2011.05.06 What is the Progression of 'Big Ideas' in Mathematics

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 Friday, 6th May 2011 @ColinTGraham Hello e Fri May 06 00:02:51 +0000 2011 - tweet id 6 @mathfour I tell you, I lo idea" anyway? #mathchat Fri May 06 00:02:54 +0000 2011 - tweet id 6 @ColinTGraham As alw with one or two people, and reme Fri May 06 00:04:13 +0000 2011 - tweet id 6 @ColinTGraham If your t or so... ;-) #mathchat Fri May 06 00:04:50 +0000 2011 - tweet id 6 @ColinTGraham Today's #mathchat Fri May 06 00:05:19 +0000 2011 - tweet id 6 @ColinTGraham So as B what we think "Big Ideas" are bef Fri May 06 00:08:20 +0000 2011 - tweet id 6 @nykat4 @ColinTGraha Fri May 06 00:08:49 +0000 2011 - tweet id 6 @ColinTGraham @nykat in mathematics?" in case you mis Fri May 06 00:09:39 +0000 2011 - tweet id 6 @nykat4 @ColinTGraha Fri May 06 00:09:48 +0000 2011 - tweet id 6 @Ideas_Factory @Colin for continental tweeps-good on yo Fri May 06 00:10:05 +0000 2011 - tweet id 6 @ColinTGraham So, for me #mathchat Fri May 06 00:11:08 +0000 2011 - tweet id 6 @mathfour Are we talkin lines? #mathchat  Fri May 06 00:11:25 +0000 2011 - tweet id 6 What is the progression of eryone, welcome to today's #mathchat 291801799143424 - #2  e #mathchat, but I get so confused at th 291814910537728 - #3  ys, if it is your first time, don't try to follo ber the hashtag>>#mathchat  292143278399488 - #4  eets are protected, you may want to un 292299600109568 - #5  topic is "What is the progression of 'Big 292421910216704 - #6  on (@mathfour) asked, (hi y'all!) we pro re talking about progression #mathchat  293178839474176 - #8  what's the topic tonight? #mathchat  293301845835776 - #9  4 Just tweeted it out, but "What is the pr ed it ;-) #mathchat  293511779131392 - #10  never mind, saw topic when I scrolled 293549368492032 - #11 Graham Agreed!But didn't know you did u! 293620336115712 - #12  xample, "zero as a place-holder" is a bi 293884363350016 - #13  big as in cute Rene and his idea of putt 293956773818368 - #14  'Big Ideas' in Mathematics? topics. What is a "big everything but interact protect them for an hour Ideas' in mathematics?" ably need to define gression of 'Big Ideas' p! #mathchat  a 'late night' #mathchat idea (or concept) to ing together a couple of

Transcript of 2011.05.06 What is the Progression of 'Big Ideas' in Mathematics

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Friday, 6th May 2011

@ColinTGraham Hello eFri May 06 00:02:51 +0000 2011 - tweet id 6 

@mathfour I tell you, I lo

idea" anyway? #mathchat Fri May 06 00:02:54 +0000 2011 - tweet id 6 

@ColinTGraham As alwwith one or two people, and remeFri May 06 00:04:13 +0000 2011 - tweet id 6 

@ColinTGraham If your tor so... ;-) #mathchat Fri May 06 00:04:50 +0000 2011 - tweet id 6 

@ColinTGraham Today's#mathchat Fri May 06 00:05:19 +0000 2011 - tweet id 6 

@ColinTGraham So as Bwhat we think "Big Ideas" are befFri May 06 00:08:20 +0000 2011 - tweet id 6 

@nykat4 @ColinTGrahaFri May 06 00:08:49 +0000 2011 - tweet id 6 

@ColinTGraham @nykatin mathematics?" in case you misFri May 06 00:09:39 +0000 2011 - tweet id 6 

@nykat4 @ColinTGrahaFri May 06 00:09:48 +0000 2011 - tweet id 6 

@Ideas_Factory@Colinfor continental tweeps-good on yoFri May 06 00:10:05 +0000 2011 - tweet id 6 

