2011.06.13 is Mathematics Unique in the Curriculum for the Deeper Thinking Skills It Develops? (follow-up discussion)

8/6/2019 2011.06.13 is Mathematics Unique in the Curriculum for the Deeper Thinking Skills It Develops? (follow-up discussion)

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Monday, 13th June 2011Is mathemati

@mathfour Guess who'sMon Jun 13 19:32:00 +0000 2011 - tweet id

@ColinTGraham Hello eMon Jun 13 19:32:07 +0000 2011 - tweet id

@ColinTGraham @mathMon Jun 13 19:32:21 +0000 2011 - tweet id

@mathfour My fav part oMon Jun 13 19:32:58 +0000 2011 - tweet id

@mathfour I'm having to#mathchat Mon Jun 13 19:33:28 +0000 2011 - tweet id

@ColinTGraham For firstinteract with one or two people. DMon Jun 13 19:33:32 +0000 2011 - tweet id

@ColinTGraham Today'sdeeper thinking skills it develops?Mon Jun 13 19:34:16 +0000 2011 - tweet id

@ColinTGraham We gotreally say what we thought deepeMon Jun 13 19:36:19 +0000 2011 - tweet id

@Janshs RT @ColinTGrcurriculum for the deeper thinkingMon Jun 13 19:36:39 +0000 2011 - tweet id

@Janshs great #mathchinvolved???Mon Jun 13 19:37:14 +0000 2011 - tweet id

@MrHonner I wasn't ther"This is somewhat offensive to noMon Jun 13 19:37:33 +0000 2011 - tweet id

@mathfour So can you cllast before that, etc.)? #mathchat Mon Jun 13 19:37:51 +0000 2011 - tweet id

@Sundayteatime #mathc

s unique in the curriculum for the deeper thinki

here... :D #mathchat 0356764226289665 - #1

eryone and welcome to today's #mathc0356794454654977 - #2

our Hi Bon! #mathchat 0356851769810944 - #3

any #mathchat - the confusing topic #m0357006636093440 - #4

construct corporate training while I chat,

0357133828358144 - #5

-timers, don't try to follow everything, itn't forget ---> #mathchat

0357152153276416 - #6

topic is: "Is mathematics unique in the" #mathchat 0357336635543552 - #7

'hung up' last time on 'defending other sthinking skills were #mathchat

0357852358787072 - #8

ham: Today's topic is: "Is mathematicsskills it develops?" #mathchat 0357934630060032 - #9

t q from @ColinTGraham might get som0358080705077249 - #10

last time, but my first impression of thisn-math teachers" #mathchat 0358163265753088 - #11

arify the question, since I missed last tim

0358237370712064 - #12

hat yes maths rules ;-)

ing skills it develops? (follow-up)

at

athchat

so y'all bear with me.

oves fast at times! Just

ider curriculum for the

bjects'... and didn't

nique in the wider

e non-Maths teachers

topic was definitely

e (and the last and the


2/17


Mon Jun 13 19:38:01 +0000 2011 - tweet id

@ColinTGraham @MrHodocument Patrick! Management aMon Jun 13 19:38:26 +0000 2011 - tweet id

@mathfour @MrHonnerof thinking than other subjects...?Mon Jun 13 19:38:46 +0000 2011 - tweet id

@jmclean77 My first thoudeveloping deeper thinking skillsMon Jun 13 19:38:47 +0000 2011 - tweet id

@Janshs I think that soci

#mathchat - but are they taught eMon Jun 13 19:39:39 +0000 2011 - tweet id

@ColinTGraham The gethat they can be developed in conMon Jun 13 19:39:39 +0000 2011 - tweet id

@mathfour I think that siin creating deeper thinking skills.Mon Jun 13 19:39:56 +0000 2011 - tweet id

@suburbanlion Dig deepshould not be limited to math clasMon Jun 13 19:40:38 +0000 2011 - tweet id

@jmclean77 When it comstudents ask what they are lookinMon Jun 13 19:40:57 +0000 2011 - tweet id

@mathfour I think math slogical thinking really blossom. #Mon Jun 13 19:40:58 +0000 2011 - tweet id

@ColinTGraham Howevdeeper levels the farther you go/nMon Jun 13 19:41:11 +0000 2011 - tweet id

@MrHonner @mathfourtruth, as opposed to empirical trutMon Jun 13 19:41:15 +0000 2011 - tweet id


0358280525918208 - #13

nner Well I just put out the questions asccepts no responsibility... #mathchat 0358384800514048 - #14

h! Now I get it! Is math unique in that it#mathchat 0358466811731969 - #15

ght is "No", are we maybe asking "is Matnd why?" #mathchat 0358473099001857 - #16

logy & social sciences must surely look

rly enough for most folks?0358689286004738 - #17

eral feeling was that all subjects have dtext, so "no", but... #mathchat 0358690871455744 - #18

ce math is often taught as algorithms, thmathchat 0358761117650944 - #19

enough in any subject & you'll find math. #mathchat

0358938012434433 - #20

es to inquiry, the work of @ddmeyer is efor and how to get there #mathchat

0359016936652800 - #22

hould be taught within every other subjeathchat 0359021718151169 - #23

r, my view was that maybe mathematicseed to go #mathchat 0359074931294209 - #24

hat's what I was thinking--it requires de#mathchat

0359093772099585 - #25


asked on the discussion

reates a different type

h effective at

at deep thinking?

