結構化教學與補救教學成效探討─以「小數的加減」為例

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The Study of the Effectiveness of Structural Teaching

and Remedial Instruction - Using Decimal Addition and

Subtraction as an example

Ya-Ling Chang

Graduate Institute of Educational Measurement and Statistics National

Taichung University

Abstract

The main purpose of this research is to find out the difference of automated remedial instruction, which based on student conceptual structure, and the remedial instruction that built by the expert and to verify the application of this structure in teaching. Beside, the research compares the learning performance of each approach and then build a computerized adaptive learning system base on automated remedial, which benchmarking the remedial instruction that recommended by the professional.

The result shows that it's a success to apply the adaptive testing algorithm of student conceptual structure on remedial instruction. Because of the structure is generated automatically, it leads to the reduction on setup time of remedial instruction and human resources involved. Comparing the performance of student on their beginning stage and pretest, pretest and posttest, the experimental group has significant improvement after normal teaching and remdial instruction. Applying online materials for remedial instruction, overall conceptual pass rate will become higher, and the order of conceptual structure presented was clear enough. Hence the teaching based on expert knowledge structure and the remedial instruction developed from conceptual structure has great teaching effectiveness.

Keyword: knowledge structure, remedial instruction, adaptive learning,

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... ...1 ...2 ...2 ...3 ... ...4 ………..12 ... ...16 ...18 ...26 ...26 ...30 ... ...32 ...38 ...43 ...47 ... ...51 ...52 1 4 16 32 51 ... 54

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 j k ... ... ... ... . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 5 8 9 9 10 10 11 13 14 14 15 18 19 21 22 22 39 40 40 41 42 42

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23 24 ... ... 42 46

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 ... ... ... ... ... ... ... ... ... ... ... ... KSAT ... KSAT ... KSAT ... ... KSAT ... KSAT ... KSAT ... ... ... ... 6 6 6 11 11 13 15 17 20 23 24 25 27 27 28 28 29 29 30 31 33 33

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23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 34 34 36 36 38 38 39 44 45 48 48 49 49 50 50

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(knowledge structure-based adaptive testing system KSAT)

( 2006)

KSAT

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(2003 2004 2005)

(knowledge structure-based adaptive testing system, KSAT)( 2006)

(ordering theory, OT) Airasian & Bart (1973)

X = ( X₁, X₂, …, X_n) n

n 0 1 X = ( X₁, X₂, …, X_n) j k (joint and marginal probabilities) 1

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1 j k Item k X_k=1 X_k=0 Total X_j=1 P(X_j=1,X_k=1) P(X_j=1,X_k=0) P(X_j=1) X_j=0 P(X_j=0,X_k=1) P(X_j=0,X_k=0) P(X_j=0) Item j Total P(X_k=1) P(X_k=0) 1 Airasian & Bart 1973

) 1 , 0 ( * = = = j k jk P X X ε j k ε (threshold) 0.02 0.04 (0.02≤ε ≤0.04) εjk <ε * j k j

k X_j → X_k(Airasian & Bart 1973) j

k j k j k ε ( 2007) KSAT KSAT OT 1. ( 1) 2. ( 2) 3. ( 3) KSAT KSAT KSAT

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( 2006) 1 2 3 2006 (2002) S6 S7 S8 S4 S1 S2 S5 S3 180 S6 S7 S8 S4 S5 S3 180 S1 S2 S6 S7 S8 S4 S1 S2 S3 180 S5

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1 2 (Dn×n) n     = = = → = = else , 0 D n ,..., 1 j ; n ,..., 1 i , D D if , 1 D D ij j i ij 3 (Mn×n) n     = = = → = = else , 0 M n ,..., 1 j ; n ,..., 1 i , M M if , 1 M M ij j i ij 4 Cpxn =Qmatrix p n 5 (Z_p_×_n) (1) Z =C×MT (2) Z ( Z_p_×_n )     = = = = ≥ = =

∑

else , 0 Z n ,..., 1 k ; n ,..., 1 j ; p ,..., 1 i , 1 M C if , 1 Z Z ij jk ik ij 6 (V_p_×_p)     = = = = ≤ = = else , 0 V n ,... 1 k ; p ,..., 1 j ; p ,..., 1 i , Z Z if , 1 V V ij jk ik ij 7 (U_p_×_p) 1 (n) 10 (p) 5 KN−i i (

