Saturday, December 13, 2014

Where Learning Happens, Being a “Math Person,” and History Class

Learning happens where you actually study the information in front of you rather than gloss over it.

Studying information doesn’t just mean reading it, or hearing it, or repeating it until you’ve memorized it. Studying can mean imagining an application for the information. It can mean trying to relate that information to other information in a way that makes sense.

Humans need air. We need water. We need reliable wi-fi. We wither and die without these things. What do information and knowledge rely on? Their air is application. Their food and water are the relationships with other pieces of information and knowledge.

Why is it hard for people to learn things? They do not actively strive to relate information to other information, nor do they seek to apply it. They gloss over and hope it sticks. When it does not stick, they assume they just aren’t smart and give up. Hey, sometimes information is hard. It's tricky to understand why something is the way it is; sometimes you struggle to find that connection. But sometimes the information is not tricky, and sometimes it's because you are not figuring out where or why it applies. You are not figuring out what you could do (or will end up doing) with that information. So, removed from the soil, it rots.

Taking college classes again made me realize this. That’s another way of saying that it made me realize what I had failed to do my first time in college. What I did in the past was learn information specifically so I could repeat it on a test, get my grade, then let the knowledge (and time spent gaining it) die. Then wondered why I hated school so much.

Nowadays I try to be more active with the information I acquire. This very blog helped me a lot, because writing it forced me to try and explain the things I thought about and read about. I had to try to make them relate (or rather, to see the relationship those facts already shared). Even if my initial guesses and ideas about those relationships were wrong, the fact that I searched for helped make the facts stick.

During this past semester (which, go figure, interfered a bit with the blog, which is why I announced a glorious return and then didn’t update) I was a lot more active during my classes. Taking statistics, I was constantly playing with my calculator, because I wanted to run equations back and forth to make sure I understood why I was getting the answers that I got. I tried--very actively--to relate every equation and concept to one another. If the teacher gave us an equation without explaining it, I began ignoring her and looking it up (okay, maybe not the #1 student role model). This had some interesting results.

Result number one: I did better in this statistics class than any math class I’d taken before.

Result number two: When I studied with other students, I was constantly explaining material to them, because I had done way more mental footwork while listening to the teacher. They called me “really smart.” That felt good.

Result number three: One of them also said, when I was explaining a concept to her, “look, I’m just memorizing it to pass, I’m not a math person like you.” This was the first time anybody had ever called me a math person, and I made a weird snorting sound at her, like if a cartoon pig was also an evil bureaucrat in pantaloons. I was never a “math person” before. It just no longer made sense to me to try and memorize something without figuring out its applications.

It’s not that I was doing something she couldn’t, because I was magically mathematical (mathemagical?) and she wasn’t. It’s that I was repeatedly doing things she wasn’t. Things that younger me also didn’t do, when he also assumed that math wasn’t his thing. Turns out, it’s not that math is fun, or that figuring out how the calculator performs its binomalpdf function and writing my own equation for it is inherently fun. It’s that finding connections is fun. Applying the knowledge of those connections in a demonstration of my ability is fun; I get to say to myself, “look what I can do!” In this regard, every subject is fun. There isn’t a single subject (as far as I can tell) that doesn’t contain those elements of forming connections and implementing applications.

I realized this very clearly during my history class. I think the reason many people struggle with history is because they feel that history requires memorization (question: what year was the 24th Amendment to the US Constitution ratified? Better question: what was the 24th amendment to begin with?). This is sort of accurate, but probably less accurate than most people think.

History is the study of people who did stuff for reasons. As your picture of the people involved becomes more clear, and your picture of the reasons and motivations they had becomes more clear, what they did and when falls into place. You can use an almanac or a textbook or scribbled notes on a sheet of paper to store the minutiae, though with enough detail, it all makes sense anyhow.

It sounds like a lot of effort to learn the “why” of a historical fact. But learning that “why” makes it progressively easier to learn everything else. A lot of people have no trouble remembering the long and drawn out details of their favorite television shows or books or movies or whatever. Yet many people struggle with history, when fundamentally your favorite TV show and your least favorite history class are the same thing. People doing stuff for reasons. Why did this character on Game of Thrones stab that one through the neck? You know because they’re both people with motivations involved in a conflict that you’ve come to understand. As long as the thing you’re reading or watching isn’t crappy fiction, the actions will make sense to you. Even when there are twists that surprise you, they (should) make sense in retrospect. Because you know why.