eper thinking skills and

en it is LESS effective

, but "digging deeper"

ffective at having

t. Then we could let the

*requires* thinking at

p thinking about logical


3/17


@mathfour Yepper! RT#mathchat Mon Jun 13 19:41:24 +0000 2011 - tweet id

@ColinTGraham @jmcleprovides more opportunity for devMon Jun 13 19:42:05 +0000 2011 - tweet id

@MrHonner @ColinTGrageneral, depth is a function of teaMon Jun 13 19:43:26 +0000 2011 - tweet id

@jmclean77 @ColinTGrmotivating students to ask questioMon Jun 13 19:43:26 +0000 2011 - tweet id

@ColinTGraham @subuthough. #mathchat Mon Jun 13 19:43:32 +0000 2011 - tweet id

@MrHonner @jmclean77really, if "taught properly". #mathcMon Jun 13 19:44:20 +0000 2011 - tweet id

@mathfour @jmclean77for that type of thing when I was aMon Jun 13 19:44:20 +0000 2011 - tweet id

@ColinTGraham @jmclemusic lessons as being deeper thiMon Jun 13 19:45:04 +0000 2011 - tweet id

@jmclean77 Inquiry, critihelp students learn? #mathchat Mon Jun 13 19:45:18 +0000 2011 - tweet id

@mathfour @jmclean77method works for everyone. @KhMon Jun 13 19:45:23 +0000 2011 - tweet id

@jmclean77 @mathfour I#mathchat Mon Jun 13 19:45:38 +0000 2011 - tweet id

@jmclean77 @mathfour I#mathchat


suburbanlion: Dig deep enough in any

0359130375794689 - #26

an77 That was a general feeling, last timeloping deeper thinking... #mathchat 0359301897662464 - #27

ham I think math requires a unique kindher and student. #mathchat 0359643980890112 - #28

ham if presented properly, math takes ons and guide their learning #mathchat 0359642508689409 - #29

banlion Digging deeper is not necessaril

0359670010748928 - #30

@ColinTGraham But the same can behat 0359868137078784 - #32

That's only if they are intrigued in that wkid. #mathchat 0359869386993664 - #33

an77 Many mentioned the analysis requinking... #mathchat 0360054657785856 - #34

al thinking, analysis what other deep thi

0360111809380352 - #35

But proper presentation depends on thenAcademy or @dydan #mathchat

0360135377158145 - #36

would have agreed with you but @ddm

0360197201215489 - #37

would have agreed with you but @ddm


ubject & youll find math

e, maybe mathematics

of deep thinking, but in

catalytic role in

y deeper thinking,

aid of most subjects,

y. I wouldn't have gone

red in, say, literature or

king skills does math

hild/learner. Not every

yer changed my mind

yer changed my mind


4/17


Mon Jun 13 19:45:38 +0000 2011 - tweet id

@mathfour @jmclean77Mon Jun 13 19:46:28 +0000 2011 - tweet id

@ColinTGraham @mathAppropriate or proper to whom orMon Jun 13 19:46:43 +0000 2011 - tweet id

@jmclean77 @ColinTGrcreates curiosity #mathchat Mon Jun 13 19:47:16 +0000 2011 - tweet id

@MrHonner @ColinTGrathe same "deep thinking" in studeMon Jun 13 19:47:45 +0000 2011 - tweet id

@mathfour @ColinTGraworld (some don't - I didn't) then...Mon Jun 13 19:48:16 +0000 2011 - tweet id

@ColinTGraham @jmcle"Inquiry, critical thinking, analysis"Mon Jun 13 19:48:16 +0000 2011 - tweet id

@mathfour @ColinTGraeveryone will take the experimentMon Jun 13 19:48:57 +0000 2011 - tweet id

@ColinTGraham @MrHoexperience to a past one? What iMon Jun 13 19:49:30 +0000 2011 - tweet id

@Janshs are we talking '

deal w/ abstract concepts for thosMon Jun 13 19:49:54 +0000 2011 - tweet id

@mathfour @jmclean77on S, not method or teacher. #maMon Jun 13 19:50:07 +0000 2011 - tweet id

@MrHonner @ColinTGratrying to understand your role in tMon Jun 13 19:50:50 +0000 2011 - tweet id

@ColinTGraham @Jansload when starting any discussion


0360197201215489 - #38

Metaphysical thinking, too. #mathchat 0360405934931968 - #39

our @jmclean77 What do you mean byto what? #mathchat 0360468266483712 - #40

ham by proper I meant in a way that eng

0360606179409920 - #41

ham Profound understanding of art (literts, I believe. #mathchat

0360727000514561 - #42

am @jmclean77 Exactly my point. If a S#mathchat

0360858831687680 - #43

an77 What other deep thinking skills wo... is that not enough #mathchat 0360861104996352 - #44

am @jmclean77 ...then math for math'sroute. #mathchat 0361029602783234 - #45

nner Do you mean reflection here, Patricprofound understanding, exactly? #mat

0361169990332417 - #46

igher order thinking skills'? #mathchat d

e? wd eg algebra help?0361269789605888 - #47

@ColinTGraham Engaging and curiosityhchat 0361323262787584 - #48

ham Trying understand the rules (of writie process. #mathchat 0361507027820547 - #49

s Well I tend to look towards Bloom's taabout thinking... #mathchat


proper" in this context?

ages the learner and

ture, music) can create

doesn't care about the

ld you add to your list

sake might be best. Not

k? Relating a newchat

o you need to be able to

provoking is dependent

ng, of music, of art),

onomy and cognitive


5/17


Mon Jun 13 19:51:02 +0000 2011 - tweet id

@MrHonner @ColinTGraapply in #math , too. #mathchat Mon Jun 13 19:51:18 +0000 2011 - tweet id

