Post B2KA3IOYBRxtEd53PU by AMS@infosec.exchange
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(DIR) Post #B2IAsek0TMLozbgfSq by futurebird@sauropods.win
2026-01-15T00:23:54Z
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Bases. (decimal, binary etc) are best explained through examples. "You can only writer 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?
(DIR) Post #B2IAwWkK8hCzM5gJHM by dancingtreefrog@mastodon.social
2026-01-15T00:24:34Z
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@futurebird "Digits"?
(DIR) Post #B2IB3D3njGmQKNyi7E by futurebird@sauropods.win
2026-01-15T00:25:49Z
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@dancingtreefrog Thing is then when we get to hex they are upset that A and F are not "digits" but ... maybe.
(DIR) Post #B2IBB7Gr8cN8glr3Ue by kw217@mathstodon.xyz
2026-01-15T00:27:11Z
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@futurebird "shapes"? "squiggles"?
(DIR) Post #B2IBFB0xA5NxSQLugy by rk@mastodon.well.com
2026-01-15T00:27:53Z
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@futurebird @dancingtreefrog I still remember calling something the Fth item the list semiseriously and a coworker about slapped me.
(DIR) Post #B2IBG1YlnbKiQMZeca by Catfish_Man@mastodon.social
2026-01-15T00:28:03Z
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@futurebird counting on fingers bypasses that specific hurdle. “Imagine if you only had two fingers, how would you count on them?”
(DIR) Post #B2IBHcz68mDWmgeZu4 by dancingtreefrog@mastodon.social
2026-01-15T00:28:25Z
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@futurebird Yeah, confuses non-techies. Hexadecimal digits make perfect sense to me, but I'm weird.Maybe Base36? https://en.wikipedia.org/wiki/Base36
(DIR) Post #B2IBKNkpDrPCPwI5tg by futurebird@sauropods.win
2026-01-15T00:28:55Z
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@Catfish_Man We have done that. I need them to be able to encode characters in binary, or understand how the system we write does that.
(DIR) Post #B2IBQkU9cblwecWrFg by ColinTheMathmo@mathstodon.xyz
2026-01-15T00:30:00Z
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@futurebird Glyphs ... Then use things other than digits.
(DIR) Post #B2IBRfv45EAOmaYebw by graydon@canada.masto.host
2026-01-15T00:30:06Z
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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.)
(DIR) Post #B2IBSlH1f6Xlg6Lddw by futurebird@sauropods.win
2026-01-15T00:30:25Z
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@rk @dancingtreefrog I will use any damn thing like a number, watch me go.
(DIR) Post #B2IBfxqQEctmQlCSNk by dancingtreefrog@mastodon.social
2026-01-15T00:32:40Z
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@futurebird @rk 👍
(DIR) Post #B2IBic9vJjwa2jaLY0 by Catfish_Man@mastodon.social
2026-01-15T00:33:16Z
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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.
(DIR) Post #B2IBzgXaHPW0YUnBJY by rk@mastodon.well.com
2026-01-15T00:36:21Z
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@futurebird @dancingtreefrog 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.
(DIR) Post #B2ICHuyFMsGkWPxQky by merms@mastodon.social
2026-01-15T00:37:58Z
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@graydon @futurebird Numeral. Yes. As in Roman numerals.
(DIR) Post #B2ICHwEafaw8RObzs0 by futurebird@sauropods.win
2026-01-15T00:39:39Z
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@merms @graydon 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.
(DIR) Post #B2ICNjsjVdMHrr9cmW by willie1foot@theblower.au
2026-01-15T00:40:37Z
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@futurebird Digits?
(DIR) Post #B2ICOQmW0cw0v1ZlYm by e@az.social
2026-01-15T00:40:49Z
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@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
(DIR) Post #B2ICUxWvAE6YDwOWyu by Bumblefish@mastodon.scot
2026-01-15T00:42:00Z
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@futurebird @dancingtreefrog Maybe use 'numbers' until you hit the letters and then see if they can solve the problem if 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!
(DIR) Post #B2ID1Qn9u8BOFETQGW by graydon@canada.masto.host
2026-01-15T00:47:52Z
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@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.@merms
(DIR) Post #B2IDDDsljA19gJiizw by meltedcheese@c.im
2026-01-15T00:50:00Z
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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.
(DIR) Post #B2IDHGTG2rkcrsiOa8 by futurebird@sauropods.win
2026-01-15T00:50:43Z
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@meltedcheese I'm hoping this helps:https://sauropods.win/@futurebird/115896355329222284
(DIR) Post #B2IDIwkYL3NeHdbfyi by simon@procrastodon.net
2026-01-15T00:50:59Z
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@futurebird Maybe not the answer you're looking for, but this got me thinking about why exactly these words are confusing, and it occrs to me that people are trying to un-learn the decimal system every time they use numbers to express things in a different base. I wonder if it would help to just use actual, unique symbols. If you give people 0, 1 and 2 and tell them to count, their brains are tripping over themselves because they have to fight the natural assumption that "10" is "the number of fingers I have" or "the number that comes after nine". Take away that association until people understand the concept of counting using fewer or more symbols, and maybe it will make more sense.
