31–40 of 139 posts
John Conway's On Numbers and Games has a great overview of infinities. And since it's about games it'll be great for teaching kids too!
I don't remember whether I was ever taught that. But I do remember the line from Marilyn Manson's "Posthuman".
> God is a number you cannot count to.
Picking the first infinite ordinal as the infinity to explain to kids might not be the best choice for every kid, though. Oridnals are tricky. I am not too comfortable with them myself, and I say that as an adult with a degree in math! The thing is, this kind of infinity just doesn't come up that often when dealing with other objects in math. Even though, as Tom Lehrer sang, one can count up to infinity - or somewher…
If the child is old enough to understand basic addition and multiplication, you can probably run through a short explanation of the different (elementary) number systems.
Why so complicated? Just ask them to do i++ and never stop. That is also infinity. (or in simpler words, imagine you have a table than you put one apple to it, then one again, amd again and again and never stop. And yes, they would also soon understand, that the table needs to be infinitly big) edit: of course it is about the sum of the process. they should imagine the pile of things or the number if you never stop a…
>Why so complicated? Because ifinity is complicated. >Just ask them to do i++ and never stop. That is also infinity. What, specifically, is infinity here? You are being vague here. Is it the process of counting up and never stopping? (that's the calculus infinity) The number you get in the end? (that's the infinite ordinal, but that is, as you noted, complicated ) The number of numbers ? (that's the cardinality of th…
"Do that process twice" "Perhaps after you're done putting apples " "..."
the point is, that the process is never finished ... just like you can never have a biggest number...just like the table has no end.
Defined as infinity. Kids do get that.
What they usually don't get are abstract mathematic concepts.
Earlier quoted context omitted.
I once read a critique of high school science textbooks which pointed out the great many "lies" that could be found even in the best of them - basically highly inaccurate or misleading descriptions and illustrations of basic scientific concepts. The thing is, though, that I recognized a great many of those same "lies" as being in my college science textbooks, too!
Like tides? What Physics Teachers Get Wrong About Tides! | Space Time | PBS Digital Studios: https://www.youtube.com/watch?v=pwChk4S99i4
- No, you can’t do 2-3. If you have 2 apples, you can’t give 3
- Well, in fact you can, it’s negative numbers. But if you have 5 apples you can’t split them equally between 2 persons.
- Well, in fact you can. They got 2.5 each. But you cannot solo 2 apples in 3 equally !!
- Well in fact you can. That’s 2/3 each.
- etc...
I like the concept, but if I may editorialize, I feel the phrasing needs work. "The smallest number you can't count to" is a negative statement, which makes it confusing right off the bat. What do you mean, a number I can't count to? If I'm 8 years old this is like throwing a null pointer exception in my brain.
Teaching mathematics is lying to kids all along, at least in France : - No, you can’t do 2-3. If you have 2 apples, you can’t give 3 - Well, in fact you can, it’s negative numbers. But if you have 5 apples you can’t split them equally between 2 persons. - Well, in fact you can. They got 2.5 each. But you cannot solo 2 apples in 3 equally !! - Well in fact you can. That’s 2/3 each. - etc...
Well, how soon is too soon to teach children about debt?
> A professor of mine once said to me that all teaching was a process of lying, and then of replacing the lies with successively better approximations of the truth. Well put! I'm in the process of explaining my 3yo daughter different molecules (there are some cheap kits on Aliexpress) and cells and life on a micro scale and this description of moving from simple but inaccurate models to more complex and accurate is s…
> Well put!
Shudder. Consider a thought experiment - a military briefing. A captain briefing generals. One must necessarily simplify. But imagine a briefing that is grossly incomplete, assortedly incorrect, very misleading, written without understanding and without mentioning and characterizing that lack, and pervasively incompetently bogus, and that captain later on the carpet before the generals, defending the briefing with "well, all briefing is a process of lying". Shudder. I consider the "teaching is lying" meme to be vile. I've heard it most often associated with pre-college chemistry. Chemistry education research describes pre-college chemistry education content as "incoherent", leaving both students and teachers deeply steeped in misconceptions. Oh well.
You mentioned microscale, so I write just to note the top "How to remember sizes" section of my slowwwly-loading wasn't-intended-to-be-public page http://www.clarifyscience.info/part/Atoms . It might help you provide a framework for your kid to think about small things. FWIW.