On the Shoulders of Giants New Approaches to Numeracy (1990) / Chapter Skim
Currently Skimming:
Uncertainty
Uncertainty
Pages 95-138
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From page 95... ...
Su~o as Or cumculum :~ detached mom that cx~e o~r Sepias hopes ~~t are d:~w Ceil in By ~~Sti05 :O t50 $~5 iS ~Ot UtOpl8~, ~~W Cal presentIv being tested 1s p=~.~y used:! and alds mther ~~n did 6~t O ~~Ct CO~tS =6 S~.
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From page 96... ...
E~s a~ concemed mth data on prompt pe - ~~:~, qu~, and reli~:~:~* Man:ufa=~g wo ~ sked to ~~ and a~ on ~~ ~r ~~ss mntr~+ The :~=lth sciences ~e w:~h da~ on co~ and c~:~s as -~11 as m~ -Gus mom median!
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From page 97... ...
{n ~e ~~ =~57 ~3 - = ~t ~0 - ~8 (~ ~ 80~ ~ be used, ~~=tLen~ hardy arm, -such ~a ~0~ : ~:—~ :~- In the bower ~7 data p~ ~ t56 ~5 t56~ ~ ~~ ~ p~0 ~~ ) ~ =~ ~~$ =~ 85 g~ ~e cl=s ("Dow Hey chlldren I:~ tn wU: house9~)
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From page 98... ...
The :~ of data analysis ow: Army probability awl index= is an impotent pn.~:~e for instmetio:n in unce~ai.~^ Artificial chance devices (=ins, dices sp:~) c~ be used to pro duce data in the cIassroo-m w:~h the i:~:*
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From page 99... ...
=~e wlm hare ln ~a ls ~ n=t n~ toward I: t~e conne~n Between S~6cS =6 pro6~li~+ ^M ~ leer see ~e mic ~ rieiitem:te ~oln~z~ion In Swish Resee ~ pro hers ~~s =~. Finally, ~~ scow Ice Us= e Car and flacks of p~babd~W to express the c=~= we =n b^e ~ -=nciu~s Own ~ ~a.
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From page 101... ...
e on other =~s O pTO6~= Sobering rig 8O ~C =~' Int0~CtiH~ the results :n their cont=~' and asking new mathematics questions s gested W~ an exe~. But it is elm tme that automated cal=~on can hide the natu~ of the work that is camed out and impede ~t ~t - ~r the wok ~s appropnate to this cite probing.
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From page 102... ...
At ~ more advanced I - ~~: some :his~gra3~s sh~d ~ maw by h=d w fuming ~ att:~lw software that chooses ~~ps and ~~ws hip di.~V - m ~e ~ ~~. Pe~s most imp eX=~ce mth Hi ciLan-ce devices and phylum simul^~ns such as braving colored b~s few ~ ~x show p=~ com - ~r s~-.
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From page 103... ...
adv~ ce to: ~ ~~y of random Elation in ~:~al summaries (~ch as the mean- of s obSe - ~tio:~- Bulb ~~sice:l random =~tion and sim.~.~icn =n O~ the other ha~d, Army statistics ::~ce requires wme under~ standing of pi There~fbm it makes =~= that the ~~n on p-~:lity be be~n ~~se ~ pm~ng ~ta and ink Because Ot t~¢ =~t CO~t I t6~t $~S C~t in p{~iitY =d in pr~il:ty based i:~:renceA fo:~1 mathematical treatment of the~ s^~s should probably be an elective mther th~ ~ core cou=e ~ secondary whOo-l, DATA ANTI - ~S Data analysis is descriptive statistics :~m, with n~ methods, r emphasis on ~,~;hics' and ~ cons:~:t philosophy due to John It t<~8 ~ 3~6 ~ 0: 7~5 ~~ ~4 Kiwi his wnt~ ings in this area.8 ~ reviewer ~~commend$ paper l: in Volume ~ as ~ good starting I:.
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From page 104... ...
Smci6c methods for data dies play -God advance in parallel mth the development of =~v qua3~titat~e con cepts~ "~0w many of-e;~ch color :n ~ bag of M&~:7- can be deter mi:~d'b~ counting and dip Blah smelts of colored bloc~ ~~r ~ stempl.~t ~ Wo~di.~t =~s can reinforce the dist1~-~n between the ~ O's and the ~ ,~ p:~ce in whole num~. ~ ~em~:lot of two~ d:~:t data lists each Is died as ~ "~- and ~~s the obsewat:~s by placing their i,5 digits as "~- on the appmpnate stem.
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From page 105... ...
In 1961 Yankee outhelder Ro~r Mans b^e 13~e -I ~~ of 60 bome ~s in ~ single season. H:~e is ~ bac~ back mmpanson of :~y bome Mars hit by Ruth (~n the :~-~)
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From page 106... ...
~ =~' Ma - s reco~ of :~:l ho~ in Age ts an o~ ~~ fans ~~y In: ho oven patted. Cat overall p=~= (~xcl~i~ ~e owner)
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From page 107... ...
