南山中學 - 2010/12/8 資優數學講座

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南南南南 - 2010/12/8 南南南南南南 南南南 南南南南南南 「」「」 南南南南南南 : 南南南南南南南南南南南南南南南南南南 南南南南南南南南南南南南南南南南南 南南南 [email protected] 1 N T U E D e p a r t m e n t o f M a t h e m a t i c s a n d I n f o r m a t i o n E D u c a t i o n ( 2 0 1 0 / 1 2 / 0 8 )

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南山中學 - 2010/12/8 資優數學講座. 【 數學之「教」與「學」 】 數學解題策略 : 以參與亞太小學數學奧林匹亞邀請賽為例 國立臺北教育大學數學暨資訊教育學系 張英傑 [email protected]. 數謎. 英文字母代表不同的印度 - 阿拉伯數字 1 ONE +1 +ONE 2 TWO. 建構數學 讓學生變笨? 數學能力 我全球第一. - PowerPoint PPT Presentation

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  • - 2010/12/8

    :

    [email protected]

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • -

    1 ONE +1 +ONE 2 TWO NTUE Department of Mathematics and Information EDucation(2010/12/08)*

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • PISA2006

    PISA2009?!

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • PISA 3 HTTP://WWW.LIBERTYTIMES.COM.TW/2010/NEW/DEC/8/TODAY-LIFE7.HTM

    NTUE Department of Mathematics and Information EDucation(2010/12/08)*

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE [email protected] FOR INTERNATIONAL STUDENT ASSESSMENT200020032006 2009

    ORGANIZATION FOR ECONOMIC COOPERATION AND DEVELOPMENT (OECD) PISA

    *

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE [email protected] AN INDIVIDUALS CAPACITY TO IDENTIFY AND UNDERSTAND THE ROLE THAT MATHEMATICS PLAYS IN THE WORLD, TO MAKE WELL-FOUNDED JUDGEMENTS AND TO USE AND ENGAGE WITH MATHEMATICS IN WAYS THAT MEET THE NEEDS OF THAT INDIVIDUALS LIFE AS A CONSTRUCTIVE, CONCERNED AND REFLECTIVE CITIZEN.

    Mathematical Literacy*

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE [email protected] AN INDIVIDUALS CAPACITY TO USE SCIENTIFIC KNOWLEDGE, TO IDENTIFY QUESTIONS AND TO DRAW EVIDENCE-BASED CONCLUSIONS IN ORDER TO UNDERSTAND AND HELP MAKE DECISIONS ABOUT THE NATURAL WORLD AND THE CHANGES MADE TO IT THROUGH HUMAN ACTIVITY.

    Scientific Literacy*

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE [email protected] INDIVIDUALS CAPACITY TO UNDERSTAND, USE AND REFLECT ON WRITTEN TEXTS, IN ORDER TO ACHIEVE ONES GOALS, TO DEVELOP ONES KNOWLEDGE AND POTENTIAL AND TO PARTICIPATE IN SOCIETY.Reading Literacy*

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE [email protected] INDIVIDUALS CAPACITY TO USE COGNITIVE PROCESSES TO CONFRONT AND RESOLVE REAL, CROSS-DISCIPLINARY SITUATIONS WHERE THE SOLUTION PATH IS NOT IMMEDIATELY OBVIOUS AND WHERE THE LITERACY DOMAINS OR CURRICULAR AREAS THAT MIGHT BE APPLICABLE ARE NOT WITHIN A SINGLE DOMAIN OF MATHEMATICS, SCIENCE OR READING.

    Problem-solving Skills*

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE [email protected]*

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE [email protected](SIMSS)1990(TIMSS) THIRD INTERNATIONAL MATHEMATICS AND SCIENCE STUDY1999 (TIMSS-R) 4 (REPEAT)

    TIMSS 2003 TREND INTERNATIONAL MATHEMATICS AND SCIENCE STUDY TIMSS 2007

    International Association for the Evaluation of Educational AchievementIEA

    *

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE [email protected]*

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*

    (2010)< NTUppt>

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • ,!!20101116

    http://www.youtube.com/watch?v=FhSCF_OlY1k

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • HTTP://WWW.LIBERTYTIMES.COM.TW/2010/NEW/DEC/7/TODAY-LIFE10.HTM

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • 12 32 2 *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • SEQUENCEFUNCTION)671,2,4, 8, 16, ?, ?,

    x = 1,2,3,4,5 y = 1, 2, 4, 8, 16 (1) x =6, y = ? (2) x =7, y = ?

