2011.06.10 is Mathematics Unique in the Wider Curriculum for the Deeper Thinking Skills It Develops

8/6/2019 2011.06.10 is Mathematics Unique in the Wider Curriculum for the Deeper Thinking Skills It Develops

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Friday, 10th June 2011 Is Mathemati

@ColinTGraham Hello eFri Jun 10 00:01:10 +0000 2011 - tweet id 78

@ColinTGraham If it's yo

one or two people. Don't forget thFri Jun 10 00:02:02 +0000 2011 - tweet id 78

@ColinTGraham If you hso it gets picked up.Fri Jun 10 00:02:34 +0000 2011 - tweet id 78

@NatBanting @ColinTGvery little to math; maybe a hint?Fri Jun 10 00:03:19 +0000 2011 - tweet id 78

@ColinTGraham Today'sdeeper thinking skills it develops?Fri Jun 10 00:03:29 +0000 2011 - tweet id 78

@stefras What do you mthinking in one manner or anotherFri Jun 10 00:03:36 +0000 2011 - tweet id 78

@delta_dc RT @ColinTGcurriculum for the deeper thinkingFri Jun 10 00:04:17 +0000 2011 - tweet id 78

@ColinTGraham @stefrwas not mine though! #mathchatFri Jun 10 00:05:08 +0000 2011 - tweet id 78

@NatBanting @stefras panswer as a necessity. diff b/w scFri Jun 10 00:05:10 +0000 2011 - tweet id 78

@stefras @NatBanting Sencountered this in a curriculum cFri Jun 10 00:05:20 +0000 2011 - tweet id 78

@stefras @NatBanting Ilinear route/schema to one. #matFri Jun 10 00:06:27 +0000 2011 - tweet id 78

@ColinTGraham I don'tthought... maybe the question is dFri Jun 10 00:06:53 +0000 2011 - tweet id 78

cs unique in the wider curriculum for the deep

eryone, and welcome to today's #mathc974953768239104 - #1

ur first time, don't try to keep up with eve

hashtag! --> #mathchat975169498054656 - #2

ve to do a long tweet, put #mathchat so

975305439657984 - #3

aham I definitely get the feeling that stanmathchat

975493453512705 - #4

topic is: "Is Mathematics unique in the"#mathchat975533504933888 - #5

an by deeper thinking? #mathchat. All s.975563821350913 - #6

raham: Today's topic is: "Is Mathematicsskills it develops?" #mathchat975737201303552 - #7

s I know what I mean by "deeper thinkin

975948829102080 - #8

eople view math's deep thinking as lineaool and real math? #mathchat

975959163875329 - #9

andard school PD extends to Universityourse. #mathchat976001056583680 - #10

elieve that real math does not ALWAYSchat

976282381127680 - #11

isagree that all subjects require more thoes mathematics require it? #mathchat976391126855680 - #12

r thinking skills it develops?

hat

ryone, just interact with

mewhere near the start,

dard school PD relates

ider curriculum for the

bjects encourage deep

unique in the wider

"... original question

. They see a future

ed courses as well. I

have an answer nor a

n surface level


2/16


@ekendriss RT @ColinTcurriculum for the deeper thinkingFri Jun 10 00:07:20 +0000 2011 - tweet id 78

@NatBanting @stefrasALWAYS does. every "deep thouFri Jun 10 00:07:39 +0000 2011 - tweet id 78

@NatBanting @stefras tFri Jun 10 00:07:54 +0000 2011 - tweet id 78

@stefras @ColinTGrahamove beyond given questions anFri Jun 10 00:08:00 +0000 2011 - tweet id 78

@ColinTGraham Or shothinking as it is about teaching 'nuFri Jun 10 00:08:04 +0000 2011 - tweet id 78

@stefras Me too. RT @N#mathchatFri Jun 10 00:08:45 +0000 2011 - tweet id 78

@stefras @ColinTGrahathinking; numbers are a cover stoFri Jun 10 00:09:51 +0000 2011 - tweet id 78

@ColinTGraham Do weon what mathematics is about? #Fri Jun 10 00:10:01 +0000 2011 - tweet id 78

@NatBanting ergh... havwill catch the archive.Fri Jun 10 00:10:03 +0000 2011 - tweet id 78

@ColinTGraham @NatBFri Jun 10 00:10:34 +0000 2011 - tweet id 78

@stefras @ColinTGraha#mathchatFri Jun 10 00:10:41 +0000 2011 - tweet id 78

@park_star @NatBantinsubjects promote deep & critical tFri Jun 10 00:10:54 +0000 2011 - tweet id 78


Graham: Today's topic is: "Is Mathematiskills it develops?" #mathchat976505060933632 - #13

e too; answers lead to more questions.ht" in my curriculum is measurable. #m976583456653312 - #15

at misconception annoys me quite a bit976646417367040 - #16

I think it does. Without being able to ansolutions. #mathchat

976673286078464 - #17

ld mathematics be as much about teachmber'? #mathchat976688322654208 - #18

atBanting: @stefras that misconception

976861631291393 - #19

I think math should be ABOUT teachiny. #mathchat977136014278656 - #20

eed to teach thinking skills to help moreathchat

977179391766528 - #21

to leave #mathchat waaaaay too early.

