!"#$%&'(
y >F ² y $ &³ &§ V | o p &7 c%
A Study to Develop the Computerized Adaptive Learning
System of Connecting Different Students’ Knowledge Structures
Abstract
This study is aimed at developing the computerized adaptive learning system of connecting different students’ knowledge structures. The system contains 2 parts. One is the computerized adaptive test of connecting different students’ knowledge structures and the other is the adaptive remedial instruction.
Under the trend of the adaptive test, the adaptive test based on knowledge structure of the independent unit has already been developed complete and maturely. In view of
this, this research takes 'the factor and multiple' theme as an example, and tries to
combine the ability indexes related to the factor and multiple. Using the adaptive test as a tool, the researcher utilizes the linking of anchor items to estimate students’ item structure. Finally, this research assesses the feasibility and effect of the adaptive test and adaptive remedial instruction.
The results of this study are as follow:
1. The effect of the adaptive learning system is good. Comparing with paper-and-pen test, the adaptive test can also save the time and items of the test. The function of offering individual diagnosing report permits learning situations to know by teachers and students. It is an efficient way to carry remedial instruction out.
2. The average prediction accuracy of the adaptive test can reach 93.11%. The average items been tested are 30. Students finish the test lessening 18 items.
3. After taking the adaptive remedial instruction, all students’ achievements of the final test are obviously higher than the pre-test (t=5.268, p<.001). The low achievement students’ progress is obviously better than other students’.
According to the results, the computerized adaptive learning system of connecting different students’ knowledge structures proposed by this research has been performed well.
Keywordsknowledge structure, computerize adaptive test, remedial instruction,
--- 01
´ nw µ ¶ !³ &--- 01 ´ w · ¸ ¹ º --- 03 ´ w » ¼ !½ ¾ --- 04--- 06
´ nw --- 06 ´ w F B !G B $ ² ¿ --- 08 ´ w T --- 12 ´ À w " # $ --- 14--- 16
´ nw q Á --- 16 ´ w  !Ã Ä --- 21 ´ w Å Æ --- 22 ´ À w U V --- 22--- 29
´ nw --- 29 ´ w _ \ 7 c--- 36 ´ w i j " # $ 7 c--- 37--- 41
´ nw Ç --- 41 ´ w È É --- 42--- 44
Ê Ë --- 44 ÌÊ Ë --- 48---
49
Í Î n P Q R S Ï Ð --- 49 Í Î s t MJ! wÑ Å Ò Ó--- 52 Í Î s t MJÔ Õ Ö × --- 54 Í Î À s t MØ--- 59 Í Î = s t MJ ¿ k --- 67! " # $ ! % & ' ( ) " # * + , - ./ 0 1 23 4 5 67 8 )9 6:; 6 < = > ?@ A B - =C D " # E F GH I " # )JK( $ ) % & 'L M N ) O PQ R S T U V W
D " # XY .Z [ )\ ] % & '^ X_ ` % & 'JK(a
b cde f g h(
i 4 C j k l m " # )n o p q r2s t ru v r)'w x y h z ) " # {| 9 } ~ " {d 2 ) I - N ) G 9 } ~ ') (
/ =/ 0 6 r " # (I)2(II)2(III).
" # ( 200320042005) z 2- = :- = D G¡¢ D £ Z r " # ¤ ¥ 'N ¦ § - N ) :¨ )% & v © ª 'N {M N \ ] « K¬ )% & '( / G« 6® N \ ] ¯ Z ° ± ) r " # ² ³ . ) r " # Y .d " # =62~ " :´ µ ¶ ~ " · ¸Y ¹ º » .¼ ¨ ½ (¾ ¿ À 2003ÁÂÃ
Ä2004ÁÅ Æ Ç 2004ÁÈ É Ê 2004)( " # )n o h.¯ Z ° ± ) " # Ë Ì Í Î ÏÐ :JÑ Ò !L M ° ± Ó Ô ) Õ .Ö l × Ø ) Ù j ° ± ¯ Z )Ú Û hÜ ! )\ ] " # d )=6: Ý Þ « ß g · { | Ð z2zà )° ± ~ " Y .d )=6: á S â ã á 4 5 )Í J " # äY .å æ D ç èÓ Ô ¤ ¥ ¨ ) % & v © Y .d é ê ë " # ¼ ) â Y . @ ì )A í H îï ð @ ñ ò - ) ( ó ñ ô l .õ )× Ø Ì z ) ./ 0 1 23 4 5 67 8 9 6:; 6< = > , - z9 6:; 6 Í {µ ö N-2-042N-3-012N-3-024 æ 5-n-0326-n-0126-n-02 " # E F ?@ A B - =) I ÷ D _ ` \ ] " # )Y ] :JK( ø GD \ ] " # Xù ¢ Ó Ô ú û \ ] % & '¤ ¥ S T U V W [ ü ý þ h® ç èÓ Ô ã ¼ ® ç èÓ Ô \ % & « K) D \ ] Ó Ô % & ') (
ñ ¼ f )g h 2 ./ 0 1 23 4 5 9 6:; 6{µ ö > ( $2H I " # JK( c2_ ` % & 'JK(
" # " # )@ )b - = A B - =(anchor item)(A B - =@ ñ 4 5 D - = ( L M / 0 1 23 4 5 9 6:; 6 Ù cs {µ ö 2cs 4 æ 9 62; 629 6:; 6) 2 9 62 ; 62 62z62 9 6§ 2^ l 9 6 ^ 0 ; 6 9 9 6:; 6 [ 9 6: ; 6 ( (knowledge structure)Y 2D ( !þ 6® ù ¢ ' :' ) # ~ " × Ø Ó Ô Gù ¢ D ) 2Ó Ô Ì Ö Ó Ô ) ¼ ® 2h® zÐ ! J) Ó Ô ( D !"@ Q R ! J)ê ë " # \ ] ~ " ù ¢ # )u $ . I ÷ ! # D % Y D - = ( " # !.D " # :& ê ë " # " # « - =¸' ¼ þ ( ) & * " # u $ G¶ D + , Ï- )- =[ Y " # Ï. (
" # / 0 1 2 3 P½ ^ 4 )¼ ® d5 = \ ] 6 Ü - N 6 7 89 : d5 .h)d5 ¸7 [ Y ; " # ÁÜ - N 6 ç è82 < h = > ? @ ° )= \ ] 6 ( A þ )2 =* BC D ¶ 7 )\ ] " # E F D ) O PG ¡ \ ] % & '(
!
