– 299 – ¯ ¯

! "#$

TIMSS, 2015)

%

&'# ()* +,* ' -./0 1 12 3 * 0! 4

56 7.8 9 0

: 1

%

" # $%

& '( ) 19

05 1440

; '( ,-).

&

16 01 1441

&'2<

0. 1-234 & 2"4 5678 9: ;2 <= "1 >? @A :

TIMSS, 2015 B$C DE -F GHI. JCK-$ &

LMN O F$ GPQ$ M2" R1AS(" . B$ B$C DE -F. T H UV &

" PQ$ ,BUV2 PQ$

,WVM2 PQ$ ,XYZ [

R4- : PQ$

\ ]^ GHI. _K- R1AS(" . G7H- 2"4 5678 ,HK2 `a27 GYb8.

%92 . %94 567^d @Z(e 02 9:

]8. ,HH-f 2"

%8 . %6 ,Hg `a27 GYb8. ,HH-f hi 2" 567^d @Z(e 02 9:

_K- T . -f G7H- 2"4 5678

]^ GHI.

%85 . %86 ]8. ,HH-f 2" 567^d @Z(e 02 9:

%15 . %14 2"4 5678 -T7 ]8. ,HH-f hi 2" 567^d @Z(e

T . -F GHI _K-$ G7H- HH-F hi

%12 . , _K- Y($ Cd8 @7d

%11 G7H- HH-F hi 2"4 5678 -T7 ]8. ,

R1AS(" . _K-$

%8 GHI _K- Y($ Cd8

%6

\

>?< $ 67j ,R4- : PQ$ ,WVM2 PQ$ ,XYZ [" PQ$ ,BUV2 PQ$ ,LMN O F$ GPQ$ :

HH-f hi 567j. ,HH-F 5

\

_________________________________________________________________________

________

Detection of response patterns in international Test of science and Math (TIMSS, 2015) for a sample of Saudi and Singapore students using the person's fit indices

Bandar Nawaf Tawfieq Jarrah⁽¹⁾ King Saud University

(Received 25/01/2019; accepted 15/09/2019)

Abstract: The aim of this study was to recognize the patterns of response in international test Mathematics and Science data (TIMSS, 2015) for the eighth grade of Saudi students and Singapore students using the person fit indices ; (capability index, misconception index, Guessing index, carelessness index),the analyses showed for responses patterns of Singapore data for science and mathematics that 92% and 94% respectively were classified as normal response patterns, 8% and 6% respectively were classified as abnormal response patterns, the analysis showed for the responses patterns of Saudi Arabia data for science and mathematics that 85% and 86% respectively were classified as normal responses patterns, 15% and 14% respectively were classified as abnormal response patterns. The proportion of the abnormal responses patterns of mathematics data to the Saudi state (12%) is more than science data (11%), the proportion of abnormal responses patterns of science data to the state of Singapore (8%) is more than mathematics data (6%).

Key Words: person fit indices, capability index, misconception index, Guessing index, carelessness index, Timss Data.

_________________________________________________________________________

________

1 k2"8 l XO2. mHO

" # $% ,H Hd ,:T (1) Assistant Professor of Educational Measurement and Evaluation, \

College of Education, King Saud University.

n.Uo p :

*(*

0. 1-234

TIMSS

J( l?

GHI u1 ,HEK2 & H Gv4 wxe ya27 z {g J2 VY G1-234 B$ . |j ;} x2T$ 9: 5".j & wh-d

& HVH2 HV ~). Ut _H€ ,. #t

12M ‚ƒF 2 DE -f B$ wHaN: B

& 1-234 GOZ B$ :V B$C `a2( #t , XY QT „O- BU. ,GHI.

… †( ]8 8 -F JOHO‡ x2T ,Cˆ

4. HH-f hi ]Ut -F B: R1E G 2"4 ,Cˆ

HV ‰F O ]^d ?JOHO‡ X2T$

_H€ ,H-$ hi OF %o .8 ‹S .8 WVM2 y7d 1-234 ? HŒ8 ]d1 4 ‚ƒF B$ whCd ]=

u1 ,HEK2 %1 & ‰T2 4 \

H$ ).

Meijer, 1996

‚-"8 B$ w-"

B$ HH-F hi 2"4 5678 1Yb C$ ƒ3

B$ ]U2 1-234 ŽA

12

‰T€ -t$ ROA

‰ej <= ,Y"j B$ Y2 e

\

@A B 6 :

%1 : ! C ()< DE F G HI. BJ*

:

%12 -(.

K

LM?<

q1 q2 q3 q4 q5 q6 q7 q8 q9 q10 q11 N2 q12

1 0 0 0 1 1 1 1 1 1 1 0 ,"U2 1

2 1 1 1 1 0 0 1 0 0 0 0 WVM2 1

3 1 1 0 1 0 1 0 0 0 1 1

‹S 1

4 1 1 1 1 1 0 1 1 0 0 0

-t F3 0

5 1 1 1 1 1 1 0 0 0 0 0 Qf-2 0

6 0 0 0 0 1 1 1 1 0 1 1

 o 1 Ja(C2"4

7 0 0 1 0 1 1 1 0 1 1 1 H:A R1) & DI 0

E 0.9

0.85 0.83 0.82 0.57 0.55 0.5 0.49 0.3 0.25 0.21 0.15

.‘ ’I

5678 z.‡ ‚-"8 -" 1

‹S. WVM2. ,"U2 J HH-F hi 2"4  o. Qf-2. %o “kV7 -t & ^F”.

H:A R1) B$ BUV2 :. Ja(C2"4 \

(.€ k=.

g z.€ ‰-"

•A 567j >?

E B$ y7

X)1 LMN %= –V7 wƒCVA ,]UV

LMN. 2

X)1 ?WVM2 B: 8 ‹S B: `t7 , 3

X)1 LMN JH-F hi –V( #?d.

1

X)1 LMN.

 o B: 8 ,"U2 B: `t7 6

?Ja(C2"4 0. —d B: R1E 1O2 <= %

$. G1-23ƒ

H6N U$8 & BF" $% & >O

PIRLS International Study Center

&

TIMSS

R1. 1-23 Ot ,O T 1-234 G1.

: ,H—7i ,H$ ,Bt1$ ] B$ { 2004

JU".2".'t

(Martin, Mullis, Gonzalez, &

Chrostowski, 2004)

-23 Ot. , GHI 1

: R1.

2004

,Bt1$. H$ ] B$

JU".2".'t ,H—7i

Mullis, Martin,

Gonzalez & Chrostowski (2004)

\ 1-23 Ot.