@ColinTGraham So, forme #mathchat Fri May 06 00:11:08 +0000 2011 - tweet id 6 

@mathfour Are we talkin

lines? #mathchat Fri May 06 00:11:25 +0000 2011 - tweet id 6 

What is the progression of

eryone, welcome to today's #mathchat 291801799143424 - #2  

e #mathchat, but I get so confused at th

291814910537728 - #3  

ys, if it is your first time, don't try to follober the hashtag>>#mathchat 

292143278399488 - #4  

eets are protected, you may want to un

292299600109568 - #5  

topic is "What is the progression of 'Big

292421910216704 - #6  

on (@mathfour) asked, (hi y'all!) we prore talking about progression #mathchat 293178839474176 - #8  

what's the topic tonight? #mathchat 293301845835776 - #9  

4 Just tweeted it out, but "What is the pred it ;-) #mathchat 293511779131392 - #10  

never mind, saw topic when I scrolled293549368492032 - #11 

Graham Agreed!But didn't know you didu!293620336115712 - #12  

xample, "zero as a place-holder" is a bi

293884363350016 - #13  

big as in cute Rene and his idea of putt

293956773818368 - #14  

'Big Ideas' in Mathematics?

topics. What is a "big

everything but interact

protect them for an hour

Ideas' in mathematics?"

ably need to define

gression of 'Big Ideas'

p! #mathchat 

a 'late night'#mathchat 

idea (or concept) to

ing together a couple of

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Friday, 6th May 2011

Fri May 06 00:16:09 +0000 2011 - tweet id 6 

@ColinTGraham @maththey can move on to the next, moFri May 06 00:16:44 +0000 2011 - tweet id 6 

@mathfour @ColinTGraof 2 and 3) #mathchat Fri May 06 00:16:48 +0000 2011 - tweet id 6 

@mathfour @ColinTGraAlgebraic systems? Or just in genFri May 06 00:17:55 +0000 2011 - tweet id 6 

@ColinTGraham @math

same if you switch the position ofFri May 06 00:17:55 +0000 2011 - tweet id 6 

@mathfour @ColinTGra(oh - and narcissistic) #mathchat Fri May 06 00:18:17 +0000 2011 - tweet id 6 

@ColinTGraham @mathFri May 06 00:18:51 +0000 2011 - tweet id 6 

@LizDk High school: quasols & graph, why you can have 0Fri May 06 00:18:57 +0000 2011 - tweet id 6 

@NathalieFytrou RT @Transformations #mathchat Fri May 06 00:19:36 +0000 2011 - tweet id 6 

@MrHonner Operations '

Adding is (2 + 3 = 3+ 2), subtr. isnFri May 06 00:19:40 +0000 2011 - tweet id 6 

@ColinTGraham @LizDgeometrically and vice versa? #mFri May 06 00:19:49 +0000 2011 - tweet id 6 

@MrHonner @ColinTGraFri May 06 00:20:33 +0000 2011 - tweet id 6 

@ColinTGraham @MrHoproperties or attributes are not uniFri May 06 00:20:39 +0000 2011 - tweet id 6 

What is the progression of

295148413321216 - #27  

our What do your students need to 'get'e advanced, topic/concept #mathchat 295296107364353 - #28  

am @MrHonner Addition is commutativ

295310128918529 - #29  

am What do students need to get...? Likeral? #mathchat 295592330072064 - #30  

our @MrHonner OK, so for some operat

the operands... #mathchat 295592216838144 - #31 

am In general? They should "get" that I'

295685938552832 - #32  

our You forgot to add Texan! ;-) #mathc295828611993600 - #33  

ratics is cornerstone of algebra. Need t,1,or 2 sols. #mathchat 295850615308288 - #34  

rHonner: Objects --> Operations --> Str

296017020133376 - #35  

ommute' if performing them in diff order

't: 2-5 <> 5-2 #mathchat 296033541492736 - #36  

So maybe the bigger idea is that algebrthchat 

296070447169537 - #37  

ham That was hard to do in 140 - #math296255478894592 - #38  

nner Yes, and students need to get thatversal... #mathchat 296278602092544 - #39  

'Big Ideas' in Mathematics?