Aid ~~n ) s double peach The peak n=r 42-5 wp~s =~$ ~n which most mIl~ bound students take the SAT, ~e 3highe~ed peak repr~ts ~~es :~n which ~-~ students m~ the Amencan ~~ Tested (~)
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From page 108... ...
Numerical descr:~on of ~ d::~-n by the median, q=~il-=, =d extreme obse - anions I=~ to ~ new Chic ~i~7 ~0 ~~* ^~ exam~ she—how u=~ Fir Chip ~ be~ AS.
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From page 109... ...
~:~Y t:~9 ~~g bra.~s of t~e ~~e t~- The ~ e:~s maw the q=~' the i) ~6 ~i~.i~ t~ 5= i~ t~6 =~:$ 306 t~6 ~h.~5 ~6 t~ t56 sm~t =d ~t indw:dual—se~.
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From page 110... ...
: : \: o:~:E ~~ ~~Y s-~:~s ~~ ~~ ~ ~~ ~~ ~~ ~~ ~~ ~~: s~ ~~ ~~ c~= : to ~e : Of the bel~d no~ Cu - ~^ St~s :~n fO~e ~ "~n mo~' on the basis of ~~r eX periled ~6 Aid. 0~: t~t ~~} into ~0 00~77 8~6 5~¢ mode} provides ~~w ex'nence mth Bin and ra - -A ~e bas:c I- of nomad =~' ~ idea ~ standardizing ~sewa Hi..
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From page 111... ...
. of the :: and ~~d Of each wn~l ~ lone ~ ~ des~ptlon of {~= I: =d pe~s the (~= =t ~ ~ ~~ ~ ~e sol of I:~ar ass~atmn.
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From page 112... ...
:~2 ~~ TO N~y Den Brie Is moM I: ~ Out On ~~ m~ - - we mt~at~y I ~r Bigamy sumac- bo~ ~~ed stratums ~ t~k ~r and explan=~= ~r ~~.~ ~~. ~~: ~~s fbrpm~:ng data to speck que~s am ~e mnce~al bake t~g ~3 8~5 t~ ~~t p=~ ~#.
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From page 113... ...
we man co.~m ou:~S with undeml=ding the -~k=~stic to be mea=:~d, w1~th d—I; ~ satin I i~$ 8~0 ~~t ~0 0~- ~~t ~~ ~ tidbit :~5 t~ -abler untts. Even ~ physical measure-~:ts the stud~ 0~f ~~se ques tion:s ex~s thro~:t the school ~= bmb in mathem=~-~s and :~n sci.~" But the Widow of physics m-: :s simple =~ed Erich the meaSur-~:t pr~Ie::m.s o;~-~e s.~.~: and I sciences.
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From page 114... ...
: Il:4 ~~.~:~ TO N~Y Brats me~:~t =d the ~ acm th~: :~: ~ ~ the ~e semnd :~or aspect Of ~ qu~t of me~ a~ ~ il~77 t~ ~~ ^~ =-~0g p=~ =~ ~ ~ by as when ~ s=le ahoy m~s 3 ~~s I~" B~ ail: ~ so ~ 1.~a On~ - ~n t~ "~e ~~- ~~ m~: ~~d M~ 05 cIe~y u~. ~~e ~~s In S~ s=~: 1s ~ m~.: ot intense ~e, ~~ce no "-~- v~= is a.vali~ie ~r =~+ ^S um~' DISK crease 1s :~ mom s~ t6= bavm~ or m~!
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From page 115... ...
~0 0tii670~- ~~t 7'~ 0{ t60 ~~ i07000 =~5 33~6 ~04 M3* =r I their tCSpOOSCS bar ~~4~g t8~5 0: t~0 0~.~$ l~3i0~6 0~ them b~ the:r
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From page 116... ...
~ ~:onvMe random ~~le caged ~~= to ~ anention p~ I.- ~ ~~m ~ =~ ~ th~ 91:% den behave thirds ~a:~is ~e n~e of wi~ -~* ~e tO at=~t pem ~~ =~ :~ ~~ pm~= 70yD "~- when the t=~ ^ :~ " - ~ S~ d~ c~ no =~l in~ - ~t *
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From page 117... ...
Recomb i:za~on amp that there \s no blaS ln assigning subjects to Amp:. The =~s aw there~e Sim:~r (:~n ~'0 aVe=~)
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From page 118... ...
~ti05 t~ 606000 0~5i~ :~s ~m ~~:~e assumptions. :n toss:~' tor eXampie, is de=~ simply as ~ sequence of ins : t:~s each yielding ~ hem mth ~rob~i1:ity ~ ~ ~ K 6~ dais unassuming ~~*
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From page 119... ...
to dislodge b~ the time students =~h secondary whorl St:~^~^ tio~s open persist even when ~~:ts =n answer typical te~ 4~ns I-:.
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From page 120... ...
