影響學童不同數學表徵樣式一般化表現因素之研究ir.lib.ksu.edu.tw/bitstream/987654321/13218/2/18陳嘉皇-影響學童不同數學... ·...

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影響學童不同數學表徵樣式ㄧ般化表現因素之研究 影響學童不同數學表徵樣式一般化表現因素之研究 陳嘉皇 摘要 本研究旨在探究影響學童不同表徵命題之樣式一般化及解題表現的解釋因 素,了解學童面對數學學習歷程及問題時,會產出何種自我調整轉化的表現,以 做為未來改善與精進樣式一般化課程與教學設計的參考。樣本為 58 位國小六年級 學童,施以樣式一般化等測驗與訪談,做為本研究分析之資料,研究分析採質、 量並重方式,研究發現: 學童在不同表徵之樣式一般化測驗表現以圖解表徵情境表現,較文字表徵情 境之解題表現佳;樣式一般化各歷程表現,隨著歷程的變化,認知能力越不足, 策略表現越差。影響樣式一般化測驗表現之解釋因素為「語文推理」、「測驗焦慮」 與「圖形推理」。學童在承諾、情感及策略等自我調整轉換等表現普遍較低。 研究者依據研究發現,提出相關建議,提供未來樣式一般化研究與教師教學 實務參考。 關鍵字:樣式一般化、表徵、情感、認知、轉化 崑山科技大學通識教育中心助理教授 59

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  • 58

    59

  • 2009 6

    A Study on the Factors Investigate of Influence Childrens Mathematic Pattern Generalized Performances among 6th Graders

    Chia-Huang Chen

    Abstract

    This study reports on a data of 58 sixth-graders performances in mathematical

    pattern generalized and affective and cognitive test and introducing two reasoning tasks

    including verbal and spatial. The analysis has revealed the following outcomes:

    performances of solving representation problem, influence factors of pattern generalized,

    transfer strategies of self-integrated. From these results, this study is supply some

    suggestion to curricula design and teaching practice of algebraic reasoning future.

    Keywords: pattern generalized, representation, affective, cognitive, transfer.

    Assistant Professor,Kun Shan University

    60

  • (Mason, 1996)

    (Friel, Curcio & Bright, 2001)

    (Kieran,

    2004)(Carpenter, Franke &

    Levi, 2003)

    Blanton Kaput

    (Blanton & Kaput, 2002)

    Kieran

    (Kieran, 2004)

    (Kieran, 2004)

    (Greeno, 1977 Schoenfeld, 1992)

    (Malmivuori, 2006)

    (Bransford, Brown,

    & Cocking, 1999)

    1

    61

  • 2009 6

    2

    3

    4

    Goldin(2000)

    ()/

    ()///

    ()

    ()

    ()

    DeBellis Goldin(2006)

    1.

    62

  • (empower)(dis-empower)

    2.

    1

    3.

    1

    2

    3

    63

  • 2009 6

    //

    //

    1

    Debellis & Goldin(2006). A representation perspective on affect. Educational

    Studies in Mathematics, 63, 135.

    4.//

    1

    2(Valence)(Arousal)

    1989

    3

    64

  • 4

    Malmivuori(2006)

    (agents)

    (self-initiative)(self-direction)Zimmerman

    (1998) 2

    1.

    2

    2.

    3.

    65

  • 2009 6

    (Goldin, 2000)

    (self-awareness)

    Shan

    Kruglanski Friedman2003

    1.(commitment transfer)

    2.(affective transfer)(flavor)

    3.(strategic transfer)

    (Debellis & Goldin, 2006)

    Blanton & Kaput, 2002

    Kieran(2004)

    1.Silver(1987) Schoenfeld(1992)

    (sensory buffers)

    66

  • 2.(Dual Coding Theory, DCT)(representation)

    (referential) (organizational/ transformational)

    1.

    (Goldin & Janvier, 1998)

    2.

    (Paivio, 1990)

    (Paivio, 1990)

    3.(Paivio, 1990)

    (Paivio, 1990)

    67

  • 2009 6

    (Friel, Curcio & Bright, 2001; Koedinger & Nathan, 2004; Nathan & Kim,

    2007)Nathan Kim(2007)

    Koedinger Nathan(2004) 6 8

    FrielCurcio Bright(2001)

    3

    1 2 3

    3

    68

  • 1.2.3.

    4.