"
#
$
%
% & '(adaptive remedial instruction)!ö - N ÏJ " #
XD ¡¢ s t ú û ?@ S T U V W H I \ ] r)% & 'J K V W L M )[ ü ý ç èÓ Ô p r7 )N Ô (
&
'
'w (2003)º 4 Õ 67 8 O P Q 4 5 º 4 5 : 9 62; 6< =Í )4 æ b « º s k ä_ ` / 0 1 23 4 5 Í cs k Ù R 9 62; 629 6:; 6) 2 9 62 ; 62 62z62 9 6§ 2^ l 9 62^ 0 ; 6 6 " # )= 8 A S =2÷ T =: Ú y ) @ =((
)
- Ö 7B~ " )U ¸V ñ W X ì þ ñ M Y )ß Z · K ½ [ (*
+
) Ù \ Ö 1 23 4 5 D )9 6:; 6< =) ] 4 4 5 ) 9 6:; 6O ¸¼ í \ ] 9 ~ " ¸3 4 5 D Í { µ ö X)hí \ ] ~ " (,
-9 " # 2 3 =* BF = - )ê ë " # :7B) " # ¸!¡¢ 2D Q R ! J)2 3 =( - )ê ë " # ~ " X þ ^ U u $ z _ ` a b z- =^ Xc \ ] 7 B ~ " (! "# $ % & ' ( ) *+ ,- . /0 1 23 4 56 7 8 9: ; < = 7 > ? @
A BCD E F /Linux G H I J < K . (Client-Server) L M (N O P 1995)Q R STU TV WXY H Z [ ; \ "] ^
_ ` a b BTU TV c d 23 e f g (2007)"hi j (2007)B Akl m I J <
K . no 23 *? p I J < K . "q H r s t "q H u v w "Tx y Cz { | } ~y C o @
I J < (Client-Server)K . n B H B L * X L AG H < (3-tier)BI J K . Q R 23 H (Client)"r s t (Server)X ¡ d 23 ¢£ ¤¥ ¦ TCP/IPBTV § ¨ TV H *H © r s t Bª < « © r s t Bu v ¬] ® ¯ F ° t ±² ³´ µ ¶F © B° t L u v w · r s t ¸ § ¨ TV ¹ u v J © u v w I ° Z [ º d » 5 ¸ ¼ - ½ ¾ ¿ À H @ < BI J K . > Á2-1 H (Client)"q H r s t (Server) Ãq H u v w @ÄH ųTU TV BÆ Ç t È É Ê ¦ Ë Ì Í Î Ï Ð Ñ Ò Ó Ô H Bu v Õ Ö ×Ø Ù - ½ ÚÄq H r s t ųApacher s t Û Ü Tx ª < Ý Þ PHP(Hypertext Preprocessor)ß à á ÚÄq H u v w Åâ³MySQLH çè é ê BÝ ë . á 0 BÝ ì Z [ u v w í î @
Aï H Tð r s t /ApacheApacheçñ ò ó Ò BTð r s t k çñ ³ô | (free software)õ ö÷ ø ù G H ú û CD E F ± ü $ H SLinux ý þ " " u z ã B à H H ¬ PHP(hypertext preprocessor)B à A2
3 B4 @
MySQLçñ " E F "î "é ê ¦ z H " - . ã ä å Ý Þ SQL(Structure Query Language, SQL)u v w r s t ¢ ü D H ±MySQL H B N z ] BE F k! ¦ q B *I J <
K . B; < È É ³ç" r s ª < MySQL×N z ] BH Bà á º d 0
SQLBl # ¢kü $ $ (% & 2004)@
AX} ' Tx Bo ï H Macromedia Dreamweaver MX 2004Tx Ü Á2-1 < I J K . Apacher s t (PHPª < Ý Þ q H r s t H u v w MySQL q H u v w Æ Ç t Tx o
Cô | PHP(hypertext preprocessor)Ý Þ @ Dreamweaver) D * Ò BTx + Î ô | (, - . / X0 2006)T ð L BK . 1 Q R é ; \ 2 3 H L B4 5 ¬ *6 n Flash} ~"a 7 8 9 z { | Tx : ; < ¦ ó @ PHPI ¥ Q . Tx q H ª < ¢ß H Bz H = > ? @ Ý Þ (scripting programming languages)÷ ø ù H Ò H STx ª < Bo ¬Ò A B Ö HTML 9 XCBÝ ì ÃC"C++"Java×PerlD E F : î ± G(H I J CK 2006)@PHPBõ L /M Ò Tð o * L Û Ü } ' Tx é ê î ß **N O N z · A Tx y CB4 @
Macromedia Flash MX 2004É W^ P Q B} ~y Cô | /Flash
*H é ê B; < È É a R S T By CU ª ¬Tx V W - n N z H * X Y B¢Z í [ ã m z { | } ~a R \ AX ] ^ _ B ^ ` 4 ¥ z [ ã B8 9: a Ò N O ^ ` Ó ^ 8 9: · Flash4 nBz { | } ~@
!
"
#
$
b c : i d (2003)e f g h çi j ª k ¥ l Sj ª k ¥ XBÄm ÅI n o p q r s t u H v w v x y > z2-1@z2-1 {"| h } t u H v w v x y (O : i d 2003) ~{h } t u H v w v x y ç] / B6 Ò 6 ´ ç6 / B@ ç] / B6 Ò 6 ´ ç6 / B@ ç6 / " *±6 B¢â /¯ è B @ ç6 / " *±B6 B¢ /¯ è B @ ~| h } t u H v w v x y ç S 1B 6 Ñ ¦ 1× " ¢ /@ n ná S 1B 6 X] @ B / B@ 4 X4 /4 4 ç/ 6 @ 4q ß ¦ X4q /4q @ 6 1µ / @ 4 é ç ã é 5(n " ) B · /4é @ Ò l t > z2-2ß A ×B A {"| h } r s h õ + /5-n-03"6-n-01"6-n-02 ""B ¡ " " ""n"x "4 "4q D + ,@ A , ¢ : £ ¤ ) ¥ b c Ò l t í î M x # B F d / õ t 5¦ c + ,- . ã = â¹ § ¨ ã ¬H : i d 1 t u H v © á » 6 + ,- . + y ª ` « ¬ 23 @
z2-2 Ò l t (O : i d 2003) h } h õ + "í î l t çh } 1-n-07 Ò c d 2" ç"5" ç"10 " çD ® } @ N-1-01" N-1-03 ¯h } 2-n-08 Ò L x g g ° ì @ N-1-06" A-1-03 h } 3-n-04 Ò L x ì B± ² G H ÷"³ C´ < µ ¶ ( ¦ · B¸ ¹ )¬x º # ® XB» n@ N-1-04 {h } 5-n-03 Ò L x "" @ N-2-04 | h } 6-n-01 Ò ¼ ,"n¬CBx (½ 20½10÷ x ½100)@ N-3-01 6-n-02 Ò ¼ , B4 "4q B± ² L x 4 "4q B¾ ¿ ; < ¬Ò ¹ á 4é @ N-3-02 À h } 7-n-09 Ò L x B± ² ¬¼ ,100*í B@ N-3-01 7-n-10 Ò L x """4 Ã4 q ¬Á  x B¾ ¿ ; ì @ N-3-02 7-n-11 Ò *4 "4q Á  G H à " "4é B¾ ¿ @ N-3-02
%
&
%
'
(
)
*
+
,
-
.
o í B ! X¦ z , A Ä ¨ ¦ BI n AI ¥ A
Å /{"| h } o q # í î È É M # ¢B & ' $ % ( ) = ¹ Æ h A6 L > z2-3@ z2-3 ! B A Ç ¥ È É > (2002) Ê " Ã4q B± ² "Ë ì Ã Ì nB x ì ¦ § ¨Í Î"§ ¨( ) ") ¦ w v L x ( ) "¦ c Ï Ì x nÝ Ð Ñ & ' D ( ) Ò @ Ó Ô Õ (2002) Ê " Ã4q B± ² ÃË ì ¦ § ¨Í Î"( ) @ Ö × Ø (2003) Ê B Ù Ú I ¥ = Û + ,XB2m G Ü § ¨] Ý @ Ì Þ ß (2004) § ¨( ) Ò / 1) Ý Þ § ¨( ) n± ) x ") ¦ w v Í Î@ 2) ¼ + § ¨( ) à 0 ( ) "á â ì âa b @ 3) ã ä § ¨( ) x nã ä ( ) "¾ å ) @ 4) " æ ' ç ( ) è é Ü ê "ë 2@ % f ì (2005) Ê BI ¥ í Ü § ¨¦ Ò 1) : ±B] Ý ( ) Ê Ñ H çû ; ì x n") ¦ w v Í Î" ì Ï Ð n± @ 2) d ( ) Bw v Í Î/ Ò ã ( ) ² î # @ ï ð ñ "È ò ó (2006) É Ê B+ ,¢ ° ì à ì B Û + ,L x ] p î m É ( ) @
b c z 2-3ô õ * É # & ' $ % ( ) M ¾ ¿ & ' µ # S) ¦ w v B² ] $ $ ö á Í Î÷ Cø ( ) @ù n±7 ! : ú í î A à ) ¥ ) ¥ + ,- . B+ y + ,- . ` nã B¨ ª X ¢û Ö ¦ L M b c B( ) Ò *ü 23 Ò ý * Ò þ B Ð # ( ) 8 9: w @
ç B ã 23 ¦ L M /0 1 *á Ò ( "h "N
2004)¶çÒ *` n q L M (Item Response Theory, IRT)/0 1 B ã 23 (Wainer , 2000)@¶¯Ò â*+ ,- . /0 1 B ã 23 (Appleby, Samuels, & Treasure-Jones, 1997; Brown & Burton,1978; Chang, Liu & Chen,1998; VanLehn, 1988; Wenger,1987)@
/
0
1
2
3
4
5
6
7
8
9
:
;
<
=
>
*` n q L M /0 1 B ã 23 · Ò B23 b c ^ ` ö ç` nBCø q Ï ? ç` n/Ì B23 @ 23 Bço > m É ¯nà nB` n^ ` Cø 523 b c *± BCø ¸ © ¾ ^ ` BÒ (initial ability)523 J nw X m * ^ ` ý m 4Ò B` n 23 B¨ ª X23 ] Ð L b c ^ ` BCø q È É m n B` n@ > · B23 ; < á ª ¾ B t u a - ç; * X c d 23 B¢Z ´ ç; * B23 - ½ ² 4523 B- ½ $ x y /^ ` Bç" Ò ´ /çm (scale score)· · Ò 2 3 $ ÷ q H Sá p 23 $ % Ö ê ` > 0 23 " Ö 23 D @/*` n q L M /0 1 B ã 23 ì þ BÐ # B( ) § ¨23 B- ½ Ñ Ò ç" Ò Cx y 8 9: B ¦ · Aï H *+ ,- . /0 1 B ã 23 / AJ @
/
?
