Appendix A Augmented TIMSS Curriculum …3A978-94-009...Appendix A Augmented TIMSS Curriculum...
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Appendix A Augmented TIMSS Curriculum Frameworks: Topics in the Third International Mathematics and Science Study (TIMSS) The most detailed categories that follow were prepared by Pinchas Tamir (Biology), Dwaine Eubanks (Chemistry), Kjell Gisselberg (Physics) and John Dossey (Mathematics) for purposes of this examination study; all other categories constitute the curriculum frameworks for TIMSS which are fully described in Robitaille et aI., 1993. This appendix only lists the topics of the Curriculum Frameworks. Some topics common to both chemistry and physics are found in both those sections of the appendix. Aspects of the frameworks not included here are Performance Expectations and Perspectives. 251
Transcript of Appendix A Augmented TIMSS Curriculum …3A978-94-009...Appendix A Augmented TIMSS Curriculum...
Appendix A
Augmented TIMSS Curriculum Frameworks:
Topics in the Third International Mathematics
and Science Study (TIMSS)
The most detailed categories that follow were prepared by Pinchas Tamir (Biology), Dwaine Eubanks (Chemistry), Kjell Gisselberg (Physics) and John Dossey (Mathematics) for purposes of this examination study; all other categories constitute the curriculum frameworks for TIMSS which are fully described in Robitaille et aI., 1993.
This appendix only lists the topics of the Curriculum Frameworks. Some topics common to both chemistry and physics are found in both those sections of the appendix. Aspects of the frameworks not included here are Performance Expectations and Perspectives.
251
Aug
men
ted
TIM
SS C
urri
culu
m F
ram
ewor
ks
Bio
logy
D
iver
sity
, O
rgan
izat
ion,
Str
uctu
re o
f L
ivin
g T
hing
s
Pla
nts
Alg
ae
Fung
i an
d m
ushr
oom
s M
osse
s Fe
rns
See
d pr
oduc
ing
plan
ts
Ani
mal
s In
vert
ebra
tes
Uni
cella
r an
imal
s C
oele
nter
ates
W
orm
s In
sect
s S
pide
rs
Ver
tebr
ates
Fi
shes
A
mph
ibia
ns
Rep
tile
s B
irds
M
amm
als
Oth
er o
rgan
ism
s M
icro
orga
nism
s D
iver
sity
of
mic
roor
gani
sms
Vir
uses
R
oles
in
recy
clin
g M
icro
orga
nism
s an
d M
an
Life
Pro
cess
es a
nd S
yste
m E
nabl
ing
Fun
ctio
ns
Lif
e P
roce
sses
an
d S
yste
ms
Pho
tosy
nthe
sis,
ene
rgy
capt
ure,
sto
rage
and
tra
nsfe
r R
espi
ratio
n, m
itoc
hond
ria
Dig
esti
on a
nd e
xcre
tion
O
ther
ene
rgy
hand
ling
Life
Spi
rals
, G
enet
ic C
onti
nuit
y, D
iver
sity
Lif
e C
ycle
s L
ife
cycl
es o
f pl
ants
, in
sect
s et
c.
Rep
rodu
ctio
n. a
ging
, de
ath
Cel
l di
visi
on,
diff
eren
tiat
ion,
suc
cess
ion
Sens
ing
an
d R
espo
ndin
g B
iofe
edba
ck a
nd h
omeo
stas
is
Sens
ory
syst
ems,
res
pons
es t
o st
imul
i
Rep
rodu
ctio
n R
epro
duct
ion
in s
eed
plan
ts
Sexu
al r
epro
duct
ion
Hum
an r
epro
duct
ion
Veg
etat
ive
repr
oduc
tion
SC
IEN
CE
Org
ans,
tis
sues
C
ompl
emen
tari
ly b
etw
een
stru
ctur
e an
d f
un
ctio
n
Cel
ls
Cel
l st
ruct
ure
and
func
tion
T
ypes
of
cells
C
ell
repr
oduc
tion
Bio
chem
ical
Pro
cess
es i
n C
ells
M
etab
olis
m,
prot
ein
synt
hesi
s, e
nzym
es
Reg
ulat
ion
of
cell
func
tion
s C
ell
wat
er r
elat
ions
hip
Var
iatio
n a
nd
Inh
erit
ance
M
eios
is
Men
deli
an g
enet
ics
Mol
ecul
ar g
enet
ics
Pop
ulat
ion
gene
tics
B
iote
chno
logy
and
app
lica
tion
of
gene
tics
Evo
lutio
n. S
peci
atio
n. D
iver
sity
V
aria
tion
E
vide
nce
of E
volu
tion
M
echa
nism
s o
f ev
olut
ion:
Lam
arck
ism
Im
plic
atio
ns o
f ev
olut
ion
Inte
ract
ions
of
Liv
ing
Thi
ngs
Bio
mes
and
Eco
syst
ems
Tun
dra
and
dese
rts
Rai
n fo
rest
and
wet
land
oth
er b
iom
es o
r ec
osys
tem
s H
abita
ts a
nd N
iche
s H
abit
ats
and
biot
opes
N
iche
s, e
ndan
gere
d sp
ecie
s
Hum
an B
iolo
gy a
nd H
ealt
h
Nut
ritio
n F
oods
, vi
tam
ins,
min
eral
s et
c.