: R1.

,Bt1$ ] B$ { 2008

lA ,H$

, h = ,;˜ ,]T.8 ~$

H% ,1.18

, with Olson (

Foy

&

, Mullis , Martin

Preuschoff, Erberber, Arora, & Galia (2008)

,

: R1. GHI 1-23 Ot.

] B$ { 2008

lA ,Bt1$ ,H$

, h = ,;˜ ,]T.8 ~$

0% ,1.18

, with Olson (

Foy

&

, Martin , llis Mu

Preuschoff, Erberber, Arora, & Galia) (2008)

\

1-23 Ot #?d.

: R1.

2011

U72" lA ,H$ ,Bt1$ ] B$ {

Martin,

Mullis, Foy & Stanco (2012)

1-23 Ot. ,

: R1. GHI

,H$ ] B$ { 2012

1.18. lA ,Bt1$

Mullis, Martin, Foy & Arora

(2012)

1-23 Ot. , : R1.

B$ { 2015

. lA ,H$ ,Bt1$ ]

Martin, Mullis, Foy

& Hooper (2016)

: R1. GHI 1-23 Ot. ,

. lA ,H$ ,Bt1$ ] B$ { 2015 Martin,

Mullis, Foy & Hooper (2016)

, 1O2 `a27 @E”.

1-234 G1. & O T :j & @%8 J2

H2

2003

. . 2007

. 2011

-f [8 GF"2 2015

. -f [8 GF"2$. T H UV R1AS("

X)1 .‘ & 6d

\2

@A B 6 :

%2 : 02 O! -./0 3 12 $P< 3 Q1 2*

:

−2003

%2015

"S *J K

-./0

12 02 TM<

U<

V8I U<

W#< B 1! V8I

2015 612

1 383

39 39

2011 613

2 394

37 42

2007 593

3 329

46

49 GHI

2003 605

1 332

43 45

2015 597

1 395

35 39

2011 590

1 436

31 42

2007 567

1 403

44

49

.‘ & R™ `a2( 9: w[( .

]•A 2

]d T . B$ -F [8 GF"2$

[8 GF"2$ ]8. ,w% 3^2$ Y-Htt. , wšZM($

O2$ Y-Htt. ,wZt$ ]d R1AS(" . B$ -F w%

\ 2" ›e x$ "1.

& -F G

.j œZ( mHO X: & ]HK($ †( 1-234

JV2( J2 :VV wOA. -F G 2" m1{t ]8

;t. , KZ  mHO & HO2 ™(

Classical Testing Theory

]8 nC „K(. ,

$ Ž1 “kV( wOA. G 2"4 #t m1t ™7 „VTt. mHO & C‡ ™( ;

ROZ 2"4

Item Response Theory) (IRT)

,

`2( WeKZ p: G 2"4 #t <= ™{7 $ k=.

p: YH= ™{7 $ k=. ,ROZ O F$ GPQ$ Y(:

LMN O F$ GPQ$ Y(: `2( GOZ

(Meijer

& Sijtima, 2001)

\

} YHA M2T{t “kV( 9: H(- GPQ

“k67 B$ W$ “kV7 B: v(

XH) Ot & IRT

x$ 9: XUK W$ #ž ~$ Y271O$. GPQ †(. ,“kV( ~$ WeKZ G 2" O F$

9: H(- <.j 567j >? "1 ›f zƒŸ

J)-

infit

.

outfit

_VT

smith, 1991

H7C. , VH) 9: H(-

„V™ HK%1j

log-likelihood

function

B 1. WZH lo

Levin & Rubin, 1979

,

†N B-2 9: H(- CC.

Expected Caution

index

B . dTt2 ECI (Tatsuoka & Linn,

1983)

\ GPQ B$ 3¡ (

:VV wOA. H(-

M2Tt J2. ,WeKZ G 2" YH= JV2(t J2 O2 mHO & HO2 ™( B$ v( } YHA PQ Y($. GPQ XH)

Caution index Sato

tT SCI

Sato, 1975

X)1 1

PQ. ,

t" P ¢

Caution Index Modified

MCI

B . ‹t1

Harnisch & Linn, 1981

PQ ,

Norm Conformity and Consistency Index

NCI

dTt2 .

dTt2

Tatsuoka & Tatsuoka, 1983

,

PQ.

Within ability index

2"d W

D’Costa, 1993a, 1993b)

X)1

2

PQ ,

Beyond ability index

:

%B

2"d

(D’Costa,

1993a, 1993b)

X)1

\3

£7 )

(Huang, 2011, 2012

:V F2

HH-F 2"4 5678 B: DNU GPQ B$

2"d 1f J2 GPQ$ 9: w62: HH-F hi.

D’Costa, 1993a, 1993b)

"1 >? Y2¤(-t J2.

. J X)1

. 4

X)1

,5

X)1

6

, X)1

\7

AZE$ 9: GPQ >? ‚T€ HV: Ot ]62%

Guttman

G1) ‰Htt 9: VaO

OZ ‰Htt. „7j <= 9:j B$ WeKZ B$ G

,‰ej <= ,Y"j X)1 ,UN

X)1 .‘ ~$ 1

#k ]KI 5

\ 1F2 J¥12 ,TT2 ¦^ 6HA.

GPQ >?

: 8XXXX +,XXXX*

Caution Index Sato

SCI

Sato, 1975

Ht¡ „F.

:

1

PQ.

Within Ability Index

2"d W

D’Costa, 1993a, 1993b)

Ht¡ „F.

:

2

PQ

Beyond Ability Index

:

%B

2"d

D’Costa, 1993a, 1993b)

:

3

B¢UV2 PQ$

Capability Index

„F.

Ht¡

:

4

PQ XYZ [" PQ$

(Misconception

Index)

Ht¡ „F.

:

5

PQ R4-$ƒ PQ$

(Carelessness Index)

:

6

PQ.

