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

Re:Marvin Minsky: What makes mathematics hard to learn? (2008) by kazinator on Tuesday January 26, 2016 @08:25AM (#10973242)

Maybe the child has simply played a doubling game before, along these lines, and memorized it:

What's 1 and 1? 2.

What's 2 and 2? 4.

What's 4 and 4? 8.

What s 8 and 8? 16.

What's 16 and 16? 32.

That's just five facts.

The game could occur socially between kids. It is natural to ask a question, then take the answer and "up the ante" by re-formulating the answer into a harder question, back into the other child's face!

Do you know 1 plus 1? Ha, two plus two? Oh yeah, how about four plus four, then?

The progression grows quickly, of course, and soon the interrogated subject breaks.

I get beaten at 65536.

Ah, if only "one twenty eight kay" were an accepted answer ... :)

[ Parent | on HN ]

Re:Marvin Minsky: What makes mathematics hard to learn? (2008) by Jtsummers on Tuesday January 26, 2016 @09:15AM (#10973438)

It's also doubling. Like ashark, I tended to play with numbers like that as a kid. Plus, not sure how old I was but I think I was 7, perhaps 8, I was introduced to the question:

  If I agreed to pay you a dollar today, and double your pay
  each day. How much would you get paid after a week? After
  30 days?

By a teacher (presented differently, but that's the question). The power of doubling just stuck with me (how quickly it grew), long before I actually knew the concepts of linear versus exponential growth. This resulted in certain arithmetic facts sticking with me better than other, perhaps more logically obvious facts. Random things like this will stick with kids when they can start to see patterns or features within the structure of it.

[ Parent | on HN ]

Re:Marvin Minsky: What makes mathematics hard to learn? (2008) by ashark on Tuesday January 26, 2016 @09:09AM (#10973418)

I used to run through this (and on up to higher powers of 2) in my head as a kid in idle moments, well before I knew it had any relevance to... anything, really.

[ Parent | on HN ]