Bal
ance
d di
ets
Dis
ease
s an
d H
ealth
P
reve
ntio
n of
dis
ease
, m
aint
aini
ng g
ood
heal
th
Cau
ses
of
dise
ases
R
emed
ies
Bio
chem
istr
y o
f Gen
etic
s S
truc
ture
of
DN
A
Rep
licat
ion
of D
NA
T
rans
form
atio
n D
NA
to
RN
A
Mut
atio
n, g
ene
expr
essi
on
Ope
ron
mod
el i
n ba
cter
ia
Impl
icat
ions
for
soc
iety
, ge
neti
c en
gine
erin
g
Inte
rdep
ende
nce
of L
ife
Food
cha
ins
web
s A
dapt
atio
ns t
o ha
bita
t co
ndit
ions
C
ompe
titio
n am
ong
orga
nism
s Sy
mbi
osis
, co
mm
ensa
lism
, pa
rasi
tism
M
an's
impa
ct o
n th
e en
viro
nmen
t
Hum
an B
iolo
gy
Org
an s
yste
ms,
org
ans,
tis
sues
C
ells
E
nerg
y ha
ndlin
g Se
nsin
g an
d re
spon
ding
L
ife
cycl
e R
epro
duct
ion
Gen
etic
s
Exa
min
ing
the
Exa
min
atio
ns
Ani
mal
Beh
avio
r T
erri
tori
alis
m
Soci
al g
roup
ing
(bee
hive
, he
rds)
M
atin
g be
havi
or a
nd s
elec
tion
Mig
rati
on o
f bi
rds,
fis
hes,
but
terf
lies
R
eari
ng t
he y
oung
L
earn
ed b
ehav
ior
Evo
luti
on
Bio
chem
istr
y of
gen
etic
s In
terd
epen
denc
e of
life
H
uman
beh
avio
r M
an's
impa
ct o
n en
viro
nmen
t
Aug
men
ted
TIM
SS C
urri
culu
m F
ram
ewor
ks
Mat
ter
Cla
ssifi
catio
n o
f Mat
ter
Ele
men
ts,
com
poun
ds,
mix
ture
s S
olut
ions
, co
lloi
ds
Stru
ctur
e o
f M
atte
r
Ato
ms,
Ion
s, M
olec
ules
E
lem
enta
ry a
tom
ic t
heor
y P
erio
dici
ty,
met
als,
non
met
als
Ioni
c co
mpo
unds
C
oval
ent
com
poun
ds
For
mul
as,
equa
tion
s, n
omen
clat
ure
Mol
e co
ncep
t
Phy
sica
l Tra
nsfo
rmat
ions
Phy
sica
l C
hang
es
Gas
es
Liq
uids
, so
lids
P
hase
cha
nges
, ph
ase
diag
ram
s S
olut
ions
C
olli
gati
ve p
rope
rtie
s
Che
mic
al T
rans
form
atio
n
Che
mic
al C
hang
es
Aci
ds,
base
s Io
nic
reac
tions
Oxi
dati
on,
redu
ctio
n
Phy
sica
l P
rope
rtie
s M
ass,
vol
ume
Den
sity
Ph
ysic
al s
tate
s
Che
mis
try
Mac
rom
olec
ules
and
Cry
stal
s C
ryst
al s
truc
ture
B
ondi
ng i
n cr
ysta
lline
sol
ids
Pol
ymer
s
Exp
lana
tions
of P
hysi
cal
Cha
nges
D
ynam
ic e
quil
ibri
um
Inte
r-pa
rtic
le f
orce
s D
ispe
rsio
n an
d fl
occu
latio
n o
f co
lloi
ds
Kin
etic
The
ory
K-M
vie
w o
f ga
ses
K-M
vie
w o
f liq
uids
, so
lids
Coo
rdin
atio
n ch
emis
try
Exp
lana
tions
of C
hem
ical
Cha
nges
Io
niza
tion
ener
gy,
elec
tron
aff
inity
, el
ectr
oneg
ativ
ity
Ioni
c an
d co
vale
nt b
onds
M
olec
ular
sha
pe
Per
iodi
c tr
ends
of
reac
tivity
Che
mic
al P
rope
rtie
s E
vide
nce
of c
hang
e C
ombi
natio
n re
actio
ns
Dec
ompo
sitio
n re
actio
ns
Add
itio
n re
acti
ons
Sub
stit
utio
n re
acti
ons
Suba
tom
ic P
artic
les
Pro
tons
, el
ectr
ons,
neu
tron
s Is
otop
es
Qua
ntum
obj
ects
E
lect
rom
agne
tic
radi
atio
n an
d m
atte
r Q
uant
um n
umbe
rs,
orbi
tal
ener
gies
E
lect
ron
conf
igur
atio
n, p
erio
dici
ty
Qua
ntum
The
ory
Pho
toel
ectr
ic e
ffec
t L
ine
spec
tra
Mat
ter
wav
es
Unc
erta
inty
pri
ncip
le
Rat
e o
f Cha
nge,
Equ
ilibr
ia
Rea
ctio
n ra
tes,
rat
e la
ws
Cat
alys
is,
acti
vati
on e
nerg
y R
eact
ion
mec
hani
sms
Equ
ilib
rium
exp
ress
ions
E
nerg
y, C
hem
ical
Cha
nge
Cal
orim
etry
F
irst
law
of
ther
mod
ynam
ics
Sec
ond
law
of
ther
mo-
dyna
mic
s
Mec
han
ics
Phy
sica
l P
rope
nies
M
ass
and
volu
me
Den
sity
P
hysi
cal
stat
es
Ene
rgy
Type
s, So
urce
s, C
onve
rsio
ns
Wor
k, e
nerg
y, p
ower
K
inet
ic a
nd p
oten
tial
ene
rgy
Ene
rgy
type
s an
d tr
ans-
orm
atio
ns
Ene
rgy
sour
ces
Ele
ctri
city
& E
lect
rom
agn
etis
m
Ele
ctri
city
E
lect
ric
char
ge,
cond
ucto
rs,
insu
lato
rs,
curr
ent
Ele
ctri
c fi
eld,
pot
enti
al,
volt
age,
res
ista
nce
Cap
acit
ors,
ser
ies
and
para
llel
, di
elec
tric
s C
harg
ing
and
disc
harg
ing
of
capa
cito
rs
Org
anic
and
Bio
chem
ical
Cha
nges
H
ydro
carb
ons
Org
anic
oxy
gen
and
nitr
ogen
com
poun
ds
Add
ition
and
sub
stit
utio
n re
acti
ons
Mec
hani
sms
of
orga
nic
reac
tion
s B
iolo
gica
lly i
mpo
rtan
t ca
rbon
com
poun
ds
Nuc
lear
Che
mis
try
Alp
ha a
nd b
eta
part
icle
s, g
amm
a ra
ys,
and
neut
rons
M
ass
defe
ct a
nd n
ucle
ar b
indi
ng e
nerg
y ni
p ra
tios
and
nucl
ear
tran
sfor
mat
ions
Type
s o
f For
ces
Gra
vita
tion
Fr
icti
on
Ten
sion
Phy
sics
Stat
ic e
quil
ibri
um (
incl
. si
mpl
e m
achi
nes,
cen
tre
of
grav
ity)
N
ucle
ar f
orce
s Ti
me,
Spa
ce a
nd M
otio
n M
easu
rem
ent
of
spac
e, t
ime
and
mas
s L
inea
r m
otio
n P
roje
ctil
e m
otio
n C
ircu
lar
mot
ion
Mot
ion
in t
wo
dim
ensi
ons
Ele
ctri
c po
wer
and