WVM2 PQ$

Guessing Index

:

7

]= _H€

: ,LMN <= —$t i

j

ROZ <= —$

\

u_ij

: KZV §€ƒ %o –V7

,0

1

\

: E Gƒ$$ V

p

¨f3 ,UN Y(: ©‰H%8 J2 GOZ

]Ut J2 0

KZ R1) BVI

\ : E Gƒ$$ V

,U P

KZ R1) BVI ]Ut J2 GOZ

\

: Gƒ$$ V

q

%= ,UN Y(: ©‰H%{8 J2 GOZ J2 KHKe

KZ R1) B: RH ]Ut

\ : Gƒ$$ V

~HV‘ q

KZ R1) B: RH ]Ut J2 GOZ \

:P.j

ROZ B: %8 B? WeKZ :

j

KHKe w %=

ªU 9: w$TO$ 1

WeKZV

\ :q.j

: %8 B? WeKZ : ROZ B

j

f3 w %=

ªU 9: w$TO$ 0

WeKZV

\

: ROZ 1Zej :

: y w:V Tth

ROZ 1Zej th

KZV T+1

9: w$TO$ i

K2

: %

$

ui

: KZV œU ]62% y2$

\i

y2$ `2(

]62%

Guttman

6d œU

X)1 ,UN & ’I$

2" ; l? 1

LMN

Person Response Function

– t J. ,

,UN Y(: %o H62€. GOZ e W R1O (: ’HKe

jθ

GOZ e @7d k= ,

LMN R1) B$ pd8 jθ

A HOHO‡ $ƒ .8 ]•

l.Tt LMN %=

,0

e @7d k=.

B$ ,)8 GOZ

jθ

l.Tt LMN %= ]•A

w€.

1

%o –V( ; $ 9: ,Eg ?«. ,

“kV7 ~$ sA2 4 l? %o –V7 ]8 l8 ,0C JH-f hi 2" –V7 p2 ]62%

\

Y$#

:

% 1 '#

&

: Person response function

%

GPQ$ ›Zt O T G"1 `a27 GYb8 KZ  JV2( J2 :VV wOA. H(- O F

9: O F hi 2"4 5678 B: DNU & ¬O ,“kV( wOA. H(- GPQ mTt 1d "1 &

Karabatsos, 2003

_H€

) W YHA ]1

36

wPQ$

9: H(- GPQ ›Zt y2"1 `a27 GYb8 ,O F hi 567j B: DNU & :V ?.

£7 yH= ,et $ wš8

Huang, 2012

K

£7 x%8 _H€

W YHA ]1) "1 2012

Ht¡ GPQ

SCI, MCI, NCI, WB

sA. H(-

2 ™(

Ht¡ GPQ ~$ mHO & HO

OUTFITz, INFITz, ECI2z, ECI4z, Lz

H(-

"1 `a27 GYb8 ,mHO & C‡ ™( sA.

GPQ ]8 @ZNd ) WB

%90

5678 B$

jθ

difficulty probability

1

0

;.™ @g HH-F hi .8 O F hi 2"4 Z2M \ £7 Db. ).

PQ 2012

1 ¢f J2 G

, , , hi 567j B: DNU "1 &

HH-F := B$ 1-234 ~ DE -f x

]Ut ). ,1TU ~I$ & GHI _K- X B$ 1-234

22

9: @O-f ROA

32

,w-f

a27 GYb8.

]8 "1 `

21

XY2 %= @7d w-f

,HH-f 4

,WV­ 567^d X¬ %= @Z¢( {e ‚ƒf

4

,R4- : 567^d XY2 %= @Z¢( {e ‚ƒf

‚ƒf 3

-d$ 567^d X¬ %= @Z¢( {e

R4-$ƒ. WV­

\

GPQ$ @Zb. J2 G"1 R17 H27.

$ B$ sOK2 & LMN O F$

G 2" ›e x

GHI 0. 1-234 & -F

TIMSS

,

"1 >? @t^A GPQ$ Db2

G7H & 2"4 5678 ;NU2"4 LMN O F$

1-23

TIMSS

\

$#*

:

,HEK2 DI & "1 UN$ LM2t

‘ & Y™ 6d T . -F 1U2 .

2

0. GHI. l1-23 9:

TIMSS

l?

®p. ,HVH2 HV 9: WVaO ›1Q{ ¯Œ ’-e8 XY QT

° `t7 ,HEK2 & ZM74 ? ]= , x38 ,$: †( ]8 8 -F x JOHO€ DI B:

.8 %o & ‘ d -F G %= 9: ŸQt G %o WV­

±

?

\

5678 B: DNU "1 >? @.€

(H & HH-F hi. HH-F -F G 2"

R1AS(" . -f [8 ~$ 71O$ R12M T p: d1N . W $O2$ ‰t$ ,2 l?.

GPQ$ DHbt ƒ3 B$ #k. ,Z2M G1.

LMN O F$

£7 1 ¢f J2

Huang, 2011

J.

, , , , Ht¡ "j B: %o :

Z :

.j QT :

HH-F 2"4 5678 -T7 $

R1AS(" .. T . B$ -F “kV( &

$”. nC JCK- ': _C.

0. 1-234 & GHI.

TIMSS, 2015

(:

~F) $ƒ:

0.05

?

nC QT :

hi 2"4 5678 -T7 $

& R1AS(" .. T . B$ -F HH-F JCK- ': _C. $”. nC “kV(

234 & GHI.

0. 1-

TIMSS, 2015

(:

~F) $ƒ:

0.05

?

[ :

¦^ 6HA "1 >? HŒ8 ¦^t :

w4.8 : WT -F x ‘ x$ A$

GHI. 0. 1-23ƒ XYHOt &

TIMSS

5678 ›e B$ sOK2 ƒ3 B$

F$ GPQ$ M2" -F G 2"

LMN O

R1AS(" . -f [8 ~$ 71O$

\

wH7Ÿ

: yH%t & "1 `a27 B$ RZ2"4

-ae G1) k­ & HVH2 HV 9: WVaO 1-234 9: [j x2T$ WTK2

\

M)S*

:

\$PXX +,XX*

:

capability index

% y —$ K

V". , KHKE G 2"4 HO y7j #? J

R1) BVI Y2 e x2T$ ]Ut J2 GOZ B:

KZ

i

\ B$ B¢Uˆ ) KZ ]8 „(V

yt1) B$ ,)8 ]Ut J2 GOZ

\

@XX]? QXX +,XX*

:

Misconception Index

%

y —$

HO y7j X"4 #? JV". ,

” G 2"4 x2T$ ]Ut J2 GOZ B: f

KZ R1) B$ 9:8 Y2 e

i

y78 „(V , HO

‰F x XYA [" †( l8 ‰F [HV 5O(

GOZ #t B:

\

-*C +,*

:

Carelessness Index

y —$ %

G 2"4 HO y7j X"4 #? JV". ,

B: f”

BVI Y2 e x2T$ ]Ut J2 GOZ KZ R1)

i

\

XXP' +,XX*

:

Guessing Index

y —$ %

G 2"4 HO y7j X"4 #? JV". , Y2 e x2T$ ]Ut J2 GOZ B: KHKE

KZ R1) B$ 9:8

i

\

XX* ^CXXW _XX(

+,XX<

+,XX*

\$PXX

:

capability index

PQ.% @X]? QX +,X*

Misconception Index

JH-F 2"4 –V7

e x2T$ @7d [" KZV BVI GOZ

x2T$

R1) x2T$ “13 .8 KZ R1)

x & B¢UV2 x$ <= ]hN 6|•A KZ KZ

\ wƒd HO PQ B$

-XX*C +,XX*

:

Carelessness Index

PQ. % XP' +,X*

:

Guessing Index

JH-F hi 2"4 –V7 %

wH .8 KZ R1) BVI ]d [" KZV KZ R1) B:

\

1`

:

− 1

o Gk GOZ 9: "1 1E2) %

RO2(

\

− 2

,e8 B$ “k67 ŸƒŸ 9: "1 1E2)

0. 1-234 & w%kV7 ': 18 : l%8 l? GHI.