977188879269888 - #22

nting Come back on Monday if you can977317334036480 - #23

Yes. That is what math is about. re tea

977348485124096 - #24

I don't think math is unique in any of it'sinking #mathchat

977403535368192 - #25


s unique in the wider

ut school maththchat

mathchat

swer "why", we cannot

ing different ways of

nnoys me quite a bit

different ways of

students get a handle

just getting started. I

Nat! #mathchat

hing thinking skills.

"thinking skills" all


3/16


@stefras @ColinTGrahaFri Jun 10 00:11:03 +0000 2011 - tweet id 78

@stefras @park_star I a

#mathchatFri Jun 10 00:11:53 +0000 2011 - tweet id 78

@ColinTGraham @parkskills are developed, not just requiFri Jun 10 00:12:09 +0000 2011 - tweet id 78

@LizDk#mathchat Hi evteachers would also argue the caFri Jun 10 00:13:08 +0000 2011 - tweet id 78

@stefras Oops. TweetDe@stefras: @ColinTGraham See yFri Jun 10 00:13:19 +0000 2011 - tweet id 78

@ColinTGraham Not nec@colintgraham isn't that the premFri Jun 10 00:13:21 +0000 2011 - tweet id 78

@lauradafinch#mathcha6000-2409, even tho we'd done itFri Jun 10 00:13:27 +0000 2011 - tweet id 78

@LizDk#mathchat I like iand also between subjectsFri Jun 10 00:13:45 +0000 2011 - tweet id 78

@stefras @ColinTGrahaneed to narrow our definition to aFri Jun 10 00:14:40 +0000 2011 - tweet id 78

@ColinTGraham Let's jusubject with deep thinking skills...Fri Jun 10 00:14:47 +0000 2011 - tweet id 78

@LizDk#mathchat MYPfor getting kids to justify rules, conFri Jun 10 00:15:13 +0000 2011 - tweet id 78

@lauradafinch#mathchayou understand, you see relationsFri Jun 10 00:15:31 +0000 2011 - tweet id 78


See you later Nat. #mathchat977441112141824 - #26

ree. To me teaching thinking skill is wha

977648671461376 - #27

star The question here, though, is wherered... #mathchat977715411230720 - #28

ryone I am Liz. Math is about thinking de for their discipline.

977965546938369 - #29

ck moved on me. It does that quitte oftenou later Nat. #mathchat#mathchat978010224668672 - #30

essarily... eg art, drama RT @park_star:ise of any learning? (ideally anyway?) #978017170427904 - #31

t Last wk one of my 5th gr's couldn't tellall year. All he has is rote memory978043665850370 - #32

most when kids can identify connection

978119494668288 - #33

I would art and drama also require deeype of deep thinkin #mathchat

978349053120512 - #34

t clarify that we are not saying that math#mathchat978380371984384 - #35

riteria B (investigating patterns) & D(reflnect ideas etc978487926521856 - #36

t I'd argue that if you memorize, you canhips and patterns, etc978562228617216 - #38


education is all about.

those deeper thinking

eply, but other subject

. @NatBanting. RT

@stefrasathchat

e AT ALL how to do

between math topics

p thinking. Perhaps we

ematics is the only

ction in math) are great

only do one thing. But if


4/16


@ColinTGraham The poirequirement in mathematics thanFri Jun 10 00:15:44 +0000 2011 - tweet id 78

@stefras RT @lauradafinone thing. If you understand, youFri Jun 10 00:16:09 +0000 2011 - tweet id 78

@ColinTGraham @stefr'deep thinking' may be consideredFri Jun 10 00:17:16 +0000 2011 - tweet id 78

@stefras @ColinTGrahaof a requiement for math than for

Fri Jun 10 00:17:18 +0000 2011 - tweet id 78

@LizDk @stefras @Colindeeper thinking than other subjecFri Jun 10 00:18:02 +0000 2011 - tweet id 78

@lauradafinch thx @steftransfers to all other subjects. #mFri Jun 10 00:18:03 +0000 2011 - tweet id 78

@stefras @ColinTGrahaour question now? #mathchatFri Jun 10 00:19:05 +0000 2011 - tweet id 78

@ColinTGraham @laurathinking, which I see as a higher lFri Jun 10 00:19:07 +0000 2011 - tweet id 78

@LizDk @stefras @Colin

depth of thought, also scientific aFri Jun 10 00:19:18 +0000 2011 - tweet id 78


@LizDk @stefras @Colinstudents?"? #mathchatFri Jun 10 00:19:57 +0000 2011 - tweet id 78

