苗栗縣國民小學四年級數學學習成就測驗試題分析–以九十八學年度為例

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Excel TestGraf98 – 100 35 .872 .61 .59 .51 TestGraf98

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Abstract

The main purpose of this study was to prepare qualified academic exam questionnaires for the purpose of improvement of student learning and educational process. According to attribute classification and various capability index of Fourth grade mathematics, a number of questions were therefore selected from the academic question bank designed for fourth grade elementary school students in Miaoli County, “98 academic Year Achievement Diagnostic Remedial Program for Elementary School and Junior High School Students”. And results were analyzed by Excel TestGraf98 software. The assessment of questionnaires mentioned above will be conducted through assessing and analyzing the results of questionnaires of each tested student and feedback to teachers for educational improvement.

In this study, two classes of the fourth grade student candidates were selected from one of the elementary schools in Miaoli County. The result of this study was analyzed though the item option characteristic curve model based on statistic of the questionnaires. This study concluded the following.

1.According to the various indexes at mathematics established for fourth grade students, 35 questions selected from the academic question bank specifically focus at number and quantity, geometry, algebra,and statistics and probability. The reliability of the questionnaires is 0.872, and the pass rate is 0.61, and the difficulty rate is 0.59, and the discrimination rate is 0.51.It shows that this is a great and worthful test.

2.Student perform less competent at number and quantity and geometry, but opposite in statistics and probability.

3.The features or the item potion characteristic curve

(1)According to the shapes,5 types of item potion characteristic curve. (2)Most of the distracters have high distraction.

Keywords: achievement diagnostic remedial plan, misconceptions, item option characteristic curve

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……….………..….1 ………...………...3 ………...………...6 ……….……….7 ………....12

……….………...……….13 ………...…….13 ……….…...18 ………....23 ………....26

………....……….……….………...35 ………....35 ………..………..36 ………....36 ………..………....42

………..……….………...43 ………....43 ….………...47

…………..……….…………...89 ..………..89 ………....93 .………….………..………..97 ..………..……....97 ..………..……..101 .……….103

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1-3-1 ………...9 2-4-1 ……….28 3-3-1 ………..37 3-3-2 ……….….40 3-3-3 ……….….41 4-1-1 ……….….43 4-1-2 ……….….45 4-1-3 ……….….45 4-1-4 ………..46 5-1-1 ………...91

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1-3-1 …………8 2-3-1 ………..24 2-3-2 ………..24 2-3-3 ………..25 2-3-4 ………..25 3-1-1 ………..……….….………..35 4-2-1 1 ………..52 4-2-2 2 ………..53 4-2-3 3 ………..54 4-2-4 4 ………..55 4-2-5 5 ………..56 4-2-6 6 ………..57 4-2-7 7 ………..58 4-2-8 8 ………..59 4-2-9 9 ………..60 4-2-10 10 ………61 4-2-11 11 ………62 4-2-12 12 ………63 4-2-13 13 ………64 4-2-14 14 ………65 4-2-15 15 ………66 4-2-16 16 ………67 4-2-17 17 ………68 4-2-18 18 ………69

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4-2-19 19 ………70 4-2-20 20 ………71 4-2-21 21 ………72 4-2-22 22 ………73 4-2-23 23 ………75 4-2-24 24 ………76 4-2-25 25 ………77 4-2-26 26 ………78 4-2-27 27 ………79 4-2-28 28 ………80 4-2-29 29 ………81 4-2-30 30 ………83 4-2-31 31 ………84 4-2-32 32 ………85 4-2-33 33 ………86 4-2-34 34 ………87 4-2-35 35 ………88

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2001 ; 2000 21 (1) (2) (3) ( ) (4)

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95 4 TestGraf98 –

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1996 80 1998 1998 2 8 100 25% 50% 25% 25 40

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TestGraf98

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98

2009

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1-3-1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

