問題解譯多媒體教學策略協助國小六年級學生學習「雞兔同籠問題」之效益研究

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-64

(1饋 ) SPSS

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The study of using problem-based multimedia teaching

strategy to assist elementary students in learning

“Chickens and Rabbits in a Cage problem”

Abstract

The purpose of this research is using problem-based multimedia teaching strategy to enhance elementary students in learning “Chickens and Rabbits in a Cage problem” mathematic curriculum. The main idea of the research is to explore the methodology of the effect for problem assumption and ponder inference towards chickens and rabbits in a cage problem.

The subjects of the study were 64 sixth grade students. The experimental group adopted the problem-based multimedia teaching strategy while the control group adopted the general multimedia teaching strategy. The experimental group’s course mainly demonstrated the problem solving approach and thinking direction with problem-based multimedia teaching materials. The purpose of the teaching strategy tried to make learners deeply investigate the problem concept, to specify the thinking direction of solving a problem, to make learners utilize their comprehension and to figure out the law of quantitative variation while facing the mathematic problem. Furthermore, the students use the law of quantitative variation and quantitative difference to solve the chickens and rabbits in a cage problem.

The experiment period was 6 weeks (12 lessons). Several statistic methods were adopted through SPSS software in the research. The counclusions of this research as following:

1. The experiment group has the significant effect in the course unit of “the quantitative variation” than the control group

2. The experiment group has the significant effect in the ability of “mathematic problem translation, simplification and problem solving” than the control group. 3. The experiment group has the positive effect of learning attitude than the control

group.

Keywords: Multimedia teaching material, Problem solving, Problem translation and Learning attitude

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t

p

( ) Levene .915 .34饋 6饋 -.567 .57饋 Levene .饋61 .611 6饋 .饋57 .798 Levene 1.34饋 .饋51 6饋 -.0饋5 .980 Levene 1饋.9饋饋 .001

(87)

58.009 -1.746 .086 *

p

<.05 4-3-7 III

F

314.831 饋 157.416 10.848 .000 8.317 1 8.317 .573 .45饋饋58.581 1 饋58.581 17.8饋0 .000 56.586 1 56.586 3.900 .053 885.169 61 14.511 4800.000 64 1饋00.000 63 *

p

<.05 4-3-5 19.09 17.50 4-3-6 (

F

=1.798

p

=.186 .05 ) 4-3-5 8.44 6.56 4-3-6 (

F

=1饋.9饋饋

p

=.001<.05 ) (

t

=-1.746

p

=.86徴.05) 4-3-5 4-3-7 (

F

=3.900

p

=.053 .05)

(88)

( )

0 1饋.5%

( )

1 饋

--

-

( )

4-3-8 14 14 14 13 15 14 14 7 17 11 15 11 18

(89)

4 0 1 0 0 0 65.63% 75.00% 78.13% 56.饋5% 1饋 10 14 14 14 14 14 8 14 8 16 1饋 6 0 4 0 饋 0 18 56.饋5% 68.75% 81.饋5% 56.饋5% 4-3-9 3饋 6.88 .83饋 4.709 3饋 8.06 .698 3.951 3饋 7.81 .74饋 4.饋00 3饋 6.38 .835 4.7饋3 3饋 6.88 .83饋 4.709 3饋 8.13 .701 3.966 4-3-8 4-3-9 6.88 8.06 7.81 6.38 6.88 8.13

( )

(90)

4-3-10 3饋 6.88 .83饋 4.709 3饋 6.19 .863 4.88饋 3饋 5.94 .835 4.7饋4 3饋 19.00 1.859 13.139 3饋 6.56 .853 4.8饋6 3饋 6.34 .841 4.756 3饋 5.75 .860 4.866 3饋 18.66 饋.389 13.516 4-3-11

tttt

F

t

p

( ) Levene .104 .748 6饋 -.103 .918 Levene .饋74 .603 6饋 .饋6饋 .794 Levene .319 .574 6饋 .130 .897 Levene .511 .477 6饋 -.156 .876 *

p

<.05 4-3-10 19.00 18.66 4-3-11 (

F

=.104

p

=.748 .05 )

(91)

( )

1 ( ) 饋 3

--

-

( )

4-3-1饋 7 3 饋3 6

(92)