@stefras @LizDk I thinkdeep thinking. #mathchatFri Jun 10 00:20:41 +0000 2011 - tweet id 78


nt is that being able to think on deeper leay be the case in other subjs #mathch

978616549064726 - #40

ch: #mathchat I'd argue that if you memee relationships and patterns978723839352832 - #41

s Art, drama, music work as much on extoo cerebral for some artists #mathchat

979003532316672 - #42

If that is our definition, then I say NO dther subjects. #mathchat

979013112111104 - #43

TGraham #mathchat yes I agree - we cas979198676504576 - #44

ras! i teach logic and reasoning as part othchat

979202761768960 - #45

In the light that deep thinking is not sp

979459935518721 - #46

afinch Memorization is more about cogvel process #mathchat

979469540458496 - #47

TGraham #mathchat surely analysing a

alysis, plus more979515648454656 - #48

Agreed, memorization is not deep thin979565833289728 - #49

TGraham How about "how do we foster

979677682810881 - #50

e already agreed that math is not the o

979861493977089 - #51


vels is more of at

rize, you can only do

pression of emotion,

ep thinking is not more

nnot claim to require

f curriculum, in part so it

cial to math, what is

itive load, rather than

ext in English requires

ing. #mathchat

eep thinking in our

ly subject that requires


5/16


@stefras @LizDk So hoFri Jun 10 00:20:48 +0000 2011 - tweet id 78

@ColinTGraham @stefr

thinking skills *developed* in matFri Jun 10 00:21:00 +0000 2011 - tweet id 78

@stefras @ColinTGrahaencouraged by Problem solving aFri Jun 10 00:21:58 +0000 2011 - tweet id 78

@stefras @ColinTGrahateaching. #mathchatFri Jun 10 00:22:26 +0000 2011 - tweet id 78

@LizDk#mathchat Deepthought rather than breadth of coFri Jun 10 00:22:34 +0000 2011 - tweet id 78

@stefras @LizDk Ah. Buneed to combine depth and breadFri Jun 10 00:23:26 +0000 2011 - tweet id 78

@lauradafinch#mathchaon their thinking and understandinFri Jun 10 00:23:54 +0000 2011 - tweet id 78

@LizDk#mathchat imporin a lack of depth of thought. InveFri Jun 10 00:24:22 +0000 2011 - tweet id 78

@ColinTGraham @LizDhigher in terms of cognitive load.Fri Jun 10 00:24:32 +0000 2011 - tweet id 78

@malynmawby Just thindeep thinkers. there is a connectiFri Jun 10 00:24:46 +0000 2011 - tweet id 78

@stefras @lauradafinch#mathchatFri Jun 10 00:24:50 +0000 2011 - tweet id 78

@LizDk @stefras #mathcconnections are a vital part of theFri Jun 10 00:25:14 +0000 2011 - tweet id 78


does math use or encourage deep thin979891185455104 - #52

s The question still remains, as in the be

ematics? #mathchat979942511149056 - #53

So it is a teaching question. I think deed rich tasks, but not drill #mathchat

980187311718400 - #54

SO the answer is yes and no dependin

980305171660800 - #55

thinking happens in math as long as thetent.980336096260096 - #56

connections can be made with breadthth strategically. #mathchat980553608663040 - #57

t @lizdk it also has to prevent children frg to "get it right"980671560876032 - #58

ant to vary assessment tasks. Tests andtigations are good.

980789106249728 - #59

Being able to analyse and reason deduasis of mathematics? #mathchat

980831984619520 - #60

... a lot of the mathematicians of old wern. #mathchat

980893011738624 - #61

o how DO we develop deep thinking? S

980907561783296 - #62

hat re breadth. Yes of course. All aboutthinking we want.981007243624449 - #63


ing? #mathchat

ginning: are the deeper

per thinking is

g on how one is

syllabus allows depth of

f content. I think we

m memorizing and rely

quizzes only, can result

tively (justify) are much

e also philosophers, i.e.

top memorization?

alance. I agree that


6/16


@malynmawby @stefrasa blog post on this, in fact. #mathFri Jun 10 00:25:35 +0000 2011 - tweet id 78

@ColinTGraham @stefrbeing the place where analytic thiFri Jun 10 00:25:59 +0000 2011 - tweet id 78

@LizDk @ColinTGrahamthough, kids survive on algorithmFri Jun 10 00:26:26 +0000 2011 - tweet id 78

@stefras @malynmawbydifferently in that continuum from

Fri Jun 10 00:26:39 +0000 2011 - tweet id 78

@malynmawby @LizDkorder process that many struggleFri Jun 10 00:26:39 +0000 2011 - tweet id 78

@lauradafinch#mathchaFri Jun 10 00:26:48 +0000 2011 - tweet id 78

@malynmawby @stefrasFri Jun 10 00:27:31 +0000 2011 - tweet id 78

@stefras @lauradafinchFri Jun 10 00:27:39 +0000 2011 - tweet id 78

@ColinTGraham @lauraunderstand (according to Bloom,Fri Jun 10 00:27:57 +0000 2011 - tweet id 78

@malynmawby interestinlater.Fri Jun 10 00:28:32 +0000 2011 - tweet id 78

@republicofmath Oh deFri Jun 10 00:28:50 +0000 2011 - tweet id 78

@stefras @ColinTGrahaBut in math, I think deep thinking i

Fri Jun 10 00:28:59 +0000 2011 - tweet id 78


@lauradafinch it is not either or? needhat

981096842330112 - #64

s That comes back to whether or not weking *should* be developed... #mathch981198696812544 - #65

#mathchat yes justify is the big deal. If tmath without justifying.981310173032448 - #66