r understand before

(2+3=3+2 for all values

e wrt commutativity?

ions the result is the

freaking awesome.

at 

understand link betw

ctures -->

yields same result.

can be represented

hat characters!

some of these

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Friday, 6th May 2011

@mathfour @LizDk Ouc#mathchat Fri May 06 00:20:56 +0000 2011 - tweet id 6 

@MrHonner @LizDk. Agbig "big" idea. #mathchat Fri May 06 00:21:11 +0000 2011 - tweet id 6 

@LizDk Commutativity comultiplication. #mathchat Fri May 06 00:21:16 +0000 2011 - tweet id 6 

@ColinTGraham @MrHofundamentals in 140 characters,

Fri May 06 00:21:31 +0000 2011 - tweet id 6 

@mathfour @MrHonner Iwow!#mathchat Fri May 06 00:21:46 +0000 2011 - tweet id 6 

@MrHonner @ColinTGrawhat it meant for commutativity toFri May 06 00:22:30 +0000 2011 - tweet id 6 

@markbethune @LizDkis more geometric than algebraicFri May 06 00:22:54 +0000 2011 - tweet id 6 

@ColinTGraham @mathquadratics rather than linear equaFri May 06 00:22:56 +0000 2011 - tweet id 6 

@mathfour @LizDk This

guess you really can say geometrFri May 06 00:23:07 +0000 2011 - tweet id 6 

@LizDk @ColinTGrahamgraph - comes into domain, rangeFri May 06 00:23:34 +0000 2011 - tweet id 6 

@MrHonner @ColinTGrasomething teachers should thinkFri May 06 00:23:41 +0000 2011 - tweet id 6 

@mathfour @ColinTGraequation/graph/set - not separate

What is the progression of

- quadratics is cornerstone of algebra.

296350253383680 - #40  

eed. Inherent connections between alge

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mes right back in high school when we l

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nner Well done, though! If we can't explaybe we need to think again.... #mathc

296495908986880 - #43  

t might be fun to try to define everything

296560065056768 - #44  

ham Right. It wasn't until grad school thfail. #mathchat 296744899645440 - #45  

ot sure what you mean by this??? I woumathchat 296846913503232 - #46  

our @LizDk To be honest, I'd prefer to ttions... it highlights concept #mathchat 296852613570560 - #47  

is why I tell parents and students that all

y is algebra. #mathchat 296899132600320 - #48  

In adv alg the main idea is link between, inverses + more. #mathchat 297012630462465 - #49  

ham @mathfour Agreed! It's a fun challebout all the time. #mathchat 297043513118720 - #50  

am @LizDk I think everything should bethe three. #mathchat 

'Big Ideas' in Mathematics?

eally? How y'figure?

ra and geometry is a

ok at matrix

in some of theseat 

in <=140 -

t I really understood

ld argue that quadratics

ach graphing using

math is the same. I

the algebra and the

nge, and concision is

taught with

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Friday, 6th May 2011

Fri May 06 00:24:09 +0000 2011 - tweet id 6 

@ColinTGraham @markgeometric.... wherein lies the probFri May 06 00:24:15 +0000 2011 - tweet id 6 

@LizDk @markbethune ISolving, manipulating, discrim is dFri May 06 00:25:02 +0000 2011 - tweet id 6 

@CutTheKnotMath @malgebraic geometry #mathchat Fri May 06 00:25:02 +0000 2011 - tweet id 6 

@mathfour @ColinTGra

and you've got a nice tri-lesson #Fri May 06 00:25:13 +0000 2011 - tweet id 6 

@ColinTGraham OK, soalg/geom, commutivaty.... what otFri May 06 00:25:31 +0000 2011 - tweet id 6 