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P difficulty PH 27 P_L 27 P= 2 L H P P + P 0 1 2002 discrimination D D= P_H −P_L H P PL -1 1 1 2008 TestGraf 98

McGill University Ramsay

1995

kernel smoothing approaches to nonparametric item characteristic curve

estimation 1991 Psychometrika Ramsay

TestGraf98 shareware

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OCC Option Characteristic Curve

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56

100

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5

1 9 2

47 105

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1322 25000 400 75 33 78 PR90 445 19 10

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1 ( E ……) 2 3 4 5 1 2 3

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4 5 1 2 3 4 5 1 2 3 1

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2 3 4 5 6 7 8 e …… 2010

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Osterlind 2001 selection-type item Haladyna,1994 86 Ramsay TestGraf98

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Stem Options

78 79

83 88 B.S.Bloom,1989 Tom Kubiszyn,Gray

Borich,1996 1. 2. 3. 4. 5.

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79 83 88 Bloom,1989 Kubiszyn,Borich,1996 1. 2. 3. 4. 5. 6. 7. 8. 9.

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84

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option characteristic function

option

characteristic curve OCC Ramsay

kernel smoothing approaches tononparametric item characteristic curve estimation 1991

Psychometrika kernel smoothing

1 0

binary variable

nonparameter

Ramsay,1991 Ramsay TestGraf98

option characteristic curve OCC 2004

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(2004) 2-3-1 3 2-3-1 2-3-2 3 5% 25% 2 50% 2-3-2

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2-3-3 4 25% 25% 25% 2-3-3 2-3-4 2 1 2 1 2 1 2 2-3-4 2004

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(1) (2) (3) ( ) (4) ( ) ( ) ( )

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91 91 N S A D 1 2 3 4 C R T S C E

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1 … 9 n s a d 2-4-1 4-n-01 ( ) N-2-02 4-n-02 N-2-03 4-n-03 N-2-05 4-n-04 N-2-06 N-2-07 A-2-02 4-n-05 ( ) N-2-07 A-2-03 4-n-06 ( ) N-2-08 4-n-07 N-2-11 4-n-08 N-2-10

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2-4-1 4-n-09 N-2-12 N-2-16 4-n-10 N-2-16 4-n-11 N-2-13 4-n-12 N-2-13 4-n-13 N-2-24 N-2-25 4-n-14 ( ) N-2-17 N-2-18 N-2-19 N-2-25 4-n-15 N-2-17 4-n-16 ( 4-s-04) N-2-20 4-n-17 N-2-21 4-n-18 ( 4-s-09) N-2-22 S-2-08 4-n-19 N-2-23

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2-4-1 4-s-01 S-2-04 4-s-02 S-2-05 4-s-03 S-2-06 4-s-04 ( 4-n-16) N-2-20 4-s-05 ( ) S-2-07 4-s-06 N-2-20 S-2-03 4-s-07 S-2-02 S-2-03 S-2-04 4-s-08 S-2-03 S-2-04 4-s-09 ( 4-n-18) N-2-22 S-2-08 4-a-01 A-2-02 4-a-02 N-2-07 A-2-01

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2-4-1 4-d-01 D-2-02 4-d-02 D-2-02

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( ) ( ) 84 83 88 79 73 82 89 89 89 89 86 Shao,1998 82 86 84 82 88 1 2 3

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82 1 2 3 4 5 89 4

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(1) 2

3 4

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TestGraf98 3-1-1 35 EXCEL SPSS TestGraf峯珉 35

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convenience sampling 88 40 56 100 25 50 25 35

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N S A D 3-3-1 3-3-1 1 A-4-n-04 饋 B- 4-s-05 3 B- 4-s-02 4 C-4-a-01 5 A- 4-n-05 6 A- 4-n-19 7 A- 4-n-09 珉 A-4-n-01 峯 A-4-n-09