\ 2015

Q6a :

XX b]0XX*

`Y( 9: "1 GV2::

"1 "8 B: %³ ªHK2 JZe \

XX -1 4 ,UN:

0. 1-23

GHI.

TIMSS, 2015 (Trends In International

Mathematics and Science)

l? G7H- 1E$

?($ 1-234 ? O. ,"1 >? yH: GV2:

: 1995

;« ,G(" ~ 18 ,d l1. ,UN

JCK-$ & -F Xt WTg & } . R:T$

% ?S2 .—t ƒ3 B$ GHI.

m1 [1$. WV [1´. -F [8 9:

\

JVHHO2 1fo 1-234 GOA 2d (: J:.1 G1-23ƒ 0. —d B: 1E 1-234 GZe

BF" Hd & >O$. H.

(Boston College,

TIMSS & PIRLS International Study Center)

Bt1$. $ ] B$

(Mullis, I.V.S. & Martin,

M.O. (Eds.) 2013).

]U2.

ΠB B$

:

J. GHI & G4 18 BVš2 x2K G7H-. "(. p‘. :j & G4 Tµ.

:. [—HZ. [HVHU. [H€j 1j

H-.

. GHI & JFS & -.

“2(2"4. sH-F2. A

& ‰T( sA. :®$ ,

X)1 .‘

3

X)1 .‘. ,

\4

B 6 :

%3 : < 4M< Bc Y$ -1M< Z< V20 K

4M<

20

<

20

:o %30

A

% 35

p‘

%30 sH-F2

% 40

"(

%20

“2(2"4 %25

G7H-

% 20

B 6 :

%4 : < 4M< Bc Y$ -1M< Z< V20 K

4M<

20

<

20

[H€j

% 35 A

%35

[HVHU %20

sH-F2 %35

[—HZ

% 25

“2(2"4 %30

14 : %20

dPc :

DE -f G7H B$ "1 ~V2 ]Ut & 0. 1-234 XO2 .h23 B? B$C

GHI.

TIMSS

: R1.

3´ |d ;2015

R1.

,R1AS(" .. T . -f  t 0. 1-23ƒ It B? -F V £ _H€

T . B$ “k6( ~HV‘ GHI.

:

%4344

Z( It B? -F V £ . R1AS(" . B$ 1-234 :

11854

`a27 Gh23. ,%

AS(" . -f |j ;T . `a27 71O R1

B$ GHI. 1-23 & .j —d @2€

G7H 9: (E€. ,R1. #t & d1N . W Ht¡ GF” sA. 1-234 :

− 1

n.Uo ~) B: G7H- ,—(t :

https://timssandpirls.bc.edu/timss2015/internatio nal-database

− 2

,Vg J2 ‚ƒF G %= GZ 1H23

—$1

BAS….

\

− 3

€. D$ & GZ ~HVv \

− 4

“kV( X)1 ‰T€ G7H- ®A

\

− 5

D$ ƒ3 B$ R€ 9: “kV7 ,d ’HKEt

’HKE2

BSASCRM6

\

− 6

d1N . ‰T€ GZ ®A \

− 7

%o Gk GOZ -2"

iE \

0!

: ]Ut ]8 G1-234 “k67 1H23 (: J:.1 ) “kV( h23 _H€ R:-2$ )18. Z2· f8 Gk

': _C. ,$”. ,nC f8 @S .

1-23 ¦¡ K( 9: G1-234

, 27

, 17

,15

GHI.

,20

,15

\20

V( ]Ut.

B$ nC “k

B$ 1H23 ROA 27

_K- 2$

, . 2$ B$ 1H23 ROA 20

WeKZ : £ . ,GHI _K-

270

w-f

B$ yTZ7 h23. ,T . B$ -f.

R1AS(" .

270

-f. w-f \

B$ $” “kV( ]Ut.

$ 1H23 ROA 17

B

_K- 2$

, . 2$ B$ 1H23 ROA 15

WeKZ : £ . ,GHI _K- w-f 258

B$ yTZ7 h23. ,T . B$ -f.

R1AS(" .

\258

B$ ': _C “kV( ]Ut.

1H23 ROA 15

_K- 2$ B$

$ B$ 1H23 ROA 20

_K- 2

WeKZ : £ . ,GHI

-f. w-f 270

R1AS(" . B$ yTZ7 h23.

270

-f. w-f \

eS>f g<

:

¦^ $ -t GPQ XH) ‚TK HO :

− 1

G7H @$M2"

TIMSS, 2015

&

Gh23. ': _C. $”. nC “kV(

GOA

o Gk GOZ -2". 2$ B$ 1H234 Gk %

,ROZ$ G7H BVš2t J2 2"4 5678. iE B$ R1AS(" . G7H B$ HaN: G(H: 1H23 XŸ

`$7 M2" Gh23 J2 “k6(

:^ SPSS

]8 #k. ;T . G7H : ~$ .T2$

:8 B$ Cd8 R1AS(" . -f B$ Wd1N :8 T . B$ Wd1N -F

\

−2

(H G7H ~$ T (H G7H `$

1AS(T \

−3

`$7 & G7H- 3=

WBstar

LMN O F$ GPQ$ XH) ‚T‡

\

b*O :

WBstar

% :

XH) @-T€

LMN O F$ GPQ$

, , ,

`$7 F"

WBStar

] B$ ‰2d l?

£7.

Lu & Huang, 2010

`$7 M2"

#TH HA

Visual Basic 6.0

\ .‘ ’I.

X)1 KZe ‚2d B$ wk3^$ wHIA w4C$ 5

77

£7® T.. ,†—(d ,BU71

2004 Rankin, Knezek,

Wallace & Zhang

yH: s-f.