@markbethune @ColinTWithout linking the algebra to geoFri May 06 00:25:35 +0000 2011 - tweet id 6 

@MrHonner @CutTheKncharacters. #mathchat Fri May 06 00:25:45 +0000 2011 - tweet id 6 

@mathfour @ColinTGra10 system. That's a huge idea. #Fri May 06 00:26:23 +0000 2011 - tweet id 6 

@ColinTGraham @CutTimportant too... Geometry is the 'hFri May 06 00:26:55 +0000 2011 - tweet id 6 

@mathfour @MrHonnerin the margin. Or so he led us toFri May 06 00:27:15 +0000 2011 - tweet id 6 

@MrHonner I think the biproblem into another, one structurFri May 06 00:27:36 +0000 2011 - tweet id 6 

What is the progression of

297160559366146 - #51 

ethune @LizDk Quadratic equations arlem if we don't present them so! #mathc297184756314112 - #52  

guess it is both. But taught in Alg 1 andef algebra. #mathchat 297381892800512 - #53  

thfour @LizDk Wile's proof of FLT is sai

297383784419329 - #54  

am @markbethune @LizDk And then c

athchat 297430525751298 - #55  

e have: zero and place-holding, quadrher 'big ideas' #mathchat 297506237124608 - #56  

Graham this is true of most maths that wetry, kids wont get it #mathchat 

297523463131136 - #57  

otMath @mathfour @LizDk Good luck e

297564680564736 - #58  

am I'm pretty impressed with the ten finathchat 297724273827840 - #59  

eKnotMath @mathfour @LizDk The ordead' noun.... #mathchat 297858151809024 - #60  

CutTheKnotMath @LizDk Fermat DIDelieve for 300 years! #mathchat 297940792197120 - #61 

gest idea, for me anyway, is transformae into another, etc. #mathchat 298027089997824 - #62  

'Big Ideas' in Mathematics?

both algebraic andat 

lg 2 courses, right?

to belong to arithmetic

nsider the set of points

tics as a link between

e teach at this level.

plaining that in 140

ers creating the base

er of words there is

explain it in <140 chars

ion. Turning one

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Friday, 6th May 2011

@ColinTGraham @mathHow often do you teach your kidsFri May 06 00:28:42 +0000 2011 - tweet id 6 

@markbethune can somFri May 06 00:29:24 +0000 2011 - tweet id 6 

@ColinTGraham We meand Distributability? #mathchat Fri May 06 00:29:55 +0000 2011 - tweet id 6 

@CutTheKnotMath @Mrthat could be described in less thFri May 06 00:29:57 +0000 2011 - tweet id 6 

@MrHonner @CutTheKnof - 1" #mathchat Fri May 06 00:31:01 +0000 2011 - tweet id 6 

@ColinTGraham @mathFermat was what some of us in thFri May 06 00:31:35 +0000 2011 - tweet id 6 

@CutTheKnotMath @mthat could be described in less thFri May 06 00:31:56 +0000 2011 - tweet id 6 

@ColinTGraham @MrHowhat you call transformation? [avFri May 06 00:32:45 +0000 2011 - tweet id 6 

@ColinTGraham @markwe are defining what we see as thFri May 06 00:33:42 +0000 2011 - tweet id 6 

@MrHonner @ColinTGra"mathematical trans." and the tecFri May 06 00:34:19 +0000 2011 - tweet id 6 

@CutTheKnotMath @Mrthe number I've been thinking ofFri May 06 00:34:39 +0000 2011 - tweet id 6 