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3-3-1 10 A-4-n-11 11 A- 4-n-01 1饋 D- 4-d-01 13 A-4-n-04 14 A- 4-n-05 15 A- 4-n-11 16 A- 4-n-18 17 B- 4-s-01 1珉 B- 4-s-02 1峯 A- 4-n-18 饋0 A-4-n-17 饋1 C-4-a-02 饋饋 A-4-n-13

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3-3-1 饋3 C- 4-a-02 饋4 B- 4-s-06 饋5 B- 4-s-04 4-n-16 饋6 B- 4-s-02 饋7 D- 4-d-01 饋珉 A-4-n-06 饋峯 A- 4-n-07 30 B-4-s-04 4-n-16 31 A- 4-n-18 3饋 A- 4-n-18 33 C- 4-a-02 34 A- 4-n-04 35 A- 4-n-06 2003

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3-3-2 4-n-01 N-2-02 8 11 2 4-n-04 N-2-06 N-2-07 A-2-02 1 13 34 3 4-n-05 N-2-07 A-2-03 5 14 2 4-n-06 N-2-08 28 35 2 4-n-07 N-2-11 29 1 4-n-09 N-2-12 N-2-16 7 9 2 4-n-11 N-2-13 10 15 2 4-n-13 N-2-24 N-2-25 22 1 4-n-17 N-2-21 20 1 4-n-18 N-2-22 S-2-08 16 19 31 32 4 N 4-n-19 N-2-23 6 1 4-s-01 S-2-04 17 1 4-s-02 S-2-05 3 18 26 3 4-s-04 N-2-20 25 30 2 4-s-05 S-2-07 2 1 S 4-s-06 N-2-20 S-2-03 24 1 4-a-01 A-2-02 4 1 A 4-a-02 N-2-07 A-2-01 21 23 33 3 D 4-d-01 D-2-02 12 27 2

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N S A D N S A D 3-3-3 3-3-3 1 5 13 14 34 5 8 11 2 28 35 2 7 29 2 9 10 15 3 32 1 16 19 20 31 4 6 1 N 22 1 2 25 30 3 24 1 S 3 17 18 26 4 A 4 21 23 33 4 D 12 27 2 3-3-3 N 5 ( )

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EXCEL SPSS TestGraf98 Excell Excell SPSS SPSS TestGraf98 Ramsay 1991 Psychometrika Ramsay

TestGraf98 option characteristic curve OCC

TestGraf98 item difficulty

index item discrimination index

item option characteristic curve IOCC 2004

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Excell SPSS Excell 27% 27% 15 15 P D 4-1-1 4-1-1 H P P_L P D 1 .93 .33 .63 .60 2 .93 .47 .70 .47 3 .60 .13 .37 .47 4 1 .33 .67 .67 5 .80 .20 .50 .60 6 .73 .40 .57 .33 7 .93 .20 .57 .73 8 .93 .53 .73 .40 9 1 .27 .63 .73 10 .80 .13 .47 .67

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4-1-1 H P PL P D 11 .87 .20 .53 .67 12 .93 .53 .73 .40 13 .93 .40 .67 .53 14 .87 .20 .53 .67 15 .87 .33 .60 .53 16 .60 .27 .43 .33 17 .80 .33 .57 .47 18 1 .20 .60 .80 19 .93 .47 .70 .47 20 .67 .13 .40 .53 21 .87 .53 .70 .33 22 .80 .27 .53 .53 23 .93 .53 .73 .40 24 .60 .33 .47 .27 25 .60 .27 .43 .33 26 .93 .53 .73 .40 27 .93 .60 .77 .33 28 .87 .13 .50 .73 29 .73 .13 .43 .60 30 1 .60 .80 .40 31 1 .47 .73 .53 32 .60 .07 .33 .53 33 .80 .47 .63 .33

