Teachers! When am I ever going to use this? @stecks talks Pythagoras in the real world. This weekend’s New Scientist or on the website. #iTeachMath#MTBoS
I had a fun little chat with Miss R (5) the other day. She asked me "What is one hundred plus two more hundreds?". When I said "three hundred", she said no, not a hundred and then three added on (or add one, add one, add one, or add one and then add two).
So we got to have a little chat about "a hundred and three" vs "three hundred".
It turns out that addition might be commutative, but the words we use to speak positional notation aren't :-)
tryin' not to be in front of computer all mornign but #mtbos reddit just had a post "best apps for college math, not for cheating" and desmos (I added geogebra), wolfram and youtube didn't suprise me but "anki for flashcards" was new. https://apps.ankiweb.net/#OER it's open source, too...
#mtbos there are people who think that audiobooks or text-to-speech are "cheating."
I wonder (no, I suspect strongly) that some people feel the same way about teaching math after ?th grade with concrete-representational-abstract structures... that somehow, if you aren't fluent in the symbol processing, you won't really be able to use math if we have to get you there via that path.
Now, you just m ight not if I don't include the structured bridges to the abstract, but maybe you can, if I do.
OK I'm trying to help plan an event. (UGH UGH UGH)
How can we communicate? Google doc? Text messages to a group? Email group? (one has said they dn't really check email; another sometimes has trouble w/ doing it).... Blog site they can comment on? #mtbos I know it's not really math but ... reaching out...
Following on from a discussion on misconceptions in Maths on Friday, gauging if there is any appetite for me finally publishing my self explanation prompts for worked examples. It'll be a slow process, but if I'm going to start the holiday is the time to start! (Poll in next post) #MTBoS#iTeachMath#MathChat#MathsEdChat
Poll - would you use them for reference (pictures only), as a resource (editable files) or not all bothered (probably wouldn't use or refer to them)? (see pictures above) #MTBoS#iTeachMath#MathChat#MathsEdChat
I solve a problem about coincidence, but really it's about problem solving and bakes in some stuff about mathematical thinking, creativity, and communication.
Here's a fun fact I just looked up: Western Australia is 2.5 times the area of Texas, but whereas Texas has 210 people for every 2 square miles, Western Australia has 5. And three-quarters of the WA population is concentrated in Perth.
Challenge: what's the average population density of WA outside Perth? What number or numbers would you need/could you use in addition to the above to calculate this? What other numbers could you calculate from the above if you had one more related number?
#mtbos so the 050 instructor brought the 5 students in the "late start" section to the tutoring lab today, and they were full of questions. They had asked whether there was anybody who "got" why / how students ... didn't get math.
So I 'splained that yes, I had a master's degree in learning disabilities and had kinda specialized in exactly that these decades.
Instructor told me that class had started w/lots of negative body language, tension but somehow somebody had started being honest and when one had said they couldn't even divide that they all started sharing their stories and being loud and laughing and ... they'll start working w/ number lines Wednesday, and they know where to go for more help...
I want to riff a bit on computable numbers. I'll start with integers, fractions, mention Egyptians, and end up at H. P. Lovecraft's Cthulhu mythos. (No, really.)
BTW, when thinking about fractions and decimal expansions, I always want to mention the Egyptian numeral system, and in particular the excellent book "Count Like An Egyptian":
The problem with our "p/q" notation for rationals is that it's hard to compare and approximate them. Say: which is bigger, 17/43 or 11/29? Hard to see, right?
But if I ask the same question for 0.3953488 and 0.3793103, it's easy.
Now think of approximation. Think of 17/43 in your typical quotitive (I think) model: you divide a circle into 43 equal sectors and you have 17 of them. But who can divide a pizza into 43 slices?? I want a smaller denominator that gets me close to 17/43.
Egyptian fractions make both tasks easy. I forget the details of how 17/43 would be done, but it turns out 17/43 is very close to 3/8 + 1/50. And 11/29 is very close to 3/8 + 1/250. So you can:
see which is bigger;
look at the denominators of the second-order terms and see how good your approximation is
Nice! But let's talk about infinity and Lovecraft.