5 饋 17 1 10 0 9.38% 4-3-13 3饋 4.84 .704 3.985 3饋饋.97 .588 3.3饋6 4-3-14

tttt

F

t

p

( ) Levene .饋47 .6饋1 6饋 -饋.043 .045 *

p

<.05 4-3-15 III

F

饋饋7.989 饋 113.995 10.481 .000 9.0饋8 1 9.0饋8 .830 .366 171.739 1 171.739 15.790 .000 56.5饋4 1 56.5饋4 5.197 .0饋6 663.448 61 10.876 1868.000 64 891.438 63 *

p

<.05 4-3-1饋

(93)

4-3-14 Levene

F

=.饋47

p

=.6饋1 .05 (

t

=-饋.043

p

=.045<.05) 4-3-15

F

=5.197

p

=.0饋6<.05

( )

4-3-16 3饋 7.31 .73饋 4.138 3饋 8.06 .698 3.951 3饋 9.69 .313 1.768 3饋饋5.06 1.饋56 7.107 3饋 6.81 .8饋7 4.680 3饋 5.56 .865 4.89饋 3饋 8.44 .65饋 3.689 3饋饋0.81 1.917 10.846

(94)

4-3-17

tttt

F

t

p

( ) Levene 1饋.饋36 .001 53.477 -1.854 .069 Levene 饋.445 .1饋3 6饋 -.453 .65饋 Levene 13.705 .000 59.370 -饋.饋49 .0饋8 Levene 14.384 .000 44.5饋4 -1.7饋9 .091 *

p

<.05 4-3-18 III

F

饋149.90饋 1 饋149.90饋 4饋.818 .000 饋91.199 1 饋91.199 5.800 .019 396.019 1 396.019 饋9.687 .000 4.11饋 1 4.11饋 .308 .581 398.1饋8 1 398.1饋8 饋9.344 .000 100.556 1 100.556 7.41饋 .008 4饋.4饋8 1 4饋.4饋8 5.433 .0饋3 饋5.091 1 饋5.091 3.饋13 .078 *

p

<.05

(95)

4-3-16 饋5.06 饋0.81 4-3-17 (

F

=1饋.饋36

p

=.001<.05 ) 4-3-18 (

F

=5.800

p

=.019<.05 ) 4-3-17 4-3-18 ( ) (

F

=-.453

p

=.65饋徴.05) (

F

=.308

p

=.581徴.05) ( ) ( ) (

F

=13.705

p

=.000<.05

F

=14.384

p

=.000<.05) ( ) (

t

=7.41饋

p

=.008<.05)

( )

11 ( 9 ) 3 (3 ) 11 13 10 16

( )

(96)

饋 3

饋饋饋 3 1 0.4 0.8 0.饋 0.4 4-4-1 3饋饋6.94 饋.9饋9 16.568 3饋 1饋.97 饋.998 16.96饋 3饋 39.91 5.336 30.187 3饋饋3.81 3.198 18.090

(97)

3饋 7.50 饋.054 11.6饋0 3饋 31.31 4.734 饋6.779 4-4-饋

tttt

F

t

p

( ) Levene .167 .684 6饋 -1.饋05 .饋33 Levene .353 .555 6饋 -.7饋1 .474 Levene 4.704 .034 54.846 -1.505 .138 *

p

<.05 4-4-1 39.19 31.31 4-4-饋 (

F

=.167

p

=.684徴.05 ) 7.88 4-4-1 4-4-饋 ( ) (

F

=.353

p

=.555徴.05) ( ) (

F

=4.704

p

=.034<.05) (

t

=-1.505

p

=.138徴.05)

(98)

5 0 5 10 0 6 6 7 70% 5 80% 3 70% 4-4-3 9 80.89 5.937 17.9饋0 14 33.64 饋.508 9.386 9 8.67 1.093 3.饋79 9 65.44 4.394 13.18饋 14 饋8.93 3.饋6饋 1饋.饋06 9 .89 .351 1.054 4-4-4 III

F

饋371饋.884 1 饋371饋.884 54.040 .000 1196.4饋7 1 1196.4饋7 饋.7饋7 .104 13.590 1 13.590 .05饋 .8饋3 980.950 1 980.950 3.7饋9 .073 950.791 1 950.791 11.15饋 .003 53饋.137 1 53饋.137 6.饋4饋 .019

(99)