@
A
5
6
7
B
8
9
:
;
<
=
>
¯ û Ò B 23 b c # + ,- . c d ¡ 2*Á2-2/ ß ¦ B¡ 2n /11n^ ` ø ( ` nA/` nA±, ` n£ ¤¸ 2` nB1" B2ÃB3 ^ ` ` nB1"B2Cø ² ` nB3Cø ( ) â! 4 ¸ 2` nB3? , ` nC5"C6"C745" M ` nB1"B2? , ` nC1"C2"C3" ÃC4« ¬ 23 # *" 4n S$ - ] h } % B# 23 ¦ & B @ · û ã 23 B; < ¢*' Ð m # B( ) § ¨þ L ( x # ( ) /Ì ¬" ¡ 2n¡ 2¢Z k : £ Ò A $ B) # B á ó c ² * + 5B# c d » 6 B8 9: @ õ ö, ¦ A É *` n- . L M /0 1 23 ª ª 2 Á2-2 # + ,- . A B2 B3 B1 C1 C2 C3 C4 C5 C6 C7þ u ç ? Ò " m ¡ 2n@- É . "/ 0 1 " "h (2006)"2 3 /"4 5 6 " "N (2006)*` n- . L M /0 1 B 23 7 ¿ ì 8 9 : Ã; ç: ú ê 8 ¡ 2u v - ½ Ø Ù ª 2þ u ç /0.95¢8 9 : Ã; ç: ú ê 8 E < " 50=*±B¡ 2nõ Ú ª 2þ u ç /0.90¢8 9 : ; ç: ú ê 8 E < " 76=*±B¡ 2nõ > *+ ,- . L M /0 1 23 ? (robustness)@ ù n±7 *+ ,- . L M /0 1 23 Bý > ? ç" ? " ã B23 Äú ¡ 2ÅBõ B@ ¯" ^ ` ² Þ " m B23 ¢Z @ A 8 9: H @ " : ² Þ ' Ð B( ) § ¨ Äú ¡ : ÅBõ t @ ² û ¾ ` n- . B; ì X "ï B C "4 D E "F G H (2005)
B A- ½ l m *I J L M (Ordering Theory, OT) (Airasian & Bart, 1973; Bart & Krus, 1973)B 23 7 ¿ ì Ä" ` nÅÃĪ 2þ u ç ů ; ! ¦ 4 K u BzÉ ý SÄ` n L - . ì Å(Item Relationship Structure Theory, IRS) (Takeya, 1991)Diagnosys(Appleby, Samuels, & Treasure-Jones, 1997)@
b c ±7 A* ¨ I J L M M 3 # + ,- . /0 1 B ã
23 / AJ Y H N ` n $ - ] # + ,- . c d ] h } #
I n Ð @
8 9: (adaptive remedial instruction)/ û Ò ¶çÒ *
H = 7 > ? @
/
C
D
5
6
7
E
;
<
F
G
C
%
*: £ /0 1 8 9: *æ [ P c d 8 9: l Q : £ £ ¤ : öÁ R : ú : ú í î ¬Ò q # Z B"  S T a Ò ¦ ó Bl Q # ) ª ü 8 9ó ½ @ l Q : £ # c d ö25b c # B"  РU V* # B( ) § ¨W n# 4 5 *j " D J c d 8 9: @¦ c · û < : £ Ò ¦ # "  S T À A X l Q , ¦ Al m · û ; < ö"52Bá Y * çØ ] Ø ] S T > 8 9: ¦ Wá ó (Z [ \ "h i j " "¡ ] ^ 2006ÚÈ X _ "Z [ \ " "hi j 2006Ú` a b"hi j " "e f g 2006Úc d e 2006Úf g á 2006)@ *: £ /0 1 8 9: BO É d q h i # æ 30æ * ±: £ æ ] ì * # ççc d 8 9: q i j B X# î É · É d 8 : D X¦ D * · 4 5 ² c d o @/
8
9
5
6
7
E
;
<
F
G
C
%
* /0 1 8 9: # c d ö25# ¦ c " Â Ð U V* ( ) § ¨* k : Û c d 8 9# Ó ^ l B ª < c d " Â B8 9l Q m ³# z { | : } ~B} # ¢B¿ n 8 9: w , ¦ Al m · û ; < ¦ çá ó (o ¯2006Ú2 X2006Ú- p q 2005)@ A: É r Ý *H B k : Û ¬b c z , ¤ ) ¥ + Ü "y C z { | : } ~· ï H * /0 1 8 9: *" æ ¢Z @! "# $ %& ' ( ) *+ , -. / 01 2 1 3 4 5 6 7 8 9 : ; )<= > ? ! "# $ @ A B ! *C D*# $ EF *-& ' ! "# $ G H I J KL 9%M)*N O L 9%P Q B ! *R # $ EF *STU V DW XYB ! B Z EF C D*[ \ 3 ] ^_7 ` a b : c d e ^_f g h iC D*STj k ^_j k XYB ! d e ^_f g h l 3-1 m n o p! "# $ q r j k ^_ j k XYB ! 3 ] ^_7 ` a b : c d e ^_f g EF M)* [ \ s t U V DW XYB ! B Z
02 1 3 4 u ( ) Linux= v # $ PHPw x y z { | MYSQL{ } ~ 8 a L 9 a -m n o p! "# $
o p^_ ^_. %L 9 C D*L & %D W -^_# $ T ^ K ^ C D* %DW %f g o p^_ %f g *% ¡ ¢ ^ K100£ ¤ ¥C D*j k o p^_%a ¦ § ¨ ^_a ¦ © ª ¥3-1 f ¤ ¥m n o p^_« ¬ = ® ¯ ^_: ° = ® ¯ %00 ± ² ³ f ¤ ¥m n o p^_« ¬ = ? ´ ^_: µ = ® ¯ %± ² ³01 f10 ¤ ¥m n o p^_« ¬ = ® ¯ ^_: µ = ? ´ %± ² ³f ¤ ¥m n o11 p^_« ¬ = ? ´ ^_: ° = ? ´ %± ² ¶ · ^ % (3.1)¸N K= %¹ ± ² ^ %¶ · K º » ¼½<¾ % ¸ ¥3-1 o p^_ ^_= ¿ À ± ² Á ¥ o p^_ = ? ´ (1) o p^_ = ® ¯ (0) ^_ = ? ´ (1) f11 f10 ^_ = ® ¯ (0) f01 f00 N f f11+ 00 ^ Â (3.1)
9: ; )5-fold Cross Validation% l3-2Ã Ä ^_%Å { } Æ Ç È KÉhÊ %h KË Ì Å (training samples); )Ë Ì Å ¶ ! Í a Î %¼h K^DÅ (testing samples); )^ DÅ 5 6 Ï Ð o p^_ Ñ Ò É± Ó É½ ^ . % ^ KÔ É± %Æ Ç Õ a L 9 a m n o p^_%f Ö K -× Ø %-¼ _¾ ^_Ù Ú Km n o p^_Ûr Ü Ý Ó Þ DW%q r ß à á â ^_% D{ } ; )o pã · (ä å æ 2007)ç è 0.96% ^_m n o p^_STÞ %DW M)% Matlab 7.0é 01 ¶ · ^ l 3-2 ¶ · ^ -5-fold CVà ê l 4 1 4 1
!