@jmclean77 RT @mathfmthd or tchr. #mathchat Really!? IMon Jun 13 19:52:15 +0000 2011 - tweet id

@Janshs #mathchat @Cinto this?Mon Jun 13 19:52:34 +0000 2011 - tweet id

@teachdig I think deeper

#mathchat Mon Jun 13 19:52:51 +0000 2011 - tweet id

@ColinTGraham @mathinterest in some areas of mathemMon Jun 13 19:53:04 +0000 2011 - tweet id

@maxmathforum Seemsanalysis help a kid get better at crMon Jun 13 19:53:55 +0000 2011 - tweet id

@ColinTGraham @teachexample... then any analysis is deMon Jun 13 19:54:39 +0000 2011 - tweet id

@maxmathforum I'm nottransfers to a general good questiMon Jun 13 19:55:26 +0000 2011 - tweet id

@ColinTGraham @maxmathematics help with approachiMon Jun 13 19:55:39 +0000 2011 - tweet id

@Janshs #mathchat @mof skills is just transfer of knowledMon Jun 13 19:56:09 +0000 2011 - tweet id

@mathfour @jmclean77different for different people. #matMon Jun 13 19:56:21 +0000 2011 - tweet id


0361553525874688 - #50

ham Reflection, absolutely, but more tha

0361620982861824 - #51

ur: Engaging and curiosity provoking ism surprised & intrigued, elaborate?0361861077401603 - #52

linTGraham I'd agree - does the ability t

0361940605599744 - #53

Thinking comes when analyzing historic

0362010788888576 - #54

our @jmclean77 I know, for example, Itics, but will never really engage #math

0362066451513344 - #55

like transfer is a big question here. Doeitical quant analysis? #mathchat 0362280239366144 - #56

dig Yes, because analysis is 'higher' ineper than comprehension... #mathchat 0362464637747200 - #57

convinced being good at asking good qon skill, for example #mathchat 0362661866516480 - #58

athforum Or does developing rational ag qualitative analysis too? #mathchat 0362715520049152 - #59

axmathforum hmm you've made me thine sometimes ...

0362843995774977 - #60

hat is engaging and curious is kinda likhchat 0362891995385856 - #61


n that. And these all

ependent on S, not

o suspend belief come

l documents as well

ay have a passinghat

critical historical

loom's taxonomy, for

estions in math class

alysis techniques in

if what we call transfer

e what is humorous -


6/17


@mathfour @jmclean77see how equations can be messeMon Jun 13 19:57:06 +0000 2011 - tweet id

@ColinTGraham @max"What if..." That may be less acceMon Jun 13 19:57:14 +0000 2011 - tweet id

@jmclean77 @mathfourthe class and, in doing so, reachMon Jun 13 19:57:32 +0000 2011 - tweet id

@MrHonner @maxmathfof the matter immediately, that caMon Jun 13 19:58:03 +0000 2011 - tweet id

@mathfour @maxmathfoquestion asking thing. Help. #matMon Jun 13 19:58:13 +0000 2011 - tweet id

@jmclean77 @mathfour Iwith @ddmeyer, we can change hMon Jun 13 19:58:31 +0000 2011 - tweet id

@maxmathforum @matsolving? #mathchat Mon Jun 13 19:58:40 +0000 2011 - tweet id

@jmclean77 @mathfourwishful thinking but he had me coMon Jun 13 19:59:01 +0000 2011 - tweet id

@mathfour @jmclean77on his/her own curiosities. #mathcMon Jun 13 19:59:02 +0000 2011 - tweet id

@jmclean77 @mathfourmaybe fail) to predict what wouldMon Jun 13 19:59:56 +0000 2011 - tweet id

@ColinTGraham @Janstransferring cognitive process, ratMon Jun 13 20:00:08 +0000 2011 - tweet id

@Janshs @ColinTGrahaqual or quant might be proved #m


I hate problem solving. I'll do it. I'll teach iwith. #mathchat

0363080177025024 - #62

athforum A 'good' question (I prefer appptable in history than ...? #mathchat 0363117405679616 - #63

h very true, but the teacher still has to pome. Agree? #mathchat 0363189799358464 - #64

rum If you can ask a good q in math, onbe applied anywhere. #mathchat

0363319214608384 - #65

rum I totally don't get what you typed thechat

0363362147512320 - #66

agree with your point, but I found that wow we deliver lessons... #mathchat 0363438215401472 - #67

four @jmclean77 why isn't messing with

0363476828172288 - #68

nd find ways to engage learners regardlvinced #mathchat

0363562907865088 - #69

Yes - and the opportunity that the teachehat 0363569287409664 - #70

on't agree with you there, when I preparngage my stdnts not me #mathchat

0363795393953792 - #71

s @maxmathforum I tend to think deeper than 'skills'/knowledge #mathchat

0363843406143489 - #72

@maxmathforum if it's about developiathchat but .....


t. But I'd much rather

ropriate) in maths is

rovide the opportunity to

e that gets to the heart

re about the good

hen i spent that day

equations problem-

ess of the topic. Maybe

r presents will be based

e a lesson I try (and

r thinkers are actually

g a sound method then


7/17


Mon Jun 13 20:00:16 +0000 2011 - tweet id

@maxmathforum @matsuggesting that critical thinking skMon Jun 13 20:00:47 +0000 2011 - tweet id