18.641 1 18.641 3.667 .075 183.4饋4 1 183.4饋4 36.084 .000 *

p

<.05 4-4-3 80.89 65.44 4-4-4 (

F

=3.7饋9

p

=.073徴.05) 4-4-3 4-4-4 33.64 饋8.93 (

F

=6.饋4饋

p

=.019<.05) 4-4-3 8.67 .89 4-4-4 (

F

=36.084

p

=.000<05)

5 0 5 10 0 6 6 1 7 70% 5 80% 3 70% 4

(100)

11 11 5 1 5

1 饋 3 50

( )

36 Likert 5 4 3 饋 1 180

(101)

4-5-1 3饋 109.47 3.518 19.90 3饋 118.7饋 4.613 饋6.09 3饋 117.16 3.8饋0 饋1.61 3饋 116.38 4.380 饋4.78 4-5-饋 III

F

14009.395 饋 7004.698 饋1.910 .000 4535.7饋9 1 4535.7饋9 14.187 .14饋 13999.6饋9 1 13999.6饋9 43.789 .000 704.631 1 704.631 饋.饋04 .143 1950饋.089 61 319.706 906101.000 64 33511.484 63 *

p

<.05 4-5-1 109.47 117.16 118.7饋 116.38 4-5-饋 (

F

=饋.饋04

p

=.143 .05

(102)

Keller ARCS (饋010) ARCS 8 40 9 45 8 40 11 55 36 180

( )

4-5-3 3饋饋3.81 .884 5.000 3饋饋5.饋饋 1.饋58 7.1饋0 3饋饋6.饋8 1.008 5.704 3饋饋5.50 1.饋饋9 6.951 4-5-4 III

F

915.518 饋 457.759 17.444 .000 417.185 1 417.185 15.898 .000 905.753 1 905.753 34.516 .000 43.饋59 1 43.饋59 1.648 .饋04

(103)

1600.716 61 饋6.饋41 45417.000 64 饋516.饋34 63 *

p

<.05 4-5-3 饋3.81 饋6.饋8 饋5.饋饋饋5.50 4-5-4

F

=1.648

p

=.饋04 .05

( )

4-5-5 3饋饋8.84 .919 5.饋00 3饋 30.饋8 1.饋饋饋 6.910 3饋饋9.50 .805 4.806 3饋饋9.09 1.010 5.716 4-5-6 III

F

43饋.761 饋饋16.380 10.164 .000 698.984 1 698.984 3饋.834 .000

(104)

16.586 1 16.586 .779 .381 1饋98.599 61 饋1.饋89 56663.000 64 1731.359 63 *

p

<.05 4-5-6 饋8.84 饋9.50 30.饋8 饋9.09 4-6-13

F

=.779

p

=.381 .05

( )

4-5-7 3饋饋4.13 .805 4.556 3饋饋6.饋8 1.030 5.8饋7 3饋饋5.7饋 .867 4.907 3饋饋5.97 .9饋7 5.饋45 4-5-8 III

F

550.544 饋饋75.饋7饋 15.994 .000 338.801 1 338.801 19.685 .000

(105)

549.544 1 549.544 31.9饋9 .000 14.643 1 14.643 .851 .360 1049.894 61 17.饋11 44346.000 64 1600.438 63 *

p

<.05 4-5-7 饋4.13 饋5.7饋饋6.饋8 饋5.97 4-5-8

F

=.851

p

=.360 .05

( )

4-5-9 3饋 3饋.69 1.356 7.668 3饋 36.94 1.479 8.366 3饋 35.66 1.457 8.饋41 3饋 35.81 1.5饋饋 8.608 4-5-10 III

F

(106)

34饋.0饋3 1 34饋.0饋3 9.089 .004 饋106.590 1 饋106.590 55.980 .000 1饋8.157 1 1饋8.157 3.406 .070 饋饋95.504 61 37.631 861饋7.000 64 440饋.484 63 *

p

<.05 4-5-9 3饋.69 35.66 36.94 35.81 4-5-10

F

=3.406

p

=.070 .05

1 2 3

(107)

4

5

6

(108)

饋6 5 4 3 饋 1 130 4-6-1 3饋 80.09 3.489 19.7饋4 3饋 86.63 3.999 饋饋.6饋4 3饋 86.53 饋.966 16.777 3饋 81.59 3.306 18.701 4-6-饋 III

F

8010.500 饋 4005.饋50 饋0.450 .000 6饋08.715 1 6饋08.715 31.700 .000 76饋0.437 1 76饋0.437 38.908 .000 1088.7饋7 1 1088.7饋7 5.559 .0饋饋 11947.饋50 61 195.857 47饋饋14.000 64 19957.750 63 *

p

<.05

(109)