o p^_XYB ! %l3-3à C D*ë ì í u j k ^_â m n o p! "# $ © ª C D*%= ¿ À î Wï Ó # $ « ] = ð C D* Sñ ò = C D*ó ô õ ö ÷ ¬ ø ù ú S C o pXYB ! o pXY B ! âû ü 1 ý í þ L 9%XY= f . C D* : c S5 6 o p^_%^m n o p! "# $ %<¥3-2à l 3-3 o p^_XYB ! %l C D* j k ^_ o p^_ õ ö ÷ ¬ ø ù D W~ XYB ! ^_a b û ü 1 ý í Ûñ ò ^_ Û¥3-2 m n o p! "# $ <¥ : c < 5 m n o p! "# $ 40 ^ m n o p^_ 40 XYB ! m n û ü 1 ý í 10 : c 40 ^ m n o p^_ ! " # $ % & ' ( ) * + ^a ¦ u ÄK u 5 6 ¼ u þ 1 C D*M)SPSS 10.0é 01 5 6 ; · ^f g ÛÝ Ó R T o pXYB ! 1 C D*Û O f Ö ¼ u ª C D* ^f g K C D* -¼ -¼Ê ! K ±
o pXYB ! -^_a ¦ ç è - ^a ¦ Û O -
© ª U - 3 ¶ " # { } $ % 7 & 5 6 - l3-4Ã l 3-4 { } ' ( ø ù m n o p^_ vs. o pXYB ! a L 9 a -m n o p! "# $ ) * o p! "# $ î W+ W> W " # ² ,² B Z $ % - ] W ) . / 0 a ! "# $ & ' a ! Í a ÷ ¬ ^_ D
12 D3 ? ¸^ 4 5 - 6 %
"
#
D% ÷ ¬ ^_7 ). ê 6 Å K 8 995! : ;: < ! Í O Ö Å ¶ 530=^: c 95! : ! >$
%
&
? ¸^Km n o p^_1? ^^7 ). ê 6 Å K 8 995! : ;: < ! Í O Ö Å ¶ 67= 95! : ! > 5 6 ^_ª & ' M)% O ÷ ¬ ^_] @ DWT a K A B -m n Co p÷ ¬ ^_m n û ü 1 ý í
'
(
)
*
â8D O B ! 3 ^_E F_%GH I J ! K / 0 L) . / 0 a (M N O ¼) / 0 a Ä DWC(M N O P) (Q R S T U V W X 2004)YDW%E § ¨ ZW[ (M N O )\TDWó ] ¥ó _^ TDó ] ¥ó ] - - ÷ ¬ ^_(M N O ) O _ ` -/ 0 Ö a b Ö Ó ! Í D{ } -TSPSS 10.0 01 Microsoft Office Excel 2003 BILOG-MG 3.0 h01 7 )c d ^_F e (CTT)x ¤ ^_F e (IRT)B 5
¼A a ¦
(¼) CTT-DW g
1. h i ² αi ² (Cronbach's Alpha)K 0.9472 Õ 0.80 -U
Yαi ² L j Kk l WØ im k a h _ ` 2. n ² o 0.942p0.677Æ Ç n ² K 0.837 3. q ² o 0.666p0.320r 0.3q _ ` (P) IRT -DW g 1. DWq (aÕ)n (bÕ)s ^(cÕ)%j ² Õt ] 2. u O 1727W%[ ó ] Õ(χ2 P-value) 0.05ó ô DW8 x Ê v ² Õt ] w ¨ / 0 ê x y k > z PB a ¦ (¼) CTT-DW g
1. h i ² αi ² (Cronbach's Alpha)K 0.9401 Õ 0.80 -U a h _ ` Yu O k l 39 Wh j { | %m k 0.0009 0.0002} ~ Ê v ² ª w ¨ / 0 ê x Kà > z 2. n ² o 0.947p0.587Æ Ç n ² K 0.797 3. q ² o 0.638p0.330r 0.3q _ ` (P) IRT -DW g 1. DWq (aÕ)n (bÕ)s ^(cÕ)%j ² Õt ] 2. u O 134 W%[ ó ] Õ(χ2 P-value) 0.05} ~ 8 x 1 W 34 W%® ¯ - K! Í ® ¯ w ¨ / 0 ê x y k > z F{ } Ã DW _ ` ì a L 9 a -m n o p! "# $ 5 6 m n o p^_
+
,
#
-L 9^_= K^_ a Ø %-)% 9DW -K] @ DW
(anchor item) ( )] @ DW a L 9%! Í a ! Í
a 5 6 m n o p^_T Tl3-5l3-6K
É: < r ] @ ;: < r
Item Item Item
1 2 3 4 5 6 7 8 9 10 1 1 0 1 1 0 1 . . . . . . . . . . . . . . . N . 1 . 1 . 1 . 1 . 1 . 0 N+1 1 1 0 1 0 1 0 . . . . . . . . . . . . . . . . . 2 N . 1 . 0 . 0 . 1 . 0 . 1 . 0 l 3-5 ] @ DW! Í = ¿ À l , - . / 0 1 2 3 4 5 (6 176)N8 9 . : ; < => ? @ [A]+ , - . A 0 1 2 3 4 5 (6 4710)N8 9 . : ; < => ? @ [B]+ , - . B C 6 (6 476)2N8 9 . : ; < => ? @ [C]+
/ 0 1 2 3 4 5 6 & B C 6 9 D N [A] B C 6 9 D 2N [C] B C 6 & A 0 1 2 3 4 5 6 9 D N [B] l 3-6 [A][B][C] l l3-5l3-66 ^_ST Ó 2N½C D*DW1p10 W% = ¿ À ÄO C D*KP ¼ = É: < r (DW1p 6)%N½== ¿ À Z K[A] ³P ;: < r (DW4p10)% N ½== ¿ À Z K[B]³Ô × %= ¿ À Z K[C]\ 3 Ê v D W%= ¿ À © ª [A][B][C] ½ %= ¿ À ( )OT01 ¶ ! Í a S Ó 3½! Í a l3-7l3-8l3-9Fâc - 9= ¿ À [C]%] @ DW a 3½! Í a l3-10Ã a f f -! Í a ^ ( ) a · î = ¿ À l 3-7 [A]-! Í a 5 4 6 1 2 3
l 3-8 [B]-! Í a l 3-9 [C]-! Í a l3-10 a -! Í a 5 4 6 5 4 6 9 7 8 10 5 4 6 9 7 8 10 1 2 3
- ] @ DW: © ª F OT01 ¶ · -! Í DWa (M x N O ;w ¨ / 0 ê x - ] r 5-n-03â ² %ê â l ² %ê ² %] ' î ² ,² %« ,² %] %6½= K] @ DW - Ø %K 8 a L 9 a -o p! "# $ o p^_ u Þ DW^: c i( )] @ DW% a STÞ ¼ ^=² ^: c %o p^_O û ¡
.