A,.s, Students Ieam the mathematics of propo~i—~, ^~ ~ pmb~tv =n be~n mth ass~s of pmb~ilitl~ to finite sets of o-~s and companion of obsewetL pmpod~s to the~ Iicomparison ~ outcomes to p0~illt:= can be—s~ if not =~v planned~ Computer sim~:ion lS w~ help~1 in ~~di.~ ;b0 I~~ DO—Ct Of t=~iS =gOi~d if -id t61811Nr<' I -my to 1:~ rel~y clow to pr~:~:~ties. T:n sho~ seq~ -of tnals, the dev:iat~ns of ~~ Czechs mom :~:ities mU o~en seem 1~*
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From page 121... ...
At this-~-~nt in the d~nt of mathem~ pm~dity~ T~ ~0 ~ ~ $~= ~ ~~ =~ ~ ~5 tt8t ~ l~ ~~ ~ ~ A ~ ng w1th =~er as=ct of math~ati~ thinking that ls ~t I ~ -in students*
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From page 122... ...
Pi SCt:~e ~~e ~ ~ c=~ ~e the ~ =~r tn ~ ~~r W~.
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From page 123... ...
:~ts 6~d the distinctions among P(~B , Pow and P(A and B~ hard to- ~~" D:~ ~ photograph of an att:~:ive and welldressed ~~an and a~ the probability that she is ~ fashion model- The Andover sho~w that the question is i- as asking the conditional prob~li:~v that ~ wOma~ k.~.~n to be ~ ~~n mode) is archive and pre - ~~ce Of ~~se positives among EuSA M~:~S antibodies ~ be =~d Wt m~ ~ 67085~-, l~t i57 t08~8 00~*
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From page 124... ...
~4 oh-: / ~ \ · ACES a:.
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From page 125... ...
but TO ~ reasoning of prob~ :~. Repe~d s~ ~ A - ~~ Spa= =~ Id ~ ~ ~ + his car: :s -Sodom in ~e techn~ 50~7 ~Ct 'God uses an explicit chan~ mechanlSm ~ :; pores mn~n -I 61~% -I ~!
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From page 126... ...
As the earlier d:~ssion of no~at distnb-utions India data ~ cscn:~o n: provides an ade quate conteXt ~ ~ ~~tic ns as i: i zed :~:~tica1 models for Donation. The core mat:~emati~ =~m tau~t to all stu~ts should include data analysis a~d an cm:pirica1 introduction to CO1NY basic pr~il~V ~~s and I~s at ~~.t the Iwe!
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From page 127... ...
ob~ ~ li ty ~~.~:ti ~ ~ ~r ~ ~
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From page 128... ...
diminution of the sm:stic gl~ the pamm~r and the con~ Aims distntutio:n of the pamm~r ~~n the a=~:y obse~d ~~e 0t t50 5~ti5~0P 'I is ~~> 5~. The su~-~w id of p—nullity is quite natu~, but it dlve~s attention—m randomness and chance as obw:~d phenomena in the ~~d whose pattems can be d-~ed mathemat:-~- A:n un~ of the behavior of ra dom phenomena Is an important goal cf teaching ~~t data and cha:~, pmbabilltv unde~od as persona:!
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From page 129... ...
w~y p—uces 230 Ian observations' ea~ m:th probability ~ ~ -of being ves~ ~e p~ni~ ~ of ~s =~= in the =~le vanes—~m -do sump:- S:~=e -id' 1000 ~m:~es ~ ~ he Gil; ng ~ ~ ~~:: on of ~ ~ T~t is app w~h mean O~ 3 and st= ~~d den i ~~ ~n ~ K 0~ 9 ~ 9—K Hi it! · ~ I ~ K at , if Repeated simulations at sampl~ o: ~~s s:~s tram :~s po~n demonstmte that ~e center ~ the w=~:~g -I r-~ai:~s at O-3 a~ that the spread ls contr~m bY tte size of the =~.
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From page 130... ...
=~t art: ~ N~y prop: ~ m:~n 85~ O-*
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From page 132... ...
In ~ random assignment of |
From page 133... ...
~? -- wa8 6185~+ J~i00 ~i$~6 tt8t ttC C3p s ma ~ ning the biro dates had ~e:3: hIled ~ month a: ~ lime and not adequately mt~d.
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From page 134... ...
s;kills~ ice meets an es=n tial ~~e ln teach i ~ and I~)
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From page 135... ...
2- ~~e n=d ~r Am: ~~: p:~^ Stad~= ~ Bedfast empt Wick r=~r ~= same - e. Looking at the data teas host pnon~.
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From page 136... ...
Data analysis in Paul blips ~o legging of basic m ^ emalics. Bu1> mod impo~1,ilis because Pistil 1bi - fig is an independent and fun eggs inte~1k~u~ method lbetit dk@erves allenlionin 1be olcu~iculum.
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From page 137... ...
gelling ~ ugly Ha Gail ~ tag $=i~i~ =~$ in big ~b-.afar CZAR Act. Amps alibis Otis, 1# 61i 19 Rubin, ate and Rota, at.
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