`$7

Wbstar

X)1 .‘ & 6d `a2( @7d.

\5

,HK2 & R™ )1j. ®$ hNt _H€

¦^ $ <=

:

: C,M Bi⁰

:

Wi¹

X) yH: 2T JH-f –V( 7 :

.1

: B Bi¹

–V( 7 X) yH: 2T WVM2

:

\ 2

Wi⁰: W

X) yH: 2T 0-$ 4 –V( 7 :

\ 3

W or B

:

Wi⁰ or Bi¹

D(e l8 ‰d$ –V( 7

X) yH: 2T 0-$ 4 .8 WV­ –V(d :

K 4

@A B 6 :

%5 : b* ' YM be WBstar

Id q1 q2 q3 q4 q5 hP< Category W B C M

1 1 1 1 1 1 5 H 1 0 0 0.6667 0

2 1 1 1 0 0 3 H 1 0 0 0.2708 0.125

3 1 1 1 0 0 3 H 1 0 0 0.2708 0.125

4 1 1 0 0 0 2 M 1' 0 0 0.1667 0.2292

5 1 1 0 0 0 2 M 1' 0 0 0.1667 0.2292

6 1 0 0 1 0 2 M 2 0.0208 0.0625 0.1458 0.1667

7 1 0 0 1 0 2 M 2 0.0208 0.0625 0.1458 0.1667

8 1 0 1 0 0 2 M 1 0.0208 0.0208 0.1458 0.2083

9 0 1 1 0 0 2 L 3' 0.1458 0.0208 0.0208 0.2083

10 0 0 0 1 1 2 L 4' 0.1667 0.2083 0 0.0208

11 1 0 0 0 0 1 L 1 0 0 0.0625 0.5417

12 0 0 0 0 0 0 L 1 0 0 0 0.7917

V 9 6 5 4 2 26 -

P.j .75 .50 .42 .33 .17 -

q.j .25 .5 .58 .67 .83 -

X)1 .‘ ’I

GPQ$ ,Hg `a27 5

LMN O F$

W, B, C, M

HIA G7H-

`$7 M2"

Wbstar

.‘ B$ ’š2 _H€ ,

5678 ŸƒŸ †( ]8 567^d @Z(e

HH-f Z BVI

H ,H1

Z BVI HH-f 567^d Z(e WFV7.

F"2 y-˜

M1'

& WV­ 567^d Z(e WFV7. , F"2 Z

,M2

Z & HH-f 567^d WFV7.

H7 ,L1

H7 y-˜ Z BVI 0-$ hi –V7.

,L3'

H7 Z BVI ‰d$ –V7.

L4'

\

‘ &.

X)1 .

’I 6

HZHd & H¡

GPQ ‚T€

, , ,

@A B 6 :

%6 : @A UP0 &'# ()* +,* i2>

:

%6 K

j3 j3 DE

R1O B: wH R1O BVI

X)1 .‘ ’I

f 6

GPQ ‚T€ O

, , , RF G4 sA.

X)1 &

, 4

,5

, 6

X)1 2"4 –V( 7

y2%1. 6

\2

_H€

= ]

VH) l.Tt q*

:

\

b*O YP! ?W :

WBstar

% :

. wH®(t w-Htt ]eKZ ‰t H(H ‰t sA

percentiles

PQV C

HOHO‡ R1O JF y7j ;

B$ H3

R4-$ƒ ,WVM2

O XŸ , DH(E2

J. ;(e8 ŸƒŸ <= WeKZ :

H R1O

 —$. ,H72. F"2.

H, M, L

sA.

Ht¡ G(H

:

W$

9:8.0.67

:H~

: R1) H

\

W W$

−0.33 0.67

:M~

F"2$ R1) \

W$

,)8. 0.33

:L~

H72$ R1)

\

Ht¡ GPQ XH) ‰tt XŸ

W, B, M

w-Htt

W$ 9: ,Eg J2 GPQ XHOA ,wH®(t

95

9:8. (

]Ut 2"4 567j VH) ‰T€ .8 O F$ hi w6H)

12­ J2 W

\ .8 PQ B$ ,d 9: : XU€ †(

W, B

6Y2VH) @7d k•A B$ pd8

wf678 p2t 0.03

PQ B$ ,d XH). ,HH-f hi pd8 C, M

0.3

HH-f wf678 p2t

\

]#A0* be :

X)1 .‘ BVš2

QT %= B$ w[—% 7

4 5678 DH(Et B: ^T l?. ,.j 2"

HH-F ^T l?. ,nC QT %= B$ w[—%.

_K- HH-F hi 2"4 5678 DH(Et B:

B$ nC “kV( & T .. R1AS(" . G7H

TIMSS, 2015

\

B 6 :

%7 : X 1 X* YXW X X X X "0SX8

-./0XX kXXJ lmXXP0 12XX :

%27 -XX(.

540

^nM?*

K

12 -./0 Z?

17 156 H1

0 12 H3

89 69 M1

9 3 M2

2 4 M3

22 2 L1

109 19 L1'

2 0 L2

15 4 L2'

4 0 L3'

1 1 L4

237 246 JH-f

26 7 WV­

6 16 R4-$ 4

1 1 ‰d$

270 270 V

I X)1 .‘ ’

2"4 5678 DH(Et 7

-F `a27. R1AS(" . -F `a27 B$ ,U B$ ]U 1-234 T .

ROA 27

WeKZ :.

`a2( @7d. ,-f. w-f 540

R1AS(" . ¦¡ K( 9:

@Z(e wFV7 246

-T( . HH-f 2" 567^d %91

GZ BVI

Ht¡

: . ,H Z & wFV7 156

Z & wFV7 69

]FV7. ,F"2

. ,H7 Z & 2

19

& wFV7

H7 y-˜ Z \

. -T( WV­ 567^d @Z(e 5678 7

%2

Ht¡ GZ BVI :

678 3

,F"2 Z & 5

Ze.

. ,H7 Z BVI 0

Z BVI 5678 4

H7 y-˜

\ . -T( H-$ hi 567^d @Z(e wFV7 16

%6

Ht¡ GZ BVI :

Z BVI wFV7 12

. ,H Ze. ,F"2 Z BVI 5678 4

0

€. 2" –V7. ,H7 y-˜ A BVI

1

‰d$

R4-$4. WV­

-T( . %0.4

H7 Z BVI \

¦¡ K( 9: WT -F `a27 @7d :

-T( . HH-f 2" 567^d @Z(e wFV7 237

%88

Ht¡ GZ BVI :

,H Z & wFV7 17

. ,F"2 Z & wFV7 89

7 Z & wFV7 22

,H

. H7 y-˜ Z & wFV7 109

\

. -T( WV­ 567^d @Z(e wFV7 26

%9

Ht¡ GZ BVI :

,F"2 Z & 5678 9

]FV7.