/
0
1
2
)
*
- ^^r 7 )m n o p÷ ¬ ^_V ¢ £ h=(2006)¤ ¥ Kh=(2006)% ¦ § ¨ T a KA B %GH ² ! K m n Co p÷ ¬ ^ _ © pê Äm n Co p÷ ¬ ^_# $ À ) ! K ª « R Ê ¬ W: f Ö _ ` STÞ DW^: c Y O ^ þ m n o p! "# $ % 8 T=pC%o u Kî 8 L 9%M)*N O L 9%P Q C D* STj k ^_d e f g j k XYB ! B ! *R# $ EF *l N O TU q r - ® STU V DWXYB ! B Z EF C D
*[ \ 3 ] ^_7 ` a b : c T ¯ M)*%} ) * ! "# $ ST K½Ï ¼) . W~ û ü 1 ý í Ï Ï ° O B ! *R # $ EF *STM)± LIJ ^_-DW( )01 Ä -l³ C´ r w x DWµ O -¥x ¸SU V ¶ { } ~ ³ U V DW% a { } ³ . U V XYB ! -)%û ü 1 ý í S f m n o p^_! Í ª õ ö ÷ ¬ ø ù ; )m n û ü 1 ý í 5 6
½ %XY · XYB ! º » : ¸ ý ¹! Í Ó º » ¹XYB ! r Ü þ
® ¯ õ ö ´ XY
Ï ° O B ! *R # $ EF *STM)M)*ß à L) * ! Í %[ \ s t # $ S¼ O L 9! Í %= ¿ À \C D*5 6 ^_ ½ ß à ë ì ¾ ¿ %[ \ s t ´ r 5 6 ^_¢ O [ \ ® ¯ R s t ® ¯ # $ ú j « ¬ M)* À j k ^_ ¼q r STÁ  ! Í ¯ ) EF ^_Ï Ï Ø %EF ^_%7 ` a b : c ¼ O C D*%= ¿ À à EF *STFâ o u -; = Ä Å ! Í j ^_%: c \Q Å ^_%M)* M): c ¹C D*L Æ ¯ )¼ O C D*%= ¿ À u # $ j © ª C D *Ç ¼DW%L 9= ¿ À È É ¼DW\¼ O C D*%O = DW1 2 DW DW%= : c O %C D{ } . j w x ! Í õ ö ÷ ¬ ø ù U ¹B ! *C D*¼Ø Ê EF ^_f g Ï l C D*%= ¿ À Ç D ! Í C ^^ST Ó ¼ ½ õ ö ÷ ¬ ø ù þ ! Í %® ¯ õ ö M Ë Ì ¥w x ¹B ! *! "*STÍ Î XYB ! 5 6 -Ï Ú Ð -EF *C D*STÑ : d e ^_%f g \Fâ# $ È É %: º » j k XYB !
3
4
5
6
7
8
þ XYB ! %<m n û ü 1 ý í × % -Ò Ó âØ G. Ô B Õ ! ² D a b K Ö ! # ! ! Í ; )Macromedia Flash MX 200401 = flashý í ý í × a b âØ B J 3 * 9E Ù = í u ' Ú ª Û ! Í Ü YÝ TÞ ß %ý í ¹C D*r Ü á âm n û ü 1 ý í 5 6 o pXYB !! "# $%&' # "# $%( ) * + ,- . &/ 0 1
* 2 34 5 6 7 89 :; <=> ? @ A ; <B BC D 9 :E F 1
G H4-1H4-2H4-3H 4-4H4-5I J "# K L M N O M P Q R S T U Q VW X=Y Z > BS T [ \ ] ^ _ ` ] ^ _ a] ^ b c O &d e f g 1h i U Q M 3j _ M W Xk l "#G H 4-6I J 1 m n o b c O 8p q r s t u F v w x 8y z 3{ 5 | } ~ i H4-78 &H4-8 s 8 x x m p q r s t 8b c 1 H 4-1 9 :M U Q t F
H 4-2 ] ^ _ ` t F
H 4-3 ] ^ _ at F
H4-5 ] ^ f g t F
H4-7 p q r s t B| }
G H4-9I J "# K L M N O M XPS T d e 9 :M 8 , - ] ^ &K L 9 :M 1 H4-9 9 :M ] ^ t F
G H4-10I J "# K L M N O M XPS T [ \ k l "#8 1 H 4-10 _ ` t F
G H4-11I J "# K L M N O M PS T X= x N 8
¡ ¢ £ ¤ ¥ ¦j _ M X= § & ¨ © t F G H4-12I J 1
H 4-11 ª " + t F
G H4-13I J m "#V8« ¬ ® ¯ ° X= j _ M m ± B5 « ¬ 8 ® + =² ³ ´ O µ ¶ ·1 ® + 8¸ ·j _ M ¹ º×¸ ·» ¹ ºj _ M m » ¹ º8« ¬ ¼ ½ ¾ j b c O j _ M ¿ 7 À [ ,Á W X ? @  à « ¬ I n o 8 p q r s t ¾ j ³ ´ Vj _ M W X,- "#8V"Ä b c O 8$%1 H4-13 j _ M « ¬ ® ¯ ° t F
* Å 8m #Æ Ç È "#É 3 "#Vi Ê Ë Ì Í Î _
a8Ï Ë Ð m ! "#8$%Ѽ ½ &Ç È "#8 + ,- Ò @
Ò @ + G > 1
G ·4-1I J h i ,- Ç È "#Ó Ô 8ª "aÕ i 48aÖ × Î aÕ &ª
"ÑØ 1¦Z Ù _ Ú : Û Ü × . m Ý Þ 0.96Ñß à ª "aÕ
á31aX=Î ª "aÕ 17aáâ 37.22%1
ã ä ,- "#å"Ù " Ý Þ Í 92.97%ß à ª "aÕ á30a
&Ç È "#æ ç X=Î ª "aÕ 18aáâ 37.5%1
V"8Ù " Ý Þ Í 93.25%ß à ª "aÕ á30a&Ç È "#æ ç è X
=Î ª "aÕ 18aáâ 37.5%1
å"&V"8Ù " Ý Þ æ é ê ë ß à XÍ 93.11% è XÎ 37.5%8
_ a1
·4-1 Ù " Ý Þ ß à ª "aÕ &Î ª "aÕ Ò ç ·
"# Ù " Ý Þ ß à ª "aÕ Î ª "aÕ (ì Ò ) Ç È "# 1.0000 48 0 (0%) Û Ü × 0.9600 30.13 17 (37.22%) "#-å" 0.9297 29.58 18 (37.50%) "#-V" 0.9325 29.36 18 (37.50%) "#ß à í 0.9311 29.47 18 (37.50%) Ð 3 ª "Ñj _ M 8x L &î L Ð ï Ö × j _ M XË x ð ñ ò î ¡ 8ó ¥ N i ª - "#8ô õ &ö ÷ ø Þ ùú û j _ M ü ý p Ð ï
ùþ Ã é 8 x 1 ´ J m * ª "& Û Ü × 8Ã é ám 0.28%ß à ª "aÕ ¿ æ é 1a "#8 Ý Þ P Û Ü × i X=p Î Ba¦ "#8åV"Ù " Ý Þ · æ ß à Æ ã * I "#$% æ : Ý Þ 1
! "
? @ Ó r j _ M &j _ M 8å"$ < / b c O @ j _ M i Ê ü $% G > 1 ·4-2 J Ó r j _ M å"8ß à $ 381.15V"8ß à $ 3 85.79ß à , Õ 34.64$@ è ' tí35.268 (p<.001) J åV"$ Í é W V"$ ß à í På"$ ß à í1 ·4-2 Ó r j _ M åV" o "# ß à Õ 5 Õ Ý é , Õ $@ è æ tí å" V" 81.1493 85.7910 67 67 17.7740 15.7004 4.6418 .914 5.268 *** ***p<.001!"#
$
%
j _ M å"$ $<<Õ 22â å B < 22â V B 233<Ò ç <j _ M m ¾ j b c OV8V"$ i Ê ü , 1 B<j _ M ·. ·4-3 J <8j _ M å"8ß à $ 396.64V"8ß à $ 397.50ß à , Õ 3.9636$@ è ' tí31.815 J åV"$ » Í é W V"$ &å"$ æ ç > » ü D , 1 ·4-3 <j _ M åV" o "# ß à Õ 5 Õ Ý é , Õ $@ è æ tí å" V" 96.6364 97.5000 22 22 1.73333 2.2200 .9636 .384 1.815 <j _ M ·. ·4-4 J <j _ M å"8ß à $ 385.91V"8ß à $ 3 89.39ß à , Õ 33.48$@ è ' tí33.757 (p<.01) J åV"$ Í é W V"$ &å"$ æ ç > ü D , 1 ·4-4 <j _ M åV" o "# ß à Õ 5 Õ Ý é , Õ $@ è æ tí å" V" 85.9130 89.3913 23 23 4.1441 4.2291 3.4783 .438 3.757 ** **p<.01
<j _ M ·. ·4-5 J <j _ M å"8ß à $ 360.68V"8ß à $ 3 70.32ß à , Õ 39.64$@ è ' tí34.630 (p<.001) J åV"$ Í é W V"$ ß à í På" ß à íü D , 1 ·4-5 <j _ M åV" o "# ß à Õ 5 Õ Ý é , Õ $@ è æ tí å" V" 60.6818 70.3182 22 22 16.0279 18.5045 9.6364 .850 4.630 *** ***p<.001
&
'
´ * + m o u F ß à , !p 8i <, Í 9.64 , " p 8i <, 33.48, !# 8i <¿ ü 0.961 50 60 70 80 90 100 H4-14 <j _ M åV"$ $ ³ H¦m $@ è T' u F Ó r j _ M 8åV"$ Í é ¿ ü
<j _ M » Í é <& <8V"$ à Í é + J
<8V"$ j b c O 8ú û !% , !p " i <!