I agree. We need both. It is a continumoncept to concept. #mathchat

981363813974016 - #67

stefras making connections require traith - teachers can facilitate #mathchat

981366619963392 - #68

t true understanding of concepts leads t981401034244097 - #69

variety in pedagogy is good. in fact, ess981581141843969 - #70

o deep thinking leads to drill (lower) thin981617409994753 - #71

afinch You probably cannot analyse, thnyway) #mathchat

981691510751232 - #72

g #mathchat but have got to dock out no

981840790233088 - #73

r! Missed #mathchat. Out to dinner with981914463186944 - #74

Mathematics is A place where deep ths the holy grail. #mathchat

981954149691392 - #75


oth I think...working on

see mathematics ast

o busy with content,

nd teachers "teach"

sference - a higher

fluency.

ntial, imho. #mathchat

king? #mathchat

ugh, unless you

w. will look back again

wife and father-in-law.

inking can be developed.


7/16


@LizDk @ColinTGrahamagain, not unique. English has lotFri Jun 10 00:29:20 +0000 2011 - tweet id 78

@stefras @malynmawbyFri Jun 10 00:29:31 +0000 2011 - tweet id 78

@ColinTGraham @repuGary! #mathchatFri Jun 10 00:29:33 +0000 2011 - tweet id 78

@stefras @republicofmatFri Jun 10 00:29:45 +0000 2011 - tweet id 78

@ColinTGraham @stefrsubject is about? #mathchatFri Jun 10 00:30:47 +0000 2011 - tweet id 78

@republicofmath Not sothought. #mathchatFri Jun 10 00:30:51 +0000 2011 - tweet id 78

@stefras Okay, I think we

subjects. We are asked how it isFri Jun 10 00:31:13 +0000 2011 - tweet id 78


@republicofmath My puYou'll have to come back on MonFri Jun 10 00:32:27 +0000 2011 - tweet id 78

@LizDk @stefras #mathcconnections eg diff fns, solving apFri Jun 10 00:32:31 +0000 2011 - tweet id 78

@stefras @republicofmatthought in math. Always expect itFri Jun 10 00:32:40 +0000 2011 - tweet id 78

@ColinTGraham @stefrdevelop the deeper thinking as aFri Jun 10 00:32:58 +0000 2011 - tweet id 78


@stefras #mathchat yes analysing v imof analysis, also sci and ss.

982039273095168 - #76

See you later. #mathchat982084647063552 - #77

licofmath Tsk, tsk! You'll have to come

982095292219392 - #78

h Just starting. #mathchat982143451201536 - #79

s Not so much the holy grail, more the e

982405326778368 - #80

sure deep thinking is it - rather persisten

982421613264896 - #81

have determined that deep thinking/Blo

eveloped in math. #mathchat982512977784833 - #82

Ran out of words. Holy grail first think t

982703113977856 - #83

ishment for two glasses of shiraz @Coliay then #mathchat

982825428254720 - #84

hat Math uses deep thinking in justifying,plications eg rates of change982841874132992 - #85

h Yes. Kids and adults do miss the persio be quick. #mathchat

982879106969600 - #86

s And also whether mathematics is uniqore part of the subject. #mathchat

982954449252353 - #87


ortant in math. But

ack on Monday then,

ssence of what the

ce and sustained

ms is essential to all

hat cam to mind.

TGraham Tsk, tsk!

communicating

tence and sustained

e in that need to


8/16


@republicofmath Thing ismall. Build from there. SustainedFri Jun 10 00:34:03 +0000 2011 - tweet id 78

@ColinTGraham "Is Matskills it develops?" No, but changFri Jun 10 00:34:09 +0000 2011 - tweet id 78

@stefras @ColinTGrahawe?#mathchatFri Jun 10 00:34:10 +0000 2011 - tweet id 78

@stefras @ColinTGraha#mathchat

Fri Jun 10 00:35:18 +0000 2011 - tweet id 78

@ColinTGraham "Is Matskills it requires?" to spell it out...Fri Jun 10 00:36:00 +0000 2011 - tweet id 78

@republicofmath Mathekaleidoscope of techniques. #matFri Jun 10 00:36:04 +0000 2011 - tweet id 78

@jmcyap RT @republicotogether a kaleidoscope of techniFri Jun 10 00:36:28 +0000 2011 - tweet id 78

@ColinTGraham @repupoint where technique needs to bFri Jun 10 00:37:09 +0000 2011 - tweet id 78

@stefras @republicofmat

empasizing problem solving, fromFri Jun 10 00:37:15 +0000 2011 - tweet id 78

@ngpestelos RT @reputogether a kaleidoscope of techniFri Jun 10 00:37:34 +0000 2011 - tweet id 78

@stefras @republicofmatdetermined that you can't learn grFri Jun 10 00:38:02 +0000 2011 - tweet id 78

@ColinTGraham @repuemotional involvement... Mathem


s, to succeed in #math, find some provathought is key #mathchat

983226340802561 - #88

ematics unique in the wider curriculum fdevelops to requires? #mathchat983253360508928 - #89

