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營造數學教師 專業對話與專業學習社群. 鍾靜 國立臺北教育大學 數學暨資訊教育學系教授. 序曲 Ⅰ. 數學教師的教學知識. 教師知識. 註: CK : Content Knowledge ; PK : Pedagogical Knowledge ;. PCK : Pedagogical Content Knowledge ; LK : knowledge of Learners and their Characteristics. 信念. 特定 脈絡 知識. 數學知識. 教學知識. 學習者數學 認知知識. 序曲 Ⅰ. - PowerPoint PPT Presentation
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CK : Content Knowledge PK : Pedagogical Knowledge PCK : Pedagogical Content Knowledge LK : knowledge of Learners and their Characteristics .
()CKPKPCK LKShulman (1986)VVVShulman (1987)VVVVVVVTamir (1991)VVVVVVReynolds (1992)VVVV(l996)VVVV(2000)VVV(2002)VVVVV(2003)VVVVV(2006)VVVVVV
Fennema & Franke1992, p.162
MK : Knowledge of Mathematics PK : Pedagogical Knowledge MTK : Knowledge of Mathematics Teaching LK : Knowledge of Learners Cognitions in Mathematics .MTKMTK
MKPKMTKLMKFennema Franke(1992)VVVVThompson (1992)VVCochran, DeRuiterKing (1993)VVVV 2001VV2000VVV2003VVVVVV2004VVVVVVV2006VVVVVVV
MKTMathematical Knowledge for Teaching
From Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers' Topic-Specific Knowledge of Students., by Hill et al., 2008, Journal for Research in Mathematics Education, 39(4), 377.
AAMTStandards for Excellence in Teaching Mathematics in Australian SchoolsSETM10NCATEStandards for Elementary Mathematics SpecialistsSEMS14INTASCModel Standards for Beginning Teachers of MathematicsMSBTM10NBPTS715Middle Childhood through Early Adolescence / Mathematics StandardsMCEAMS12()NCETMTDATDA Professional Standards for Mathematics TeachersTDAPSMT33()
2012203217-239
A.A-1 2A-2 4A-3 3A-4 3B.B-1 2B-2 2B-3 2B-4 2C.C-1 2C-2 2C-3 2
1. 2. 12342012203217-239()
A-1 A-1-1 3~4444A-1-2 3444A-2 A-2-1 1~32~444A-2-2 2~32~43~44A-2-3 2~33~444A-2-4 2344A-3 A-3-1 2344A-3-2 3444A-3-3 2344A-4 A-4-1 233~44A-4-2 2~33~444A-4-3 2~33~444
()1. 2. 12342012203217-239
B-1 B-1-1 1344B-1-2 1444B-2 B-2-1 1344B-2-2 1344B-3 B-3-1 12~344B-3-2 44B-4 B-4-1 12~444B-4-2 114
()1. 2. 12342012203217-239
C-1C-1-1 2~3444C-1-2 144C-2C-2-1 2~33~44C-2-2 2~34C-3C-3-1 2~344C-3-2 4
(professional dialogue)(curriculum development)(peer supervision)(peer coaching)(action research)
Types of Cooperative Development (Glatthorn, 1987)
TypeFocusDistinguishing features1. Professional dialogueReflection about practiceGuided discussion, focusing on teaching as thinking2. Curriculum developmentProduction of materialsCollaborative development of curriculum, using naturalistic processes3. Peer supervisionAnalysis of teachingObservation of instruction, followed by analysis and feedback4. Peer coachingMastery of skillsDevelopment of specific skills, usually based on models of teaching and supported with staff development5. Action researchSolving of problemsDevelopment and implementation of feasible solution to teacher-identified problems
Isaacs (1999) --Listening --Suspending --Respecting --Voicing
Glatthorn1987
Scharmer (1998) --/politeness (Talking nice)/breakdown (Talking tough) /inquiry (Reflective dialogue)/flow (Generative dialogue)
1.2.3.
based on a 5-point scale 4.94.64.6
Scharmer study (1998)/ Politeness/Breakdown/Inquiry /Flow
vs.1.2.3.
based on a 5-point scale 4.64.5
109/21209/28310/05410/12510/19610/26711/02811/09911/16
A / B
Stage Date109/21AB209/28ABB310/05AB410/12AB
Stage Date510/19AB610/26ABB711/02AB811/09ABB911/16AB
Level 0 Kimberly H.A., Karen C. F.,& Miriam G. S.(2004) .Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education. 35(2), 81-116.