ene
rgy
Exa
min
ing
the
Exa
min
atio
ns
Kin
etic
s of
nuc
lear
dec
ay
Fis
sion
, fu
sion
B
iolo
gica
l ef
fect
s E
lect
roch
emis
try
Ele
ctro
lysi
s E
lect
roch
emic
al c
ells
F
ree
ener
gy,
cell
pote
ntia
ls
Pra
ctic
al e
lect
roch
emis
try
corr
osio
n
Dyn
amic
s o
f Mot
ion
Law
s of
line
ar m
otio
n L
inea
r m
omen
tum
, co
nser
vati
on o
f m
omen
tum
and
lor
ener
gy
Law
s o
f ci
rcul
ar m
otio
n A
ngul
ar m
omen
tum
, m
omen
t of
iner
tia,
rot
atio
nal
kine
tic
ener
gy
Flu
id B
ehav
iour
P
ress
ure,
Arc
him
edes
' pr
inci
ple
Liq
uid
flow
, co
ntin
uity
equ
atio
n B
erno
ulli
the
orem
DC
cir
cuit
s A
C c
ircu
its
Ele
ctro
nics
, se
mic
ondu
ctor
s E
lect
rom
agne
tic
osci
llat
ions
Aug
men
ted
TIM
SS C
urri
culu
m F
ram
ewor
ks
Ele
ctro
mag
netis
m &
Mag
netis
m
Mag
neti
c fo
rces
, m
agne
tic
fiel
ds
Ele
ctro
mag
neti
sm
Indu
ctio
n S
elf
indu
ctan
ce
Cha
rges
in
elec
tric
and
mag
neti
c fi
elds
Wav
es,
Soun
d, L
ight
Wav
e P
heno
men
a S
impl
e ha
rmon
ic m
otio
n, p
endu
lum
s T
rans
vers
e w
aves
L
ongi
tudi
nal
wav
es
Sup
erpo
siti
on o
f w
aves
, in
terf
eren
ce
Dop
pler
eff
ect
The
rmop
hysi
cs
Hea
t an
d Te
mpe
ratu
re
Hea
t an
d en
ergy
, ch
ange
s o
f st
ate
The
rmal
exp
ansi
on
The
rmal
equ
ilib
rium
, co
nduc
tion
T
herm
oele
ctri
city
E
mis
sion
and
abs
orpt
ion
of h
eat
radi
atio
n P
hysi
cal
Cha
nges
G
aseo
us s
tate
P
ress
ure,
vol
ume
and
tem
pera
ture
rel
atio
nshi
ps
Par
tial
pre
ssur
es
Dif
fusi
on,
effu
sion
R
eal
gase
s P
rope
rtie
s o
f liq
uids
P
rope
rtie
s o
f so
lids
Ato
mic
and
Qua
ntum
Phy
sics
Ato
ms,
Ion
s, M
olec
ules
D
alto
n's
atom
ic t
heor
y A
tom
ic m
asse
s
Dif
frac
tion
, th
e el
ectr
omag
neti
c sp
ectr
um
Rad
iow
aves
, ra
dio
tran
smis
sion
So
und
and
Vib
ratio
n St
andi
ng w
aves
In
fras
onic
and
ultr
ason
ic w
aves
In
tens
ity o
f so
und
Cry
stal
str
uctu
re
Pha
se c
hang
es
Hea
ting
and
coo
ling
cur
ves
Pha
se d
iagr
ams
For
mat
ion
of s
olut
ions
So
lutio
n co
ncen
trat
ion
Eff
ects
of
tem
pera
ture
and
pre
ssur
e on
so
lubi
lity
Col
liga
tive
pro
pert
ies
Exp
lana
tions
of P
hysi
cal
Cha
nges
Fr
eezi
ng a
nd b
oili
ng o
f pu
re s
ubst
ance
s In
term
olec
ular
for
ces
Dyn
amic
equ
ilib
rium
Suba
tom
ic p
arti
cles
N
ucle
ar a
tom
M
etal
s, n
onm
etal
s Pe
riod
icity
Ligh
t R
efle
ctio
n an
d re
frac
tion
L
ight
int
ensi
ty,
lum
inos
ity
Fib
re o
ptic
s P
olar
ized
lig
ht
lon-
dipo
le a
nd d
ipol
e-di
pole
for
ces
Hyd
roge
n bo
ndin
g Fr
eezi
ng p
oint
dep
ress
ion
Osm
osis
, di
alys
is
Col
loid
al d
ispe
rsio
ns
Kin
etic
The
ory
K-M
vie
w o
f ga
ses
K-M
vie
w o
f liq
uids
and
sol
ids
Ene
rgy
and
Che
mic
al C
hang
e C
alor
imet
ry (
chem
ical
rea
ctio
ns)
Firs
t L
aw o
f th
erm
odyn
amic
s Se
cond
Law
of
ther
mod
ynam
ics
Ioni
c co
mpo
unds
M
olec
ular
com
poun
ds
Nam
ing
com
poun
ds
For
mul
as a
nd e
quat
ions
Mol
e co
ncep
t M
acro
mol
ecul
es,
Cry
stal
s Io
nic
crys
tals
N
etw
ork
soli
ds
Met
alli
c so
lids
O
rgan
ic p
olym
ers
Inor
gani
c po
lym
ers
Bio
poly
mer
s Su
bato
mic
pan
icle
s P
roto
ns e
lect
rons
and
neu
tron
s Is
otop
es
Pro
pert
ies
of
quan
tum
obj
ects
E
lect
rom
agne
tic
radi
atio
n an
d m
atte
r E
xclu
sion
pri
ncip
le a
nd q
uant
um n
umbe
rs
Orb
ital
sha
pes,
ene
rgie
s M
ulti
-ele
ctro
n at
oms
Ele
ctro
n co
nfig
urat
ions
E
lect
ron
stru
ctur
e an
d pe
riod
icit
y Q
uant
um T
heor
y U
nspe
cifi
ed
Pho
toel
ectr
ic e
ffec
t L
ine
spec
tra
Mat
ter
wav
es
The
unc
erta
inty
pri
ncip
le
Qua
ntum
eff
ects
, tu
nnel
ing
Nuc
lear
Phy
sics
Alp
ha a
nd b
eta
part
icle
s, g
amm
a ra
ys a
nd n
eutr
ons
Mas
s de
fect
and
nuc
lear
bin
ding
ene
rgy
Rel
ativ
ity
and
Cos
mol
ogy
Cos
mol
ogy
Bey
ond
the
sola
r sy
stem
E
volu
tion
of
the
univ
erse
Che
mic
al C
hang
es
Aci
d-ba
se r
eact
ions
A
cid-
base
sto
ichi
omet
ry
Aci
d-ba
se d
efin
itio
ns
Ioni
c re
actio
ns
Com
bust
ion
reac
tion
s
N /p
rat
ios
and
nucl
ear
tran
sfor
mat
ions
K
inet
ics
of
nucl
ear
deca
y F
issi
on,
fusi
on
Rel
ativ
ity
Bas
ic p
ostu
late
s o
f th
eory
M
ass-
ener
gy c
orre
spon
denc
e
Exa
min
ing
the
Exa
min
atio
ns
Oth
er o
xida
tion
-red
ucti
on r
eact
ions
O
xida
tion
num
bers
B
alan
cing
red
ox e
quat
ions
Bio
logi
cal
effe
cts
of
radi
atio
n N
ucle
ar e
nerg
y tr
ansf
orm
atio
ns
Nuc
lear
mod
els
Rel
ativ
istic
ene
rgy
and
mom
entu
m
Lor
entz
tra
nsfo
rmat
ions