I think we have detemined it is not uniq

983256527212545 - #90

Sorry. What do you mean by "change

983542155128832 - #91

ematics unique in the wider curriculum fmathchat

983717204410368 - #92

atics is like aikido, Practice basics. Strichat

983733755133952 - #93

math: Mathematics is like aikido, Practicues. #mathchat

983837421547520 - #94

licofmath The same can be said of anytreplaced by something else tho' #math

984007475404800 - #95

h In Western Canada, we are getting ou

which need for ... #mathchat984034318942209 - #96

licofmath: Mathematics is like aikido, Prues. #mathchat

984110391042048 - #97

h ... skills developes. There is a drawbacmmar by writing essays. #mathchat

984229832241153 - #98

licofmath Musicians, artists, actors, etc.ticians? clarity of thought? #mathchat


le fact, no matter how

r the deeper thinking

ue, haven't

evelops to requires?"


g together a

e basics. String

ing, there comes ahat

of practicing skills and

ctice basics. String

k . It has been

are expected to show


9/16


Fri Jun 10 00:38:10 +0000 2011 - tweet id 78

@Benwturner Can we intskills that Maths is best predisposFri Jun 10 00:38:54 +0000 2011 - tweet id 78

@ColinTGraham Paul MBeethoven... doesn't stop him beiFri Jun 10 00:39:10 +0000 2011 - tweet id 78

@stefras @ColinTGraha@davidwees and @rvdemerchanFri Jun 10 00:39:38 +0000 2011 - tweet id 78

@dmarain Perhaps one c

math IS problem-solving! #mathcFri Jun 10 00:39:40 +0000 2011 - tweet id 78

@republicofmath @Colion reflection and development. #Fri Jun 10 00:40:04 +0000 2011 - tweet id 78

@stefras @ColinTGrahamusic. #mathchatFri Jun 10 00:40:06 +0000 2011 - tweet id 78

@stefras RT @dmarain:areas, but math IS problem-solvinFri Jun 10 00:40:35 +0000 2011 - tweet id 78

@LizDk @ColinTGrahamcannot say that music, arts etc doFri Jun 10 00:41:02 +0000 2011 - tweet id 78

@ColinTGraham @BenFri Jun 10 00:41:03 +0000 2011 - tweet id 78

@souzatharsis RT @reptogether a kaleidoscope of techniFri Jun 10 00:41:42 +0000 2011 - tweet id 78

@republicofmath @ColiPowerful, Can turn people into lotFri Jun 10 00:42:10 +0000 2011 - tweet id 78

@ColinTGraham @LizDbeing a good artist vs being a goo


984261683785728 - #99

erpret this question differently. Are thereed to develop? #mathchat984449764757504 - #100

Cartney would be totally crap at analysig a good songwriter though #mathchat

984514260582400 - #101

Interesting analogy. I just participated iabout Mathematician's ... #mathchat

984633810825216 - #102

an apply problem-solving strategies to al

at984641893244928 - #103

TGraham Didn't mean focus on techniqathchat

984741939986432 - #104

... Lament that touches on math being

984750366339072 - #105

erhaps one can apply problem-solvingg! #mathchat984870025641985 - #106

#mathchat Some create music, some anot involve analysis.

984985163464704 - #107

turner Or that maths has to develop... #984989290676224 - #108

ublicofmath: Mathematics is like aikido,ues. #mathchat

985152558145536 - #109

TGraham Thrill of discovery in #math iss-eaters (= mathematicians) #mathchat

985271802208257 - #110

Never said they didn't... BUT is analysisd mathematician? #mathchat


some deeper thinking

g a symphony by

n a webinar with

l content areas, but

e. Au contraire, focus is

an art like painint and

trategies to all content

alyse. I really think you

athchat

ractice basics. String

highly emotional.

a key component of


10/16


Fri Jun 10 00:42:25 +0000 2011 - tweet id 78

@stefras @Benwturner Ithink of an example though. #matFri Jun 10 00:42:42 +0000 2011 - tweet id 78

@ColinTGraham I am nothough, that expression of emotioFri Jun 10 00:43:34 +0000 2011 - tweet id 78

@stefras @ColinTGrahait to analysis or broaden it to patteFri Jun 10 00:43:56 +0000 2011 - tweet id 78

@Benwturner @ColinTG

students (beyond numeracy) for tFri Jun 10 00:43:59 +0000 2011 - tweet id 78

@LizDk @ColinTGrahamAs a creator - that would depend.Fri Jun 10 00:44:23 +0000 2011 - tweet id 78

@republicofmath SolvinSome light appears, little by little.Fri Jun 10 00:44:41 +0000 2011 - tweet id 78

@LizDk @ColinTGraham#mathchatFri Jun 10 00:45:04 +0000 2011 - tweet id 78

@dmarain Basic problemdevelop as students try more comFri Jun 10 00:45:14 +0000 2011 - tweet id 78

@ColinTGraham Deductithe construction of mathematicalFri Jun 10 00:45:25 +0000 2011 - tweet id 78

@stefras @LizDk That isTrue for all subjects. All also problFri Jun 10 00:45:25 +0000 2011 - tweet id 78