@mathfour @jmclean77pants. The energy is contagious.Mon Jun 13 20:01:00 +0000 2011 - tweet id

@Janshs @ColinTGrahaas maths to develop logic, speculMon Jun 13 20:01:12 +0000 2011 - tweet id

@Janshs @ColinTGraha

as maths to develop logic, speculMon Jun 13 20:01:12 +0000 2011 - tweet id

@jmclean77 @mathfourMon Jun 13 20:01:38 +0000 2011 - tweet id

@mathfour @maxmathfosolving - especially when you takMon Jun 13 20:01:49 +0000 2011 - tweet id

@Janshs @ColinTGrahathat process? #mathchat Mon Jun 13 20:02:21 +0000 2011 - tweet id

@mathfour @maxmathfoeverything. #mathchat Mon Jun 13 20:02:26 +0000 2011 - tweet id

@ColinTGraham @max

required for thinking to be consideMon Jun 13 20:02:59 +0000 2011 - tweet id

@maxmathforum @mrhpersistence seems universal yet iMon Jun 13 20:03:09 +0000 2011 - tweet id

@ColinTGraham @maxproof is based on reasoned logicaMon Jun 13 20:03:44 +0000 2011 - tweet id

@mathfour @maxmathfoof ways. It is creating that place o


0363880852897792 - #73

four we're wondering if math teachers crills in math may not transfr #mathchat 0364010490429441 - #74

I gotta present what makes me so excitemathchat 0364064278196224 - #75

@maxmathforum ..... Do other subjecttion, reflection? #mathchat 0364111795453952 - #76

@maxmathforum ..... Do other subject

tion, reflection? #mathchat 0364111795453952 - #77

aha that is awesome, I get that. #mathc0364221023526912 - #78

rum @jmclean77 It is. Messing with equof the "right way" stigm #mathchat

0364268196872192 - #79

@maxmathforum how do you feel mat

0364403119239168 - #80

rum Critical thinking skills in math transf

0364426267602944 - #82

athforum @mathfour The transferable a

red "critical" in subjects... #mathchat 0364564549603328 - #83

nner hard to separate cognitive processpersist mathematically, don't musically #0364604001226752 - #84

athforum @mathfour For example, 'tradl deduction... anything else is 'demo' #m0364753268117504 - #85

rum You create new brain passages/rivetside the box. #mathchat


itical thinking. I'm

I'm gonna wet my

s help in the same way

s help in the same way

at

tions is very problem

hs curriculum helps with

r to

spect is maybe what is

from domainmathchat

itional' mathematicalthchat

rs by thinking in all sorts


8/17


Mon Jun 13 20:03:48 +0000 2011 - tweet id

@maxmathforum @matnot)Mon Jun 13 20:03:54 +0000 2011 - tweet id

@mathfour Once you thiyour brain so you can go out of thMon Jun 13 20:04:37 +0000 2011 - tweet id

@mathfour @maxmathfoMon Jun 13 20:05:06 +0000 2011 - tweet id

@ColinTGraham @maxhope!), music tends to emotionalMon Jun 13 20:05:16 +0000 2011 - tweet id

@Janshs @CafeRico jusyouMon Jun 13 20:05:54 +0000 2011 - tweet id

@MrHonner @maxmathfMon Jun 13 20:05:59 +0000 2011 - tweet id

@MrHonner @maxmathfMon Jun 13 20:05:59 +0000 2011 - tweet id

@ColinTGraham @maxvery analytic and mathematical inMon Jun 13 20:06:01 +0000 2011 - tweet id

@mathfour @maxmathfopathways for other things. And I tMon Jun 13 20:06:09 +0000 2011 - tweet id

@maxmathforum @matI'm saying math skills (like provingMon Jun 13 20:06:10 +0000 2011 - tweet id

@mathfour @jmclean77#mathc hat Mon Jun 13 20:07:08 +0000 2011 - tweet id

@maxmathforum #mathmath problems persistently. The sMon Jun 13 20:07:09 +0000 2011 - tweet id


0364768464084992 - #86

four prove it! #mathchat (can't decide if t

0364795370536962 - #87

k in ways you wouldn't normally think, ybox whenever #mathchat

0364973133545472 - #88

rum No irony here, all passion. #mathch0365094441193472 - #89

athforum @mrhonner With experiencexpression for performers #mathchat 0365138175213568 - #90

wondering if you have noticed #mathch

0365295537094656 - #91

rum I'm not sure what you are saying th0365316558946304 - #92

rum I'm not sure what you are saying th0365316558946304 - #93

athforum @mrhonner Musicology, thouappearance, though... #mathchat 0365327212494848 - #94

rum I teach math as if they'll never use itll them that. #mathchat 0365359688986624 - #95

four I meant my post was ironic. I want ystuff) don't transfer #mathchat

0365363128311808 - #96

Most of the time they think I'm nuts, but t

0365607568154624 - #97

hat I mean that I didn't learn how to perskill doesn't transfer to learning piano0365612391608320 - #98


his tweet is ironic or

u've made a path in

t

f both, at higher level (I

t might be of interest to

ere. #mathchat

ere. #mathchat

h, tends to become

- they only use the

ou to use proof and yet

hey still get excited.

ist from doing hard


9/17


@MrHonner @ColinTGraunderstanding the rules, whetherMon Jun 13 20:07:26 +0000 2011 - tweet id

@mathfour @maxmathfoday-job and do this too. #mathchMon Jun 13 20:07:38 +0000 2011 - tweet id

@ColinTGraham @maxfallacies in argument during a debMon Jun 13 20:07:38 +0000 2011 - tweet id