and
add
itio
n o
f ve
loci
ties
Min
kow
sky
spac
e
Aug
men
ted
TIM
SS C
urri
culu
m F
ram
ewor
ks
Sta
ndar
d un
its
(cus
tom
ary
and
met
ric)
Q
uoti
ents
and
pro
duct
s of
uni
ts
Dim
ensi
onal
ana
lysi
s E
stim
atio
n of
mea
sure
men
ts a
nd e
rror
s of
mea
sure
men
ts
Pre
cisi
on a
nd a
ccur
acy
of m
easu
rem
ents
P
oint
s, l
ines
, se
gmen
ts,
half
-lin
es a
nd g
raph
s C
ircl
es a
nd t
heir
pro
pert
ies
Scie
nce
and
Oth
er D
isci
plin
es
Con
cept
of
vect
ors
Vec
tor
oper
atio
ns (
addi
tion
and
sub
trac
tion
) V
ecto
r do
t an
d cr
oss
prod
uct
Slo
pe a
nd g
radi
ent
in s
trai
ght
line
grap
hs
Tri
gono
met
ry o
f ri
ght
tria
ngle
s R
epre
sent
atio
n of
rel
atio
ns a
nd f
unct
ions
In
terp
reta
tion
of
func
tion
grap
hs
Log
arit
hmic
and
exp
onen
tial
equ
atio
ns a
nd t
heir
sol
utio
ns
Unc
erta
inty
and
pro
babi
lity
L
imits
and
fun
ctio
ns
Gro
wth
and
dec
ay
Dif
fere
ntia
tion
In
tegr
atio
n D
iffe
rent
ial
equa
tion
s
Who
le N
umbe
rs
Mea
ning
U
ses
of n
umbe
rs
Pla
ce v
alue
and
num
erat
ion
Ord
erin
g an
d co
mpa
ring
num
bers
Fra
ctio
ns a
nd D
ecim
als
Com
mon
Fra
ctio
ns
Mea
ning
-rep
rese
ntat
ion
of c
omm
on f
ract
ions
C
ompu
tati
ons
wit
h co
mm
on f
ract
ions
and
mix
ed n
umbe
rs
Dec
imal
Fra
ctio
ns
Mea
ning
-rep
rese
ntat
ion
of
deci
mal
s C
ompu
tati
ons
wit
h de
cim
als
Inte
gers
, R
atio
nal,
and
Rea
l N
umbe
rs
Neg
ativ
e N
umbe
rs,
Inte
gers
, an
d th
eir
Pro
pert
ies
Con
cept
of
inte
gers
O
pera
tion
s w
ith
inte
gers
C
once
pt o
f ab
solu
te v
alue
P
rope
rtie
s of
int
eger
s
Ope
ratio
ns
Add
ition
S
ubtr
acti
on
Mul
tiplic
atio
n D
ivis
ion
Mix
ed o
pera
tion
s
Nu
mb
ers
Rel
atio
nshi
ps B
etw
een
Com
mon
and
Dec
imal
F
ract
ions
C
onve
rsio
n to
equ
ival
ent
form
s O
rder
ing
of
frac
tion
s an
d de
cim
als
Per
cent
age
Perc
ent
com
puta
tions
P
erce
ntag
e pr
oble
ms
(inc
reas
e, d
ecre
ase,
... )
Rat
iona
l Num
bers
and
the
ir P
rope
rtie
s C
once
pt o
f ra
tion
al n
umbe
rs
Ope
ratio
ns w
ith r
atio
nal
num
bers
P
rope
rtie
s o
f ra
tion
al n
umbe
rs
Equ
ival
ence
of
diff
erin
g fo
rms
of
ratio
nal
num
bers
R
elat
ion
of r
atio
nal
num
bers
to
term
inat
ing
and
recu
rrin
g de
cim
als
Exa
min
ing
the
Exa
min
atio
ns
Pro
pert
ies
of O
pera
tions
A
ssoc
iativ
e pr
oper
ties
C
omm
utat
ive
prop
erti
es
Iden
tity
prop
erti
es
Dis
trib
utiv
e pr
oper
ty
Oth
er n
umbe
r pr
oper
ties
Mat
hem
atic
s
Pro
pert
ies
of C
omm
on a
nd D
ecim
al F
ract
ions
A
ssoc
iativ
e pr
oper
ties
C
omm
utat
ive
prop
erti
es
Iden
tity
prop
erti
es
Inve
rse
prop
erti
es
Dis
trib
utiv
e pr
oper
ties
C
ance
llat
ion
prop
erti
es
Oth
er n
umbe
r pr
oper
ties
Rea
l N
umbe
rs,
thei
r Su
bset
s, a
nd t
heir
P
rope
rtie
s C
once
pt o
f re
al n
umbe
rs (
incl
udin
g co
ncep
t o
f ir
ratio
nals
) Su
bset
s of
rea
l nu
mbe
rs (
Z,
Q,
W,
N)
Ope
rati
ons
with
rea
l nu
mbe
rs
Pro
pert
ies
of r
eal
num
bers
(de
nsity
, or
der,
com
plet
enes
s)
Ope
rati
ons
with
abs
olut
e va
lue
Aug
men
ted
TIM
SS C
urri
culu
m F
ram
ewor
ks
Oth
er N
umbe
rs a
nd N
umbe
r C
once
pts
Bin
ary
Ari
thm
etic
or
Oth
er N
umbe
r B
ases
E
xpon
ents
, R
oots
, an
d R
adic
als
Inte
ger
expo
nent
s an
d th
eir
prop
erti
es
Rat
iona
l ex
pone
nts
and
thei
r pr
oper
ties
R
oots
and
rad
ical
s an
d th
eir
rela
tion
to
rati
onal
exp
onen
ts
Rea
l ex
pone
nts
Est
imat
ion
and
Num
ber
Sens
e
Est
imat
ing
Qua
ntity
and
Siz
e R
ound
ing
and
Sign
ifica
nt F
igur
es
Uni
ts
Con
cept
of
mea
sure
(in
c!.
non-
stan
dard
uni
ts)
Sta
ndar
d un
its (
Cus
tom
ary
and
Met
ric)
Per
imet
er,
Are
a, V
olum
e, a
nd A
ngle
s
Com
puta
tion
s, f
orm
ulas
, an
d pr
oper
ties
of
leng
th a
nd p
erim
ete
r C
ompu
tati
ons,
for
mul
as,
and
prop
erti
es o
f ar
ea
Est
imat
ion
and
Err
ors
Com
plex
Num
bers
and
thei
r P
rope
rtie
s C
once
pt o
f co
mpl
ex n
umbe
rs
Alg
ebra
ic f
orm
of
com
plex
num
bers
and
the
ir p
rope
rtie
s T
rigo
nom
etri
c fo
rm o
f co
mpl
ex n
umbe
rs a
nd t
heir
pro
per
ties
Rel
atio
n of
alg
ebra
ic a
nd t
rigo
nom
etri
c fo
rms
of
com
plex
nu
mbe
rs-D
eMoi
vre'
s th
eore
m
Est
imat
ing
Com
puta
tions
M
enta
l ar
ithm
etic
R
easo
nabl
enes
s of
resu
lts
Mea
sure
men
t
Use
of
appr
opri
ate
inst
rum
ents
(ru
ler,
pro
tr.)
C
omm
on m
easu
res
(len
gth,
are
a, v
olum
e, c
apac
ity,
ti
me/
cale
ndar
, te
mpe
ratu
re,
angl
es,
wei
ght/
mas
s, ..