Vi <1& * ' Ð Ð 3<ß à Õ 396( i æ ) * 8$ X
!" # $
%& ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 :( ) 8 9 ; < = > ? @ A B @ A C ( D E F G 4 5 H %I J H K L $:4 5 M NO 6 ; < P Q R S T U ? V O6 !W6 7 !X Y Z [ P Q \ ] 6 7 ^ _ ` a G bc M N? d ebf g $
%& ' ( ) * + 2 3 4 5 ( ) h ( i ( j k l m 92.97%n( i ( j k l m 93.25%o p i ( j k l m 93.11%q ? m @ A 37.50r B L @ A C ( s 18@ A C ( D E ebt$ %u v w * + 2 3 4 5 ( ) @ A s + x y z u v w { v | } 2 3 4 5 ( ) ebf g $
:~ B !; < ~ B ! 2 3 4 5 M NO6 n9 { m | k e t 5.268(p<.001) ~ B !: 4 5 M NO6 n G | ` $ : WW ; < M Nb |y z
(t=3.757, p<.01) (t=4.630, p<.001))p m | k ` l ` l 4 5 M NO6 z % 6 G | $ - . / 0 1 2 3 4 5 6 7 8 9 :( ) ; < ? m ¡ C ( ¢ :M NO6 ; < ? m ¡ C O¢ £ F G f g eb$
, - . / 0 1 4 5 ( ) %M NO6 ¤ G * ¥ e b: ¦ § WD E ¨© ª « ? ¬ $
!
"
:® ¯ ° s 6 6 7 :± ² ¯ ° ³ G , ´ 5 µ ¶ · ? ¸ B - . L § ¹ º » ¼ ½ ¾ s ¿ À Á v W à < Ä WÅ Æ %Å Ç ¨È É :2 3 4 5 ( ) Ê Ë eb$#
$
%
&
'
(
"
)
*
+
i B 2 3 C ( Ì Í z Î Ï Ð ? & ' i B Ñ Ò C ( s Ó Ô i ( j k l { v Õ k =$,
-
.
Ö × Ø Ù Ú H Û Ü Ý Þ ÈÖ × ß à Ü Ù á %Ü â ? ã 4 5 6 7 ( ) 8 9 ` ² ä å æ ç â %è é ê ë Õ Ü Õ ì O6 !% B ! í î$
/0
1
2
3
4
5
6
7
8
` a M NO6 D x ï ð ñ * ¥ ò ó ² ß x ï ð ñ ô õ ö O÷ 6 s ø ù ú Ø Ù 6 8 6 û ü ý þ ? ô õ û ü ¦ û ü : b%ñ < * Ó Õ B !` a M N6 7 $9
:
;
<
=
7
8
>
?
, - . / 0 1 4 5 ( ) B « ø S ? ` a ½ ? Õ x × $9 : ; (2004) !"!"!"!" #### $$$$ %%%% &&&& '''' (((( )))) **** ++++ ,,,, ---- 6< =
> ? @ 4AB C D EF G 68
9 H (2004) .... //// 0 0 0 0 1111 2222 3333 6< = >
? @ 4AB C D EF G 68
I J K (2005)4444 5555 6666 7777 8888 9999 :::: ;;;; <<=<<=== >>>> ???? @@@@ AAAA %%%% &&&& 6
< = > L C D EF G 68 I M N (2004)PHPMySQLBBBB CCCC DDDD EEEE FFFF GGGG 678OP Q R S T (2003)6666 7777 HHHH IIII JJJJ >>>> K K K K 3333 AAAA LLLL MMMM ==== NNNN OOOO PPPP- . / Q " # % & . / Q " # % & . / Q " # % & . / Q " # % & 6< = > L C D EF G 68 U V W (200611) RRRR SSSS TTTT UUUU VVVV WWWW - -
- - - QQQQ """" #### %%%% &&&&
X Y Z @ [ \ / ]^ @ [ \ _ P ` / ! " # $ %
&TANET20066a P b P ` 245 ]^ 8
U c d (2002) XXXX %%%% YYYY ZZZZ [[[[ \\\\ ---- e f < = > L 0 4AB C
D EF G e f 8 jk l m (n) (2006) ]]]] UUUU ^^^^ ____ ``aQ``aQaQaQ b6joOjkbbb l m jk l m (n) (2006) ] ]]] UUUU ^^^^ ____ cccc ddaddaaa!!b!!bb6joOjkb l m p q r (2006) .... //// """" #### eeee ffff ++++ ,,,, UUUU gggg K K K K 3333 AAAA hhhh iiii OOOO PPPP6 ? @ 4AB C D EF G 6 8 p s d I h t u v w (2004)Y x y z { | } %4A 1 1 1 1 EEEE """" jjjj kkkk 1261-99 ~ (2003) llll (I) > 4A@ (NSC-91-2520-S-142-001)68O6< = > ? @ 4AB ~ (2004) llll (II) > 4A@ (NSC-92-2521-S-142-003)68O6 < = > ? @ 4AB ~ p (2005) llll (III) > 4A@ (NSC-93-2521-S-142-004)6 8O6< = > ? @ 4AB (20055)HHHH IIII mmmm nnnn oooo pppp q b0 1 qq b0b0 11 q b0 1 rrrr 6a < = # $ %&TWELF2005 6a L 245 678 X (n)(2003) ] ]]] ssss `"`"`"`" dtdtdtdt uuuu vvvv wwww xxxx yyyy .... // 678O // X (2004) .... //// A A A A 0000 1111 zzzz {{{{ |||| AAAA
} P
}} PP
} P-~~~~ 6< = > ? @ 4AB C D E
¡ (1995)P ` 1 ¢ £ O¤ ¥ & ¦ § ¨ © 2ssss ---- EEEE ssss **** kkkk11 (9) ª« ¬ (n) (2006) ]]]] UUUU ^^^^ ____ ``aQ``aQaQaQ bbbb67oOª« ¬ ª« ¬ (n) (2006) ]]]] UUUU ^^^^ ____ cccc ddddaaaa!!!!bbb67oOª«b ¬ ® ¯ ° ± J ² (200611) RRRR SSSS TTTT UUUU V VV V ³ a ´ µ ¶ · 6a < =
6a < = ¸ ´ µ 6a < = 4A/ ¹
º » ¼ ! " # $ %&2006'6a ´ µ ¶ · 23 45 678 ± J ² ½ ¾ ¿ (200611)6666 7777 HHHH IIII oooo pppp 0 1 2 0 0 11 22 0 1 2 X Y Z @ [ \ / ]^ @ [ \ _ P ` / ! " # $ %&TANET20066a P b P ` 245 ]^ 8 ± J ² (2007)6666 7777 HHHH IIII oooo pppp >>>> 0 0 0 0 1111 AAAA 6 L C D EF G 68 u c À Á Â Ã ~ (20063) llll - - - - Ä Å > Æ ! " # $ %&2006'Y x 1 P ` · Ç È É Ê Ë 245 Ä Å 8 u v w (2005)++++ ,,,, UUUU gggg HHHH IIII oooo pppp >>>> K K K K 3333 AAAA hhhh iiii OOOO P PP P- .... //// """" #### ++++ ,,,, UUUU gg 6<gg = > L C D EF G 68 ½ ¾ ¿ Ì Í (20064)}}}} (((( HHHH IIII mmmm nnnn oooo pppp ( - (( - - ( - ÆÎ Ï £ Ð 0 ÆÑ Ï