A. QuestingB. Explaining mathematical thinkingC. Source of mathematical ideasD. Responsibility for learning
Level 1 Kimberly H.A., Karen C. F.,& Miriam G. S.(2004) .Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education. 35(2), 81-116.()
A. QuestingB. Explaining mathematical thinkingC. Source of mathematical ideasD. Responsibility for learning()
Level 2 Kimberly H.A., Karen C. F.,& Miriam G. S.(2004) .Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education. 35(2), 81-116.()
A. QuestingB. Explaining mathematical thinkingC. Source of mathematical ideasD. Responsibility for learning
Level 3 Kimberly H.A., Karen C. F.,& Miriam G. S.(2004) .Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education. 35(2), 81-116.()
A. QuestingB. Explaining mathematical thinkingC. Source of mathematical ideasD. Responsibility for learning()
2010-312-333
2010-312-333
Level 0Level 1Level 2Level 3Level 4
Level 0 Level 1 ()
Level 2 ()
Level 3 ()
Level 4 ()
1. 2. 3.
1.2.3.
1.2. 3.4.
problem-based learning [PBL] 3.4.5.6.
1.2.
2009
/20075223-47
765
2009(N=85)
N35N16N34MinMaxMSMinMaxMSMinMaxMS354.46.561254.44.892254.35.734354.34.591354.50.632254.47.706254.31.676354.13.719254.35.812254.17.618354.00.730254.29.871253.91.702253.94.929253.88.880253.77.770253.81.981253.41.821153.631.003253.50.894253.53.929253.80.833253.441.031253.50.788253.94.725354.00.632253.94.776354.34.591354.25.577354.32.684254.37.731354.31.602354.29.719354.26.701354.31.602354.21.687354.34.725354.44.629254.56.705254.14.879354.13.806254.29.760254.00.939153.941.181153.941.043253.97.822254.00.816254.09.933153.74.980153.751.183153.681.007153.741.010253.56.964153.531.022
--
01N3425N386N13MinMaxMSMinMaxMSMinMaxMS254.41.783254.42.642354.38.650354.35.646254.45.686454.54.519354.35.597254.16.886454.54.519354.21.687254.11.863454.38.506254.09.712253.79.905353.77.725253.76.781253.55.828253.541.050153.591.019253.55.921253.54.877253.62.985253.63.786253.54.776254.00.778253.84.638354.15.801354.35.646354.26.644454.38.506354.38.652254.24.751354.46.660354.26.618354.21.741354.31.630354.41.609354.50.688254.38.961254.03.904354.26.760354.46.660154.031.029153.891.034254.001.000253.97.969253.95.769354.38.768153.651.098153.681.042354.00.707153.381.101153.76.971353.85.689
2009.06217-239
/20075223-47
-/M.
M.M-0M-0-1M-1M-1-1M-1-2 M-2M-2-1 M-2-2 M-2-3 M-2-4 M-3M-3-1 M-3-2 M-3-3 M-4M-4-1 M-4-2 M-4-3
-/A./T.
A.A-0A-0-1A-1A-1-1 A-1-2 A-2A-2-1A-2-2 A-3A-3-1 A-3-2 A-4A-4-1 A-4-2 T.T-0T-0-1T-1T-1-1 T-1-2 T-2T-2-1T-2-2 T-3T-3-1 T-3-2
-/H.
H.H-0H-0-1H-1 H-1-1H-1-2H-2H-2-1H-2-2H-2-3H-3H-3-1H-3-2H-3-3H-4H-4-1H-4-2
2010(N=84) M.A.T.H.
N=39N=16N=29MinMaxMSMinMaxMSMinMaxMSM.354.28.605354.19.834354.59.568454.69.468454.63.500454.83.384454.64.486354.63.619354.52.574354.64.537254.31.873354.41.628354.59.549354.44.629354.55.632454.74.442254.50.894454.79.412454.62.493354.63.619354.59.568454.64.486454.56.512354.52.574354.59.595354.63.619354.38.622354.79.469454.75.447354.55.572454.64.486454.63.500354.48.688454.64.486254.44.814354.62.561454.56.502154.381.025354.59.568
M.A.T.H.
N=39N=16N=29MinMaxMSMinMaxMSMinMaxMSA.254.23.667154.001.095354.24.577354.41.637153.941.181354.17.711354.51.601354.50.632354.55.572354.15.670154.001.033253.93.842354.31.694354.38.619354.34.670354.69.521454.63.500454.76.435253.85.587153.871.088254.03.731254.15.630354.19.655354.45.632354.62.590354.37.719354.69.604T.353.95.686153.941.181353.93.593354.33.577154.001.317354.10.673354.41.677354.44.629254.24.786354.64.537254.06.772254.48.738354.59.595354.37.619354.48.574454.51.506354.31.704354.28.702354.54.600454.50.516354.28.751
M.A.T.H.