    CarpenterFranke Levi(2003)1(explore)2

    (conjecture)3(test)4(generalize)

    1

    2

    3

    4

    5

    2 58

    29

    20 24

    69

  • 2009 6

    16 23 45

    5 6 30

    Cronbach .93

    .86.90.82.86.79.90 KMO

    .91.83.84.88.89.98

    .86 40

    50

    2001 Cronbach

    .89 Cronbach

    .75 .85

    30

    1.

    5 Likert

    .57 Cronbach

    .75.75.76

    2.

    Likert 5

    .52

    Cronbach .74.85.67

    1986

    70

  • 1 1

    4346 .77.924603

    .82.87.42.82.30.76

    SPM1994

    12 60

    1 1

    .53-.92.49-.93

    .31-.79.37-.78

    ShanKruglanski Friedman2003

    1.

    2.

    3.

    20

    .05

    2007 11 2008

    2

    40

    71

  • 2009 6

    1

    1 M SD M SD

    36.3 10.2 42.5 7.0

    8.1 2.9 3.0 2.2

    1.1.63.63.78

    8.42.92.72.7

    1.6.68.68.60

    1 36.3

    42.5 10.2 7.0

    2.5 .63

    2.5

    .78

    2.5

    2 19.7 30

    72

  • t3.6p.01

    (Friel, Curcio & Bright,

    2001; Koedinger & Nathan, 2004; Nathan & Kim, 2007)

    p.05

    2

    M SD M SD

    3.3 3.4 2.9 3.6 3.7 2.8

    1.11.11.51.11.11.5

    4.95.64.53.01.7

    19.7

    1.1.671.41.92.4

    5.56

    3

    .49

    (Paivio, 1990)

    (Debellis & Goldin, 2006)

    73

  • 2009 6

    3

    R 2 R 2 F

    .39 .39 36.38 .000 .46 .06 6.19 .016 .49 .04 4.14 .047

    .42.48

    .42

    .0640.375.95

    .000

    .018

    .21.32

    .21

    .1115.158.80

    .000

    .004 .19 .19 13.38 .001 .40 .40 37.49 .000 .09 .09 5.83 .019 .23 .23 17.03 .000

    4

    .22

    .16

    .26

    .29

    .38

    1.

    2.

    74

  • 3.

    4

    R 2 R 2 F

    1

    .13

    .22.13.09

    8.246.75

    .006

    .0122 .16 .16 10.34 .0023

    .18.26

    .18

    .0812.556.05

    .001

    .0074 .29 .29 22.73 .0005 .38 .38 33.92 .000

    5

    5 (%)

    1.

    3764

    2.

    1322

    3.

    3460

    75

  • 2009 6

    4.

    1119

    5.

    3662

    5

    60

    19

    62

    6 41

    28

    6 (%)

    1. 2441

    2. 1526

    3. 1628

    4. 1628

    5. 1119

    7

    76

  • 15

    7

    1. 4781

    2. 4577

    3. 1119

    4. 3866

    5. 915

    8

    70

    ShanKruglanski Friedman2003

    1.

    2.

    3.

    77

  • 2009 6

    8

    %

    1. 4171

    2. 2848

    3. 814

    4. 4577

    5. 814

    78

  • 79

  • 2009 6

    (1994)

    (1989)

    (2001)

    51-71

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    Blanton, M., & Kaput, J.(2002). Developing elementary teachers algebra eyes and

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    and experience. Washington, DC: National Academy Press.

    Carpenter, T. P., Franke, M. L., & Levi, L.(2003). Thinking mathematically: Integrating

    arithmetic & algebra in elementary school. Portsmouth, NH: Heinemann.

    DeBellis, V. & Goldin, G.(2006).Affect and meta-affect in mathematical problem

    solving: A representational perspective. Educational Studies in Mathematics, 63,

    131-147.

    Friel, S. N., Curcio, F. R., & Bright, G. W.(2001). Making sense of graphs: Critical

    factors influencing comprehension and instructional implications. Journal for

    Research in Mathematics Education, 32, 124-158.

    Goldin, G. A.(2000). Affective pathways and representations in mathematical problem

    solving. Mathematical Thinking and Learning, 17, 209-219.

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    Chick., & M. Kendal(Eds.), The future of the teaching and learning of algebra(pp.

    21-33). Dordrecht, The Netherlands: Kluwer Academic.

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    the cognitive and motivational aspect of self-regulation. In s. J. Spencer, S. Fen., M.

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