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4-1-1 H P PL P D 34 .93 .33 .63 .60 35 .93 .53 .73 .40 =.59 =.51 4-1-2 0.0~0.2 0.2~0.4 0.4~0.6 0.6~0.8 0.8~1.0 0 2 16 17 0 0% 6% 46% 48% 0% .50 4-1-2 .40 .60 16 .60 .80 17 .20 .40 2 .59 4-1-3 0.2~0.3 0.3~0.4 0.4~0.5 0.5~0.6 0.6 1 6 10 5 13 3% 17% 29% 14% 37% .60 13 .30 .60 21 .3 97 .51 .25 Noll,Scannell, Craig,1979

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s Cronbach' α SPSS 4-1-4 Cronbach' s α .872 4-1-4 1 .868 19 .871 2 .866 20 .868 3 .870 21 .871 4 .868 22 .867 5 .870 23 .867 6 .874 24 .873 7 .865 25 .871 8 .868 26 .868 9 .865 27 .869 10 .864 28 .868 11 .867 29 .868 12 .868 30 .870 13 .867 31 .868 14 .865 32 .868 15 .869 33 .871 16 .871 34 .866 17 .869 35 .870 18 .864 Cronbach' s α .872

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TestGraf98

items option characteristic curve IOCC

Std.Normal Latent Trait 0

5 . 2 ± Probability 7 4-2-7 18 22 28 4-2-7 7

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35 4-2-35 1 12 21

23 26 27 31

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3 4-2-3 24 25 32

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4 4-2-4 6 8 9 10 11

13 14 15 16 17 20

33

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2 4-2-2 5 19 29 30 34

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1 4-2-1 1 1. 100 饋3 (1窳100 饋3 (饋窳100×饋3 (3窳100×饋3 饋3 (4窳100 100×饋3 A-4-n-04 1 2 3 100 23 4

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2 4-2-2 2 2. 3 5 (1) 10 (2) 60 (3) 10 (4) 60 B-4-s-05 1 2 3 4

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3 4-2-3 3 3. (1)6cm 6cm 15cm (2)6cm 7cm 8cm (3)6cm 6cm 5cm (4)6cm 5cm 4cm 4-s-02 1 2 3 1 4

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4 4-2-4 4 4. 108 6 3 (1)108÷6÷3 (2)108÷ 6÷3 (3)108÷3÷6 (4)108÷ 6×3 C-4-a-01 1 2 4 3 4

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5 4-2-5 5 5. 636 36×10 (1)27 (2)36 (3)600 (4)6000 A-1. 2. 3. 4-n-05 1 3 4 2 3 4

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6 4-2-6 6 6. 4 (1)9 (2)12 (3)36 (4)48 1 4-n-19 1 2 3 4

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7 7. (1) 2 1 (2) 4 2 (3) 6 4 (4) 10 5 A-4-n-09 1 2 3 4

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8 8. (1)70650 (2)700650 (3)7006500000 (4)70065000000000 4-n-01 1 2 3 4

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9 9. 10 2 10 2 1 0.饋 (饋窳0.珉 (3窳1.饋 (4窳1饋 A-4-n-09 1 2 3 4

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10 10. 0.51 0.499 0.5 0.49 (1)0.51 0.499 0.49 0.5 (2)0.51 0.5 0.499 0.49 (3)0.499 0.51 0.49 0.5 (4)0.499 0.51 0.5 0.49 A-4-n-11 1 2 3 499 51 49 5 0.499 0.51 0.49 0.5 4

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11 11. (1) (2) (3) (4) 4-n-01 1 2 3 4

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12 12. (1) (2) (3) 220 (4) D-4-d-01 1 2 3 4

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13 13. 83 72 12 (1)83 72×12 (2) 83 72 ×12 (3)83 72×12 (4) 83 72 ×12 A-4-n-04 1 2 3 4

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14 14. 21 12 ×7 (1)21 12×7 (2)21×7 12 (3) 21×12×7 (4)21×7 12×7 4-n-04 1 2 3 4

