Is it possible that when John Smith moved from Apple to Microsoft, this raised the average IQ of both companies?
Ouch... I guess Minsky was a Mac guy.
Marvin Minsky: What makes mathematics hard to learn? (2008)
121–130 of 175 posts
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#122While kids may find arithmetic to be boring and demotivating, they're able to do it. It's when math gets symbolic that you get the permanent attrition. For instance, most people never get to calculus. When you progress from arithmetic to abstract, it hardly gets easier . Moreover, memorizing. You go from memorizing multiplication tables to other kinds of tables, like tables of equations giving various identities, row…
Potentially unpopular opinion: Maybe our math teachers just suck? If we all had Marvin as our professor I doubt attrition would be as high, whereas most High School math teachers are simply analytically inclined people who realized they had better job security teaching math than english
If Richard Feynman taught our children physics that would be great too. Your bar is unrealistically high I feel. I'm pretty sure there's a large percentage of math teachers that want to teach math and enjoy teaching it. I'm not sure how much freedom they have to teach it their way though.
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#123I had dinner with Prof Minksy, about 15 years ago. He asked what I was working on (evolutionary algorithms) we got talking about domains of knowledge. He said all knowledge has a half-life, the time it takes for half of what you know to be redundant or wrong. Math, he said, is the longest, measured in centuries or millennia. One should feel sorry for neuroscientists: they can go to the bathroom and half their knowled…
That's a pretty interesting way to put it. I feel that the math-related fields also have a long half-life: EE, ME, Statistics, Physics, etc.
The EE and ME stuff won't exactly be wrong, but could become out of date because of new device types and materials. Imagine studying EE before solid-state devices and ICs, for example. But it's still a pretty long half-life compared to biology!
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#124Earlier quoted context omitted.
Disagree. Kids disengage from math for many different reasons. There is no single pattern to it. If it were that simple, it would not have remained an issue since schools were commonplace. Minsky solidly makes the point that when math is taught as nothing more than an endless series of tedious drills with no purpose in sight, of course it demotivates kids. No one likes pointless Sisyphean tasks. Many students, howeve…
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 sa…
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)
#125> Anecdote: I asked a certain 6-year-old child “how much is 15 and 15”and she quickly answered, “I think it’s 30.” I asked how she figured that out so fast and she replied, “Well, everyone knows that 16 and 16 is 32, so then I subtracted the extra two 1’s.” Wait, is this girl some kind of base-2 native?
As much as I regret that humans don't have 8 fingers at each hand and count in base 16, I think it's more likely that she simply is/knows a computer nerd.
If you learn Egyptian method of counting you can get to 12 on 1 hand and with a single small tweak to it. We could count to 16 on each hand. If we taught kids how to count differently
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#126Mathematics is hard to learn because it's a 'solved' problem.
Everything is taught as a convention through brutally boring rote memorization and repetitive mechanical operation.
Unfortunately, the people creating the training materials are usually so far removed from a basic level of understanding, they're blind to their own expert bias.
What we need sre training materials that bridge basic to advanced understanding theough practical application. Except practical application is hard to measure so it'll never be used. In a traditional teaching environment.
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#127While kids may find arithmetic to be boring and demotivating, they're able to do it. It's when math gets symbolic that you get the permanent attrition. For instance, most people never get to calculus. When you progress from arithmetic to abstract, it hardly gets easier . Moreover, memorizing. You go from memorizing multiplication tables to other kinds of tables, like tables of equations giving various identities, row…
Disagree. Kids disengage from math for many different reasons. There is no single pattern to it. If it were that simple, it would not have remained an issue since schools were commonplace. Minsky solidly makes the point that when math is taught as nothing more than an endless series of tedious drills with no purpose in sight, of course it demotivates kids. No one likes pointless Sisyphean tasks. Many students, howeve…
It's just one anecdote, but this jibes with my personal experience. I hated algebra (high school algebra) because it was endless tedious, mechanical manipulations and there didn't seem to be any real elegance or beauty to it. It was just memorizing "stuff" like the quadratic formula, how to rationalize denominators, blah, blah, blah. But high-school geometry was actually interesting. Seeing how the various proofs were formed and built up from pieces, and how one thing followed logically from another, that was fun.