. )
Com
puta
tions
, fo
rmul
as,
and
prop
erti
es o
f su
rfac
e ar
ea
Com
puta
tions
, fo
rmul
as,
and
prop
erti
es o
f vo
lum
e
Est
imat
ion
of m
easu
rem
ents
and
err
ors
of
mea
sure
men
t
Num
ber
Theo
ry
Pri
mes
and
fac
tori
zatio
n E
lem
enta
ry n
umbe
r th
eory
(pr
imes
, lc
m,
gcf,
dio
phan
tine
prob
lem
s)
Syst
emat
ic C
ount
ing
Tre
e di
agra
ms,
lis
ting,
and
oth
er f
orm
s P
erm
utat
ions
C
ombi
nati
ons
Gen
erat
ing
func
tions
Exp
onen
ts a
nd O
rder
s o
f Mag
nitu
des
Quo
tient
s an
d pr
oduc
ts o
f un
its (
lan/
hr.
, m
/s')
D
imen
sion
al a
naly
sis
Com
puta
tion
s, f
orm
ulas
, an
d pr
oper
ties
of a
ngle
s
Pre
cisi
on a
nd a
ccur
acy
of m
easu
rem
ents
Tw
o-D
imen
sion
al G
eom
etry
Coo
rdin
ate
Geo
met
ry
Lin
e an
d co
ordi
nate
gra
phs,
mid
poin
ts
Equ
atio
n of
line
s in
the
pla
ne
Con
ic s
ectio
ns a
nd t
heir
equ
atio
ns
Par
abol
a E
llips
e H
yper
bola
(in
clud
ing
asym
ptot
es)
Thr
ee-D
imen
sion
al g
eom
etry
3-di
men
sion
al s
hape
s an
d su
rfac
es a
nd t
heir
pro
pert
ies
Pla
nes
and
lines
in
spac
e
Vec
tors
Con
cept
of
vect
ors
Vec
tor
oper
atio
ns (
addi
tion
and
sub
trac
tion
) V
ecto
r do
t an
d cr
oss
prod
uct
Tra
nsfo
rmat
ions
Pat
tern
s, T
esse
llatio
ns,
Fri
ezes
, St
enci
ls,
etc.
Geo
met
ry-F
orm
(P
osit
ion,
Vis
uali
zati
on,
and
Shap
e)
Bas
ics
Poin
ts,
lines
, se
gmen
ts,
half
-lin
es,
and
rays
A
ngle
s Pa
ralle
lism
and
per
pend
icul
arit
y P
aral
lel
post
ulat
e P
erpe
ndic
ular
ity
Bas
ic c
ompa
ss/s
trai
ghte
dge
cons
truc
tion
s
Spat
ial
perc
epti
on a
nd v
isua
liza
tion
C
oord
inat
e sy
stem
s in
thr
ee d
imen
sion
s
Nor
m a
nd r
esol
utio
n of
vec
tors
N
orm
al v
ecto
r to
lin
e/pl
ane
Mat
rix
oper
atio
ns G
eom
etry
-Rel
atio
n (S
ymm
etry
, C
ongr
uenc
e, a
nd S
imila
rity
)
Sym
met
ry
Lin
e sy
mm
etry
Exa
min
ing
the
Exa
min
atio
ns
Pol
ygon
s an
d C
ircl
es
Tri
angl
es a
nd q
uadr
ilat
eral
s: c
lass
ific
atio
n an
d pr
oper
ties
T
rian
gles
, Q
uadr
ilat
eral
s P
ytha
gore
an t
heor
em a
nd i
ts a
ppli
cati
ons
Oth
er p
olyg
ons/
pro
pert
ies
Cir
cles
and
the
ir p
rope
rtie
s L
ocus
pro
blem
s
Equ
atio
ns o
f lin
es,
Pla
nes,
and
Sur
face
s in
Spa
ce
Equ
atio
n of
line
in
spac
e E
quat
ion
of
plan
e in
spa
ce
Equ
atio
n of
qua
dric
sur
face
in
spac
e E
quat
ion
of a
sph
ere
Eig
en v
alue
s/ei
gen
vect
ors
Vec
tor/
mat
rix
form
of
tran
sfor
mat
ion
Ref
lect
iona
l sy
mm
etry
R
otat
iona
l sy
mm
etry
Aug
men
ted
TIM
SS C
urri
culu
m F
ram
ewor
ks
Tra
nsfo
rmat
ions
T
rans
lati
ons
Ref
lect
ions
R
otat
ions
D
ilat
ions
C
ongr
uenc
e an
d Si
mila
rity
Con
grue
nces
C
once
pt o
f co
ngru
ence
(se
gmen
ts,
angl
es, .
.. )
Tri
angl
es (
SSS,
SA
S, .
... )
Q
uadr
ilat
eral
s P
olyg
ons
Sol
ids
Con
stru
ctio
ns u
sing
Str
aigh
tedg
e an
d C
ompa
ss
Pro
port
iona
lity
Con
cept
s
Mea
ning
of R
atio
and
Pro
poni
on
Pro
port
iona
lity
Pro
blem
s
Sol
ving
pro
port
iona
lity
equ
atio
ns
Sol
ving
pra
ctic
al p
robl
ems
wit
h pr
opor
tion
s Sl
ope
and
Tri
gono
met
ry
Slo
pe a
nd g
radi
ent
in s
trai
ght
line
gra
phs
Lin
ear
Inte
rpol
atio
n an
d E
xtra
pola
tion
In
terp
olat
ion
Ext
rapo
lati
on
Com
posi
tion
s o
f tr
ans-
form
atio
ns
Gro
up s
truc
ture
of
tran
s-fo
rmat
ions
Fi
xed
poin
ts o
f tr
ansf
orm
atio
n
Sim
ilari
ty
Con
cept
of
sim
ilar
ity
(pro
port
iona
lity
) T
rian
gles
(A
A,
SSS,
SA
S, .
... )
Q
uadr
ilat
eral
s P
olyg
ons
Soli
ds
Pro
port
iona
lity
Dir
ect a
nd I
nver
se P
ropo
nion
D
irec
t va
riat
ion
Indi
rect
var
iatio
n O
ther
pro
port
iona
l re
latio
nshi
ps
Scal
es (
map
s an
d pl
ans)
and
Rat
es
Pro
port
ions
bas
ed o
n si
mila
rity
Tri
gono
met
ry o
f ri
ght
tria
ngle
s
Pat
tern
s, R
elat
ions
, an
d F
unct
ions
Num
ber
patt
erns
R
elat
ions
and
the
ir p
rope
rtie
s F
unct
ions
and
the
ir p
rope
rtie
s (r
ange
/dom
ain,
....