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15 15. 5÷8 1 6.25 (2)1.6 (3)0.625 (4)0.16 A-4-n-10 1 2 5÷8 8÷5=1.6 3 2 4 4

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16 16. (1)7290 (2)360 (3)270 (4)189 A-4-n-18 1 2 3 4

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17 17. (1) (2) 90 (3) 90 (4) B-4-s-01 1 2 3 1 2 4 4

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18 18. 30 60 90 (1) (2) (3) (4) B-90 4-s-02 1 2 90 3 4

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19 19. 10 11 9 (1) (2) (3) (4) A-4-n-18 1 2 11 9 20 10 3 4

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20 20. 15 500 (1)2000 (2)15500 (3)150500 (4)1500500 A-1 1 4-n-17 1 1 100 2 1 1000 3 1 2 4 4

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21 21. 48÷ 4 (1) 48 4 (2) 48 (3) 48 4 (4) 48 4 C-… 4-a-02 1 2 3 4

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22 22. 10 30 5 30 (1) 10 30 5 30 15 60 16 (2) 10 30 5 30 5 0 5

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(3) 12 5 30 10 30 1 30 1 30 4 0 4 (4) 12 5 30 10 30 1 30 1 30 6 60 7 7 A-4-n-13 1 2 1 3 4

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23 23. 68×12 816 60 12 1 12 (2)60 (3)63 (4)65 C-4-a-02 1 12 12 2 1 3 1 2 4

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24 24. (1) (2) (3) (4) 4-s-06 1 2 3 4

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25 25. (1)40 (2)80 (3)100 (4)140 B-0 4-s-04 4-n-14 1 2 3 2 4

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26 26. (1) (2) (3) 60 (4) ×2 4-s-02 1 2 3 4

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27 27. (1)9 10 (2)10 11 (3)11 12 (4)12 13 D-4-d-01 1 2 3 11 12 4

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28 28. 72516478 14503296 (1)5799 (2)5800 (3)5801 (4)5802 4-n-06 1 2 3 4 2 3

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29 29. 1÷3 3 1 1 3 4 3 1 2 3 1 3 3 3 3 1 (4) 3 3 1 A-4-n-07

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1 4 2 1 3 3 3 3 3÷3 1 1 4

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30 30. (1) (2) (3) (4) 4-s-04 4-n-14 1 2 3 4

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31 31. (1) × (2) ×4 (3) (4) × A-4-n-18 1 2 3 4 1 2

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32 32. 2 40 4 3 (1)7 20 (2)80 (3)60 (4)20 A-×4 4-n-18 1 2 40 3 2 3 ÷4 4

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33 33. 315÷3 105 (1)3×105 (2)105×3 (3)105÷3 (4)315÷105 C-4-a-02 1 2 3 4

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34 34. 12 4 500 (1) 452 (2) 484 (3) 76 (4) 76 A-4-n-04 1 4 4 2 3 576 76 4 1 3

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35 35. 48550 (1)48550 (2)48600 (3)49000 (4)50000 A-4-n-06 1 2 3 4 50000

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35 SPSS s Cronbach' α .872 .60 13 .30 .60 21 .30 97 .59 .50

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7 18 22 28 1 12 21 23 26 27 31 35 3 24 25 32 4 6 8 9 10 11 13 14 15 16 17 20 33 2 5 19 29 30 34 35 21 8 4 2

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5-1-1 .63 .72 .56 .47 .61 .27 .60 .55 N .55 .55 .68 .48 S .63 .60 A .67 .67 D .80 .80 5-1-1 .55 .60 .67 .80

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( 2000) – 29 .38 – 32 .27 46 A 23 C 1294 684 47.14 – 24 .48

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– 33 .52 – 2010 – 2010 – 1 1

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– (2005) N( ) N (2005) () N ( ) – 2006 (1997) 2003 2006