. ,H7 Z BVI 2

Z BVI wFV7 15

H7 y-˜

\ -T( H-$ hi 567^d @Z(e 5678 6

%2

Ht¡ GZ BVI :

V7 ]F Z BVI 2

. ,F"2

–V7. ,H7 y-˜ Z BVI 5678 4

€. 2"

‰d$ 1

WV­

. R4-$4

-T(

%0.4

H7 Z BVI

\

X)1 .‘ BVš2

QT %= B$ w[—% 8

2"4 5678 DH(Et B: ^T l?. .j HH-F QT %= B$ w[—%.

B: ^T l?. nC

_K- HH-F hi 2"4 5678 DH(Et & T .. R1AS(" . GHI G7H B$ nC “kV(

TIMSS, 2015

\

B 6 :

%8 : -./0X X 1 X* Y$ "0S8

kJ lmP0 12 :

%20 -(.

^nM?* 540 K

1 -./0 Z?

4 185 H1

90 55 M1

3 0 M2

9 6 M3

12 2 L1

116 15 L1'

3 0 L2

24 0 L2'

6 6 L3'

3 1 L4'

222 257 JH-f

30 0 WV­

15 12 R4-$ 4

3 1 ‰d$

270 270 V

X)1 .‘ ’I 5678 GZH(Et 8

`a27 B$ ,U 2"4 R1AS(" . B$ -F

GHI 1-234 T . B$ -F `a27.

B$ ]U WeKZ :. ROA 20

w-f 540

K( 9: R1AS(" . `a2( @7d. ,-f.

¦¡

: ,HH-f 2" 567^d @Z(e wFV7 257

-T( . %95

Ht¡ GZ BVI :

Z & wFV7 185

. ,H ]FV7. ,F"2 Z & wFV7 55

& 2

. ,H7 Z

H7 y-˜ Z & wFV7 15

\

]d WV­ 567^d @Z(e 2" 5678 % 4 wZe l.T WVM2 5678 : \

. @Z(e wFV7 12

-T( H-$ hi 2" 567^d

%4.4

Z BVI G

Ht¡

: . ,F"2 Z BVI 5678 6

5678 6

H7 A y-˜ BVI \

€. 2" –V7.

‰d$ 1

R4-$4. WV­

-T(

%0.4

H7 Z BVI \

¦¡ K( 9: WT -F `a2( @7d :

-T( ,HH-f 2" 567^d @Z(e wFV7 222

%82

Z BVI Ht¡ G

: Z & 2" 5678 4

. ,H . ,F"2 Z & wFV7 90

wFV7 12

&

. ,H7 Z

. ,H7 y-˜ Z & wFV7 116

30

-T( WV­ 567^d @Z(e wFV7

%11

GZ BVI

Ht¡

: . ,F"2 Z & 5678 3

Z & 5678 3

,H7 . H7 y-˜ Z & wFV7 24

\ . wFV7 15

-T( H-$ hi 2" 567^d @Z(e

%5.6

BVI

Ht¡ GZ :

. ,F"2 Z & 5678 9

5678 6

H7 y-˜ A &

\ . 2" 567^d @Z(e 5678 3

-d$

R4-$4. WV­

-T(

%1

y-˜ Z BVI

H7 \

X)1 .‘ BVš2

QT %= B$ w[—% 9

HH-F 2"4 5678 DH(Et B: ^T l? .j DH(Et B: ^T l? nC QT %= B$ w[—%. . _K- HH-F hi 2"4 5678 B$ $” “kV( & T .. R1AS("

G7H

TIMSS, 2015

\

B 6 :

%9 : -./0X X 1 X* YXW X X "0S8

_*o lmP0 12 :

%17 -(.

^nM?* 516 K

1 -./0 Z?

17 152 H1

76 60 M1

6 1 M2

7 17 M3

0 1 M4

23 1 L1

105 23 L1'

24 3 L2'

221 236 j3

30 4 Pp

7 17 -*

0 1 VW*

258 258 hP<

X)1 .‘ ’I

2"4 5678 DH(Et 9

. -F `a27. R1AS(" . -f `a2(

]U 1-23 & T

:. ROA 17

WeKZ . `a27 @7d. ,-f. w-f 516

¦¡ K( 9: R1AS("

: 567^d @Z(e wFV7 236

-T( . ,HH-f 2"

%91

Ht¡ GZ BVI :

. ,H Z & wFV7 152

Z & wFV7 60

–V7. ,F"2

. ,H7 Z & 1

Z & wFV7 23

H7 y-˜

\ -T( WV­ 567^d @Z(e 5678 4

%2

BVI

Ht¡ GZ :

€. –V7

. F"2 Z & 1

3

H7 y-˜ Z BVI 5678 \

567^d @Z(e wFV7 17

-T( H-$ hi

%7

Ht¡ GZ BVI :

wFV7 17

€. –V7. ,F"2 Z BVI

‰d$ 1

WV­

R4-$4.

-T(

%0.4

Ht¡ GZ BVI :

€. –V7

F"2 Z & 1

\

@7d.

¦¡ K( 9: T . `a2(

:

-T( . HH-f 2" 567^d @Z(e wFV7 221

%86

Ht¡ GZ BVI :

,H Z & wFV7 17

. . ,F"2 Z & wFV7 76

Z & wFV7 23

. ,H7 H7 y-˜ Z & 5678 105

\

­ 567^d @Z(e wFV7 30

-T( WV

%12

Ht¡ GZ BVI :

. ,F"2 Z & 5678 6 24

H7 y-˜ Z BVI wFV7 \

567^d @Z(e 5678 7

-T( H-$ hi

%3

Ht¡ GZ BVI :

5678 3

567^d 2" 5678 D(E{t }. ,F"2 Z BVI -d$

R4-$4. WV­

\

BVš2 X)1 .‘

QT %= B$ w[—% 10

HH-F 2"4 5678 DH(Et B: ^T l? .j

DH(Et B: ^T l? nC QT %= B$ w[—%. . GHI _K- HH-F hi 2"4 5678 B$ $” “kV( & T .. R1AS("

G7H

TIMSS, 2015

\

B XX6 :

%10 : XX 1 XX* YXXW XX XX XX XX "0SXX8

_*o lmP0 12 -./0 :

%15 -(.