@mathfour @ColinTGraFri May 06 00:34:49 +0000 2011 - tweet id 6 

What is the progression of

our The big concept there was the inven0, 1, 2,... do you start 1, 2 #mathchat 298304891330560 - #63  

one remind me of the topic so I don't ge298482079711232 - #64  

tioned commutativity... how about the ot

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Honner @mathfour @LizDk BTW, what in 40 characters? #mathchat 298619095031810 - #66  

otMath @mathfour @LizDk "whatever n

298887031361537 - #67  

our @MrHonner @CutTheKnotMath @Le North would call a blagger! [TX = BSer299031885840384 - #68  

thfour @MrHonner @LizDk BTW, what in 140 (sorry) characters? #mathchat 299118485643265 - #69  

nner Would you accept redefinition as aiding terminology problems] #mathchat 299326812532736 - #70  

ethune "What is the progression of 'Bige 'Big Ideas' first, Mark. #mathchat 299564600209408 - #71 

ham Guess I'm using transformation tonique of "changing your perspective". #299719063838720 - #72  

Honner "whatever number you are thinkimathchat 299802211717120 - #73  

am Well, alas, I teach Daughter starting299845085888512 - #74  

'Big Ideas' in Mathematics?

tion of zero, though.

t off base?#mathchat 

her two? Associativity

s the smallest integer

mber you are thinking

izDk Yeah, as if!#mathchat 

s the smallest integer

other way of describing

Ideas' in mathematics?"

ean bothathchat 

ng of - 1" ~ but this was

with 0. #mathchat 

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Friday, 6th May 2011

@ColinTGraham @mathprobably start with 1 when countiFri May 06 00:36:01 +0000 2011 - tweet id 6 

@ColinTGraham @markare linked or that a picture/visualiFri May 06 00:37:18 +0000 2011 - tweet id 6 

@ColinTGraham @MrHodifferentiation, I have to say I'm nFri May 06 00:38:08 +0000 2011 - tweet id 6 

@mathfour @ColinTGranumbers so I can teach her to co

Fri May 06 00:38:24 +0000 2011 - tweet id 6 

@oldak @ColinTGrahamPutting all fingers down to represFri May 06 00:38:33 +0000 2011 - tweet id 6 

@MrHonner @CutTheKnbegan with me saying "I think 15,Fri May 06 00:38:42 +0000 2011 - tweet id 6 

@halebone Hm, don't lootrue? How num 0 - 9 got their shaFri May 06 00:38:45 +0000 2011 - tweet id 6 

@ColinTGraham OK, spFri May 06 00:39:01 +0000 2011 - tweet id 6 

@CutTheKnotMath A regroup, you always get the same rFri May 06 00:39:32 +0000 2011 - tweet id 6 

@MrHonner What aboutetc.#mathchat Fri May 06 00:39:51 +0000 2011 - tweet id 6 

@mathfour @ColinTGraFri May 06 00:39:55 +0000 2011 - tweet id 6 

@ColinTGraham @oldaktwoness and threeness etc. is cerFri May 06 00:40:08 +0000 2011 - tweet id 6 

What is the progression of

our That is probably uncommon though,g... 0 as a 'Big Idea' is lost #mathchat 300147738488832 - #75  

ethune So what is the big idea here... isation is important? #mathchat 300469470969856 - #76  

nner Yes, well I always have problems tt talking about calculus! #mathchat 300679177781248 - #77  

am I'm really trying to figure out how to "nt from -3. #mathchat 

300747817558016 - #78  

@mathfour Don't most kids start countinnt 0 must be 2ndary. #mathchat 300785276895232 - #79  

otMath This reminds me of the chat I ha00 is the biggest number". #mathchat 300822576824320 - #80  

k like the arabic num I std in Egypt MTe http://bit.ly/kHUnlt #mathchat 

300833704329216 - #81 

aking of calculus.... is that a big idea? #300903992475648 - #82  

lly big idea is that, however you count thsult #mathchat well, with a proviso301032942141440 - #83  

modeling" as a 'big idea'? Interpreting, r

301110985572352 - #84  

am Calculus is dumb. #mathchat 301127263649792 - #85  

@mathfour It may be secondary, recogainly fundamental #mathchat 301182326480896 - #86  

'Big Ideas' in Mathematics?

since most parents

it that alg and geom

lking about

display" negative

g with their fingers?