4-6-1 80.09 86.53 86.63 81.59 4-6-饋

F

=5.559

p

=.0饋饋<.05

饋6 - - - -- - - -- - -t

( )

4-6-3

III

F

36.833 1 36.833 13.170 .001 饋4.459 1 饋4.459 8.746 .004 90.196 1 90.196 33.8饋8 .000 30.390 1 30.390 11.398 .001 *

p

<.05

(110)

- (

F

=8.746

p

=.004<.05

F

=11.398

p

=.001<.05)

( )

t

4-6-4

tttt

t

p

a. - 5.03 5.7饋饋.饋79 1.955 .688 1.431 .16饋 b. - 7.84 7.38 1.936 饋.181 -.469 -.987 .33饋 c. - 5.59 5.84 1.6饋4 1.886 .饋50 .751 .458 d. - 7.88 7.69 1.79饋 1.533 -.188 -.454 .653 e. - 5.66 6.饋8 饋.0饋6 1.9饋饋 .6饋5 1.51饋 .141 f. - 6.59 6.91 1.68饋 1.838 .313 .76饋 .45饋 g. - 5.69 6.34 饋.饋9饋饋.073 .656 1.877 .070 h. - 5.63 6.63 饋.15饋饋.47饋 1.000 饋.饋50 .03饋 i. - 6.31 6.81 饋.40饋饋.饋9饋 .500 1.01饋 .319 j. - 5.13 6.19 饋.044 1.958 1.063 饋.89饋 .007 k. - 7.饋5 7.饋8 1.741 1.464 .031 .104 .918 l. - 5.34 6.44 饋.饋95 1.983 1.094 饋.384 .0饋3 m. - 6.16 7.03 1.986 1.555 .875 饋.301 .0饋8 *

p

<.05 4-6-4 - - - -

(111)

-- - - -- - --

-( )

t

4-6-5

tttt

t

p

a. - 6.饋5 5.7饋饋.369 饋.饋03 -.531 -1.357 .184 b. - 8.06 7.03 1.848 饋.087 -1.031 -饋.953 .006 c. - 5.7饋 4.66 饋.饋18 1.771 -1.063 -饋.771 .009 d. - 7.38 6.78 饋.196 1.736 -.594 -1.7饋4 .095 e. - 6.63 6.50 饋.311 1.934 -.1饋5 -.407 .687 f. - 6.06 6.饋5 饋.031 1.6饋6 .188 .619 .540 g. - 6.59 6.16 饋.340 饋.411 -.438 -1.407 .169 h. - 6.13 6.03 饋.311 1.94饋 -.094 -.饋83 .779 i. - 6.59 6.56 饋.108 1.831 -.031 -.109 .914 j. - 6.63 5.53 饋.47饋饋.079 -1.094 -3.467 .00饋 k. - 7.38 7.16 1.755 1.饋饋1 -.饋19 -.8饋7 .415 l. - 6.饋饋 6.19 1.913 1.71饋 -.031 -.095 .9饋5 m. - 7.00 7.03 1.83饋 1.805 .031 .099 .9饋饋 *

p

<.05 4-6-5

(112)

- - - -- - - -- -

t

4-6-6 a. - 5.03 5.7饋 6.饋5 5.7饋 b. - 7.84 7.38 8.06 7.03 c. - 5.59 5.84 5.7饋 4.66 d. - 7.88 7.69 7.38 6.78 e. - 5.66 6.饋8 6.63 6.50 f. - 6.59 6.91 6.06 6.饋5 g. - 5.69 6.34 6.59 6.16 h. - 5.63 6.63 6.13 6.03 i. - 6.31 6.81 6.59 6.56 j. - 5.13 6.19 6.63 5.53 k. - 7.饋5 7.饋8 7.38 7.16 l. - 5.34 6.44 6.饋饋 6.19 m. - 6.16 7.03 7.00 7.03 4-6-6

(113)

1 2 3 - -4 (5) ( )

(114)

(115)

5-1-1

(116)

0.4 0.8 0.2 0.4 - - - -- - - - - - - -- - ( )

(117)

- - - -

-- - -

(118)

(p=0.2~0.4)

(119)

(饋007)

饋010 6 15 http://freedownloadbooks.net/ (饋007) EEE-E---JournalJournalJournalJournal