@LizDk @republicofmathmathematics.Fri Jun 10 00:45:53 +0000 2011 - tweet id 78

@LizDk @stefras #mathc


985330853814272 - #111

think math does develop unique deep thichat

985403377524736 - #112

saying that mathematicians are unemotis not a requirement of maths #mathch

985621753962496 - #113

I guess it depends on how you envisiorn play. #mathchat985714066407424 - #114

raham absolutely, I think Maths is most v

e deeper skills it develops #mathchat985726083080193 - #115

in school, yes. Go to art, music class - t#mathchat985826574417920 - #116

#math problem like being in dark room,Then illumination #mathchat985902206091264 - #117

re emotion. Interesting point. I had neve

986000390553600 - #118

s develop basic skills. Reasoning/conceplex non routine problems #mathchat986041603788800 - #119

ve reasoning, logic, Socratic dialogue, porlds, as a beginning... #mathchat

986088458371073 - #120

how I envision math -- you can analyzeem solving. #mathchat986089485967361 - #121

#mathchat. Persistence therefore a key

986205567520768 - #122

hat "Like". I wish there was a "like" butto


nking skills. I have to

ional. I am saying,t

math. You can narrow

aluable to most

ey analyse art, music.

banging into furniture.

thought of that.

tual understanding

oof, etc. are basic to

nd you can create.

component of good

.


11/16


Fri Jun 10 00:46:26 +0000 2011 - tweet id 78

@stefras @LizDk Yes. Bdevelop it? #mathchatFri Jun 10 00:46:38 +0000 2011 - tweet id 78

@stefras @LizDk There iFri Jun 10 00:47:24 +0000 2011 - tweet id 78

@dmarain @republicofmFri Jun 10 00:47:29 +0000 2011 - tweet id 78

@republicofmath Physicproblem solving, .... #math is ... ?Fri Jun 10 00:47:57 +0000 2011 - tweet id 78

@LizDk @stefras #mathcin discussion. High school all tooFri Jun 10 00:48:04 +0000 2011 - tweet id 78

@stefras @dmarain @reFri Jun 10 00:48:12 +0000 2011 - tweet id 78

@ColinTGraham @stefr

have with mathematics? They doFri Jun 10 00:48:34 +0000 2011 - tweet id 78

@republicofmath @dmaFri Jun 10 00:48:41 +0000 2011 - tweet id 78

@stefras @LizDk I agreethinking). #mathchatFri Jun 10 00:48:58 +0000 2011 - tweet id 78

@LizDk @republicofmathsolving, analysing, connecting, ...Fri Jun 10 00:49:05 +0000 2011 - tweet id 78


@LizDk @ColinTGrahamFri Jun 10 00:49:51 +0000 2011 - tweet id 78


986345191706624 - #123

t how often do we teach persistence or

986392163725312 - #124

s a favorite option/button. #mathchat986585391120384 - #125

th Beautiful analogy! #mathchat986609881657344 - #126

is problem solving, car repair is proble#mathchat986724633608193 - #127

hat Not enough. Hence my lament re breuch of a rush.

986756497752064 - #128

ublicofmath It is beautiful, but not uniqu986786872889344 - #129

s @LizDk Is this not at the root of the pr

't learn to go deep enough... #mathchat986881831927808 - #130

rain Stole it from Andrew Wiles #mathch986908155392000 - #131

. We rush over content at the expense of

986981673148416 - #132

Math is .. making sense of the world we#mathchat987010169249792 - #133

Yes. That is what I thought the original

987117774110720 - #134

@stefras #mathchat re root of problem:987205342793728 - #135


rovide opportunity to

solving, architecture is

adth of content earlier

to math. #mathchat

blem many people

t

exploration (deep

live in through problem

question was about.

Totally!


12/16


@ColinTGraham "Is Matskills it develops?" or should be dFri Jun 10 00:50:09 +0000 2011 - tweet id 78

@republicofmath Yes, almany people have with math? DoFri Jun 10 00:50:33 +0000 2011 - tweet id 78

@stefras @ColinTGrahadeep, & broad, to teach thinking rFri Jun 10 00:52:03 +0000 2011 - tweet id 78

@ColinTGraham I wouldmathematical way of thinking... w

Fri Jun 10 00:52:11 +0000 2011 - tweet id 78

@Benwturner @ColinTGpersist and can manage frustratioFri Jun 10 00:52:48 +0000 2011 - tweet id 78

@republicofmath Fatherhelp him do that & drink whisk(e)yFri Jun 10 00:52:49 +0000 2011 - tweet id 78


@LizDk @stefras #mathcissue right there.Fri Jun 10 00:53:09 +0000 2011 - tweet id 78

@stefras @republicofmatFri Jun 10 00:53:23 +0000 2011 - tweet id 78

@ColinTGraham @stefrmathematics... analytic thinking mFri Jun 10 00:54:11 +0000 2011 - tweet id 78

@ColinTGraham @repuFri Jun 10 00:54:31 +0000 2011 - tweet id 78

@dmarain As long as mocoverage the culture we're descriFri Jun 10 00:54:59 +0000 2011 - tweet id 78


ematics unique in the wider curriculum fveloping but isn't... #mathchat

987280387289091 - #136

ways dig deeper @ColinTGraham Is this't learn to go deep enough #mathchat987380006199296 - #137