with my niece,which

davidwees: Is this

athchat 

e number of objects in a

fining, altering,

izing oneness and

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Friday, 6th May 2011

@mathfour @ColinTGrathe thing that lets us know that TeFri May 06 00:40:21 +0000 2011 - tweet id 6 

@markbethune @ColinTimpt for stud at this level. This is eFri May 06 00:40:46 +0000 2011 - tweet id 6 

@ColinTGraham @oldakthing in terms of manipulating nuFri May 06 00:41:12 +0000 2011 - tweet id 6 

@mathfour @oldak @Cobe negatives. Husband didn't agr

Fri May 06 00:41:22 +0000 2011 - tweet id 6 

@markbethune @ColinTthan when I went to school #mathFri May 06 00:41:31 +0000 2011 - tweet id 6 

@LizDk Calculus itself iscurved function by zooming in, isFri May 06 00:41:41 +0000 2011 - tweet id 6 

@ColinTGraham @mathdown... -3, -2, -1, 0, then start putFri May 06 00:42:39 +0000 2011 - tweet id 6 

@mathfour @ColinTGraFri May 06 00:43:26 +0000 2011 - tweet id 6 

@ColinTGraham @CutTbase... #mathchat Fri May 06 00:43:39 +0000 2011 - tweet id 6 

@mathfour RT @CutThenumber of objects in a group, youFri May 06 00:44:04 +0000 2011 - tweet id 6 

@MrHonner @LizDk @mcontinuous from discrete snapshoFri May 06 00:44:17 +0000 2011 - tweet id 6 

@ColinTGraham @MrHounless you are suggesting constrFri May 06 00:44:33 +0000 2011 - tweet id 6 

What is the progression of

am Okay, maybe calculus isn't dumb, wxas is the biggest. #mathchat 301238316244992 - #87  

Graham of course alg and geo are linkedssence of tech use #mathchat 301343966568448 - #88  

@mathfour However, using zero as a plbers... It's not intuitive. #mathchat 301451235885056 - #89  

linTGraham I figured counting on someoe. #mathchat 

301494697271296 - #90  

Graham tech allows studs to visuallize thhat 

301532005613568 - #91 

ot a big idea. Idea that we can get the sbig idea. #mathchat 

301571654369280 - #92  

our Counting from -3, start with 3 fingersing fingers up => directed #mathchat 301815796416512 - #94  

am I like it! #mathchat 302014048579584 - #95  

eKnotMath You do need to assume a 'c

302066708070402 - #96  

KnotMath: A really big idea is that, howealways get the same result #mathchat 302172605845504 - #97  

athfour S. Strogatz describes calculus ats, as a film. Big idea! #mathchat 302226397806592 - #98  

nner Modeling is more about methodoloction of mathematical models? #mathch302294148399104 - #99  

'Big Ideas' in Mathematics?

en I calm down. It is

but the picture is also

aceholder is a 'huge'

ne else's fingers could

e maths. far different

lope at a point for a

up and take them

ounting system' or

er you count the

piecing together the

y or teaching practice,at 

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Friday, 6th May 2011

@ColinTGraham @mathnumber" when talking about +veFri May 06 00:45:36 +0000 2011 - tweet id 6 

@oldak @ColinTGrahamRight hand: 1 (thumb) to 5 (pinkieFri May 06 00:46:03 +0000 2011 - tweet id 6 

@CutTheKnotMath @Cobase... Why? Just state consistenFri May 06 00:46:07 +0000 2011 - tweet id 6 

@ColinTGraham @marklinked to recognizing numbers of t

Fri May 06 00:47:14 +0000 2011 - tweet id 6 

@MrHonner @ColinTGraproblem--how to interpret, represFri May 06 00:48:00 +0000 2011 - tweet id 6 

@ColinTGraham @oldaknumbers have a position AND a dFri May 06 00:48:11 +0000 2011 - tweet id 6 

@ColinTGraham @CutToneness, twoness, etc. is certainlFri May 06 00:49:18 +0000 2011 - tweet id 6 

@CutTheKnotMath @Coprepared to share the laurels #maFri May 06 00:50:32 +0000 2011 - tweet id 6 