(DIR) Post #B2IDxcl7ZKMa9jGk0O by gooser3000@mastodon.social
2026-01-15T00:58:19Z
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@futurebird there are only 10 numer keys on the keyboard... Imagine of there were more or fewer. Also consider a clock where we count by 12s and 60s and use : to separate.
(DIR) Post #B2IG7xGyM0C2aADlrs by CaptMorgan@freeradical.zone
2026-01-15T01:22:38Z
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@futurebird Mathematical A number in base n is a polynomial xn^0 + yn^1 + zn^2 + …where x,y,z, … are whole numbers < n
(DIR) Post #B2IGRBIyPG3jbYKCTg by futurebird@sauropods.win
2026-01-15T01:26:10Z
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@CaptMorgan This is great for students who have strong algebra. But that idea of using increasing powers? It's really not obvious that's what's going on when you first start. But could one do something with... physical cubes and literal flat squares? That's Cuisenaire rods for decimal. Are there... base 16 Cuisenaire rods? Why not? hmm....
(DIR) Post #B2IM0z1E3z8ThAulQu by thomas_decker@mastodon.online
2026-01-15T02:28:37Z
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@futurebird In German we have a useful word: Ziffer (single digit number) - as opposed to Zahl (any number)
(DIR) Post #B2IO4wjUhjCDfjddJI by itgrrl@infosec.exchange
2026-01-15T02:51:44Z
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@futurebird maybe you could start by introducing the concept of character sets (ASCII probably being the most “obvious” one to start with) so that the students get familiar /comfortable with the idea that even “simple” things like numbers & letters are encoded in computer-land, which could then flow into a discussion of both bases & variables 🤔 ^ I’d suggest also the Unicode emoticons / emoji block for the fun factor but then you’re into multi-byte encodings & modifiers which seems you’d probably be throwing students into the deep end waaay too soon
(DIR) Post #B2ISFLWfmJL1HNr768 by Burn_this_@beige.party
2026-01-15T03:38:28Z
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@futurebird Digits?
(DIR) Post #B2IWNXtE5rNDl4ZPVI by grant_h@mastodon.social
2026-01-15T04:24:45Z
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@futurebird I go with "symbols" in Yr10 when I teach it. Certainly avoid "number", because one of the big ideas is to separate the notion of "number" from its representation.Fun if I have Arabic or Korean or Chinese students. I ask them to write up their digits.
(DIR) Post #B2IhXyccepwP3fyqRM by mansr@society.oftrolls.com
2026-01-15T06:29:53Z
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@futurebird @merms @graydon I once saw a demonstration (by some maths guy on TV) of doing long division with Roman numerals. It was indeed strange.
(DIR) Post #B2It1VsDCvlw4zYhw8 by oblomov@sociale.network
2026-01-15T08:38:29Z
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@futurebird @dancingtreefrog I vote for digits too. And you can make an example of weird digits even before getting to base 16 if you want to try your luck at teach them about balanced ternary after showing them the classic unbalanced version (use the the upper-side down 1 for the -1 value in writing, or T if typing: «why T?» «Because the Setun never gained commercial success»).
(DIR) Post #B2IxBv38rCuesIt9kG by david_chisnall@infosec.exchange
2026-01-15T09:25:10Z
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@futurebird @dancingtreefrog Semi serious, but the only real reason we use letters in hex is that they’re convenient. Modern Unicode has a load of digit-like symbols. There’s no reason you couldn’t use superscript digits. Or bold. And there’s no reason you have to use any existing symbols if your students are using pen and paper. You could start with Church numerals (good American number representation, none of this Arabic nonsense) and then have them define shorthand symbols for s(😶), s(s(😶)) and then build binary, decimal, base 60, or whatever out of those symbols. (No-face emoji is zero).There might be a reason I’m not allowed to teach maths.
(DIR) Post #B2IxikSLGTERZlKW3M by ColinTheMathmo@mathstodon.xyz
2026-01-15T09:31:07Z
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@futurebird Have you seen James Tanton's "Exploding Dots" done properly? He targets it for kids, and at the beginning I thought "Huh, this is just binary" ...But by the end he was doing polynomial division and non-integer bases. Might be worth looking at
(DIR) Post #B2JKGrlIo2v74Vs8iu by Ehay2k@mastodon.social
2026-01-15T13:43:47Z
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@futurebird Units?
(DIR) Post #B2KA3IOYBRxtEd53PU by AMS@infosec.exchange
2026-01-15T23:24:00Z
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@futurebird @dancingtreefrog That's usually ok after you ask them what to use for bases beyond 10.
(DIR) Post #B2KJJVbFkscKPTpOMq by thezerobit@anticapitalist.party
2026-01-16T01:07:45Z
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@futurebird @dancingtreefrog In a hex number, the symbols A - F are considered digits and this is confirmed by Merriam-Webster definition of "digit" (1a). Symbol, element, character and digit are all correct terms. Of these, "digit" is the most specific.