£ Ð 0 ÆÎ Ò > ÆÎ \ Y Ò Ó # $ %&2006L · 1 Ô Ä Ð 0 2b 45 67Õ ½ (2006) QQQQ """" #### .... //// ++++ ,,,, UUUU gggg K K K K 3333 AAAA hhhh iiii O P OO PP O P6 ? @ 4AB C D EF G 6 8 Ö × Ø (2006) RRRR SSSS TTTT UUUU VVVV WWWW - 6 L C D EF G 68 L Ù · 3 / (n) (2006) Dreamweaver 8 ssss 67oOÚ Ù (2007)(((( NNNN 0 0 0 0 1111 2222 6 ? @ 4 AB C D EF G 68
Û (2004) .... //// A A A A 0000 1111 zzzz {{{{ |||| AAAA
} P
}} PP
} P- = <=== <<< = === 6< = > ? @ 4AB C D
EF G 68
Ü Ý Ò Þ ß (n) (2006)Dreamweaver & PHP BBBB CCCC FFFF GGGG OOOO PPPP67oO
à Ï £
á â (2006)SSSS TTTT RRRR - >>>> ???? @@@@ 6
? @ 4AB C D EF G 68
ã ä U å æ (2006)ç è é Þ ¹ ê y %L ë L 1 ì L í î Y x ï ð ñ ò ó @ %4Ammmm ---- ¡¡¡¡ kkkk40(1)
Airasian, P.W., & Bart, W.M.(1973). Ordering theory: A new and useful measurement model. Journal of Educational Technology, 5, 56-60.
Appleby, J., Samuels, P., & Treasure-Jones, T.(1997). Diagnosys--A knowledge-based diagnostic test of basic mathematical skills. Computers & Education, 28(2), 113-131.
Bart, W.M., & Krus, D.J.(1973). An Ordering-Theoretic Method to Determine
Hierarchies Among Items. Educational and Psychological Measurement, 33(2), 291-300.
Brown, J.S., & Burton, R.R.(1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2, 155-191.
Chang, K.E., Liu, S.H., & Chen, S.W.(1998). A testing system for diagnosing
misconceptions in DC electric circuits. Computers & Education, 31(2), 195-210. Takeya, M.(1999). Structure Analysis Methods for Instruction. Tokyo: Seizansya. Takeya, M.(1991). New Item Structure Theorem. Tokyo: Waseda University.
VanLehn, K.(1988). Student Modeling. In Polson, M.C., & Richardson, J. J.(Eds.),
Foundations of Intelligent Tutoring Systems (p.p. 55-78). NJ: Lawrence Erlbaum
Associates.
Wainer, H., Dorans, N.J., & Flaugher, R.(Eds.) (2000). Computerized Adaptive Testing:
A Primer (2nd ed.). NJ: Lawrence Erlbaum Associates.
Wenger, E.(1987). Artificial Intelligence and Tutoring Systems: Computational and
Cognitive Approaches to the Communication of Knowledge. CA: Morgan
1 6-n-01 4 2 5 3 6 5 6-1 5 5-1 3 4-1 2 1 1-1 3-1 3 3-1-2 2-1, 3-1-1 2-1-1,3 -1-1-1, 3-1-2-1 2 20
2 6-n-02 4 4-1 4-1-1 1 ! 1-1 ! 1-1-1, 2-1-1, 3-1-1 ! 3 " 2 # $ % 2-1, 3-1 "
3 5-n-03 1-2, 2-2, 3-1-2, 4-1-1-2, 5-1-1-2, 6-2 &' ( ) 1-1, 2-1, 3-1-1, 4-1-1-1, 5-1-1-1,6-1 &* ( ) 1 +, -1 2 +, ! -./ 3-1, 4-1-1 5-1-1 6 &* ' ( 0 1 5-1 4-1 2 ' 4 3 4 ' 5 5 6 3 5 6 7-1-1 +, -./ 8-1-1 9-1-1, 10-1-1 9 7 8 9 6-3, 7-1-1-1, 8-1-1-1, 9-1-1-1, 10-1-1-1 &* ( ) 6-4, 7-1-1-2, 8-1-1-2, 9-1-1-2, 10-1-1-2 &' ( ) 7-1 +, ! -: ; ! 8-1 7 8 9 9-1 10-1 < * = > -< ) 7 +, ?: ; @ , 8 7 8 9 10 < * = > -<
1 A 126 ! "# $ 227 %& ! "' ( ! )1 328 * ! "# $ 429 %& ! "' + ! ), -530 ! ". / 631 0 ! "1 $ 732 2 3 4 5 ! 833 ! "6 7* 8 9 : 934 ! "; < * 8 9 : 1035 0 ! ". / 1136 2 3 4 5 0 ! 1237 = ! "# $ 1338 %& ! "' ( = ! ), -1439 * = ! "# $ 1540 %& ! "' + = ! )> ? + 1641 %& ! @ > ? A & = ! 1742 = ! ". / 1843 0 = ! "1 $ 1944 2 3 B 1 C D E "= ! 2045 B 1 C D "= ! 8 9 : 2146 F ! G H )F ! 0 = ! I# $ 2247 0 = ! ". / 2348 F ! G H )F ! 0 = ! I. / 2449 2 3 B 1 C D E "0 = ! 2550 * = ! J K
2 B 124 ' + 0 ! "1 $ 225 2 3 ' + 0 ! 326 L M "1 $ 427 N 7! O P ' Q 7! 528 ' + 0 ! "8 9 : 629 L M ". / 730 2"= ! / R 831 S ! "1 $ 932 3"= ! / R 1033 M ! "1 $ 1134 5"= ! / R 1235 S ! ". / 1336 T ! U V IP W 2"= ! 1437 M ! ". / 1538 T ! U V IP W 3"= ! 1639 M ! "1 $ 1740 T ! U V IP W 5"= ! 1841 M ! ". / 1942 M ! 7 2043 2 3 20 X E "M ! "= ! 2144 ' ( 0 = ! "1 $ 2245 2 3 ' ( 0 = ! 2346 ' ( 0 = ! "8 9 :
!