@jmclean77 @mathfour#mathchat Mon Jun 13 20:07:56 +0000 2011 - tweet id

@maxmathforum #mathbut I'm not convinced we becomeMon Jun 13 20:08:03 +0000 2011 - tweet id

@mathfour @MrHonner#mathchat Mon Jun 13 20:08:23 +0000 2011 - tweet id

@maxmathforum #mathcognitive skills across domainsMon Jun 13 20:08:26 +0000 2011 - tweet id

@NatBanting #mathchat math? #math #edchat #mathed Mon Jun 13 20:08:56 +0000 2011 - tweet id

@mathfour @jmclean77need your & @dydan's methods.Mon Jun 13 20:09:02 +0000 2011 - tweet id

@mathfour @ColinTGramath profs go off to law school asMon Jun 13 20:09:58 +0000 2011 - tweet id

@ColinTGraham @maxa 'deep' skill... evaluation/judgmeMon Jun 13 20:10:00 +0000 2011 - tweet id

@MrHonner @ColinTGra-play, find patterns, make rules, d


ham @maxmathforum Math and musicollowing them or breaking them. #mathc0365680729403392 - #100

rum Sorry - sarcaso-meter is down todat 0365732474519552 - #101

athforum @mathfour So being able to aate is not transferred maths skill? #math0365734307434496 - #102

ell with that motivation I can see why th

0365807028289536 - #103

hat I think we can teach kids how to tranmore logical thinkers by doing math0365836543590400 - #104

ColinTGraham @maxmathforum So is

0365920039612416 - #105

hat unless we are helped to reflect and

0365933901783042 - #106

I need your opinions. Do cheatsheets he

0366060875943937 - #107

nd still there are many I don't reach. Prmathchat

0366084028506112 - #108

am @maxmathforum Yes - debate is ma retirement project) #mathchat 0366321740681216 - #109

athforum I don't think being able to thint/justification...? #mathchat 0366327319105536 - #110

ham @maxmathforum Musical explorativiate, reflect, repeat #mathchat


re both fund. abouthat

. Trying to work the

nalyse the logicalhat

ey get so excited

sfer skills and concepts,

learning a language! :D

ee the relevance of

lp students in grade 11

bably because they

th. (The reason most

'logically' is necessarily

n is akin to math. expl.-


10/17


Mon Jun 13 20:10:31 +0000 2011 - tweet id

@mathfour @NatBantingwhat they have on them and howMon Jun 13 20:10:34 +0000 2011 - tweet id

@maxmathforum @Coliknwlg of what counts as rigor. r allMon Jun 13 20:10:38 +0000 2011 - tweet id

@mathfour @ColinTGragotta take from one place to anotMon Jun 13 20:11:07 +0000 2011 - tweet id

@ColinTGraham I think t

burden that was added in the reviMon Jun 13 20:12:22 +0000 2011 - tweet id

@maxmathforum #mathyou've been trained in logic couldMon Jun 13 20:12:48 +0000 2011 - tweet id

@Janshs @maxmathforuIMO #mathchat do ss receive morMon Jun 13 20:13:53 +0000 2011 - tweet id

@NatBanting @mathfourexamples. Basic. What are your tMon Jun 13 20:13:57 +0000 2011 - tweet id

@ColinTGraham @maxwhich relies on synthesis/evaluatiMon Jun 13 20:14:21 +0000 2011 - tweet id

@mathfour @ColinTGrawords, don'cha think!? #mathchat Mon Jun 13 20:14:36 +0000 2011 - tweet id

@Janshs @informed_ed(#mathchat )Mon Jun 13 20:15:13 +0000 2011 - tweet id

@mathfour @NatBantingMon Jun 13 20:15:16 +0000 2011 - tweet id

@ColinTGraham @mathKnowledge = low level, How do I


0366459963965440 - #111

Depends on all the other stuff around thyou're teaching... #mathchat 0366471976464384 - #112

TGraham @mathfour not sure. there's cmathematicians gd at it? #mathchat

0366486975299584 - #113

am @maxmathforum Depends on hower. #mathchat 0366610862440448 - #114

o many people also ignore the second

ion of Bloom's taxonomy #mathchat 0366922264358912 - #115

hat recognizing need for proof, and maytransfer... But making args is hard!0367033358876672 - #116

m reflection 1 of key attributes (avoidinge guidance in this in maths?0367307318247425 - #117

What "other Stuff" They could have ruleoughts? yes or no? #mathchat 0367320618369025 - #118

athforum That's because it is the creativn not just regurgitation #mathchat

0367421843709953 - #119

am second dimension of cognitive burd0367485865558016 - #120

or - does learning always come from a

0367639733612544 - #122

I always allow a "cheat sheet" in every s0367652865970176 - #123

our Yep! It's the meta-thinking you referrnow I know... meta-knowledge! #mathc


ose "cheat sheets" and

ntnt knwlg involved and

any logical steps you

imension of cognitive

be seeing bad logic if

skills or knowledge)

, formulas, and

e end of the scale...

n


11/17


12/17


Mon Jun 13 20:23:55 +0000 2011 - tweet id

@Janshs @ColinTGrahapenny dropped for me (was aboutMon Jun 13 20:24:42 +0000 2011 - tweet id

@ColinTGraham @inforterms of thinking is the "Doh!" moMon Jun 13 20:25:18 +0000 2011 - tweet id

@Janshs @informed_edAt appropriate time I'm the marginMon Jun 13 20:25:36 +0000 2011 - tweet id