The question is clear; its meaning is nther than doing. #mathchat

987756650508288 - #138

argue that any analytic act in any subjecether you're teaching maths or not #mat

987792486629377 - #139

raham YES should be! but you have to hto develop those skills. #mathchat

987945788452865 - #140

in-law keen to watch Miami Heat play MBye till next time. #mathchat

987950507036672 - #141

SO part of your definition of math is an

988010754027521 - #142

hat "..teach thinking rather than doing" S

988034468626432 - #143

h Bye. #mathchat988091746041856 - #144

s Not as such, but recognizing patternsay be best developed there. #mathchat988294746148864 - #145

licofmath Bye Gary. #mathchat988377956950016 - #147

st 2ndary teachers believe that curriculuing will not happen #mathchat

988496215347200 - #148



not at root of problem

t. I think we need to go

requires ahchat

ave resilient stdnts who

vericks (NBA) Must

alytical thinking?

o true. You nailed the

nd comparing them is

and instr = content


13/16


@stefras @ColinTGrahatopic, is mathematical? I am unsuFri Jun 10 00:55:13 +0000 2011 - tweet id 78

@LizDk#mathchat. I ambut it turned out to be very thoughFri Jun 10 00:55:17 +0000 2011 - tweet id 78

@ColinTGraham @Benstudents become more resilient aFri Jun 10 00:55:27 +0000 2011 - tweet id 78

@stefras @LizDk Bye. SFri Jun 10 00:55:46 +0000 2011 - tweet id 78

@ColinTGraham @LizDFri Jun 10 00:56:00 +0000 2011 - tweet id 78

@LizDk @dmarain #mathproblem.Fri Jun 10 00:56:05 +0000 2011 - tweet id 78

@stefras @ColinTGraha

thinking. #mathchatFri Jun 10 00:56:25 +0000 2011 - tweet id 78

@LizDk @ColinTGrahamFri Jun 10 00:56:37 +0000 2011 - tweet id 78

@Benwturner @ColinTGelsewhere. Maths is the best vehiFri Jun 10 00:56:56 +0000 2011 - tweet id 78

@LizDk @stefras re MonMonday one. #mathchatFri Jun 10 00:57:10 +0000 2011 - tweet id 78

@ColinTGraham @stefrwhen you analyse something... it'Fri Jun 10 00:57:24 +0000 2011 - tweet id 78

@Benwturner @ColinTG

valued and recognised alongsideFri Jun 10 00:58:04 +0000 2011 - tweet id 78


DO you think the act of analyzing, rege of that. #mathchat

988555896111106 - #149

ff now too. Nice chat - Initially I thoughtt provoking. Thx.988569737302016 - #150

turner Or we have to structure methodold persistent in their approaches. #math

988612137529345 - #151

e you MOnday? #mathchat988694635290624 - #152

Bye Liz, thanks for joining us! #mathch988750646030336 - #153

chat re content coverage. I agree totally

988774062825472 - #154

Yes, we have to structure how we teac

988854937395200 - #155

Thanks. :) #mathchat988906829320192 - #156

raham Some examples of maths thinkinle to dvlp these as it IS this thnkng #ma

988987653558273 - #157

ay. Unlikely - it is middle of night in Jap

989046709370880 - #158

s If you get meta-cognitive and think ababout comparison, at 1st #mathchat

989103697367040 - #159

raham of course these are learnable qua

ontent skills... #mathchat989272878821376 - #160


rdless of subject and

e were going nowhere

gy towards helpinghat

t

- that is the crux of the

h to emphasize deep

can be foundhchat

n when you do the

ut what you are doing

lities and should be


14/16


@ColinTGraham @stefrmaybe, deciding why differencesFri Jun 10 00:58:44 +0000 2011 - tweet id 78

@ekendriss#mathchat Duses every opportunity 2 make stFri Jun 10 00:58:53 +0000 2011 - tweet id 78

@stefras @ColinTGrahadefinition of science. How does thFri Jun 10 00:59:38 +0000 2011 - tweet id 78

@ColinTGraham @ekenmathematics... if it is done properl

Fri Jun 10 01:00:17 +0000 2011 - tweet id 78

@stefras @ColinTGrahagaps within it. This opens doors fFri Jun 10 01:00:56 +0000 2011 - tweet id 78

@ekendriss#mathchat hPolitics teacher one day about INFri Jun 10 01:00:56 +0000 2011 - tweet id 78

@Benwturner @ColinTGtraits including slf dscipline are thFri Jun 10 01:01:03 +0000 2011 - tweet id 78

@ColinTGraham @stefrI see it, anyway, so fundamentallyFri Jun 10 01:01:36 +0000 2011 - tweet id 78

@ekendriss#mathchat o

photography, perspective. only wFri Jun 10 01:01:58 +0000 2011 - tweet id 78

@stefras @ColinTGrahaScience generally uses hypothesiFri Jun 10 01:02:54 +0000 2011 - tweet id 78