) R
epre
sent
atio
n o
f re
lati
ons
and
func
tion
s
Equ
atio
ns a
nd F
orm
ulas
Rep
rese
ntat
ion
of
num
eric
al s
itua
tion
s In
form
al s
olut
ion
of
sim
ple
equa
tion
s O
pera
tion
s w
ith e
xpre
ssio
ns
Equ
ival
ent
expr
essi
ons
(fac
tori
zati
on,
sim
plif
icat
ion,
par
tial
fr
acti
on d
ecom
posi
tion
, an
d so
luti
on t
ests
) L
inea
r eq
uati
ons
and
thei
r fo
rmal
(cl
osed
) so
luti
ons
Qua
drat
ic e
quat
ions
and
the
ir f
orm
al (
clos
ed)
solu
tion
s P
olyn
omia
l eq
uati
ons
and
thei
r so
luti
ons
Tri
gono
met
ric
equa
tion
s an
d id
enti
ties
(in
clud
ing
law
of
cosi
nes
and
sine
s)
Dat
a re
pres
enta
tion
an
d a
naly
sis
Col
lect
ing
Dat
a fr
om E
xper
imen
ts a
nd S
urve
ys
Dat
a fr
om e
xper
imen
ts
Dat
a fr
om s
urve
ys
Rep
rese
ntin
g da
ta
Bar
, li
ne,
circ
le,
and
hist
ogra
phs
Ste
m-a
nd-l
eaf,
box
-and
-whi
sker
, ...
S
catt
erpl
ots
Mul
tiva
riab
le p
lots
Fun
ctio
ns,
Rel
atio
ns,
and
Equ
atio
ns
Fam
ilies
of
func
tion
s (g
raph
s an
d pr
oper
ties
) O
pera
tions
on
func
tion
s R
elat
ed f
unct
ions
(in
vers
e, e
xp/l
og,
deri
vati
ve, .
.. )
Rel
atio
nshi
p o
f fu
ncti
ons
and
equa
tion
s
Log
arith
mic
and
exp
onen
tial
equ
atio
ns a
nd t
heir
sol
utio
ns
Sol
utio
n of
equ
atio
ns r
educ
ing
to q
uadr
atic
s, r
adic
al e
quat
ions
, ab
solu
te v
alue
equ
atio
ns,
...
Oth
er s
olut
ion
met
hods
for
equ
atio
ns (
succ
essi
ve a
ppr
oxim
atio
ns,
bise
ctio
ns, .
.. )
Ineq
ualit
ies
or t
heir
gra
phic
al r
epre
sent
atio
n
Dat
a R
epre
sent
atio
n, P
roba
bilit
y, a
nd S
tati
stic
s
Inte
rpre
ting
tabl
es,
cham
, pl
ots,
and
gra
phs
Bar
, lin
e, c
ircl
e, a
nd h
isto
grap
hs
Stem
-and
-lea
f, b
ox-a
nd-w
hisk
er, .
..
Scat
terp
lots
M
ultiv
aria
ble
plot
s K
inds
of s
cale
s N
omin
al
Ord
inal
In
terv
al
Rat
io
Exa
min
ing
the
Exa
min
atio
ns
Inte
rpre
tati
on o
f fu
ncti
on g
raph
s F
unct
ions
of
seve
ral
vari
able
s R
ecur
sion
H
yper
boli
c fu
ncti
ons
Syst
ems
of e
quat
ions
and
thei
r so
lutio
ns
Sub
stit
utio
n L
inea
r co
mbi
nati
ons/
Gau
ss-J
orda
n M
atri
x so
luti
on
Sys
tem
s o
f in
equa
liti
es
Sub
stit
utin
g in
to o
r re
arra
ngin
g fo
rmul
as
Gen
eral
equ
atio
n o
f th
e se
cond
deg
ree
and
its i
nter
pret
atio
n P
aram
etri
c eq
uati
ons
Rat
iona
l eq
uati
ons
Mea
sure
s o
f cen
tral
tend
ency
M
ean
Med
ian
Mod
e M
easu
res
of d
ispe
rsio
n R
ange
V
aria
nce
Sta
ndar
d de
viat
ion
Inte
rqua
rtil
e ra
nge
Aug
men
ted
TIM
SS C
urri
culu
m F
ram
ewor
ks
Sam
plin
g, r
ando
mne
ss,
and
bias
T
ypes
of
sam
plin
g R
ando
mne
ss
Bia
s--d
etec
tion
and
avo
idan
ce
Var
iabi
lity
of
sam
plin
g m
ean
Pre
dict
ion
and
infe
renc
es f
rom
dat
a
Unc
erta
inty
and
Pro
babi
lity
Info
rmal
lik
elih
oods
and
voc
abul
ary
Num
eric
al p
roba
bili
ty a
nd p
roba
bili
ty m
odel
s C
ount
ing
as i
t ap
plie
s to
pro
babi
lity
M
utua
lly
excl
usiv
e ev
ents
C
ondi
tion
al p
roba
bili
ty &
ind
epen
dent
eve
nts
Inde
pend
ent
even
ts
Con
diti
onal
pro
babi
lity
Inrm
ite
Pro
cess
es
Ari
thm
etic
, G
eom
etri
c, a
nd G
ener
al S
eque
nces
A
rith
met
ic s
eque
nces
: n
Ih t
erm
s G
eom
etri
c se
quen
ces:
n
Ih t
enns
G
ener
al s
eque
nces
: n'
" te
rms
Ari
thm
etic
, G
eom
etri
c, a
nd G
ener
al S
erie
s A
rith
met
ic s
eque
nces
: su
ms
Geo
met
ric
sequ
ence
s:
sum
s G
ener
al s
eque
nces
: su
ms
Fitt
ing
lines
and
cur
ves
to d
ata
Gra
phic
al m
etho
ds
Lea
st s
quar
es m
etho
ds
Ana
lysi
s o
f fit
lin
es/c
urve
s C
orre
lati
ons
and
othe
r m
easu
res
of r
elat
ions
U
se a
nd m
isus
e o
f st
atis
tics
Bay
es'
theo
rem
C
onti
ngen
cy t
able
s P
roba
bili
ty d
istr
ibut
ions
for
dis
cret
e ra
ndom
var
iabl
es
Pro
babi
lity
dis
trib
utio
ns f
or c
onti
nuou
s ra
ndom
var
iabl
es
Exp
ecta
tion
and
the
alg
ebra
of
expe
ctat
ions
Sa
mpl
ing
and
prob
abil
ity
Est
imat
ion
of p
opul
atio
n pa
ram
eter
s
Ele
men
tary
Ana
lysi
s
Bin
omia
l Th
eore
m
Bin
omia
l se
ries
O
ther
Seq
uenc
es a
nd S
erie
s P
atte
rns
to r
ules
D
iffe
renc
e eq
uati
ons
desc
ript
ion
Lim
its a
nd C
onve
rgen
ce o
f Seq
uenc
es &
Ser
ies
Lim
its/
conv
erge
nce
of s
eque
nces
L
imit
s/co
nver
genc
e o
f se
ries
M
acla
urin
and
Tay
lor
seri
es
Hyp
erbo
lic
trig
onom
etri
c se
ries
Hyp
othe
sis
test
ing
Con
fide
nce
inte
rval
s B
ivar
iate
dis
trib
utio
ns
Mar
kov
proc
esse
s M
onte
Car
lo m
etho
ds a
nd c
ompu
ter
sim
ulat
ions
Lim
its a
nd fu
nctio
ns
Lim
it of
fun
ctio
n as
x -
-> a
L
imits
at
infi
nity
L
imits
for
seq
uenc
e of
fun
ctio
ns
The
orem
s ab
out
limits
C
ontin
uity
C
once
pt a
nd d
efin
itio
n In
term
edia
te v
alue
the
orem
Cha
nge
Gro
wth
and
Cec
ay
Dif
fere
ntia
tion
C
once
pt a
nd d
efin
itio
n (a
lgeb
raic
&
geom
etri
c)
Der
ivat
ive
of
pow
er f
unct
ions
D
eriv
ativ
e o
f el
emen
tary
fun
ctio
ns
Der
ivat
ives
of
sum
s, p
rodu
cts,
and
quo
tien
ts
Der
ivat
ives
of
com
posi
te f
unct
ions
(C
hain
rul
e)
Der
ivat
ives
of
impl
itic
tly
defi
ned
func
tion
s D
eriv
ativ
es o
f hi
gher
ord
er
Rel
atio
nshi
p be
twee
n de
riva
tive
beh
avio
r an
d m
axim
a an
d m
inim
a R
elat
ions
hip
betw
een
deri
vati
ve b
ehav
ior
and
conc
avit
y an
d in
flec
tion
poi
nts
Val
idat
ion
and
Just
ific
atio
n
Log
ical
con
nec
tive
s Q
uant
ifie
rs (
For
eac
h, t
here
exi
sts,
...
