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Re:Marvin Minsky: What makes mathematics hard to learn? (2008) by kazinator on Tuesday January 26, 2016 @10:09AM (#10973720)
Humanity as such absolutely loves pointless repetition, and abhors thinking about something hard, which involves focusing intensely on one subject in which where no repeatable progression of simple successes is taking place, leading to a mounting sense of discomfort.

Just look at various cultural traditions, popular (and even serious) music, crafts, sports, ... sneeze ligion. Mindless repetition is everywhere.

The same kid that hates doing arithmetic will play the same video game for hours in which a small variation on the same set of events happens over and over again.

The kids you're describing are the smart minority, of whom a portion will go on into STEM type fields. They too will hit their mathematics ceilings. Most will go as far as a couple of third year undergrad math courses and that's where it ends.

Re:Marvin Minsky: What makes mathematics hard to learn? (2008) by Fordrus on Tuesday January 26, 2016 @02:23PM (#10975315)
I think your assumptions are fundamentally wrong. The examples of repetition you describe are specifically designed, whether by a video game producer, a musician, or a priestly class- to feel important and be generally pleasant. Video game creators spend thousands of hours researching the best ways to turn their systems into Skinner Boxes, priestly sorts have spent untold amounts of time preparing sermons to instill a sense of the criticality of religious ritual- in other words, no, humanity doesn't like repetition in and of itself, but it designs repetitions that it does like.

Meanwhile, that dual sense- the pleasure the video game designer tries to create and the sense of importance the priest creates- these are fundamentally absent from our teaching methods in early arithmetic, which, at least in America, we call 'math,' not differentiating the symbolic thought processes from the repetitive arithmetic, incorporating little if any fun, and constantly failing to appropriately create a sense of importance (the most common teenage question in math classes is, "Why do I have to learn this? When am I ever going to use this?").

While there Do exist efforts to instill a video game's sense of fun to arithmetic exercises and a sense of near-religious importance to the symbolic thought of math, we are functionally applying a tourniquet to the mathematical understanding of the young by just force-feeding arithmetic drills and emphasizing mistake avoidance instead of proper thinking- and it's very little wonder that only some few students' mathematical passion survives the tourniquet.

Re:Marvin Minsky: What makes mathematics hard to learn? (2008) by kazinator on Tuesday January 26, 2016 @03:35PM (#10975824)
Yes, of course people don't like repetition per se abstracted from the particulars of what it is that is repeating. Someone likes repeated palm-muted metal guitar riffs; but thinks that someone else who likes knitting sweaters, loop by loop, should get a life.
Re:Marvin Minsky: What makes mathematics hard to learn? (2008) by marincounty on Tuesday January 26, 2016 @02:01PM (#10975168)
For myself, I found math difficult. Never understood, even now, the need to spend so much time memorizing multiplication tables.

That said, I started over in a community college, and finished up to trig. with ease. I found trigonometry, surprisingly straight forward. I went on to finish a year of physics. I didn't need calculus for my major, and heard it was really hard. Plus, I didn't want to ruin my grade point average with a class I didn't need. I now regret not taking calculus, but it's so much easier to learn something these days.

My struggle with math was two fold. I didn't care in high school, and I never had a firm grasp on basic math. I look back , and once I truly inderstood basic math, especially fractions, and percentages; it all became so easy.

I see a lot of kids still struggling with math. They get pushed along, and avoid any class that has math in it. I do blame our U.S. teaching system in this case. Keep teaching basic math until the kid can teach it to to their classmates.

Then, and only then move on to algebra, and trig? As to calculus, I didn't take it so I won't comment, but when I was applying to health professional schools, I didn't find one that required Calculus. Probally for good reason. My physics classmates biggest, silent stumbling block was they were horrid in math, and looking back--they just didn't know the basics, so every step up the ladder became more mysterious. Most of my classmates seemed to the solving problems in physics by memorizing the homework; not truly understanding the problems.

Re:Marvin Minsky: What makes mathematics hard to learn? (2008) by mindcrime on Tuesday January 26, 2016 @05:27PM (#10976700)
I now regret not taking calculus, but it's so much easier to learn something these days.

It's funny to hear you say that. I don't know how old you are, but lately I've been trying to teach myself some additional math that I never took before (like Linear Algebra) and refreshing on Calculus, and now - at the ripe old age of 42 - I swear I find it easier to learn this stuff than I did when I was in college 20 some odd years ago.

Maybe it's just a question of motivation, or maybe I have more context available now, or, hell, maybe I've gotten smarter... but whatever it is, I'm not going to complain, considering how you always hear about how our minds slow down as we age and things are supposed to get harder to learn.

Re:Marvin Minsky: What makes mathematics hard to learn? (2008) by seba_dos1 on Tuesday January 26, 2016 @03:41PM (#10975871)
For myself, I love math. I also never understood, even now, the need to spend so much time memorizing multiplication tables.

In fact, I've never learnt it. From time to time I still find myself multiplying on fingers; as a kid I used it a lot, now the table went into my head automatically simply from continued usage. The way to multiply two natural numbers from <6; 9> on fingers was one of the most important things my mom tought me :)

There's also a way as presented in the article (87 = 88-8), but I mostly use it when double checking, as I find it slightly more error-prone when doing it in head (and obviously very inefficient when done on paper). Works great for bigger numbers though.

Once in junior high school my math teacher caught me on multiplying on fingers and ordered me to learn the table for the next lession. Managed to pass it, but quickly forgot in following days. I never cared - I was always doing very fast and well on math classes anyway.

Re:Marvin Minsky: What makes mathematics hard to learn? (2008) by krmboya on Thursday January 28, 2016 @03:18PM (#10990957)
I view memorization as a shortcut that allows one to operate on higher level concepts with ease. Much like abstraction mechanisms in programming.
Re:Marvin Minsky: What makes mathematics hard to learn? (2008) by crispyambulance on Tuesday January 26, 2016 @12:23PM (#10974521)
The kids I am describing are somewhat lucky for not having "checked out" before progressing beyond fractions. But they're not extraordinary, they're just kids who have been taught competently and who have been motivated in one way or another to get that far.

Kids are naturally curious and fighting against their curiosity can easily lead to losing their interest.