Bases.
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Bases. (decimal, binary etc) are best explained through examples.
"You can only write three symbols in base 3. These are: 0, 1, 2"
So you count: 0, 1, 2, 10, 11, 12 ...
I think the word "symbols" is confusing, but so is "characters"? Students don't think of numbers or letters as "symbols" or characters. The card sorting puzzle helps with this. But I'm always refining the language:
How would you put this as plainly as possible?
@futurebird Glyphs ... Then use things other than digits.
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Bases. (decimal, binary etc) are best explained through examples.
"You can only write three symbols in base 3. These are: 0, 1, 2"
So you count: 0, 1, 2, 10, 11, 12 ...
I think the word "symbols" is confusing, but so is "characters"? Students don't think of numbers or letters as "symbols" or characters. The card sorting puzzle helps with this. But I'm always refining the language:
How would you put this as plainly as possible?
@futurebird In base 3, there are only three numerals; 0, 1, and 2.
(A number is the thing you write down by using one or more numerals.)
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I still remember calling something the Fth item the list semiseriously and a coworker about slapped me.
I will use any damn thing like a number, watch me go.
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Bases. (decimal, binary etc) are best explained through examples.
"You can only write three symbols in base 3. These are: 0, 1, 2"
So you count: 0, 1, 2, 10, 11, 12 ...
I think the word "symbols" is confusing, but so is "characters"? Students don't think of numbers or letters as "symbols" or characters. The card sorting puzzle helps with this. But I'm always refining the language:
How would you put this as plainly as possible?
@futurebird I am trying to remember how I adjusted to the terminology
I think on some level I just had to commit hard to the idea that something notated as 12 doesn't necessarily map to the WORD "twelve"
Then you can call symbols, characters, etc. whatever you want
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I will use any damn thing like a number, watch me go.
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We have done that. I need them to be able to encode characters in binary, or understand how the system we write does that.
@futurebird yeah, tricky. “View this abstraction you’re comfortable with as an entirely different category of abstraction” is always a tall order.
It reminds me a little of the confusion I’ve seen in beginners about the distinction between variables themselves and the values of variables.
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Bases. (decimal, binary etc) are best explained through examples.
"You can only write three symbols in base 3. These are: 0, 1, 2"
So you count: 0, 1, 2, 10, 11, 12 ...
I think the word "symbols" is confusing, but so is "characters"? Students don't think of numbers or letters as "symbols" or characters. The card sorting puzzle helps with this. But I'm always refining the language:
How would you put this as plainly as possible?
-
Bases. (decimal, binary etc) are best explained through examples.
"You can only write three symbols in base 3. These are: 0, 1, 2"
So you count: 0, 1, 2, 10, 11, 12 ...
I think the word "symbols" is confusing, but so is "characters"? Students don't think of numbers or letters as "symbols" or characters. The card sorting puzzle helps with this. But I'm always refining the language:
How would you put this as plainly as possible?
@futurebird
Have you ever read "How To Count On Your Fingers" by Frederick Pohl? I taught myself to count in binary on my fingers one night when I was driving on a dark highway after reading that! It's an article, not a short story. -
I will use any damn thing like a number, watch me go.
In all seriousness maybe different written random symbols like Zener cards?
Be like “oh look, add one to star and you get wavy lines but oh shit you add one to wavy lines and you gotta bring another card in” and later “but what if we wrote the star as (dramatic pause) 1”
(This may be the card sorting exercise you referred to earlier, in that case ignore me.)
But the distinction between sign-and-signified is the single biggest aha moment you can get in CS, IMHO.
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@futurebird In base 3, there are only three numerals; 0, 1, and 2.
(A number is the thing you write down by using one or more numerals.)
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Bases. (decimal, binary etc) are best explained through examples.
"You can only write three symbols in base 3. These are: 0, 1, 2"
So you count: 0, 1, 2, 10, 11, 12 ...
I think the word "symbols" is confusing, but so is "characters"? Students don't think of numbers or letters as "symbols" or characters. The card sorting puzzle helps with this. But I'm always refining the language:
How would you put this as plainly as possible?
@futurebird while "symbols" might be confusing initially, it seems like the most straight forward, especially as you develop examples, eg you get to hexadecimal 1a = 26 in decimal and your symbols include numbers and letters even though you are still talking about numbers...so symbols would be my approach.
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@graydon @futurebird Numeral. Yes. As in Roman numerals.