^nM?*516 K

12 -./0 Z?

4 171 H1

72 68 M1

4 0 M2

4 15 M3

17 0 L1

123 4 L1'

32 0 L2'

1 0 L3'

1 0 L4'

216 243 JH-f

36 0 WV­

5 15 R4-$4

1 0 ‰d$

258 258 V

X)1 .‘ ’I

5678 DH(Et 10

-F `a27. R1AS(" . -f `a2( 2"4 B$ ]U GHI 1-23 & T .

15

WeKZ :. ROA

@7d. ,-f. w-f 516

9: R1AS(" . `a27

¦¡ K(

: wFV7 243

-T( . ,HH-f 2" 567^d @Z(e

%94

BVI

Ht¡ GZ :

. ,H Z & wFV7 171

wFV7 68

. ,F"2 Z &

H7 y-˜ Z & 5678 4

\ }.

WV­ 567^d 2" 5678 D(E{t \

-T( H-$ hi 567^d @Z(e wFV7 15

%6

Ht¡ GZ BVI :

,F"2 Z BVI wFV7 15

-d$ 567^d 2" 5678 DH(Et D(Et }.

WV­

R4-$4.

K( 9: T . `a2( @7d. ,

¦¡

: ,HH-f 2" 567^d @Z(e wFV7 216

-T( . %84

Ht¡ GZ BVI :

Z & 5678 4

. ,H –V7. ,F"2 Z & wFV7 72

& 17

. ,H7 Z

H7 y-˜ Z & wFV7 123

\

-T( WV­ 567^d @Z(e wFV7 36

%14

Ht¡ GZ BVI :

. ,F"2 Z & 5678 4 32

H7 y-˜ Z BVI wFV7 \

567^d @Z(e 5678 5

H-$ hi -T(

%2

Ht¡ GZ BVI :

4

5678

–V7. ,F"2 Z BVI

,H7 y-˜ Z BVI 1

€. –V7.

‰d$ –V(d D(e 1

R4-$4. WV­

H7 Z BVI \

X)1 .‘ BVš2

QT %= B$ w[—% 11

HH-F 2"4 5678 DH(Et B: ^T l? .j w[—%. DH(Et B: ^T l? nC QT %= B$

. _K- HH-F hi 2"4 5678 B$ _C “kV( & T .. R1AS("

G7H

TIMSS, 2015

\

B 6 :

%11 : -./0X X 1 X* YXW "0S8

J lmP0 12 q! T

: %17 -(.

^nM?* 540 K

12 -./0 Z?

28 147 H1

0 2 H3

88 60 M1

3 0 M2

14 11 M3

17 6 L1

86 40 L1'

29 3 L2'

3 1 L3'

2 0 L4'

219 253 JH-f

32 3 WV­

17 14 R4-$4

2 0 ‰d$

270 270 V

X)1 .‘ ’I 678 DH(Et 11

2"4 5

. -F `a27. R1AS(" . -f `a2(

]U 1-234 T :. ,ROA 17

KZ

. `a27 @7d. ,-f. w-f 270

¦¡ K( 9: R1AS("

: 567^d @Z(e wFV7 253

-T( . ,HH-f 2"

%94

Ht¡ GZ BVI :

. ,H Z & wFV7 147

Z & wFV7 60

. ,F"2

. ,H7 Z & 5678 6

& wFV7 40

H7 y-˜ Z \

-T( WV­ 567^d @Z(e 5678 3

%1

BVI

. ,H7 y-˜ Z

H-$ hi 567^d @Z(e wFV7 14

-T(

%5

Ht¡ GZ BVI :

]FV7 & 2

Z

,H D(Et }. ,F"2 Z BVI wFV7 11

-d$ 2" 5678

R4-$4. WV­

\

¦¡ K( 9: T . `a27 @7d.

:

-T( . ,HH-f 2" 567^d @Z(e wFV7 219

%81

Ht¡ GZ BVI :

,H Z & wFV7 28

. Z & wFV7 88

. ,F"2 

Z & wFV7 17

. ,H7 H7 y-˜ Z & wFV7 86

\

-T( WV­ 567^d @Z(e wFV7 32

%12

Ht¡ GZ BVI :

. ,F"2 Z & 5678 3 29

€. 2" –V7. ,H7 y-˜ Z BVI wFV7

1

‰d$ –V(d D(e

R4-$4. WV­

BVI Z

H7 \ -T( H-$ hi 567^d @Z(e wFV7 17

%6

Ht¡ GZ BVI :

,F"2 Z BVI wFV7 14

. WFV7 @Z(e ,H7 y-˜ Z BVI 5678 3

-d$ 567^d 2" 2

R4-$4. WV­

-T(

%0.7

\(

X)1 .‘ BVš2

QT %= B$ w[—% 12



HH-F 2"4 5678 DH(Et B: ^T l? .j DH(Et B: ^T l? nC QT %= B$ w[—%.

. GHI _K- HH-F hi 2"4 5678 B$ ': _C “kV( & T .. R1AS("

G7H

TIMSS, 2015

\

B XX6 :

%12 : XX XX "0SXX8 XX 1 XX* YXXW XX XX

q! TJ lmP0 12 -./0 :

%20 -(.

^nM?* 540 K

1 -./0 Z?

7 169 H1

0 13 H3

77 65 M1

2 0 M2

4 4 M3

16 2 L1

145 14 L1'

11 0 L2'

4 2 L3'

4 1 L4'

245 250 JH-f

13 0 WV­

8 19 R4-$4

4 1 ‰d$

270 270 V

X)1 .‘ ’I 5678 DH(Et 12

`a27. R1AS(" . -F `a27 B$ ,U 2"4 ]U GHI 1-234 T . -F WeKZ :. ,ROA 20

,-f. w-f 540

¦¡ K( 9: R1AS(" . `a27 @7d.

:

250

-T( . ,HH-f 2" 567^d @Z(e wFV7

%93

Ht¡ GZ BVI :

. ,H Z & wFV7 169

65

]FV7. ,F"2 Z & wFV7 ,H7 Z & 2

. H7 y-˜ Z & wFV7 14

\

WV­ 567^d 2" 5678 D(Et }.

\

567^d @Z(e wFV7 19

-T( H-$ hi

%7

Ht¡ GZ BVI :

. ,F"2 Z & wFV7 13

4

€. 2" –V7. ,F"2 Z BVI 5678

1

‰d$ –V(d D(e

R4-$4. WV­

y-˜ Z BVI

H7 \

¦¡ K( 9: T . `a27 @7d.