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KN) Ii i _{KN−1→KN−2} KN−2 KN−1 KN−1→KN−2 KN−1→KN−7 KN−2→KN−3 KN−2→KN−4 KN−2→KN−6 KN−7→KN−9 KN−7→KN−8 KN−3→KN−5 KN−4→KN−5 KN−8→KN−10 2 (D_n_×_n)( 2) 2 KN-1 KN-2 KN-3 KN-4 KN-5 KN-6 KN-7 KN-8 KN-9 KN-10 KN-1 1 1 0 0 0 0 1 0 0 0 KN-2 0 1 1 1 0 1 0 0 0 0 KN-3 0 0 1 0 1 0 0 0 0 0 KN-4 0 0 0 1 1 0 0 0 0 0 KN-5 0 0 0 0 1 0 0 0 0 0 KN-6 0 0 0 0 0 1 0 0 0 0 KN-7 0 0 0 0 0 0 1 1 1 0 KN-8 0 0 0 0 0 0 0 1 0 1 KN-9 0 0 0 0 0 0 0 0 1 0 KN-10 0 0 0 0 0 0 0 0 0 1 2002 3 (M_n_×_n)( 3)

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3 KN-1 KN-2 KN-3 KN-4 KN-5 KN-6 KN-7 KN-8 KN-9 KN-10 KN-1 1 1 1 1 1 1 1 1 1 1 KN-2 0 1 1 1 1 1 0 0 0 0 KN-3 0 0 1 0 1 0 0 0 0 0 KN-4 0 0 0 1 1 0 0 0 0 0 KN-5 0 0 0 0 1 0 0 0 0 0 KN-6 0 0 0 0 0 1 0 0 0 0 KN-7 0 0 0 0 0 0 1 1 1 1 KN-8 0 0 0 0 0 0 0 1 0 1 KN-9 0 0 0 0 0 0 0 0 1 0 KN-10 0 0 0 0 0 0 0 0 0 1 2002 4 (Cpxn =Qmatrix)( 4) I1 KN-1 I2 KN-4 KN-7 I3 KN-6 I4 KN-6 KN-9 I5 KN-5 KN-10 4 KN-1 KN-2 KN-3 KN-4 KN-5 KN-6 KN-7 KN-8 KN-9 KN-10 I1 1 0 0 0 0 0 0 0 0 0 I2 0 0 0 1 0 0 1 0 0 0 I3 0 0 0 0 0 1 0 0 0 0 I4 0 0 0 0 0 1 0 0 1 0 I5 0 0 0 0 1 0 0 0 0 1 2002

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5 (Z_p_×_n)( 5) 5 KN-1 KN-2 KN-3 KN-4 KN-5 KN-6 KN-7 KN-8 KN-9 KN-10 I1 1 0 0 0 0 0 0 0 0 0 I2 1 1 0 1 0 0 1 0 0 0 I3 1 1 0 0 0 1 0 0 0 0 I4 1 1 0 0 0 1 1 0 1 0 I5 1 1 1 1 1 0 1 1 0 1 2002 6 (V_p_×_p)( 6) ( 4) 6 I1 I2 I3 I4 I5 I1 1 1 1 1 1 I2 0 1 0 0 1 I3 0 0 1 1 0 I4 0 0 0 1 0 I5 0 0 0 0 1 2002

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4 2002 7 (U_p_×_p)( 7) ( 5) 7 I1 I2 I3 I4 I5 I1 1 1 1 0 0 I2 0 1 0 0 1 I3 0 0 1 1 0 I4 0 0 0 1 0 I5 0 0 0 0 1 2002 5 2002 I5 I2 I1 I3 I4 I5 I2 I1 I3 I4

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(2008) 1 Q_n_×_p n p 2 OS_p_×_p(order structure) 3 Q×(R+I_p )T ( ) CI p p I =1 T     = + × >= + × = • • • • 0 ) I R ( Q if , 0 1 ) I R ( Q if , 1 CI _T j p i T j p i ij 4 C n      = = = ≤ = = • • else , 0 C n ,..., 2 , 1 j ; n ,..., 2 , 1 i , CI CI if , 1 C C ij j i ij KN-1 KN-4 I1 I5 KN-1 1 KN-2 2 1 Q_n_×_p( 8) I1

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KN-1 I2 KN-1 KN-3 I3 KN-2 I4 KN-3 KN-4 I5 KN-4 8 I1 I2 I3 I4 I5 KN-1 1 1 0 0 0 KN-2 0 0 1 0 0 KN-3 0 1 0 1 0 KN-4 0 0 0 1 1 2008 2 OS_p_×_p(order structure) OS( 6) R ( 9) 6 2008 I1 I2 I3 I4 I5