They don't have place value. And they use... subtraction. But our students are very familiar with roman numerals for some reason (I think the PE staff uses them a lot?)
I want to bring them out when it can be more obvious how strange they are.
Change the symbols and I don't even know if you could do a sorting problem with them.
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@futurebird yeah, tricky. “View this abstraction you’re comfortable with as an entirely different category of abstraction” is always a tall order.
It reminds me a little of the confusion I’ve seen in beginners about the distinction between variables themselves and the values of variables.
@futurebird ok EXTREMELY off the wall suggestion: warm them up to thinking like this by having them read a bit of Through The Looking Glass
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Bases. (decimal, binary etc) are best explained through examples.
"You can only write three symbols in base 3. These are: 0, 1, 2"
So you count: 0, 1, 2, 10, 11, 12 ...
I think the word "symbols" is confusing, but so is "characters"? Students don't think of numbers or letters as "symbols" or characters. The card sorting puzzle helps with this. But I'm always refining the language:
How would you put this as plainly as possible?
@futurebird Digits?
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Bases. (decimal, binary etc) are best explained through examples.
"You can only write three symbols in base 3. These are: 0, 1, 2"
So you count: 0, 1, 2, 10, 11, 12 ...
I think the word "symbols" is confusing, but so is "characters"? Students don't think of numbers or letters as "symbols" or characters. The card sorting puzzle helps with this. But I'm always refining the language:
How would you put this as plainly as possible?
@futurebird
uhm...as a thought experiment, and based on the principle that a rose by any other name would smell as sweet, I wonder how it would go to pick three random actual symbols, for instance ^,&,* and count with them, then repeat with three characters like F,K,T, in hope that they could eventually relax with the specific visual representations of the counting operations -
Thing is then when we get to hex they are upset that A and F are not "digits" but ... maybe.
@futurebird @dancingtreefrog Maybe use 'numbers' until you hit the letters and then see if they can solve the problem of what to call them. Explain that you also had trouble about what to call them, and that their ideas might help next years' class, and hey presto you're also teaching empathy! Win-win!
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@futurebird Glyphs ... Then use things other than digits.
@ColinTheMathmo @futurebird glyphs are fancy symbols, so that would be a more advanced approach
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They don't have place value. And they use... subtraction. But our students are very familiar with roman numerals for some reason (I think the PE staff uses them a lot?)
I want to bring them out when it can be more obvious how strange they are.
Change the symbols and I don't even know if you could do a sorting problem with them.
@futurebird Roman numerals are like that because it's a finger counting system being written down, essentially a record of hand positions. (So four is traditionally IIII, not the compact for monuments IV.)
If I understand the discussion at all, which I might well not, the history-of-writing folks think positional notation and zero are effectively the same concept; it's difficult to do the one without the other. And, oddly, given the Babylonians did have it, Classical Antiquity didn't.
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Bases. (decimal, binary etc) are best explained through examples.
"You can only write three symbols in base 3. These are: 0, 1, 2"
So you count: 0, 1, 2, 10, 11, 12 ...
I think the word "symbols" is confusing, but so is "characters"? Students don't think of numbers or letters as "symbols" or characters. The card sorting puzzle helps with this. But I'm always refining the language:
How would you put this as plainly as possible?
@futurebird Symbol. It means “stands for”. The trouble comes because are reusing 1 and 0 together to mean something different. Somehow you need to convey that the symbol “represents” a concept, it is itself not the concept. The symbol alone carries no meaning except that which we agree to assign it.
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@futurebird Symbol. It means “stands for”. The trouble comes because are reusing 1 and 0 together to mean something different. Somehow you need to convey that the symbol “represents” a concept, it is itself not the concept. The symbol alone carries no meaning except that which we agree to assign it.
@meltedcheese
I'm hoping this helps:myrmepropagandist (@futurebird@sauropods.win)
I don't know how well this puzzle will translate to a toot. Imagine each line is on a card: □□▷ □□□ ■■ ■ □■ □▷▣ ▣ □▣ ■▷ ■▣ ▣▷ □□■ □▷ ▣▣ □□ □ ▣□ □□▣ ■□ ▷ □▷□ □▷■ ▣■ □▷▷ Put them in order. (The 5th graders could do it, but they did have a helpful example first... There may be more than one solution, but I think there is ONE really good order. Can you find it?) (I should also mention that every adult I've shown this to gives up. But I only showed it to two rather grouchy teachers.)
Sauropods.win (sauropods.win)