@maxmathforum @Coli

writing? Or scientific method? #mMon Jun 13 20:26:04 +0000 2011 - tweet id

@Janshs @ColinTGrahaMon Jun 13 20:26:11 +0000 2011 - tweet id

@informed_edu @Colinnot jump in when they say "Doh!".Mon Jun 13 20:27:19 +0000 2011 - tweet id

@Janshs @maxmathforusimilar? #mathchat Mon Jun 13 20:27:38 +0000 2011 - tweet id

@ColinTGraham @maxcommunicating abstraction, so mMon Jun 13 20:27:49 +0000 2011 - tweet id

@ColinTGraham @max

metacognition... analysis is perceiMon Jun 13 20:28:54 +0000 2011 - tweet id

@delta_dc Agreed! >> Rthinking linguistics might be similaMon Jun 13 20:29:21 +0000 2011 - tweet id

@ColinTGraham @maxanalyse a symphony by BeethoveMon Jun 13 20:30:02 +0000 2011 - tweet id

@docdcc @ColinTGraharelates to metacognition. Math as


0369830829637633 - #137

@informed_edu always remember wh40 yo!) was about metacognition #math0370028779802624 - #138

ed_edu @Janshs Equally important, buent... the 'anti-' Aha! #mathchat

0370179195944961 - #139

@colintgraham yes! I sometimes get s#mathchat

0370254269779968 - #140

TGraham why best developed in maths

thchat 0370373727752192 - #141

:-) #mathchat 0370400432898048 - #142

Graham @Janshs It strains every teachSo hard! #mathchat 0370687423942656 - #143

m @colintgraham I cannot help thinking

0370765270228992 - #144

athforum Maths is about noticing and cybe 'best suited' to application #mathch0370812321927168 - #145

athforum I see it more as a purposeful

ved as being a part of mathematics. #m0371083630493696 - #146

@Janshs: @maxmathforum @colintgrr? #mathchat 0371198889951232 - #147

athforum The fact that Paul McCartneyn does not impede his musicianship or...0371370680266753 - #148

m @maxmathforum Back to Skemp. Matsubject typically does not. #mathchat


en my tutor said thehat

t often overlooked, in

to actually write aha!

why not reading &

rly bone in my body to

linguistics might be

mparing patterns,t

pplication of

thchat

ham I cannot help

ay not be able? #mathchat

hematics as discipline


13/17


Mon Jun 13 20:30:45 +0000 2011 - tweet id

@maxmathforum Numbourselves in. But science, anthro,Mon Jun 13 20:30:58 +0000 2011 - tweet id

@ColinTGraham So, oncsee as "deeper thinking"... any taMon Jun 13 20:31:11 +0000 2011 - tweet id

@ColinTGraham @docdin the way that mathematics is apMon Jun 13 20:32:27 +0000 2011 - tweet id

@ColinTGraham @infor

Gardner-like puzzles... finding theMon Jun 13 20:33:50 +0000 2011 - tweet id

@delta_dc @ColinTGrahand explain why? #Mathchat Mon Jun 13 20:33:55 +0000 2011 - tweet id

@maxmathforum @Colitaught. Y not make every subjectMon Jun 13 20:34:12 +0000 2011 - tweet id

@ColinTGraham @maxdo in getting thinking put onto schMon Jun 13 20:34:55 +0000 2011 - tweet id

@Janshs @ColinTGrahaengender that or does it help to dMon Jun 13 20:34:58 +0000 2011 - tweet id

@Janshs @delta_dc @mLinguistics? Other? #mathchat Mon Jun 13 20:35:48 +0000 2011 - tweet id

@informed_edu @Janshbetween training the builder and gMon Jun 13 20:36:14 +0000 2011 - tweet id

@Janshs @ColinTGraha#mathchat Mon Jun 13 20:36:40 +0000 2011 - tweet id


0371548854292481 - #149

rs are the other language besides languetc. are also ways to analyze #mathchat 0371604714029056 - #150

e again, we are successfully skirting aroers? #mathchat 0371657646161920 - #151

c @maxmathforum My feeling too... a troached and taught... #mathchat

0371976572649473 - #152

ed_edu @Janshs The "Doh!" is often a

'trick' or cognitive shortcut #mathchat 0372325815566336 - #153

am Would it help to consider people we t

0372347638513664 - #154

TGraham @docdcc a missed opportunitbout learning & metacognition? #mathc

0372417331077121 - #155

athforum @docdcc Part of what Edwarool curricula. #mathchat 0372600366313473 - #156

well is it simply learning to learn? #mavelop ppl who will be prone to?0372612231999488 - #157

axmathforum @colintgraham finding pat0372819212509184 - #158

s @ColinTGraham I guess it's about striiving him/her more bricks... #mathchat 0372929363312641 - #159

@informed_edu can you have a "doh-

0373038067093504 - #160


ge that we express

nd defining what we

tally missed opportunity

big part of Martin

hink of as deep thinkers

y in the way *school* isat

deBono was trying to

hchat & does maths

erns? Maths?

ing the balance

ha!" moment?!