@ColinTGraham @MrHo

many ways and visualizing. It maFri May 06 00:50:34 +0000 2011 - tweet id 6 

@teachersharetp RT @kfun!http://bit.ly/i4DLqg #mathchat Fri May 06 00:51:34 +0000 2011 - tweet id 6 

@earlsamuelson @maththemselves! #mathchat Fri May 06 00:51:45 +0000 2011 - tweet id 6 

@ColinTGraham @CutTdefining or noticing patterns is a b

What is the progression of

our It also supports the mathematician'snd -ve integers etc. #mathchat 302559954010112 - #100  

@mathfour Hold up both hands, palms, left: -1 (thumb)... #mathchat 302673342828544 - #101 

linTGraham You do need to assume a 'c#mathchat Important that magnitude ex

302686907203584 - #102  

ethune I think that visualization is a 'bighings... #mathchat 

302969032880128 - #103  

ham I'm thinking of modeling as the waynt, and solve it. #mathchat 303161517875200 - #104  

@mathfour That would work too, the unirection maybe? #mathchat 303207604887553 - #105  

eKnotMath The concept of magnitude,very important/big idea #mathchat 

303490850430976 - #106  

linTGraham what I referred to as onenesthchat 303799245029376 - #107  

nner OK, that's maybe a combination of

be farther along... #mathchat 303810716446720 - #108  

bkonnected: 60+ math sites for makingspedchat #elemchat #edchat 

304060378189825 - #109  

four I like showing negative numbers as

304107165646848 - #110  

eKnotMath ;-) Grouping like and separaig idea too, maybe! #mathchat 

'Big Ideas' in Mathematics?

 jargon of "directed

ut as a number line?

ounting system' orists

idea', and probably

one interacts with a

erlying idea being that

hat I referred to as

s, twoness, etc. ~ I am

defining a problem in

ath

ransformations

ing unlike as part of

8/6/2019 2011.05.06 What is the Progression of 'Big Ideas' in Mathematics

http://slidepdf.com/reader/full/20110506-what-is-the-progression-of-big-ideas-in-mathematics 10/11

 

Friday, 6th May 2011

Fri May 06 00:51:55 +0000 2011 - tweet id 6 

@ColinTGraham TBH, ifor twenty-one would be written asFri May 06 00:53:44 +0000 2011 - tweet id 6 

@oldak @CutTheKnotM"2ness", "3ness", etc... are 2nd orFri May 06 00:53:47 +0000 2011 - tweet id 6 

@LiveBinders RT @kbk#mathchat #spedchat #elemchat Fri May 06 00:54:01 +0000 2011 - tweet id 6 

@ColinTGraham @oldak

several approach, too. The key pFri May 06 00:55:01 +0000 2011 - tweet id 6 

@MrHonner How big an iFri May 06 00:55:55 +0000 2011 - tweet id 6 

@ColinTGraham OK, fivlet alone the progression... ;-) #mFri May 06 00:56:10 +0000 2011 - tweet id 6 

@ColinTGraham Hmm, iHow big an idea do you think "infiFri May 06 00:56:58 +0000 2011 - tweet id 6 

@CutTheKnotMath @Mrone? #mathchat Fri May 06 00:57:40 +0000 2011 - tweet id 6 

@mathfour Sorry y'all. D

Husband to tuck her in. #mathchaFri May 06 00:58:46 +0000 2011 - tweet id 6 

@CutTheKnotMath @Mr#mathchat Fri May 06 00:59:06 +0000 2011 - tweet id 6 

@mathfour @ColinTGraFri May 06 00:59:08 +0000 2011 - tweet id 6 

@ColinTGraham OK, togrouping=>counting, zero as placFri May 06 01:00:02 +0000 2011 - tweet id 6 