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9 I1 I2 I3 I4 I5 I1 0 0 0 0 0 I2 1 0 0 0 0 I3 1 1 0 0 0 I4 1 1 0 0 0 I5 1 1 0 1 0 2008 3 Q×(R+I_p )T CI ( 10) 10 I1 I2 I3 I4 I5 KN-1 1 1 1 1 1 KN-2 0 0 1 0 0 KN-3 0 1 1 1 1 KN-4 0 0 0 1 1 2008 4 C( 11) ( 7) KN-1 KN-2 KN-1 KN-2

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11 KN-1 KN-2 KN-3 KN-4 KN-1 0 0 0 0 KN-2 0 0 1 0 KN-3 1 0 0 0 KN-4 0 0 1 0 2008 7 2008 Q KN-1 KN-3 KN-2 KN-4

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(2008) 16 ( 12) ( 13) 30 ( 9) ( 14) ( 15) ( 16) ( 10) ( 11) ( 12) 12 S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11

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S12 S13 S14 S15 S16 13

I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13 I14 I15 I16 I17 I18 I19 I20 I21 I22 I23 I24 I25 I26 I27 I28 I29 I30 KN-1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 KN-2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 KN-3 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 KN-4 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 KN-5 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 KN-6 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 KN-7 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 KN-8 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 KN-9 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 1 0 KN-10 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 KN-11 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 KN-12 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 KN-13 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 KN-14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 KN-15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 KN-16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1

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9

I1 I2

I6

I3.I4.I5.I7.I8.I9.I10.I11.I18.I19 I12

I13 I14 I16 I17

I20 I15

I21 I22

I23 I24 I26

I27 I28 I29

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14

I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13 I14 I15 I16 I17 I18 I19 I20 I21 I22 I23 I24 I25 I26 I27 I28 I29 I30 I1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I3 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I4 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I5 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I6 1 0 0 0 0 0 0 0 0 0 0 1 0 0 3 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 I7 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I8 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I9 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I10 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I11 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 I13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I18 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 I19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 I20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 I21 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 I22 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 I23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I27 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 I28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 I29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 I30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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15

I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13 I14 I15 I16 I17 I18 I19 I20 I21 I22 I23 I24 I25 I26 I27 I28 I29 I30 KN-1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 KN-2 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 KN-3 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 KN-4 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 0 KN-5 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 KN-6 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 KN-7 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 KN-8 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 KN-9 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 KN-10 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 KN-11 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 KN-12 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 KN-13 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 KN-14 0 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 KN-15 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 KN-16 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 16 KN-1 KN-2 KN-3 KN-4 KN-5 KN-6 KN-7 KN-8 KN-9 KN-10 KN-11 KN-12 KN-13 KN-14 KN-15 KN-16 KN-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 KN-2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 KN-3 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 KN-4 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 KN-5 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 KN-6 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 KN-7 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 KN-8 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 KN-9 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 KN-10 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 KN-11 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 KN-12 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 KN-13 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 KN-14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 KN-15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 KN-16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

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10 S1 S2 S5 S3 S6 S4 S14 S15 S16 S11 S10 S8 S7 S9 S12 S13

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11 S1 S2 S5 S3 S6 S13 S14 S15 S16 S9 S10 S4 S7 S8 S11 S12

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12 2008 S1 S2 S5 S3 S6 S4 S14 S15 S16 S11 S10 S8 S7 S9 S12 S13

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109 56 53 KSAT ( 13) ( 14) KSAT ( 15) 16 KSAT ( 17) ( 18) ( 19)

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6 7 8 9 11 12 13 7 8 9 11 12 13 7 8 9 7 9 8 13 KSAT 14 KSAT

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15 KSAT

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17 KSAT

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19 KSAT

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20 20 40 160 40 40 40 10

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1 2

57% 82% 1 2

1

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( 22) 1 1 2 21 22 3 4 7 94% 90% 94% 4 7 S1 S饋 S1 S2

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0 7 4 7 4 3( 23) 3 4 7 3 4 ( 24) 23 24 S7 S4 S3 S7 S4 S3

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5 6 10 94% 73% 86% 6 0 ( 25) ( 26) 6 10 5

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25 26 8 9 11 12 13 94% 89% 81% 59% 81% 12 S10 S5 S6 S5 S6 S10

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9 12 13 ( 27) 9 11 12 13 9 11 12 8 ( 28) 0 7 8