. )
Boo
lean
alg
ebra
Stru
ctur
ing
and
Abs
trac
ting
Set
s, s
et n
otat
ion,
and
set
ope
rati
ons
Equ
ival
ence
rel
atio
ns,
part
itio
ns,
and
clas
ses
Gro
ups
Rin
gs
Rel
atio
nshi
p be
twee
n di
ffer
enti
abil
ity
and
cont
inui
ty
Mea
n va
lue
theo
rem
!,
Hop
ita!
's R
ule
App
lica
tion
s o
f th
e de
riva
tive
D
eriv
ativ
e o
f po
lar
func
tion
D
eriv
ativ
e o
f ve
ctor
val
ued
func
tion
s N
ewto
n's
met
hod
Inte
grat
ion
Con
cept
and
def
init
ion
Bas
ic i
nteg
rati
on f
orm
ulas
In
tegr
atio
n by
sub
stit
utio
n In
tegr
atio
n by
par
ts
Inte
grat
ion
by t
rig
subs
titu
tion
In
tegr
atio
n by
par
tial
fra
ctio
ns
Val
idat
ion
and
Stru
ctur
e
Con
diti
onal
sta
tem
ents
I e
quiv
alen
ce o
f st
atem
ents
(co
nver
se,
cont
rapo
siti
ve,
inve
rse,
... )
In
fere
nce
sche
mes
(e.
g.,
mod
us p
onen
s, m
odus
tol
ens,
sy
llog
ism
....
. )
Fie
lds
Vec
tor
spac
es
Sub
grou
ps,
subs
pace
s, a
nd t
heir
pro
pert
ies
Oth
er a
xiom
atic
sys
tem
s (f
init
e ge
omet
ries
, ...
)
Exa
min
ing
the
Exa
min
atio
ns
Def
init
e in
tegr
als-
-Iim
it o
f su
ms
Pro
pert
ies
of
inte
gral
A
ppro
xim
atio
ns o
f de
fini
te i
nteg
ral
Fun
dam
enta
l T
heor
ems
App
lica
tion
s o
f de
fini
te i
nteg
ral
Ant
ider
ivat
ives
In
tegr
atio
n o
f po
lar
func
tion
s
Dif
fere
ntia
l E
quat
ions
P
arti
al D
iffe
rent
iati
on
Num
eric
al A
naly
sis
Con
side
rati
ons
Mul
tipl
e In
tegr
atio
n
Dir
ect
dedu
ctiv
e pr
oofs
In
dire
ct p
roof
s an
d pr
oof
by c
ontr
adic
tion
P
roof
by
mat
hem
atic
al i
nduc
tion
C
onsi
sten
cy a
nd i
ndep
ende
nce
of a
xiom
sys
tem
s
Isom
orph
ism
H
omom
orph
ism
Aug
men
ted
TIM
SS C
urri
culu
m F
ram
ewor
ks
Info
rmat
ics
Ope
rati
on o
f co
mpu
ters
F
low
cha
rts
His
tory
and
Nat
ure
of M
athe
mat
ics
Spec
ial
App
lica
tion
s o
f Mat
hem
atic
s
Kin
emat
ics
Net
owia
n m
echa
nics
Pro
blem
Sol
ving
Heu
rist
ics
Oth
er C
onte
nt
Pro
gram
min
g la
ngua
ge
Pro
gram
s
Net
wor
ks (
grap
h th
eory
) L
inea
r pr
ogra
mm
ing
Alg
orit
hms
with
app
lica
tion
to
the
com
pute
r
Cri
tica
l pa
th a
naly
sis
Eco
nom
etri
cs
Non
-Mat
hem
atic
al N
on-S
cien
ce C
onte
nt (
asso
ciat
ion
of m
athe
mat
ics
with
con
tent
and
act
ions
in
non-
scie
nce
area
)
AppendixB
Technical Notes
Cautions About Unwarranted Conclusions
Guarding against overgeneralization of results. Reiterating a caution provided in Chapter 1, study results should not be overgeneralized into statements that a given country's curricula or examinations include (or do not include) specific topics because: (1) only two years of examinations were analyzed; we have no specific knowledge of topics in other years of the examinations; (2) while examinations in other countries undoubtedly have tremendous influence on the topics studied in school, research on the specific linkages between examination topics and school topics has not been done. Because the structure of examinations probably is more stable than their topics over the years, cautious generalizations about length, choice, item type and performance expectations are more appropriate than about specific content.
Countries not included in the study. Resource constraints limited the study to seven countries, although many others have university entrance examinations. The included countries generally were chosen because they are strategic economic partners of the United States, and we had preliminary information that there were interesting contrasts between their examinations and the Advanced Placement examinations with respect to both their internal characteristics and their examination systems. We do not know whether examinations of some other countries would have similar or even more striking contrasts.
Percentages of Topic Coverage in England/Wales examinations. Because the England/Wales examinations are so long, 1.5 to 3 times longer than examinations from the other countries, seemingly small percentages of topic coverages in the England/Wales examinations actually represent significant amounts. Only a few percent of an England/Wales examination can represent several examination questions; in contrast, a few percent of other countries' examinations represent only one or two questions.
