1361 * * 75% 60% 25%
1362 A Research on the Performance of Probability Concepts on Sixth-Grade Students Hsin-Chien Tsai Chi-Tsuen Yeh National University of Tainan Abstract This research paper focuses on questioning the Probability concepts for elementary school's sixth grade. The main study methodology focuses on the quantity while the quality is the supplement. Test-survey method is used to research the Probability concepts in the sixth grade revealing the variance between different gender and different region. Semi-structured interviews are used for the children's solve strategies when they have a problem with Probability. The result of this research shows the variation Children have different performances on different Probability concepts. For the concept test of Probability the correct rate is approximately 75%. For the concept test of The law of large numbers and Probability, the correct rate is approximately 60%For the concept test of Sample space, the correct rate is approximately 25%, noticeably less than as mentioned. This result indicates there are some unclear thoughts requiring clarification for the students. From the ANOVA, we can determine there is no significant difference between gender and location on Probability performancethere is also no significant difference from regions in the learning of Probability concepts. Lastly, according to the literature, process, and result of this study, the researcher provides future suggestions and research to the Probability course's arrangement in the primary school. Keywords: probability, sample space, event, the law of large numbers.
1363 92 D-4-04 Mendoza Swift(1992)
1364 () () () () () () () () Jacob Bernoulli ()
1365 (trial) ( 85) n A a A a/n( 85) (Konold, 1993) (85) ( 85p421)
1366 Piaget & Inhelder Bognar & Nemetz Jones ()Piaget & Inhelder(1975) ( 85) 1. 2. 3. ()Bognar & Nemetz(1977) 1. (certain events) (impossible events) (mutually exclusive events) 2. (more likely events) (less likely events) (order
1367 events) 3. (relative frequencies) (diagrams) 4. (independent) (correlated) ()Jones, Thornton, Langrall, & Tarr(1999) 1. 2. 3. 4. () ( 85 87) 1.Jones(1974) 2.Leffin(1971), Jones(1974) IQ IQ 3.White(1974), Mckinley(1960), Shulte(1968) 4.Fischbein(1975)
1368 ( 91) 64 82 89 92 (81) Jones
1369 / 64 82 ( ) ( ) ( ) (1) (2) 89 D-3-31 D-4-3 D-4-4 92 9-d-092 9-d-10 1D-3-3 D 3 ( ) 3 29-d-09 9 d 09 ( 81)
1370 Tversky Kahneman(1973) ( 84) (Konold, 1993) (85) () (representiveness) () (availability) () () (outcome approach)
1371 (Konold, 1983) 20 639 12 () () () 47 () 20 12 ()
1372 ( ) 47 20 22 639 50% 50% 3 12 ( ) 14 ( )Jones
1373 11012 14 58 2 4 9 367 1113 4 3 2 5 9 5 14 ( ) () 30 14 1 14 N W S E B G N7B01 7 1 S2G25 2 25
1374 ( ) 15~25 DV 639 14 7.97 2.269
1375 75% 60% 25% ( ) 1 10 12 14 89% 51% 92% 67% 75% 1 12 90% 10 51% 14 67% 14% () 2 5 8 31% 7% 36% 25% 2 31% 26% 5 7% 66% 1/3 1/3 8 36% 40% (56)(65)
1376 ( ) 4 9 51% 71% 61% 4 51% Jacob Bernoulli 9 70% () 3 6 7 11 13 60% 54% 74% 57% 59% 61% 3 60% 26% 5 4 6 54% 38% 7 74% 11 57% 13 60% J 4
1377 52 4 4/52 4 J 1 1/4 52 1 1/52 12 ( ) 10 14 1 2 3 4 10 8 2 4 3 2 3 1 2 3 4 14 4 4 5 2 3 3 4