14/17


@ColinTGraham @Jansdoes it make me a good driver? DMon Jun 13 20:36:44 +0000 2011 - tweet id

@Janshs @ColinTGrahalearning? Is that the deep skill? #Mon Jun 13 20:37:55 +0000 2011 - tweet id

@ColinTGraham @Janswhere you recognize something yMon Jun 13 20:38:01 +0000 2011 - tweet id

@maxmathforum #mathit's so miserable to be forced to dMon Jun 13 20:38:41 +0000 2011 - tweet id

@delta_dc Deep thinkerspossibilities, create something neMon Jun 13 20:38:44 +0000 2011 - tweet id

@informed_edu @ColinDoh! Hmmm... Aha! Doh!"... etc?Mon Jun 13 20:38:54 +0000 2011 - tweet id

@ColinTGraham Knowinobvious. Making decisions basedMon Jun 13 20:38:56 +0000 2011 - tweet id

@Janshs @informed_edMon Jun 13 20:40:45 +0000 2011 - tweet id

@informed_edu @kalinsstrategies-for-struggling-successfMon Jun 13 20:41:03 +0000 2011 - tweet id

@ColinTGraham @maxon thinking ... we do Ss a dis-servMon Jun 13 20:41:06 +0000 2011 - tweet id

@ColinTGraham @deltanoticing, etc. tied in with that too.Mon Jun 13 20:42:36 +0000 2011 - tweet id

@informed_edu Do we nquestions? Or do we just need toMon Jun 13 20:44:05 +0000 2011 - tweet id


s I don't think it's as easy as that... eg lio I continue learning? #mathchat 0373056001933312 - #161

absolutely! Yes! So how do we encourathchat 0373355945005056 - #163

s @informed_edu The doh-aha! is the iou should have known & 'forgot' #mathc0373379219202048 - #164

hat maybe what makes math so good fomath w/out being supportd to think

0373545795989505 - #165

are metacognitive, able to make connec... am I getting close? #Mathchat

0373558802513920 - #166

Graham @Janshs Is the perfect lessonmathchat :)

0373603236974592 - #167

when to stop, maybe? RT @cherraolthon critical thought & analysis? #mathcha0373609973035008 - #168

@colintgraham hehe I love it :-) #math0374066929868800 - #169

ki1970 Me too. I need to start teaching mlly, I think. #mathchat 0374140619599873 - #170

athforum As so much of mathematics aice if we don't support theirs #mathchat 0374154129448961 - #171

dc I think there is a lot of evaluation, judwareness of limits #Mathchat

0374534401818624 - #172

eed maths textbooks that are more thanuse them better? #mathchat 0374904213606402 - #174


ensed to drive a car...

age desire to keep on

eal... or the aha-doh!at

r learning 2 learn is that

tions, consider

"Aha! Doh! Hmm... Aha!

of: Not going with thet

hat

ore metacognition and

a discipline is based

gment, comparison,

lists of repetitive


15/17


@ColinTGraham How mthinking skills as more 'knowledgeMon Jun 13 20:44:32 +0000 2011 - tweet id

@mathfour Crumb - whatMon Jun 13 20:45:05 +0000 2011 - tweet id

@ColinTGraham @inforDoes it have a 'life' in its present fMon Jun 13 20:45:10 +0000 2011 - tweet id

@ColinTGraham @mathMon Jun 13 20:45:41 +0000 2011 - tweet id

@ColinTGraham @Jansacross everything... eg Paul McCMon Jun 13 20:46:54 +0000 2011 - tweet id

@earlsamuelson @Colintheory to "real world" applicationsMon Jun 13 20:47:38 +0000 2011 - tweet id

@ColinTGraham @earls

taxonomy) than just applying or uMon Jun 13 20:48:56 +0000 2011 - tweet id

@Janshs @ColinTGrahadisciplinary skill or develops ppl wMon Jun 13 20:50:47 +0000 2011 - tweet id

@ColinTGraham @Jansenough thinking about anything inMon Jun 13 20:52:07 +0000 2011 - tweet id

@ColinTGraham @Jansanalysis, comparison, evaluation,Mon Jun 13 20:52:53 +0000 2011 - tweet id

@ColinTGraham @JansShakespeare plays will necessarilMon Jun 13 20:54:44 +0000 2011 - tweet id

@ColinTGraham @Jansable to analyse characters in draMon Jun 13 20:55:43 +0000 2011 - tweet id


ch more important is it going to be to de /fact' appears online? #Mathchat

0375017950552064 - #175

'd I miss? #mathchat 0375159357308928 - #176

ed_edu Do we need to rethink what therm? #mathchat

0375180131704833 - #177

our The cheerleaders and the rodeo clo0375309018472448 - #178

s For me the deeper skill is expanding crtney is studying orchestration. #mathch0375614426722304 - #179

TGraham .....could deeper thinking invol#mathchat

0375799408107520 - #180

muelson Knowing when to apply is 'hig

derstanding or knowing... #mathchat 0376127658541056 - #181

so is it that maths enables us to encouho can? #mathchat 0376593985445888 - #183

s Ah, that is the question, Jan! For me, Iany subject.... #mathchat 0376927944310784 - #184

s What mathematics gives us is a platfoetc. "makes sense" #mathchat 0377119770812416 - #185

s For example, I'm not sure that analysiy 'improve' audience experience... #mat0377586294853633 - #186

s However, if I want to perform Shakesas *is* important #mathchat 0377831951044608 - #187


elop deeper (critical)

textbook is for, too?

n... ;-) #mathchat

ognitive awarenessat

e applying known

er' (in Bloom's

rage that cross

don't think we teach

rm where teaching

g characters inchat

eare, then maybe being


16/17


@informed_edu I wondestance through maths? #mathchaMon Jun 13 20:56:34 +0000 2011 - tweet id

@ColinTGraham @Jans'soundness' or validity is 'perfectlyMon Jun 13 20:56:51 +0000 2011 - tweet id