:

2" 567^d @Z(e wFV7 245

-T( . ,HH-f

%91

Ht¡ GZ BVI :

,H Z & 5678 7

. . ,F"2 Z & wFV7 77

Z & wFV7 16

. ,H7 H7 y-˜ Z & wFV7 145

\

-T( WV­ 567^d @Z(e wFV7 13

%5

Ht¡ GZ BVI :

]FV7 ,F"2 Z & 2

. ,H7 y-˜ Z BVI wFV7 11

@Z(e 5678 4

‰d$ –V(d

R4-$4. WV­

y-˜ Z BVI

H7 \ X)1 .‘ BVš2

QT %= B$ w[—% 13

HH-F 2"4 5678 DH(Et B: ^T l? .j DH(Et B: ^T l? nC QT %= B$ w[—%.

hi 2"4 5678 . _K- HH-F

$”. nC “kV( & T .. R1AS("

G7H B$ ': _C.

TIMSS, 2015

\

B 6 :

%13 : 1!

F ) DE ) O!

lmP kJ _*o TJ q!

K hP<

9 = ,61 t

= 1596

mP0 q! TJ l

9 = ,17 t = 540

_*o lmP0 9

= t ,17 = 516

kJ lmP0 9 = ,27 t = 540

1 -./0 1 -./0 1 -./0 1 -./0 Z?

677 735 219 253 221 236 237 246 JH-f

88 14 32 3 30 4 26 7 WV­

30 47 17 14 7 17 6 16 R4-$4

3 2 2 0 0 1 1 1 ‰d$

798 798 270 270 258 258 270 270 V

X)1 .‘ ’I -f `a2( 567j : 13

“k6( p: T . -F `a27. R1AS(" . 1-234 ': _C. $”. nC Z2M 1-234 ]U

OA 61

WeKZ :. ,R

w-f 1596

-f.

\

¦¡ K( 9: R1AS(" . `a27 @7d.

:

-T( HH-f 2" 567^d @Z(e wFV7 735

%92

,

. -T( WV­ 567^d @Z(e wFV7 14

%2

. ,

47

-T( R4-$ : 567^d @Z(e wFV7

%6

]FV7. ,

2

-d$ 567^d Z(e

­ R4-$4. WV -T(

\%0.3

¦¡ K( 9: T . `a27 @7d.

: -T( HH-f 567^d @Z(e wFV7 677

%85

. ,

88

-T( WV­ 567^d wZ(e

%11

. , @Z(e wFV7 30

-T( H-$ 4 567^d

%4

. , 567^d @Z(e 5678 3

-d$

R4-$4. WV­

-T(

\%0.4

X)1 .‘ BVš2

QT %= B$ w[—% 14

HH-F 2"4 5678 DH(Et B: ^T l? .j DH(Et B: ^T l? nC QT %= B$ w[—%. . GHI _K- HH-F hi 2"4 5678 $”. nC “kV( & T .. R1AS("

C.

G7H B$ ': _

TIMSS, 2015

\

B 6 :

%14 : 1!

F ) DE ) O!

lmP kJ _*o TJ q!

K hP<

9 = ,55 t = 1596

q! TJ lmP0 9 = t,20 = 540

_*o lmP0 9 = t ,15 = 516

kJ lmP0 9 = ,20 t = 540

1 -./0 1 -./0 1 -./0 1 -./0 Z?

683 750 245 250 216 243 222 257 JH-f

79 0 13 0 36 0 30 0 WV­

28 46 8 19 5 15 15 12 R4-$4

8 2 4 1 1 0 3 1 ‰d$

V

)1 .‘ ’I X

`a2( 567j : 14

p: T . -F `a27. R1AS(" . -f ': _C. $”. nC Z2M 1-234 “k6(

B$ ]U GHI 1-234 :. ,ROA 55

WeKZ

-f. w-f 1596

\ . `a27 @7d.

¦¡ K( 9: R1AS("

: 567^d @Z(e wFV7 750

-T( HH-f 2"

%94

WV­ –V7 l8 D(E }. ,

%0

. , 46

-T( R4-$ : 567^d @Z(e wFV7

%6

]FV7. ,

-d$ 567^d Z(e 2

WV­

R4-$4.

-T(

\%0.3

¦¡ K( 9: T . `a27 @7d.

:

H-f 567^d @Z(e wFV7 683

-T( H

%86

. ,

79

-T( WV­ 567^d wZ(e

%10

. @Z(e wFV7 28

-T( H-$4 567^d

%3

. , 567^d @Z(e 5678 8

-d$

R4-$4. WV­

-T(

\%1

be0 #A0*

: ^ @Z(e :

%92

.

%85

2" 5678 B$

-f 567^d 02 9: T. R1AS("

2"

#t ]8 l8 ,ŸƒC G1-234 “k67 p: HH-f & WeKZV HOHO‡ G 2"4 ,Cˆ 567j & & BUV2 <= #k x— ). , _K-$

y($ 9:8 R1AS(" -f x ‘. _K-$

T . B$ -F x

\ : ^u

@Z(e

%94

.

%86

678 B$ % 2" 5

-f 2" 567^d 02 9: T. R1AS("

#t ]8 l8 ,ŸƒC G1-234 “k67 p: HH-f & WeKZV HOHO‡ G 2"4 ,Cˆ 567j & BUV2 <= #k x— ). ,GHI _K-$

9:8 R1AS(" -f x ‘. GHI _K-$ &

y($

T . B$ -F x

\

^Ju @Z(e :

%8

.

%15

-f 2" 5678 B$

567^d 1-234 02 9: T. R1AS("

,Cˆ 4 567j #t ]8 l8 ,HH-f hi 2"

Zt1 x— ). ,WeKZV HOHO‡ G 2"4 F x HH-F hi 567j -T7 & WT -

BUV2 :. ,1-234 624 : <= _K-$

"j B: G %o WV­ <= -F ~A ¸ ,&

\

: ^XX @Z(e

%6

.

%14

2" 5678 B$

1-234 02 9: T. R1AS(" -f #t ]8 l8 ,HH-f hi 2" 567^d GHI WeKZV HOHO‡ G 2"4 ,Cˆ 4 567j \

).

-F x HH-F hi 567j -T7 Zt1 x—

624 : <= GHI _K-$ & WT WV­ <= -F ~A ¸ & BUV2 :. 1-234

"j B: G %o

\

^2*

hi 2"4 5678 -T7 ]= : & HH-F