1378 2 3 ( ) 1 2 3 4 2 2 3 10 2 1 4 ( ) 3 2
1379 4 ( ) 1 2 3 4 8 6 1 5 6 6 3 1 5 6 3 ( ) ( ) ( ) 1 2 3 4
1380 9 10 3 2 4 3 4 ( ) 1 2 3 4 6 7 3 5 2 3 2
1381 ( ) 8.03 8.21 8.13 2.434 2.212 2.312 96 114 210 (46%) (54%) (100%) 7.79 7.84 7.81 2.494 2.075 2.275 76 85 161 (47%) (53%) (100%) 8.29 7.89 8.11 2.261 2.025 2.162 116 96 212 (55%) (45%) (100%) 7.65 6.84 7.29 2.589 2.075 2.387 31 25 56 (55%) (45%) (100%) 8.03 7.91 7.97 2.403 2.130 2.269 319 320 639 (50%) (50%) (100%)
1382 (P<.05) ( )LSD Scheffe Scheffe P =.047 40.884 7.205 *16.581 3226.410 43862.000 III F 3 1 3 631 639 13.628 7.205 5.527 5.113 2.665 1.409 1.081.047*.236.357
1383 95% (I) (J) (I-J).31.02.84.237.220.340.184.927.013* -.15 -.41.18.78.45 1.51 -.31 -.29.53.237.236.351.184.213.133 -.78 -.76 -.16.15.17 1.22 -.02.29.82.220.236.340.927.213.016* -.45 -.17.16.41.76 1.49 LSD -.84 -.53 -.82.340.351.340.013*.133.016* -1.51-1.22-1.49 -.18.16 -.16.31.02.84.237.220.340.622 1.000.106 -.35 -.60 -.11.98.64 1.80 -.31 -.29.53.237.236.351.622.670.520 -.98 -.96 -.46.36.37 1.51 -.02.29.82.220.236.340 1.000.670.120 -.64 -.37 -.13.60.96 1.78 Scheffe -.84 -.53 -.82.340.351.340.106.520.120-1.80-1.51-1.78.11.46.13 * p<.05
1384 ( ) 14 7.97 ( ) ( ) (a,b)(b,a) 1/3 () 8.03 7.97
1385 ( ) () Bognar & Nemetz (1977) Fischbein (1970)Piaget 9-10 Green(1987, 1988)
1386 (92.11.14) ( )
1387 ( )1. 1234 ( )2. ( ) ( ( ) 1 2 34 ( )3. 1 2 3 4 ( )4. 200 45 500 125 9 1 1 1 2 3 4 40 4 2 ( )5. 1 1 2 2 3 1 4 1 3 9 2 9 ( )6. ( ) 1234 ( )7. 1234
1388 ( )8. 5 6 3 1 5 6 2 3 3 4 ( )9. 1 2 3 4 ( )10. 1 2 3 4 ( )11. ( )10 2 1234 ( )12. 1 2 3 4 ( )13. 52 ( ) J 1 1 2 1 3 1 4 11 4 13 52 13 ( )14. 1 2 4 3
1389 (85) 85 127-153 (81)1116 (91) (91) 8133-158 (85) (92) (87) ( ) 257-266 (85) 407-442 (84) 143-55 Bognar, K. & Nemetz, T. (1977). On the teaching of probability at secondary level. Educational Studies in Mathematics, 8, 399-404. Fischbein, E. (1991). Factors affecting probabilistic judgments in children and adolescents. Educational Studies in Mathematics, 22(6), 523-549. Fischbein, E. & Gazit, A. (1984). Do the teaching of improve probability intuitions? Educational Studies in Mathematics, 15, 1-24. Jones, G. A., Thornton, C. A., Langrall, C. W., & Tarr, J. A. (1999). Understanding students probabilistic reasoning. In Stiff L. V. & Curcio F. R. (Eds.), Developing Mathematical Analyzing in Grades
1390 K-12 : 1999 year book (pp.146-155). Reston, Va: National Council of Teachers of Mathematics. Jones, G. A., Thornton, C. A., Langgrall, C. W., & Mogill, A. T. (1997). A Framework for assessing and nuturing Young Children s Thinking in Probability. Educational Studies in Mathematics, 32, 101-125. Konold, C. (1993). Inconsistencies in students reasoning about Probability. Journal for Research in Mathematics Education,24(5), 392-414. Kahneman, D. & Tversky, A. (1973). Availability: A heuristic for judging frequency and probability. Cognitive Psychology, 5, 207-232. Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. InD. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp.465-494). New York: Macmillan.