@ColinTGraham @ekenfairly new concept, how/why doesFri Jun 10 01:03:10 +0000 2011 - tweet id 78

@stefras RT @ekendrisssimilar to one in photography, per


s Noticing whether something is the sare there... mathematics #mathchat

989439208132608 - #161

on't think mathematics unique. We havedents think deeply. Admire her.989477468573696 - #162

I agree with that definition of mathemaat fit into posing? #mathchat989664345796608 - #163

riss Again, the claim is that these skillsy. Use is universal... #mathchat

989827583913984 - #164

I think before one can pose a problemr questions. #mathchat989991937716225 - #165

ad fab discussion w/Sp teacher and HuERENCE. We could form a panel,3 of u

989990947856385 - #166

raham it is becoming increasingly moreaccelerators of learning #mathchat

990022275121152 - #167

s Science is probably an outgrowth of thmathematical! #mathchat

990160095748096 - #168

ne of the hardest concepts for my studen

are looking at data.990251548344320 - #169

I think science is a branch of math. Maschema / induction. #mathchat

990485993164800 - #170

riss The whole idea of a "grammar of vicomposition work in art... #mathchat

990556558147584 - #171

: #mathchat one of the hardest conceptspective. We are looking at data.


e or different and then,

a Spanish teacher--

ics. It is also the

re *developed* in

must see a pattern and

eography/Gov't &s!

pparent that these

e Socratic method... as

ts is similar to one in

th uses more schema.

ualisation" is also a

for my students is


15/16


Fri Jun 10 01:03:19 +0000 2011 - tweet id 78

@Benwturner @ColinTGand concepts should be using apFri Jun 10 01:03:21 +0000 2011 - tweet id 78

@stefras @Benwturner SFri Jun 10 01:04:06 +0000 2011 - tweet id 78

@ColinTGraham OK, westart! Thanks for your contributionFri Jun 10 01:04:57 +0000 2011 - tweet id 78

@stefras @ColinTGraharecognition. So there is a link betFri Jun 10 01:05:14 +0000 2011 - tweet id 78

@stefras @ColinTGrahafashion. Yeah! #mathchatFri Jun 10 01:05:59 +0000 2011 - tweet id 78

@ColinTGraham @stefrfor #RSCON3 in July! ;-) #mathchFri Jun 10 01:06:09 +0000 2011 - tweet id 78

@rowiematti RT @repubtogether a kaleidoscope of techniFri Jun 10 01:06:15 +0000 2011 - tweet id 78

@Benwturner @ColinTGFri Jun 10 01:06:23 +0000 2011 - tweet id 78


@k8nowak @dmarain Socover too much content, we don'tFri Jun 10 01:06:48 +0000 2011 - tweet id 78

@stefras @Benwturner BFri Jun 10 01:06:56 +0000 2011 - tweet id 78

@ColinTGraham @BenFri Jun 10 01:07:16 +0000 2011 - tweet id 78

@ColinTGraham @stefrFri Jun 10 01:08:11 +0000 2011 - tweet id 78


990592285212672 - #172

raham and I agree, the way we guide sturoaches that develop them.. #mathchat

990602548674560 - #173

O model deep thinking and problem solv990788306010112 - #174

are out of time, just when we're gettings everyone. #mathchat991005692608512 - #175

"grammar of visualization" is pattern aeen math, science and art. #mathchat

991073858420737 - #176

This was a good chat. I kept up and co

991261696147457 - #177

s Yep, totally agree! That's the main focat991304608067584 - #178

licofmath: Mathematics is like aikido, Praues. #mathchat

991330914742272 - #179

raham Class arriving got to go #mathcha991365912010752 - #180

I agree it was too short. It always see991375726686208 - #181

long as these punishing state (next: cohave much of a choice. #mathchat991470966751232 - #182

ye. #mathchat991502734393344 - #183

turner Bye Ben, glad you could join us!991587333517312 - #184

s Time flies when you're having fun, Sh991819165274112 - #185


dents through ideas

ing? #mathchat

oing -- after a shaky

d pattern gap

ntributed in a timely

s of my presentation

ctice basics. String

t

s so ... :-( #mathchat

mon core) exams

mathchat

wn! #mathchat


16/16


@stefras @ColinTGrahaOther subjects do the same thingFri Jun 10 01:09:00 +0000 2011 - tweet id 78

@stefras ;-) RT @ColinTShawn!#mathchatFri Jun 10 01:09:11 +0000 2011 - tweet id 78


@ColinTGraham @stefrFri Jun 10 01:10:42 +0000 2011 - tweet id 78

@stefras Just finished aif we teach deep thinking. ContinuFri Jun 10 01:15:10 +0000 2011 - tweet id 78


I think math develops deeper thinkingtheir way. #mathchat992023557902336 - #186

raham: @stefras Time flies when you'r

992069145792512 - #187

Have a good day. See you Monday. #992337870655488 - #188

s You too! #mathchat992450093449216 - #189

reat #mathchat. Getting down to what mes on Monday!993572728274945 - #190


kills mathematically.

having fun,

athchat

ath really is and asking

Documents

2011.06.10 is Mathematics Unique in the Wider Curriculum for the Deeper Thinking Skills It Develops