T o wa rds a sha re d fra me wo rk? A. Ga rdine r (E . Orr, C. - - PowerPoint PPT Presentation

T

• wa rds a sha re d fra me wo rk?
• A. Ga rdine r

(E . Orr, C. Nyle )

T he F ra me wo rk

(Ca mb ridg e Ma the ma tic s q uo te , my a dditio n in ita lic s)

Wha t it is

“a cohe r e nt and fle xible pre se nta tio n o f the ma the ma tic s with whic h stude nts a g e d 5 to 19 c o uld b e r e asonably e xpe cte d to e ng a g e ”

Wha t it do e s

• Ma ps do ma in kno wle dg e
• Org a nise s pro g re ssio ns in c o nc e pts a nd skills
• Pro vide s a nc ho rs fo r linking do ma in kno wle dg e

to imple me nta tio n”

Mathe matic s e duc atio n vs Me dic ine

• Primitive : he rb s; e xpe rie nc e / tra ditio n; ma g ic / Go d
• Pse udo -sc ie nc e : ‘mo de ls’, but no me tho d/

c he c k

• Gre e k/

Re naissanc e : “Go lo o k/ think fo r yo urse lf” (H ippo c rate s; Gale n; Ve salius, H arve y, …)

• Prac titio ne rs (barbe r-surge o ns) vs ‘pro fe ssio nals’
• T
• war

ds a Sc ientific Method (E

dwa rd Je nne r, Jo hn Sno w, F lo re nc e Nig hting a le , L

• uis Pa ste ur,…)
• “Mo de rn me dic ine ”

“Who se c urric ulum is it a nywa y? ” Who g a ins?

T he q ue stio n:

• de nie s a b so lute s: “e le my ma ths = inde p o f c ulture ”
• re je c ts the o nly pa th to g ra dua l impro ve me nt (thro ug h re spe c ting ,

re fle c ting o n, le a rning fro m, a nd impro ving o n pa st e xpe rie nc e )

Co nve nie nt fo r a dvo c a ting o ne ’ s pre fe rre d ‘ mo de l’

• first to insist o n the rig ht to one ’s own pla c e in the sun
• the n to re -de fine one se lf to b e the “Go o d Guy”, a nd e ve ryo ne e lse

to b e (mo re -o r-le ss) “Ba ddie s” (o f diffe re nt a lle g e d pe rsua sio ns)

T he Ma g ic a l M*ste ry T

• ur …

I s c o ming to ta ke yo u a wa y … T he y’ ve g o t e ve rything yo u ne e d … Sa tisfa c tio n g ua ra nte e d.

Choose: t***s; o r t***s; o r T ***S (+ …);

• Na tio na l Curric ulum use s the F
• wo rd (x24; M-wo rd x0):

re se nte d b y so me a s to o spe c ific / na rro w

• Sing a po re / Sha ng ha i/ … fo c us a tte ntio n o n long-te r

m te ac hing; b ut “M******” ne ve r c la rifie d

• Re -inte rpre te d a s so me thing le ss spe c ific  slo g a n
• Ge ts c o nfuse d with a n a ma lg a m o f:

(a ) a die t o f “ric h” t***s (disjo inte d, non-c umulative) (b ) “Big I de a s” (a ppe a ling to ma ny, b ut no me aning) (c ) sha llo w b e ha vio urist b ra inwa shing + t***s (Skinne r, Blo o m: dic e / te st/ re wa rd = “tic k o ff sub le ve ls”. Doe sn’t wor

k)

L

• o k fo r a n a lte rna tive to : Big -e nde rs a nd

L ittle -e nde rs, Co wb o ys a nd I ndia ns, “Us” a nd “T he m”

• Re je c t c rude dic ho to mie s (pro g re ssive -c o nse rva tive , e tc ),

g ro te sq ue c a ric a ture s, a nd ha lf-b a ke d slo g a ns

• Re c o g nise : e ffe c tive syste ms b uild o n c onsensus + a na lysis

T he n lo o k to se e

• to wha t e xte nt e le me ntar

y maths ma ke s c o nse nsus e asy;

• a nd whe re the re is g e nuine sc o pe fo r disa g re e me nt.

T he n

• ide ntify the e ffe c tive a lte rna tive s; e xplo re ; ma ke c ho ic e s

T

• wa rds a n a lte rna tive ?
• Ca nno t pre -e mpt the pa th to c o nse nsus; so b e te nta tive
• L

a y a side pe rso na l pre fe re nc e s; fo c us o n the

goal = inde pe nde nt yo ung a dults within so c ie ty

• Be pra g ma tic : disting uish a small numbe r o f pa thwa ys
• sha re d up to a po int, the n dive rg ing (to re fle c t g o a ls)
• My re a ding o f the e vide nc e (first thre e pha se s):
• E

Y: physic a l, so c ia l a nd ling uistic pre pa ra tio n fo r K

S1

• KS1/ 2: la ng ua g e , se e ing / do ing / dra wing / ma king ,

numb e r / me a sure me nts – fro m Co nc re te to Abstr

ac t

• KS3A/ B: (A: c o nso lida ting K

S1/ 2 a nd le a ding to “Voc ”

B: b uilding o n K

S1/ 2 to GCSE +)

T

• wa rds a c o nse nsus: De ta ils  unive rsa l T

***S?

• Conc r

e te -Abstr ac t: So rt o ut why KS1/ 2 “Abs” is “fo r all”

• Voc ational/ Ac ade mic : pre pa re all fo r c hoic e (a t 13-15? )
• E

Y: T

ry to a g re e g o a ls; pro s/ c o ns o f “fo rma l wo rk”

• KS1/ 2: T

ry to a g re e o n “to g e the r” vs “g ro up/ individua l” (“to g e the r/ g ro up”  c la ss-te a c hing + inte rve ntio n; “individua l”  le ss c la ss-te a c hing + o ut o f pha se )

• Po stpo ne de ta ils o f “la ng ua g e , do ing / dra wing / ma king ”

until e ndpo ints a g re e d fo r K S1/ 2

• “Numb e r/ me a sure me nt”: So rt o ut e sse ntia l ing re die nts

+ e ndpo ints, a nd ho w the se a re effec tively ta ug ht to all

• KS3A/ B:

A – o ur e xpe rie nc e is limite d (le a rn fro m o the rs); B – fa irly c le a r (ne g s, fra c s, pro pn, a lg , func , g e o m? , pro b / sta ts)

Ca mb ridg e Ma the ma tic s 1 Hills Ro a d, Ca mb ridg e Unite d K ing do m CB1 2E U

c a mb ridg e ma ths.o rg info @ c a mb ridg e ma ths.o rg @ Ca mb ridg e Ma ths L inke dIn