Marvin Minsky: What makes mathematics hard to learn? (2008) • Hacker News Board

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#171

Post by franciscop » Thu, Jan 28, 2016, 1:49 AM UTC

ScottBurson wrote: post #128

crispyambulance wrote: post #42

Earlier 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…

> 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…

This resonated a lot with me. I never memorized 6+7 nor 7+8, I couldn't bring myself to do it. Instead I found an easier alternative: make it 7+7 or 8+8 and substract 1.

Luckily I didn't say that out loud, otherwise they might have made me hate mathematics and I wouldn't love science now (:

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#172

Post by JadeNB » Thu, Jan 28, 2016, 5:10 PM UTC

JadeNB wrote: post #164

throwupper247 wrote: post #35

Earlier quoted context omitted.

In the decimal system it is just as easy to associate 5+5=10. 5xN is easier to remember than 16xN on account of 5 being the smaller number. 2^n is logarithmic whereas 5*n is linear. Arguably, logarithms are not too complicated, even if linear seems to be a degree easier, seeing that the decimal system is also logarithmic as that's a denser representation. edit: how to enter an aterisk as the multiplication operator s…

> 5xN is easier to remember than 16xN on account of 5 being the smaller number. By that logic, shouldn't it be easier to remember 7 * n than 10 * n, because 7 is the smaller number? > 2^n is logarithmic Also, as Jtsummers ( https://news.ycombinator.com/item?id=10973381 ) points out, the function `n \mapsto 2^n` is exponential : its growth is significantly faster , not significantly slower , than exponential.

Please read 'linear' in place of the last word 'exponential' in my reply. Oops.

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#173

Post by krmboya » Thu, Jan 28, 2016, 8:18 PM UTC

seba_dos1 wrote: post #144

marincounty wrote: post #119

Earlier quoted context omitted.

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 ave…

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 on fingers was one of the most important things my mom t…

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)

#174

Post by throwupper247 » Sun, Jan 31, 2016, 12:47 PM UTC

JadeNB wrote: post #164

throwupper247 wrote: post #35

Earlier quoted context omitted.

In the decimal system it is just as easy to associate 5+5=10. 5xN is easier to remember than 16xN on account of 5 being the smaller number. 2^n is logarithmic whereas 5*n is linear. Arguably, logarithms are not too complicated, even if linear seems to be a degree easier, seeing that the decimal system is also logarithmic as that's a denser representation. edit: how to enter an aterisk as the multiplication operator s…

> 5xN is easier to remember than 16xN on account of 5 being the smaller number. By that logic, shouldn't it be easier to remember 7 * n than 10 * n, because 7 is the smaller number? > 2^n is logarithmic Also, as Jtsummers ( https://news.ycombinator.com/item?id=10973381 ) points out, the function `n \mapsto 2^n` is exponential : its growth is significantly faster , not significantly slower , than exponential.

I didn't talk about growth, i was specifically thinking about a comment that called our number system logarithmic and it stands to reason, if you wan't to find x in 10^x=y, unless you do calculus in your head at the age of five, you may as well look at a grap of the exponential progression. now that's two incoherent arguments, but the latter should point out that it doesn't really matter which way, and the first alludes that there is something more basic to the logarithm, something easier to capture. If I look at the grid pattern in logarithmic plots, it's not a runaway progression but a nice repetition where the zeros in the end of the numbers at each 10^n interval behave like the unary number system, which is the basic positional system and arguably easier even then binary.

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#175

Post by ddingus » Sun, Jan 31, 2016, 6:55 PM UTC

agumonkey wrote: post #15

elementalest wrote: post #11

Earlier quoted context omitted.

This is how i often work with things. I break them down into things that i know how to work with. I search my knowledge for elements that most closely represents the problems and then combine them. For example, rather than remembering 12 * 6 = 72, i recall that 10 * 6 = 60 and 2 * 6 = 12, hence 60 + 12 = 72. I don't need to remember as many things and for me i can do that much faster than trying to recall it. My memo…

That's how I felt about math for a long time. The so-called good laziness. You don't bother doing the hard way, you search for tricks. Symmetries, difference from simple cases as the girl did. Instead of memorizing algorithms, kids should be shown this. It's free gamification and, after some years, I believe it's a core idea of what is, and why math can be pleasing.

Parents can do it and it can really help.

I actually was taught this and a number of other "tricks" in primary school. Estimation was a defined thing, and the idea of getting quick math results in your head was a real goal. Reasons given: job interview, pricing goods and services to understand value, fuel consumption, making things (that deck, how many boards, cost, etc...), navigation.

They took us through a lot of those cases. The first time I applied this was powers of 2 for computing. Learn the first 16 bits worth, and that helps with all sorts of things in computing, same as powers of ten and common easy to compute things do in most other areas of life.

So, what I did was make it a car game. Figure out how tall things might be, or prices, whatever comes up. Practice doing it helps to actualize the skill and once it's done, they will apply in in ways they find useful.