For the same reason, you can easily learn why one country invades another, or why one politician doesn’t get elected. These “why” questions force you to form a better picture. The more facts you acquire and the more you understand why those facts are true, the better the picture synchronizes with itself. Then, if you don’t actually remember something, the things you do know can help you recreate the fact. It will be the only thing left that makes sense, given what you know.

History is the biography of everybody. Knowing this, history should be significantly more interesting to significantly more people. When you look at how obsessed some folks can be on social media over the most minor happenings, it’s a surprise they’re not more interested in history. People love politics and drama! Just ask high-school students.

But to be fair to the high-schoolers, the classes and textbooks and sometimes teachers do a tremendous disservice to history. They present a series of facts in the dullest manner possible and say “go forth and forget.” How are you supposed to remember the year Texas broke from Mexico without something to relate it to? Imagine trying to put a puzzle together by memorizing the coordinates of every piece without ever looking at the picture. That's how many people study history, and--coincidence?--why many people don't like it. Without a why, your puzzle pieces are blank.

Be the annoying child. “Why?” your world to death.

Not just “why?” but “how?” And not just “how did that happen?” but “how can I use that?” and “how does that fit?” Not just “how does that fit?” but “what does it fit with?”

Life is full of information that you gloss over. And in truth, that is totally fine; if you didn’t gloss over a lot of the world, you would get very little done. Your questions would spiral down to the quantum level in an endless cycle of why and how and then you would notice that you forgot to eat. Then you would be too busy finding your hunger a curious happenstance, and something else would eat you instead.

But you don’t get to gloss over the stuff you want to keep and use. Many of us go through the “why” process automatically when we’re excited; we look for applications of things when we’re having fun. We ask questions just because we are curious, we search for applications because it’s fun. Once novelties wear off, however, once the obligations set in and you just want to clock in and get it done and go home, the learning stops too. Being an auto-mechanic for twenty years doesn’t mean you’re good with cars, it means you spent twenty years in a garage. Being an auto-mechanic who spent twenty years learning, tinkering, exploring, researching, asking questions, and making all that information relate to each other is what makes you a good auto mechanic. In fact, it’s probably what makes you a great one.

So do that! You learn a new fact, “how could I use this?” You learn another one, “how can this be used with the other one? How do they relate?” Even if your guesses are wrong, attempting to relate them is a form of using them, and helps them stick.

This is how learning happens. When you learn consistently and automatically, you develop something that looks a bit like genius, but is really just unconscious, persistent effort.

Thanks for reading.


  1. Well said Rob, I love your work

  2. Our brain physically works this way too. The more synaptic connections we have to something, the more accessible and retrievable the information or function is.

  3. This blog entry is singlehandedly and positively influencing me more than it ought to. WHY are your words so good to me?

  4. Your views on statistics runs parallel to my own views on calculus.
    People call me crazy for finding ways to derive all the formulas used, but I find it comforting to know that if my memory fails to recall the derivative of arcsin, I can derive it myself by drawing a triangle.

    Good stuff.

  5. I needed this. Thank you.

  6. How interesting! These thoughts are completely identical to what i've pondered about since my start of taking classes. Glad to see someone sharing my thoughts. Good read!

  7. I'm a 'math person' and this is why I rarely had to study much for math tests. If the class is taught correctly, it goes through the progression of ideas and gets more and more complex throughout the year, building off what you already know. Since tests are usually set up in the same way, the first question would jog my memory about the easy stuff, and I would simply re-derive equations as I needed them. This method failed in Calc 2, and I did poorly in it, because infinite series, trig integration, etc, was not so much explained as presented, and I failed to see the connections. Calc itself was the first math class I took, where I wasn't figuring out equations a step ahead of the teacher explaining them; it was the first class where the progression from simple to complex wasn't intuitive to me, so when I got to the parts I struggled with, I figured "oh well, I guess I'm not an 'integration person'". Same with stats and prob, though those classes were taught as merely a presentation of mathematical 'tools' with very sparse explanation as to how or why they were derived, and very little explanation as to how the different distributions are connected (at least that was my experience). As a 'math person' I'm just now (in uni) learning how to study for math, because it was all so intuitive to me before, and I've found that rote memorization means I forget it all the next semester (looking at you Calc 2).

    Thanks for the post, I enjoy reading them.

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