit much to blame a 15-year-old kid for making poor lifetime decisions – even if said kid was yourself.

I actually have a job where geometry is vital part of what I do. Part of the software that I develop and maintain involves the layout of HVAC ductwork onto flat patterns. If you look at various heating and air conditioning system especially where they change size and/or direction all those fittings has to be cut out of a flat sheet of metal.

To develop the flat pattern for these fittings you need geometry. So I use geometry on a daily basis to create and maintain fittings for our software. Geometry provides the step by step rules to do the layout and trig provides the numbers for the x-y coordinates of the final flat patterns.

I found geometry fascinating, and got good grades in the class, but I never thought I would have a practical use for it. You just never know.

When I learned math in junior high school, it was all rote memorization, a skill I am still terribly bad at. My teachers suggested I take remedial math in high school.

Fortunately, my 9th grade remedial math teacher recognized that my problem was memory-related and not skill-related, and on my third week called me after class and asked me to try a couple of simple algebra problems. I completed both in under a minute with correct answers. He started giving me algebra tests instead of the usual math tests. A month later he had convinced the principle that I should be transferred to pre-algebra since I was doing the work anyway. This is how I discovered there was more to math than arithmatic and memorizing the decimal equivalents for fractions.

*Wince.* While there are certainly more painful things to look back on than a missed learning opportunity, that does sting quite a bit. I can empathize, although I was about as different from you in my high school days, in terms of interest, as I could be. I can’t *stand* math. Never could, and at my age, I probably never will. I’ve always been a writer who understands how words and sentences and paragraphs go together intuitively, but I just can’t understand relationships between numbers. I’m one of those weirdos who can memorize a sonnet in under 15 minutes, but I STILL (and not for lack of trying) have been unable to memorize all of the basic times tables. I really regret that, mostly because I DO love computers, and would love to learn how to program; at this point in my life though, I’ll stick to programming vicariously through reading blogs like yours. :D

These autoblography posts just made something click in the back of my head. I am reminded of your 2 part piece about visiting Seven Springs. Now I realize why it was such a big deal for you to work harder in high school. This brings more meaning to a story that I loved when I read it the first time. It really helps me to read this from an adult, because as a seventeen year old kid, it seems that no one that’s older really understands my willingness to be lazy. I am successful in all of my schoolwork, yet I never actually make an attempt to do an ounce of the work. So it’s nice to hear it from somebody who’s been there. So thanks, Shamus. Always a pleasure visiting your blog.

I find it rather interesting how many people are commenting that they only started to like math after they became aware of its utility as I find that my feeling is rather orthogonal to that. While I admire and appreciate how useful trig and calc are in my physics class I find examples of applied math in my math classes aggravating. I would much rather learn math in the abstract, in its pure form, then put it to practical use outside the math classroom, than have the purity of the math impinged upon with examples inside the classroom.

Word problems as practice are annoying, but do something to lessen the boredom of repeated drills, which is good. However, using examples to explain and introduce a topic for the first time seems downright counterproductive and confusing to me, as it forces one to sift through the context of the problem to get at the mathematics underneath. This, personally at least, obscures the math and makes its principles much harder to discern.

I love math (high school senior taking AP Stat and AP Calc BC here), but I find its applications nothing but a distraction when it comes to the initial presentation of a topic.

I always hated story problems. I could never figure out all the things I needed to about which numbers where which things in the question and which formula I was supposed to use. Didn’t help that I generally didn’t get how or why it worked and just had to memorize formulas. I have a lot of trouble remembering things or applying them when I don’t know why they work. :P

See, I don’t even call all that stuff “math”. That’s “arithmetic”. “Math” is manipulating formulas, formalizing insight, applying existing rules and coming up with your own, and inventing or discovering what you need to solve your problem.

It’s a semantic thing, but I find it a very useful semantic thing. Arithmetic is what computers are good at. Math is what humans are good at.

I once had a fun project in math where I had to draw a picture on a t-83 calculator using only formulas. That is my only fond memory of math.

Math was, oddly enough, one of my strongest subjects back in school (although, to toot my own horn -massively-, there was nothing I was bad at), but I’ve just never had much interest in it for the same reason. It’s repetition of endless problems with some sort of transparent “you’ll get graded for this” at the end.

There are two contexts in which I’ve found mathematics interesting: The first is when it’s used to solve a (hypothetical) practical problem. The other is when it’s applied to physics, chemistry and so on, for the same reasons.

Although I’m currently studying music (and psychology after that), so I probably won’t need my mathematics beyond what you learn in music theory (surprise, even music contains math. THERE IS NO ESCAPE!)

Shamus, I’m curious. How did your school experiences shape your thoughts and actions when it came to helping your children through school?

(I can’t remember if you said your kids are homeschooled, so if they are please disregard this post.)

I came to this site back in the DMotR days, and have been enjoying your posts all along. Your autobiographical blogs have resonated with me. I had a much more stable family life than you did, but school was always a chore. I hated the repetition, horribly. In Biology in high school, I did one piece of homework the entire year and got a B in the class thanks to an awesome, understanding teacher that made most of the grade related to test scores rather than the drudge work.