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– 35 TestGraf98

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2010 2010 98 1993 1996 1996 1998 2003 2009 1996 1997 2007 1991 , 8 , 6 ,13-18 1992) -, 9 , 1 ,5-9 1992 -, 9 , 2 ,6-10 2002 2001

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2005 2002 1993 1993 2001 — 2002 2008 1990 4 295-347 2000 189 P.29-35 2006 2002

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2008 1993 2001 17 85-106 2003 2005 -2010 2008 2008 1989 43 29-33 2004 (2001) 2002 100 86-100 2003 2006 287(4) P2-19

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2010 2005 2000 2008 2009 1996 13 45-47 91 96 17-22 2004 Testgraf98 93-104 1990 23 265-290

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01 100 23 (1) 100 23 (2) 100×23 (3) 100×23 23 (4) 100 100×23 02 3 5 (1) 10 (2) 60 (3) 10 (4) 60 03 (1) 6cm 6cm 15cm (2) 6cm 7cm 8cm (3) 6cm 6cm 5cm (4) 6cm 5cm 4cm 04 108 6 3 (1) 108÷6÷3 (2) 108÷ 6÷3 (3) 108÷3÷6 (4) 108÷ 6×3

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05 636 36×10 1 276 (2) 360 (3) 600 (4) 6000 06 4 (1) 9 (2) 12 (3) 36 (4) 48 07 (1) 2 1 (2) 4 2 (3) 6 4 (4) 10 5 08 (1) 70650 (2) 700650 (3) 7006500000 (4) 70065000000000 09 10 2 10 2 1 0.2 (2) 0.8 (3) 1.2 (4) 12 10 0.51 0.499 0.5 0.49 (1) 0.51 0.499 0.49 0.5 (2) 0.51 0.5 0.499 0.49 (3) 0.499 0.51 0.49 0.5 (4) 0.499 0.51 0.5 0.49

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11 (1) (2) (3) (4) 12 (1) (2) (3) 220 (4) 13 83 72 12 (1) 83 72×12 (2) 83 72 ×12 (3) 83 72×12 (4) 83 72 ×12

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14 21 12 ×7 (1) 21 12×7 (2) 21×7 12 (3) 21×12×7 (4) 21×7 12×7 15 5÷8 1 6.25 (2) 1.6 (3) 0.625 (4) 0.16 16 (1) 7290 (2) 360 (3) 270 (4) 189 17 (1) (2) 90 (3) 90 (4)

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18 30 60 90 (1) (2) (3) (4) 19 10 11 9 (1) (2) (3) (4) 20 15 500 (1) 2000 (2) 15500 (3) 150500 (4) 1500500 21 _{48÷□ 4} (1) 48 4 (2) 48 (3) 48 4 (4) 48 4

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22 10 30 5 30 (1) 10 30 5 30 15 60 16 (2) 10 30 5 30 5 0 5 (3) 12 10 30 1 30 4 (4) 12 10 30 1 30 7 5 30 1 30 4 0 5 30 1 30 6 60 7

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23 68×12 816 60 12 1 12 (2) 60 (3) 63 (4) 65 24 (1) (2) (3) (4) 25 (1) 40 (2) 80 (3) 100 (4) 140 26 (1) (2) (3) 60 (4) ×2

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27 (1) 9 10 (2) 10 11 (3) 11 12 (4) 12 13 28 72516478 14503296 (1) 5799 (2) 5800 (3) 5801 (4) 5802

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29 1÷3 3 1 (1) 3 4 3 1 2 3 1 3 3 3 3 1 (4) 3 3 1 30 (1) (2) (3) (4) 31 (1) × (2) ×4 (3) (4) × 32 2 40 4 3 (1) 7 20 (2) 80 (3) 60 (4) 20 33 315÷3 105 (1) 3×105 (2) 105×3 (3) 105÷3 (4) 315÷105

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34 12 4 500 (1) 452 (2) 484 (3) 76 (4) 76 35 48550 (1) 48550 (2) 48600 (3) 49000 (4) 50000