267
268 Technical Notes
Information on Methods
Topic stability between years. We included two years of examinations and reported their aggregate characteristics in order to provide as much generalization about countries examinations as possible. There was some variance in examination topics between years, but overall there was more stability than variance for the more general topics. More between-year variance existed for very detailed topics. Tamir and Dossey have provided analyses for year-to-year stability at a general topic level for biology and mathematics examinations. Biology: Except for the Associated Examining Board in England and Wales, topic stability ranged from 60 to 95 percent, and averaged 80 percent. Mathematics: Pearson product-moment correlations ranged from 0.64 to .98 except for the examinations of Aix (France), Sweden, and Tokyo University, which each had little commonality among topics across the two years. Because these examinations contain a small number of questions, changes in the topics of only a few questions can result in large variances in these examinations' topic coverages.
Analytical techniques in Chapter 6, mathematics. The comparisons in Chapter 6 are supported by especially extensive mathematical analyses that the editors mostly omitted to make results accessible to as many readers as possible. For example, averages for topic coverage over two years were subjected to a median polish (Hoaglin, Mosteller, and Tukey, 1983). Topic patterns among countries were derived from a cluster analysis (SAS Institute, 1994). Further analysis and description of the clusters was done through dendograms that were not included in the chapter (Milligan, 1980).
Distinction between short and extended answers. Short answers were defined to be 1-3 sentences of text or quantitative answers requiring only one formula or equation in a single-calculation step. Extended answers were identified as four or more sentences of text or quantitative answers requiring multiple-calculation steps and/or more than one formula or equation. Although authors encountered some ambiguity between short- and extended- answer questions within their subjects, they felt the distinction was sufficiently clear to report these two item types separately in Chapters 3 through 6. Because this delineation between short and extended answers was not always easy to maintain in similar ways among the different subjects, however, Chapter 2 discusses the study's findings about these types of items in the aggregate.
Examining the Examinations 269
Within-country reporting for England/Wales, France, and Germany. The examinations from the Associated Examining Board and the University of London usually were different enough to warrant separate reporting of their characteristics in many tables and figures. Because differences between the Aix and Paris examinations in France and the BadenWiirttemberg and Barvaria examinations in Germany were less pronounced, often the aggregate data for France and Germany are reported. However, readers will find some separate reporting of French and German regions for examination topics.
Scorable events. The unit of analysis in the study was scorable events as described in Chapter I-the smallest question in an examination that could not be broken down into more subquestions. Many examinations had questions that were numbered as a single item yet had several subquestions embedded within them. The authors analyzed each subquestion separately, i.e., these were the scorable events for coding, analysis and reporting. The data in tables or figures were compiled from the coding of scorable events.
Estimated weightings for scorable events. While many examinations provided the points allocated to whole questions or subquestions, as they were numbered by the examinations themselves, we often had to estimate the points corresponding to the embedded subquestions that we identified as scorable events. Sometimes this information could be gleaned from scoring rubrics. When scoring rubrics were unavailable, however, we had to divide the available points evenly across the scorable events, or estimate a weighting if the scorable events embedded in a question obviously required different amounts of student effort, e.g., one scorable event required a short answer while the other necessitated an extended answer.
Influence of choice on weightings. When students were afforded a choice among questions, each scorable event was weighted accordingly. For example, if students were to answer any three of eight questions, then the contribution of each scorable event when compiling the examinations' topics, etc., was multiplied by 3/8.
Terms in Text
Scorable events, items, questions. All specific data reported are referring to compilations of scorable events. To make the text more accessible to readers, however, authors often used more common words-items or questions.
270 Technical Notes
Papers, sections. Most examinations contained discrete subparts that are described in Chapters 3 to 6. Parts that are separately timed are called papers, while parts with no formal timing requirements are referred to as sections. This particular usage was adopted in part because examinations in England and Wales have separately timed parts that are called "Papers."
Points, marks, grades, scores. Examination questions have assigned values that we refer to as points. We used the term scoring for referencing the process of awarding points for students' answers to individual questions. The total number of points given for a student's performance on the examination was called the score. Grading is the process of translating a total examination score into some reporting scale such the AP scale of 1-5. The resulting value assigned is called the examination grade. Obviously, these terms are often used in alternative ways, or interchangeably-so much so, that we may have inadvertently failed to be consistent with our intended use of them in the book. A final confusion is that in England and Wales, the points awarded for individual questions are called marks and the process of scoring the examinations is called marking.
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Index of Sample Examination
Questions
Example 3-5 ................................................... 67 Example 3-9 ................................................... 70 Example 3-ll .................................................. 77 Example 3-13 ................................................... 79 Example 4-ll .................................................. 109 Example 4-20 .................................................. ll8 Example 5-2 .................................................. 131 Example 5-3 .................................................. 132 Example 6-12 .................................................. 189 Example 6-17 .................................................. 191
EngiandIWales, University of London Example 4-1 .................................................... 95 Example 4-3 ................................................... 101 Example 4-9 ................................................... 106 Example 5-4 .................................................. 133 Example 5-8 ................................................... 149 Example 5-ll .................................................. 152 Example 5-16 .................................................. 159 Example 6-2 ................................................... 173 Example 6-3 ................................................... 174 Example 6-8 ................................................... 178 Example 6-10 .................................................. 187
France,Aix Example 4-8 ................................................... 103 Example 5-1 .................................................. 129
France, Paris Example 3-6 .................................................... 67 Example 4-12 ................................. ; ................ 109 Example 6-13 .................................................. 189
Germany, Baden-Wiirttemberg Example 3-15 ................................................... 80 Example 5-6 ................................................... 142 Example 6-6 ................................................... 177 Example 6-16 .................................................. 191
277
278 Index
Germany, Bavaria Example 3-10 ................................................... 74 Example 3-14 ................................................... 79 Example 4-6 ................................................... 102 Example 4-13 .................................................. 110 Example 5-10 .................................................. 151 Example 5-13 .................................................. 155 Example 6-9 ................................................... 184 Example 6-19 .................................................. 194
Israel Example 3-4 .................................................... 66 Example 3-7 ................................................... 67 Example 3-8 ................................................ 68 - 69 Example 4-4 ................................................... 101 Example 4-14 .................................................. 110 Example 4-18 .................................................. 113 Example 5-9 ................................................... 149
Japan Example 3-2 .................................................... 64 Example 3-3 ................................................... 65 Example 4-7 ................................................... 103 Example4-15 .................................................. 111 Example 5-7 ................................................... 147 Example 5-14 .................................................. 156 Example 6-7 ................................................... 177
Sweden Example 4-2 ................................................... 101 Example 4-16 .................................................. 111 Example 4-19 .................................................. 117 Example 5-15 .................................................. 157 Example 6-5 ................................................... 175 Example 6-15 .................................................. 190
United States Example 3-1 .................................................... 63 Example 3-12 ................................................... 78 Example 3-16 ................................................... 80 Example 4-5 ................................................... 102 Example 4-10 .................................................. 107 Example 4-17 .................................................. 112 Example 5-5 ................................................... 141 Example 5-12 .................................................. 154 Example 6-1 ................................................... 173 Example 6-4 ................................................... 175 Example 6-11 .................................................. 187 Example 6-14 .................................................. 190 Example 6-18 .................................................. 192