I was undiagnosed ADD all through school, so instead of being on too many medications, I was on too few. In classes that I had an interest, I could be in the top few students. In classes that I was uninterested, well, those didn’t turn out so well. I just wanted to thank you for a consistently well written blog. I do miss the articles on your procedurally generated world, but I know that you have a LOT of projects going simultaneously.

I made the same mistake, although my parents & I listened to my counselor who suggested I take Chemistry rather than Physics because Physics was probably “too hard”. Having a brain wired for maths I did not do well in the Chemistry environment but suspect I would have excelled at Physics, at which point my life probably would have taken a completely different course. I’m happy in my personal life, but on the work-side of things not so much, and at 42-years old have little-to-no desire to go back to school to make a change.

I did the same thing, honestly. Thankfully, I didn’t have that bad math classes; what really threw me was Chemistry. (He’d assign us fifty of problem A, fifty of problem B, fifty of problem C, and then fifty more of problem A each week, and expect us to grade ourselves according to the answer key. I always did, because even then I was Lawful, but I wasn’t happy about it.) But it wasn’t until my last year of high school that I took my first “harder” math class.

In the first week, I’d been assigned to a teacher that I’ve come to like, not for his teaching style or for his treatment of students later in the year, but for how the first thing he did was test us on the material he’d be covering that year. Students who tested well enough would get pulled aside, and told that he thought this class was wasting our opportunities; if we were willing, he’d get us sent to the harder math class.

All through my life, I’d been told that I was smart- particularly at math. I’d find that, with classwork, I’d often finish ahead of the curve, turn in my work, and then pull out my book and read. Sometimes, I’d miss the middle step; at the beginning of the year, teachers would ask if I was done, to which I would always reply “yes.” So it wasn’t a shock to me that I got enough of the test right that I was in the top three considered for going to Precal Honors.

What was a shock was how engaging this harder work was. I’d assumed that this stuff was for “the smarter kids,” and more than that, the ones who were driven; people who wanted to be in school. I didn’t want to be in school, and I didn’t make friends easily- I still don’t- so being able to be given a piece of paper with one problem on it and told, “solve this,” was an entirely new experience. Often, I would get the answers wrong; more often, though, I would get them right.

This changed when I made my friend, who goes by Stick of Butter- at least, he did last I knew. (I haven’t actually talked to him in a while- I’m terrible at talking to people first, and he’s terrible at getting on Skype.) We were both nerds, even among the people in Precal Honors. He had a laptop, and I believe was in Special Ed, like my other friend Jordan; he didn’t act like the other kids did. Sometimes he would have trouble with enumerating concepts, and he would do things with his arms, but he never treated me with anything but respect and goodwill, so I latched on.

We’d always wind up sitting at the same table together, even when that wasn’t the seating chart. I found it was always useful to ask him about things I was having trouble with, and he did the same for me; our work got done sooner, more accurately, and then we could play video games together (not the same one, but beside each other) or read or chat about our other interests. He brought his laptop to school, I believe because he had some trouble with writing by hand- one of my other friends did as well, and he had a special thing that would only show one line of text at a time and seemed terribly inconvenient to me- and often, he would bring Playstation controllers as well, and after school or during lunch he’d hook them up and we’d play Bomberman, or that one Touhou fighting game. A few times, I made noises about hanging out at houses, but his parents weren’t okay with that.

Tables tended to evacuate slowly when people were assigned to sit with me and Stick. Often, there’d be other spots open- more as the school year progressed- and they’d swap out to sit with their other friends. I didn’t mind. I had my friend, so I didn’t care if they had theirs; I’d value their input if they stayed, and help if they asked, but I never formed relationships with any of them. I don’t think I even knew their names, honestly; or if I did, I forgot them soon after. I didn’t do the best in class, but that wasn’t the fault of Stick or of the teacher; sometimes, I just wouldn’t grasp concepts, especially when we were made to do without our cheat sheets. More often, I wouldn’t get the rote down. I’d understand what this was, but I’d have to use the cheat sheet for a long time until I grocked it. Tests were easy, but apart from Japanese- which was almost all rote memorization- tests were always easy for me. I’ve come to understand how lucky that made me. But it also meant that I didn’t get help where I needed it, because I completed the test- often before anyone else in the class- even if I had to guess. Sometimes I guessed right. Often, when I would get the process wrong, I would fill in whichever answer was closest to mine- I’d assume that I rounded where the test writers hadn’t, or vice versa.

That’s one of the things that saw me through high school on time. Having that time to destress with someone I considered a close friend- even though we never really talked about our home lives- was important, with me taking three math-heavy classes (even though I loved them all) and a few others I wasn’t too interested in.

Jeeze, this is almost as long as the chapter up there. If you’ve gone and read it, thanks.

We think it’s a problem if we don’t do our work, because then we don’t get to play computer games! We thought learning plus was boring before we learned it, but it’s really easy! All you have to do is add up the numbers.