@earlsamuelson True Rtaxonomy) than just applying or uMon Jun 13 20:57:23 +0000 2011 - tweet id

@Janshs @ColinTGrahavideo & analyse choreo - I thoughMon Jun 13 20:57:55 +0000 2011 - tweet id

@ColinTGraham @inforto declare a (somewhat skewed)Mon Jun 13 20:58:12 +0000 2011 - tweet id

@Janshs @ColinTGrahathinking #mathchat Mon Jun 13 20:58:50 +0000 2011 - tweet id

@ColinTGraham @earlsbe more difficult for many than knMon Jun 13 20:59:06 +0000 2011 - tweet id

@Janshs RT @informedencourage a critical stance througMon Jun 13 20:59:19 +0000 2011 - tweet id

@Rolfster @informed_edsay I haven't used a textbook yeaMon Jun 13 20:59:23 +0000 2011 - tweet id

@ColinTGraham @Jansproduction, then you need to devMon Jun 13 21:00:06 +0000 2011 - tweet id

@Janshs @informed_edmost creative aspects of mathsMon Jun 13 21:00:15 +0000 2011 - tweet id

@Janshs @informed_edmost creative aspects of maths


if a greater emphasis on stats wouldn't

0378045554372609 - #188

s Whereas, analysing the steps in a manatural' [purposeful] #mathchat 0378117243416577 - #189

@ColinTGraham Knowing when to apderstanding or knowing... #mathchat 0378253503770624 - #190

interesting; in a dance cover lesson toI did rather well :) #mathchat

0378388400967680 - #191

ed_edu Ah, now, as a statistician, I supias in favour of that! #mathchat 0378456415809536 - #192

back to research skill perhaps then (q

0378616457867264 - #193

muelson The same is true of knowing "wing "when" #mathchat

0378684363653120 - #194

edu: I wonder if a greater emphasis onh maths? #mathchat 0378739480985600 - #195

u I'm an Assistant Head and Head of ms. #mathchat 0378757831073793 - #196geo info: Point - lat = 51.4

s If you want to preserve performing artlop notations (symbols) #mathchat 0378938303586305 - #197

interesting q #mathchat I sometimes thi

0378972935954432 - #198

interesting q #mathchat I sometimes thi


elp encourage a critical

hematical proof for

ly is 'higher' (in Bloom's

ay we had to watch

ose, at heart... I have

al or quant) .... Hmmm

hat to apply" and may

tats wouldn't help

ths and I can honestly

201013 - long = -0.1946497

or pass on a particular

nk probability is 1 of

nk probability is 1 of


17/17

Monday 13th June 2011Is mathemati

Mon Jun 13 21:00:15 +0000 2011 - tweet id

@ColinTGraham @JansMon Jun 13 21:00:56 +0000 2011 - tweet id

@Janshs @ColinTGrahaMon Jun 13 21:02:29 +0000 2011 - tweet id

@earlsamuelson cont)#mathchat Mon Jun 13 21:02:44 +0000 2011 - tweet id

@earlsamuelson #mathc@ColinTGraham The same is truMon Jun 13 21:02:45 +0000 2011 - tweet id

@ColinTGraham OK peomaking us think! ;-) Vote for next tMon Jun 13 21:02:57 +0000 2011 - tweet id

@ColinTGraham Watchbrush up on thinking, I'm one of thMon Jun 13 21:03:59 +0000 2011 - tweet id

@mathfour I agree. RTanything in any subject.... #mathcMon Jun 13 21:04:26 +0000 2011 - tweet id

@Janshs RT @ColinTGrThank you all for making us think!Mon Jun 13 21:05:53 +0000 2011 - tweet id

@mathfour @ColinTGragoing to present on August 3. #mMon Jun 13 21:06:33 +0000 2011 - tweet id

@mathfour @ColinTGraMon Jun 13 21:06:55 +0000 2011 - tweet id

@informed_edu I crashemore regular participant. ThanksMon Jun 13 21:07:16 +0000 2011 - tweet id

@ColinTGraham @inforMondays... ;-)Mon Jun 13 21:08:01 +0000 2011 - tweet id


0378972935954432 - #199

s @informed_edu With a 99.9% certain0379145372172288 - #200

hehe it's about trust and belief though0379536956592128 - #201

and may be more difficult for many than

0379598537375744 - #202

hat Project scenarios are helpful with thiof knowing "what to apply" (cont

0379605260840961 - #203

ple, that's it for another #mathchat (probopic here: http://bit.ly/e72g8r 0379652425793536 - #204

ut for #TMThink on Wednesday: http://be presenters! #Mathchat 0379912661377024 - #205

ColinTGraham: I dont think we teach enat 0380025735610370 - #206

ham: OK people, that's it for another #;-) Vote for next topic here ...0380392821104640 - #207

am Oooo! Can I plug @MariaDroujkova'thchat 0380560110919680 - #208

am Thanks for hosting! #mathchat 0380650988908544 - #209

the end of a very interesting #mathchaveryone0380739690037248 - #210

ed_edu Thanks for joining us Dave. #m0380927158665216 - #211

ing skills it develops? (follow up)

y? ;-P #mathchat

isn't it? ;-) #mathchat

knowing "when"

.....to some extent RT

bly) Thank you all for

it.ly/gKl6ih if you want to

ough thinking about

athchat (probably)

s MathFuture? I'm

. I shall try and be a

thchat it's not just for

Documents

2011.06.13 is Mathematics Unique in the Curriculum for the Deeper Thinking Skills It Develops? (follow-up discussion)