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27 28 ( 17) ( 29) S9 S7 S8 S11 S12 S13 S9 S7 S8 S11 S12 S13

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17 56 81.46 19.016 53 72.89 14.297 56 85.16 11.750 53 75.51 16.815 56 91.27 9.471 53 81.42 15.151

81.46

85.16

91.27

72.89

75.51

81.42

50

60

70

80

90

100

29 ANCOVA

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4 109 18 18 : III df F * 130.612 1 130.612 1.391 .241 9861.037 105 93.915 18 F 1.391 p .241 .05 19 III df F 442.188 1 442.188 4.691 .033 9991.649 106 94.261

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19 F 4.691 p .033 .05 20 (I-J) (I) 82.492a 1.318 (J) 78.330a 1.356 4.162 1.922 0.33 a. ( ) 20 82.492 78.330 4.162 21

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21 : III df F * 76.916 1 76.916 1.793 .183 4505.012 105 42.905 21 F 1.793 p .183 .05 22 III df F 176.645 1 176.645 4.087 .046 4581.927 106 43.226 22 F 4.087 p .046 .05 23 (I-J) (I) 87.784a 0.903 (J) 85.096a 0.929 2.688 1.330 0.46 a. ( ) 23 87.784

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2.688

( 29) ( 30)

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30 30 1 3 4 5 8 10 11 14 8 100% 6 7 9 12 90% 4 6 12 14 8 2 13 15 16 13 16 10% 2 15 20% （S5） 100.0% 100.0% （S3） 100.0% 100.0% S6 92.86% 91.07% （S4） 100.0% 98.21% S15 60.71% 89.29% S16 69.64% 87.50% S11 100.0% 100.0% S10 100.0% 100.0% S8 100.0% 100.0% S7 96.43% 100.0% S9 96.43% 100.0% S12 98.21% 96.43% S13 78.57% 91.07% S14 100.0% 96.43% S2 73.21% 94.64% S1 100.0% 100.0%

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31 31 1 10 100% 2 13 15 16 60% 80% 2 20% 15 16 15% 13 8 10 12 90% 100% 2 13 15 16 13 13 67.92% 13 78.57% 91.07% 13 （S5） 96.23% 96.23% （S3） 96.23% 98.11% S6 81.13% 90.57% （S4） 92.45% 92.45% S15 60.38% 75.47% S16 64.15% 81.13% S11 94.34% 96.23% S10 100.0% 96.23% S8 96.23% 92.45% S7 84.91% 90.57% S9 83.02% 86.79% S12 94.34% 90.57% S13 67.92% 67.92% S14 86.79% 94.34% S2 67.92% 90.57% S1 100.0% 96.23%

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100% 4 6 12 14 ( 24) 24 ( ) ( ) 4 0 0 0 0 1 1 6 3 1 4 3 2 5 12 1 0 1 2 0 2 14 0 0 0 2 0 2 4 6 4 91 6 91 97 97 76 83

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12 52 14 100% 15 4 20% 32 33

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1 4 7 8 9 11 12 13 9 32 33 ( 34) ( 35) 1 1 14 10 11 12 S1 S3 S4.S7.S8 S2 S6 S10 S11.S12.S13 S14 S15.S16 S9 S5 S1 S2 S3.S5 S4.S7.S8.S9 S6 S10 S11.S12.S13 S14 S15.S16

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14 34 35 36 37 2 3 5 2 14 S1 S2 S3.S5 S4.S7.S8 S6 S10 S11.S12 S14 S15.S16 S9.S13 S1 S2 S3.S5 S4.S7.S8 S6 S10 S11.S12.S13 S14 S15.S16 S9

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36 37 1 14 15 16 2 10 11 12 S1 S2 S3 S4.S7.S8 S6 S10 S11.S12 S14 S15.S16 S9.S13 S5 S1 S2.S3.S5 S4.S7.S8 S6.S10 S11.S12.S13 S14 S15.S16 S9

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82.492

78.330 87.784

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20%

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(2003) (I) (NSC-91-2520-S-142-001) (2004) (II) (NSC-92-2521-S-142-003) (2005) (III) (NSC-93-2521-S-142-004) (2006) KSAT -14 53-135 (2006) 14 17-35 (2007) 15 1-11 (2008) (2008)

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Airasian, P.W, & Bart, W.M. (1973). Ordering Theory : A new and useful measurement model. Journal of Educational Technology, Vol.5. pp. 56-60.