Needless to say, my geometry grade was much better than my algebra grade.
Then, in college, taking pre-calc/Trig, it was back to a lot of boring repetition (except trig, that was actually interesting). But then in Calc I, it was fun again. The idea behind derivatives was actually interesting, and hooked me early on in Calc I.
Anyway, I always found that, other than tedium, the biggest challenge I had with math was being put off by cryptic notation. I tend to want to read things to myself in my head as I look at them on a page, and when I'm looking at (new/unfamiliar) math notation, and I don't know how to "pronounce" it to myself, my mind wants to just blank out and skip it.
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#128While kids may find arithmetic to be boring and demotivating, they're able to do it. It's when math gets symbolic that you get the permanent attrition. For instance, most people never get to calculus. When you progress from arithmetic to abstract, it hardly gets easier . Moreover, memorizing. You go from memorizing multiplication tables to other kinds of tables, like tables of equations giving various identities, row…
Disagree. Kids disengage from math for many different reasons. There is no single pattern to it. If it were that simple, it would not have remained an issue since schools were commonplace. Minsky solidly makes the point that when math is taught as nothing more than an endless series of tedious drills with no purpose in sight, of course it demotivates kids. No one likes pointless Sisyphean tasks. Many students, howeve…
> Kids disengage from math for many different reasons. There is no single pattern to it.
I agree with a lot of what you're saying, but not this. The pattern is depressingly clear. People are taught math by teachers who don't really understand it and didn't like it themselves; most of the students wind up in the same place, and so each generation poisons the next. Elementary school teachers especially tend to be drawn from the subset of the population that doesn't like math.
And it starts with the idea that math is all about rote memorization. I would go farther than Marvin did with the flash cards. I would say, for each fact, let's work it out by the standard algorithm, then see if we can find two or three more ways to arrive at it: by distributing multiplication over addition (e.g. 7 × 6 = (6 + 1) × 6 = 6 × 6 + 6 = 36 + 6) or by factoring one multiplicand and reassociating (e.g. 7 × 6 = 7 × 2 × 3 = (7 × 3) × 2 = 21 × 2, which is easy because you can double both digits of 21 without generating a number bigger than 10).
So when I read the reply of the "traditional teacher" to the 6-year-old who had a novel way of computing 15 + 15 -- "Your answer is right but your method was wrong" -- I think that if this was a real anecdote, the teacher should have been fired on the spot, for not understanding the first thing about mathematics! But sadly, no one could probably have been found to replace this teacher who wouldn't have suffered from the same fundamental misconception. It's not about knowing the "right" way: it's about knowing many ways.
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#129I think early math education suffers from the lack of awareness about how important is exactness in math. People come to math from real world, where they don't mind to be rigorous about the meaning of every word. Most newcomers tend to skip words they don't find interesting and then penalty seems to come from nowhere. And education even encourages such error-prone behaviour, by giving wrong exercises and poor materia…
This resonates very strongly with my experience helping my two kids (11,13) with their math work. Their teachers have not always been as helpful as they might in this respect, for example marking test solutions as entirely incorrect when the student has made a stupid arithmetic mistake in the working but otherwise demonstrated a proper understanding of how to solve the problem. I'm not arguing that incorrect answers should be rewarded, but it does seem to demotivate the student when they are punished for a mistake performing a task that no adult would need to perform (we use computers and calculators for our arithmetic, and have done since I was my kids age in the 1970s).
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#130Earlier quoted context omitted.
>neuroscientists: they can go to the bathroom and half their knowledge will be out of date Web development seems to be even worse than neuroscience in this regard. I feel like I have to perpetually study to be abreast of best practices.
Well, at least the languages you use stay pretty much the same? Javascript, HTML, and CSS are always going to be there. Although.. I suppose that could be considered both good and bad..
While that's half-true, compare ES3 to ES2015, or DHTML to HTML5.