What is the progression of

304148617961472 - #111 

I had my way, either the coordinate syst12...! #mathchat 304605591580672 - #112  

th @ColinTGraham Isn't concept of "1neer? #mathchat 

304619395035136 - #113  

nnected: 60+ math sites for making matedchat 304676215271425 - #114  

@CutTheKnotMath You could argue th

int is the grouping, though #mathchat 304929568006144 - #116  

ea do you think "infinity" is? #mathchat 305153669677058 - #117  

minutes to go and we haven't even defithchat 305218878513152 - #118  

infinity bigger than zero, as big as zeroity" is? #mathchat 305420309962752 - #119  

Honner what I referred to as oneness, tw

305595698982912 - #120  

ughter's losing her mind not wanting to

t 305872057466880 - #121 

Honner How big an idea do you think "in

305955524120576 - #122  

am This is definitely a fun topic, though!305964944535552 - #123  

ummarize... commutativity, quadratics aholder, infinity, calculus #mathchat 306189323010048 - #124  

'Big Ideas' in Mathematics?

m would be reversed,

ss" fundamental, where

fun!http://bit.ly/i4DLqg 

t. There is the one, two,

ed all of the 'Big Ideas'

or... ;-) RT @MrHonner:

oness, etc. ~ Which

o to sleep without

inity" is? ~ Which one?

#mathchat 

s basis for algebra,

8/6/2019 2011.05.06 What is the Progression of 'Big Ideas' in Mathematics

http://slidepdf.com/reader/full/20110506-what-is-the-progression-of-big-ideas-in-mathematics 11/11

 

Friday, 6th May 2011

@oldak @ColinTGrahammagnitude represent? #mathchat Fri May 06 01:00:46 +0000 2011 - tweet id 6 

@MrHonner @CutTheKnFri May 06 01:00:49 +0000 2011 - tweet id 6 

@ColinTGraham visualizproblems), anything else to add toFri May 06 01:01:14 +0000 2011 - tweet id 6 

@MrHonner @ColinTGra#mathchat Fri May 06 01:01:31 +0000 2011 - tweet id 6 

@CutTheKnotMath @Mrof them #mathchat Fri May 06 01:01:41 +0000 2011 - tweet id 6 

@ColinTGraham @oldakideas, getting into the sematics ofFri May 06 01:02:21 +0000 2011 - tweet id 6 

@ColinTGraham Well, Ithanks for your contributions, oncFri May 06 01:03:38 +0000 2011 - tweet id 6 

@ColinTGraham We'll se#mathchat Fri May 06 01:04:29 +0000 2011 - tweet id 6 

@MrHonner Thanks, @CMonday's#mathchat.Fri May 06 01:05:06 +0000 2011 - tweet id 6 

@ColinTGraham You cayou like... and today's archive shoFri May 06 01:06:26 +0000 2011 - tweet id 6 

@ColinTGraham BTW, ifback and 'tart up' some older oneFri May 06 01:08:31 +0000 2011 - tweet id 6 

What is the progression of

When you say that an "idea" is "big", wh

306377370443776 - #125  

otMath Seems like you agree that infinity306387080261632 - #126  

tion, modeling (combining visualizationthe list before we end? ;-) #mathchat 306493036756992 - #127  

ham @mathfour I agree: a fun topic, but

306562582515712 - #128  

Honner Seems like you agree that infinit

306608187179008 - #129  

Ah, well given that we didn't get on to di'Big' may be tricky! #mathchat 306772209631232 - #130  

uess today's topic has got us all beat! Jagain! #mathchat 

307097670860800 - #131 

e how we get on with this on Monday, w

307309927804929 - #132  

olinTGraham, and others. Maybe we'll s

307464097824769 - #133  

vote on next week's topic http://bit.ly/e7uld be online by Sat. #mathchat 307802095824896 - #134  

you like the format of the archives now, ltoo! #mathchat 

308324840312832 - #135  

'Big Ideas' in Mathematics?

at property does that

is a big idea.#mathchat 

ith redefining

hard to get a grasp on.

is a big idea. I do; all

scussing progression of

st for a change...

en we come back to it!

lve this on

2g8r (yes, already!) if

et me know... I may go