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"?

@dancingtreefrog

Thing is then when we get to hex they are upset that A and F are not "digits" but ... maybe.

@futurebird @dancingtreefrog

I still remember calling something the Fth item the list semiseriously and a coworker about slapped me.

@rk @dancingtreefrog

I will use any damn thing like a number, watch me go.

@futurebird counting on fingers bypasses that specific hurdle. “Imagine if you only had two fingers, how would you count on them?”

@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.

@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:

https://sauropods.win/@futurebird/115896355329222284

@futurebird Mathematical

A number in base n is a polynomial

xn^0 + yn^1 + zn^2 + …

where x,y,z, … are whole numbers < n

@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....

@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.

@futurebird @dancingtreefrog i think at that point the upset about learning something new that violates a socially constructed rule is unavoidable and possibly even harmful to shield the kids from

...i remember the first time in english class when the teacher told us the author we were studying was gay...

@futurebird @rk @dancingtreefrog i think this is the perfect way to explain it

@meltedcheese @futurebird this is good

one thing that isn't taught nearly enough (and some religious or reactionary parents might even actively obstruct such learning) is the arbitrariness of the signifier's relationship to the signified and how you need to learn to be able to untangle that to get to higher levels of thinking about anything

...this is kinda starting to feel like that previous discussion https://brain.worm.pin...

@apophis @futurebird Thanks. Understanding the concept of symbol reallly does unlock a lot of reasoning.

@apophis @futurebird Hmm, never bothered me, but I went to high school in the late 1960s and studied English in university through the 1970s. I guess I'm just weird.

@dancingtreefrog @futurebird i went to high school in the 90s in a neighbourhood where "castrate (rather than kill) all the f.ggots" was considered a slightly spicy moderate position among my peers...

@apophis
I was in California, in a middle class neighborhood, mostly white. There as no such talk. In fact, nobody talked about sexual orientations at all in high school. I didn't encounter that until I was in college studying creative writing. I don't know what other majors might have been like. I knew a bisexual woman that called herself Lorrainbow. She was fun!
@futurebird