饋饋饋饋饋010 饋饋 http://140.1饋7.36.饋51/e-journal/95 /01 .pdf。饋009 1 11 1----4444 3饋6-346 1998 11 1111 11 391-4饋0 1998 6(3)6(3)6(3)6(3) 63-77 饋003 9饋 9饋9饋 9饋 1111 1-8 饋005 46464646 103-110 1995 16161616 16-饋5 (饋000) 饋010 1 1饋 http://episte.math.ntu.edu.tw/articles/mm/mm_0饋_3_05/page5.html 饋004 (饋004) 饋004 饋1 (4)饋1 (4)饋1 (4)饋1 (4) 693-696 (饋005 (饋009) 50 50 50 50 106-114 (饋008) 53(1) 53(1)53(1) 53(1) 1-饋6 ( ) 饋010 7 饋 http://www.wretch.cc/blog/iamevolve/1饋5饋饋655

(120)

(饋004) 17 17 17 17----饋饋饋饋 1-饋饋 (饋004) (饋008 4141-4141---5555 (饋008 (饋010) (饋007) 4040 4040 (饋) (饋) (饋) (饋) 3饋-41 (饋001) 11饋11饋11饋11饋 5饋-58 (饋003) 116 116 116 116 64-76 (饋007) 饋003 饋00饋饋00饋 (饋003) (饋006) 饋饋 16饋-168 (饋008 (饋009 10101010 饋010 饋 1 http://www.cnxz.com.cn/epaper/xzrb/html/饋009-08/饋6/content_3饋0756.htm (饋003) 饋010 1 30 http://140.1饋饋.140.4/~cyc/_private/mathedu/me9/nineyear/index.htm (饋003 9999饋饋饋饋饋010 8 6 http://teach.eje.edu.tw/9CC/index_new.php (饋005)

(121)

(饋006 (饋000) 饋(饋) 饋(饋) 饋(饋) 饋(饋) 45-60 (饋00饋) (饋00饋) 饋3-3饋饋004 -18(饋) 18(饋) 18(饋) 18(饋) 71-88 (饋004) 36 3636 36 饋010 饋 3 http://www.docin.com/p-8571430.html (饋005) --- --(饋007) 饋3 1饋5-150 (饋008) (饋009) 饋5 饋5 饋5 饋5 饋饋5-饋31 (饋010) (饋001 (饋003 (饋004) 饋73饋73 饋1-41 饋73饋73 (饋009) 6 饋009 11 9 http://www.modernmgz.com/forum/viewthread.php?tid=1038 (饋00饋) 饋6饋6(饋6饋6(((4444)))) 60-68 (饋001 饋001 (1995) ( ) 301(1)301(1)301(1)301(1) 饋010 饋 18

(122)

(1995) ( ) 30饋(饋)30饋(饋)30饋(饋)30饋(饋) 饋010 饋 18 http://163.20.22.161/Science/content/1995/00020302/0015.htm。 (2007) -(1993 31(1) 31(1) 31(1) 31(1) 55-66 饋010 1 17 http://joemls.dils.tku.edu.tw/fulltext/31/31-1/55-66.pdf (1993) “ ” 17(4)17(4) 74-83。 17(4)17(4) (1997) 33 3333 33 饋0-饋7 (饋004) (饋004) 37(5)37(5)37(5)37(5) 7-13 (饋006) 饋饋 418-4饋4 (饋001) 饋010 1 30 http://image.cse.nsysu.edu.tw/research/Math/%C0%B3%A5%CE%B8%EA%B0T%AC%E C%A7%DE%B6i%A6%E6%A4j%B3W%BC%D饋%BC%C6%BE%C7%BE%C7%B饋%DF%AF%E0%A4O%B5%FB %B6q%A4%A7%AC%E3%A8s.doc (饋007) (饋00饋) : : : : 饋饋5-饋44 : (饋003) ---- 饋010 1 30 http://140.1饋饋.140.4/~cyc/_private/mathedu/me9/nineyear/philosophy/Appe ndix_A5.doc (饋004) (饋006) 40 4040 40(1)(1)(1) 饋3-45 (1) (饋003) (饋006) (饋010)

(123)

饋010

http://cnte2010.cs.nhcue.edu.tw/pdf/www/index.html。 G. Polya(1945/饋006).

How To Solve It.

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John A Van De Walle(饋001/饋005).

Elementary and Middle School

Mathematics:Teaching Develpmentally

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