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • (GENERALIZATION)223448(1) 66(2) 77(3) nn*NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • (TOWER OF HANOI)

    64()64(1)(2)

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • Geroge Ploa How to solve it?

    () WIN: What- If- Not*NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *http://www.naer.edu.tw/study/math/ana/index.htmhttp://content.edu.tw/primary/math/tp_pc/main.htm-http://mathseed.ntue.edu.tw/http://www.shes.hcc.edu.tw/~oddest/http://www.mathland.idv.tw/http://sctnet.edu.tw/index.phpHercules ttp://residence.educities.edu.tw/mario123/http://www.paps.kh.edu.tw/aspx/math_menu/math_source.aspx/

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • 200996 95/12/15

    --Benchmark 2010: Collaborative Inquiry and Co-create Quality Elementary Mathematics and Science Teacher Education Program

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • 2009

    3 444////:////:////:////

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • EX1-5: 2009

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • Test1-3:

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • EX2-6: 12244812.........

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • Test1-4: 25

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • EX2-3:

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • Ex1-1: ?

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • EX1-2: 199111

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • () *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • 1.2.3.4.5.6.7.8.

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • 9.10.11.12.13.14.15.

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • http://model.math.scu.edu.tw/ (2010 March

    *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*

    Question:?

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*

    http://mag.udn.com/mag/campus/storypage.jsp?f_ART_ID=21240

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*:Formosahttp://www.nownews.com/2007/11/15/515-1768980.htm

    ?? !!

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*1x1x1x1 = ?

    11

    1

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)* 1.1x1.1x1.1x1.1 = ?

    1.11.1

    ?!

    :

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*1.11.12.591.1x1.1= 1.211.1x1.1x1.1 = 1.3311.1x1.1x1.1x1.1 = 1.46411.1x1.1x1.1x1.1x1.1 = 1.610511.1x1.1x1.1x1.1x1.1 x1.1 = 1.7715611.1x1.1x1.1x1.1 x1.1x1.1x1.1 = 1.94871711.1x1.1x1.1x1.1 x1.1x1.1x1.1x1.1 = 2.1435866 1.1x1.1x1.1x1.1 x1.1x1.1x1.1x1.1x1.1 = 2.35794761.1x1.1x1.1x1.1 x 1.1x1.1x1.1x1.1x1.1 x1.1 = 2.5937423

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)* 0.9x0.9x0.9x0.9 = ?

    0.90.9

    ?!

    :

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*0.90.90.35 0.9x0.9 = 0.810.9x0.9x0.9 = 0.7290.9x0.9x0.9x0.9 = 0.65610.9x0.9x0.9x0.9x0.9 = 0.590490.9x0.9x0.9x0.9x0.9x0.9 = 0.5314410.9x0.9x0.9x0.9x0.9x0.9x0.9= 0.47829690.9x0.9x0.9x0.9 x0.9x0.9x0.9x0.9= 0.43046720.9x0.9x0.9x0.9x0.9x0.9x0.9x0.9x0.9 = 0.38742040.9x0.9x0.9x0.9 x0.9x0.9x0.9x0.9x0.9x0.9= 0.3486783

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*: ? 1.11.12.59

    0.90.90.35

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*:

    ! !

    ! !

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*: 3CCompetence Cooperation Confidence

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*ATTITUDE: WAY OF THINKING OR BEHAVING

    :

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*

    :

    Putting Together!

    Making Difference!

    Showing Significance!

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*() M.(Mathematics)A.(Art)T.(Test)H.(Head)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)* (JANE GOODALL)Only if we can understand can we care.Only if we care will we help.Only if we help shall we be saved.

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)* Just do it >>>

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • NTUE Department of Mathematics and Information EDucation(2010/12/08)*Ing-Jye Chang*

    NTUE Department of Mathematics and Information EDucation(2010/12/08)

  • *NTUE Department of Mathematics and Information EDucation(2010/12/08)

    NTUE Department of Mathematics and Information EDucation(2010/12/08)