Marvin Minsky: What makes mathematics hard to learn? (2008)
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Marvin Minsky: What makes mathematics hard to learn? (2008)
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Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#2> 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?
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#3> 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.
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#4> 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?
It might "just" (not to be little it) be shortcut she has learned, I also used tons of my own shortcuts for answers when I was smaller (read: used to not use calculator). I could do smaller calculations like that fast and when my parents asked how I came up with them and when I answered they didn't believe me.
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#5> 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?
A lot of cooking, at least in the US, is base 2.
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#6> 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?
It might "just" (not to be little it) be shortcut she has learned, I also used tons of my own shortcuts for answers when I was smaller (read: used to not use calculator). I could do smaller calculations like that fast and when my parents asked how I came up with them and when I answered they didn't believe me.
I think parent wondered how it's possible that she remembered 16+16=32.
Children raised on positional decimal arithmetic are "supposed" to figure that 10+10=20 or 20+20=40 and then add/subtract 5+5.
Of course it's easier to associate 15 with 16 than with 10 or 20, but the fact that she immediately knew 2·16 and was able to proceed further says something about either her experience with binary arithmetic or some tendency to spontaneously count in binary.
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#7> 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?
Maybe finds it easier to remember one large addition and to correct it with smaller additions.
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#8He makes a really good point about traditional teaching methods. What's the point with the obsession over 'the correct method'? If the answer is correct, and the method in question can reliably reach the correct answer, in my opinion, the correct method is that one, and it differs from person to person.
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#9> 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?
A lot of cooking, at least in the US, is base 2.
Yeah, I think imperial units are good explanation as well, if this is what you meant.
Re: Marvin Minsky: What makes mathematics hard to learn? (2008)
#10> 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?
There is a popular [citation needed] children's song called Inchworm[0] that has a chorus that lists powers of two.
Two and two are four
Four and four are eight
Eight and eight are sixteen
Sixteen and sixteen are thirty-two