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

T o 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’ • ds a Sc ientific Method (E dwa rd Je nne r, T owar • Jo hn Sno w, F lo re nc e Nig hting a le , L o uis Pa ste ur,…) “Mo de rn me dic ine ” •

“Who se c urric ulum is it a nywa y? ” T he q ue stio n: de nie s a b so lute s: “e le m y 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) Who g a ins?

T he Ma g ic a l M*ste ry T o 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 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 o 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 +)

o wa rds a c o nse nsus: De ta ils  unive rsa l T T ***S? ac t: So rt o ut why KS1/ 2 “ Abs ” is “fo r all ” Conc r e te -Abstr • Voc ational/ Ac ade mic : pre pa re all fo r c hoic e (a t 13-15? ) • Y : T ry to a g re e g o a ls; pro s/ c o ns o f “fo rma l wo rk” E • 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 info @ c a mb ridg e ma ths.o rg @ Ca mb ridg e Ma ths L inke dIn c a mb ridg e ma ths.o rg