1 Y Z A B C D E F G H I JK L M JN O P (2004E92) ! "# $ % & '( ) * + , - . / 0 1 2 3 4 5 6 0 7 2 ( 8 . / 6 7 9 : ; < = > ? @ A BCD E F G H I 6 J 9 2 @ A K * L M N * OP M QR S T U V * W L X L Y Z L [ ; L \ L V * ] ^ _ ` M a b c d _ ` E e f M a 6 g h i j k l h 9 * m n M a 6 o p < W Oq r M U M a o p s t u v w x 4 5 y z e f { ) p | } ~ @ _ ` p | p K K K "K " " [ p K K K K 'K ' [ p K K K K K V * O K K K K K ' V # $ + , V p K V ¡ V * ¢ / £ ¤ ¥ ¦ Ob £ * § ¨ £ ¤ © p U ª « V * q ¬ A V * _ ® q ¬ A Ol ¯ 7 ° ± c d _ V * ] ^ U R ² ¬ A Ob l ¯ 7 ° U2 Y [ \ -E ] 5 7 Y [ \ -E ] 5 7 ) ^ % E ] _ ` )^a S b c d e If g h 9 i )^Q j k l g m n o n )^p q g r a )^s 9 t o a g u v V 9 "w n x i )^X y z v { | "} ~ W g )^ : F & X ": g )^ ; < % v / " g " o o x )^p q g )^ v I g )^ < @ ¡ "¢ £ g % )^a S ¤ ¥ ¦ , § | "¨© C D X ª P « ¬ g h _ ` )^ ® ¯ ° " x ± W ² ³ "´ g A B C D E F G H I JK L M JN O P (2004E93)
3 Y [ \ -µ 5 7 Y [ \ -µ 5 7 ) ^ % µ )^W ¶ · k ¸ ¹ : "E ] g h µ t IJ º i x ^1 i )^» ¼ ¢ g m x )^½ ¾ µ I¿ À Á I g r à ¤ À Á t ¨© o U )^½ ¾ µ E g u µ )^ V 9 Ä Å ^1 g µ )^ Æ Ç c d e "È É Ê g \ Ë É Ê )^3 Ì Ã µ It g µ Æ Ç )^Í Î Ï Ð Ñ e A g µ "Ò%& U )^ ! U x )! { a g : ¶ " 3 )^Ã Ó Ô Õ ½ Ö O à µ It g A B C D E F G H I JK L M JN O P (2004E93)
4 Y [ \ -À Á 5 7 Y [ \ -À Á 5 × )Ø ^Ø %Ø À Ù p q À Á )^Ú ¾ y z Û Ü b c d e f I gØ Ø Ø hØ Ý p q À Á )^Ú ¾ y z Þ Û Ü b d e f I gØ Ø Ø mØ À Á "9 i ß o )^ µ %à gØ Ø Ø rØ À Á )^a S µ : "á â gØ Ø Ø uØ À Á I ¹ R ã )^ä å %à gØ Ø Ø Ø À Á æ "E ] )^L W ç è Å é "Ì ê gØ Ø Ø Ø À Á E ] )^ë á â ì í î ï gØ Ø Ø Ø À Á )^ð @ %& p q gØ Ø Ø Ø À Á )^ V 9 ñX ò ó ôñX ò )ôñÞ õôñ* ö I÷ ô"9 n gØ Ø Ø Ø À Á æ )^ ø Ã á â "ù ú gØ Ø Ø %Ø À Á û )^ À Á Æ Ç ü ý þ gØ Ø Ø hØ À Á æ E ] Æ Ç )^ Ï gØ Ø Ø mØ À Á æ E ] Æ Ç )^ % gØ Ø Ø rØ À Á E ] )^@ gØ Ø Ø uØ À Á E ] )^W Q n ¶ Ï gØ Ø Ø Ø µ @ 3 Ì Õ À Á )^ Þ 3 Ì Õ gØ Ø Ø A B C D E F G H I JK L M JN O P (2004E94)
5 [ \ [ \ Ø )Ø ^Ø %Ø "_ ` )^ 1 Ø Ø Ø hØ "_ ` )^ 1 Ø Ø Ø mØ )^6 ¤ { | E ] "É Ê Ø Ø Ø rØ )^ Å É Ê " 8 9 Ø Ø Ø uØ x : R ã )^ ù A ü © Ø Ø Ø Ø © %I )^ @ A " Ø Ø Ø Ø )^3 Ì @ 8 ! ö Þ ç è " ü # $" % & Ø Ø Ø Ø ' ( æ ) ® æ "* + )^S Ø Ø Ø Ø , ¡ I7- )^ . Ø Ø Ø Ø î ï )^W ² / 0 1 î Ø Ø Ø %Ø µ À Á )^1 î Ã © %23 Ø Ø Ø hØ ¤ " ! )^ë 4 5 6 ½ Ø Ø Ø mØ )^ 7 8 "0 ã ß 9 9 I Ø Ø Ø A B C D E F G H I JK L M JN O P (2004E95)
"
#
u:; ! { } ~ < ! = ! =A > / ?@AB@C D(E) F ( : G H ? I ? J K ?L Þ È M N O P Ã N R Q ` R S %À Ù T 27$ Ò 12/¨ 42 Q R1. S T U7×9V63WXY 7-63 Z [\ Q R2. +,] 5 6 ^ X -@ _\ 0 1 ./ : ; ! Q R3. S T U64÷4V16WX` 16-64 Z [\ Q R4. +,] 5 6 ^ X ! -@ _\ 0 1 ./ : ; ! Q R5. a b c d -45 \ 135 13 9 4 Q R6. ef T g U14 ?1J2J7J 14WXU21 ?1J3J7J21WX h [1J7-14i21Z [\ ! Q R7. Y 635 6 ?j k \ 1J3J7J9J21J63 1J3J7J9J31J63 1J2J3J8J31J63 1J2J3J9J21J63 Q R8. l104,m n o 2 p q r Xs t u vXw ?x a ys p @ _z\ 12 13 14 16 Q R9. #108{ | } ~ 3 + @ X w ?x a y+3 ?@ _{ | } \ 8 12 14 16 Q R10.a b c d -48i64 \ 12 14 16 18 Q R11.Y 54i42 ?j k \ 1J4J6J8J18 1J4J6J9 1J3J6J9J12 1J2J3J6 Q R12.S T U9×5V45WX` 45-9 Z [\Ò 22/¨ 42 Q R13. ) +,] -@ _\ : ; 1 ./ : ; ! Q R14.S T U36÷3V12WX` 36-12 Z [\ Q R15.+,] 5 6 ^ X ! -@ _\ 0 1 ./ : ; ! Q R16.+,] @ ?@ _, \ : ; @ i + @ 1 0 Q R17.a b c d -8 \ 1 14 44 104 Q R18.S T U3 ?3J6J9J12…WX U6 ?6J12J18J24…WX ^ 6J12-3i6Z [\ Q R19. 150250 ` ?26 \ 156J182J206 104J156J182 156J182J208J234 182J208J234J260 Q R20. ! $ 450550 X36 +Xt u vy s ?@ _ \ 468J504J540 450J550 450J504J540 432J468 Q R21.S T U4×5V20WX20-4i5 Z [\ Q R22.a b c d -28i42 \ 56 112 168 196 Q R23.a b c d -9i24 \ 3×8 924 9×12 9×24 Q R24.100600 ] ^ X39i 65 + ?j k \ 195J351J585 195J390J585 260J390J585 390J585J780 Q R25.S T U252V12×21X252÷12V21WX a b c d \ 21-12 X12-21 12-21 X21-12 21-252 X252-21 252-12 X12-252
Ò 32/¨ 42 Q R26. ^ U11×13V143WX` 13 -143Z [\ Q R27.+,] -@ _\ : ; ! ./ 1 0 Q R28. U54 ÷ 9= 6…0WX` 9-54 Z [? Q R29.+,] ! -@ _\ : ; ! ./ 1 0 Q R30.a b c d -32 \ 128 8 7 3 Q R31.ef T g U16 ?1J2J4J 8J16WXU30 ?1J2J3J 5J6J10J15J30WX^ 1J2 -16i30Z [\ ! Q R32.a b c d -785 6 \ 1J2J3J4J19J26J39J78 1J2J3J6J13J26J39J78 1J2J6J7J11J13J39J78 1J2J6J8J11J13J39J78 Q R33.l95{ } 2 p q r Xs t u vXw ?x a ys p @ _z\ 19 17 13 9 Q R34.#112 ~ + @ X w ?x a y+ ?@ _ \ 11 12 13 14 Q R35.a b c d -36i60 \ 8 9 12 15 Q R36.Y 72i56 ?j k \ 1J2J4J7J14 1J4J7J8 1J2J4J8J12 1J2J4J8 Q R37.S T U6×7V42WX` 42-7 Z [\ Q R38.+,] 5 6 ^ X -@ _\ : ; ! ./ : ; 1 Q R39.S T U100÷25V4WX` 100 -25Z [\