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James Tanton
An Aussie fellow promoting uplifting joyful genuine math thinking and doing for students & teachers alike. Honored: reaching millions!
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James Tanton retweeted
Ralph Pantozzi 8h
Replying to @Mathgarden @NCTM and 2 others
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James Tanton 8h
A unit on quadratics is about Power of Symmetry in math. Factoring inherently asymmetrical,not part of that story. But,re picture,you can still deduce info about a rectangle in one other case:I tell you area is zero. My take when forced to teach factoring:
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James Tanton 8h
Replying to @PixelQuilter
Is it possible to create a math classroom culture with some dual focus on questions and ideas, seeking understanding, probing examples and counter-examples, all along with the standard growth of numerical fluency and accuracy and facility to answer traditional exercise questions?
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James Tanton 9h
In case interesting, here are some informal thoughts on student assessment qus I wrote up a while back when in the HS classroom. This rough piece resurfaced again after a twitter conversation a year or so ago. The "Classic Error Head-On" idea is there.
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James Tanton 9h
Replying to @CsmcPhlospher
Sit with this for a bit. There is something cool and mysterious/troubling here!
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James Tanton retweeted
Benjamin Dickman 10h
For your Q: Yes! I mentioned yesterday Borasi's book on exploring such errors [] and once before []. One benefit is explicitly valuing S work when they [oftentimes: bravely] make a false conjecture: Beyond "No" to "Is it ever true?"
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James Tanton retweeted
Mike Lawler 11h
Replying to @jamestanton
We explored the first one a while back via 3d printing - it was a fun way to see that the equations were different:
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James Tanton retweeted
Benjamin Dickman 11h
There is a nice post on MESE, which links to an earlier post on MSE, about errors of the type above:
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James Tanton 11h
The last one is particularly cool.
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James Tanton 11h
Would taking classic and tempting errors "head-on" be a worthwhile classroom activity and discussion?
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James Tanton 11h
Galileo: Sum of first k odd numbers equals one-third sum of next k odd numbers: 1/3=(1+3)/(5+7)=(1+3+5)/(7+9+11)=...Visual proof by HS students. Can you prove other interesting ratios? eg alternating sums?or 1/(3+5)=(1+3)/(5+7+9+11)=(1+3+5)/(7+9+11+13+15+17)=...?or sums of evens?
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James Tanton 20h
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James Tanton retweeted
LilMathGirl May 18
Replying to @jamestanton
By the way Mr.Tanton would be the first person to warn about the consistency of patterns.
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James Tanton retweeted
Mardalee Burwitz May 18
Replying to @jamestanton
Yep. Spending stormy afternoon wrapping my head around this and... nuthin’...though lower corner was intriguing for a bit... back to watching Star Wars on the tv..... 🤔😕
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James Tanton May 18
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James Tanton May 18
Replying to @prairieveep
Play with it. Do you believe it? Cool fun!
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James Tanton May 18
It doesn't take long to realise that something is terribly awry here.
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James Tanton May 18
Replying to @Dr_Kreisberg
"Anomalous cancellation"is classic&cool. Lot's to explore.(Eg Why 26..6/6..65=2/5 no matter # of 6s) But one comment here is what means to "teach." To "teach" this rule can only mean"tell." But teaching is about encouraging thinking&questioning, how do I know what I think I know?
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James Tanton May 18
That makes for an very rich conversation. The word "teach" here, I wonder, can only mean "tell." But maybe having our fabulous kiddos explore the mysteries of this, find counterexamples, find other instances where, by luck, it works, explore why 1/5=19/95=199/995=.., is teaching?
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James Tanton May 18
Replying to @RWA_Maths
Careful!
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