N=39N=16N=29MinMaxMSMinMaxMSMinMaxMSH.354.03.628253.94.854353.93.651354.51.556254.37.885354.52.634454.69.468454.75.447354.61.567454.62.493154.371.025354.34.670454.49.506154.371.025354.38.677354.74.498454.56.512354.62.677354.46.643154.251.065354.55.632354.13.656154.061.124254.28.702354.41.595154.191.109354.38.677454.62.493154.631.025354.62.622354.21.615154.311.078354.34.670
M.A.T.H.
01N=3425N=316N=19MinMaxMSMinMaxMSMinMaxMSM.354.26.666354.48.626354.37.684454.65.485454.71.461454.89.315354.53.563454.61.495354.68.582354.41.657254.52.677354.63.597354.50.615354.55.568354.63.597354.65.544254.74.631454.79.419354.41.609454.74.445454.74.452454.59.500454.55.506354.63.597354.47.563354.52.626354.63.684354.71.524454.74.445354.63.597354.44.613354.65.551454.74.452454.59.500254.55.675354.68.582454.62.493154.42.807354.58.607
M.A.T.H.
01N=3425N=316N=19MinMaxMSMinMaxMSMinMaxMSA.254.12.686154.19.792354.32.749254.24.781154.23.845354.26.806354.44.613354.55.624454.63.496253.97.717153.97.983354.32.582354.32.727354.32.653354.37.597354.65.544454.74.445454.74.452253.91.753153.77.805354.16.602254.09.712354.26.575454.58.507354.47.748454.71.461354.63.597T.153.76.890254.00.632354.16.688154.12.844154.29.824354.16.688254.18.797354.52.570354.42.692254.35.734254.52.724454.63.496354.44.613354.55.568354.58.607354.32.638354.42.620354.47.612354.47.662354.42.672354.42.607
M.A.T.H.
01N=3425N=316N=19MinMaxMSMinMaxMSMinMaxMSH.353.94.694253.97.706354.05.621354.47.615254.52.677354.47.697454.68.475454.65.486354.72.575354.53.563154.39.844354.53.612354.41.557154.35.839354.58.607354.62.604354.74.514354.63.597354.38.652154.42.886354.63.597354.15.702154.13.885354.26.733354.44.660154.29.824354.32.749354.65.544154.58.807354.63.597354.32.684154.16.820354.37.684
M.A.T.H.
01N=5423N=223N=8MinMaxMSMinMaxMSMinMaxMSM.354.41.659354.23.685454.50.535454.81.392454.50.512454.75.463354.69.507354.36.581454.63.518254.54.665354.36.658454.63.518354.69.507354.18.664454.63.518254.74.589454.68.477454.63.518354.61.564454.59.503454.63.518454.65.482354.45.596454.50.535354.59.567354.32.716454.63.518454.72.452354.64.658454.75.463354.61.596454.55.510454.50.535254.69.577354.36.581454.63.518154.59.687354.36.581454.63.518
M.A.T.H.
01N=5423N=223N=8MinMaxMSMinMaxMSMinMaxMSA.154.28.763254.00.756454.13.354154.20.786254.27.935454.38.518354.57.570354.41.666454.50.535154.04.889354.05.653354.13.641354.35.677354.27.703454.38.518454.74.442354.59.590454.75.463153.83.818354.00.617454.25.463254.22.634354.27.703454.50.535354.61.627354.45.671454.88.354T.153.89.816354.05.722354.00.535154.15.899354.27.550354.25.707254.39.712354.41.666354.00.756254.44.744354.41.590454.88.354354.46.605354.59.590454.63.518354.39.627354.41.590354.38.744354.39.685354.50.598454.62.518
M.A.T.H.
01N=5423N=223N=8MinMaxMSMinMaxMSMinMaxMSH.253.94.685354.14.640353.75.707254.41.714454.64.492454.63.518354.70.503454.64.492454.62.518154.44.744354.59.590454.38.518154.43.742354.45.596454.38.518354.72.492354.59.666354.50.756154.50.771354.36.727454.38.518154.17.841354.09.684454.38.518154.31.820354.45.596454.38.518154.63.734454.59.503454.63.518154.24.799354.32.646454.38.518
***1.Isaacs Listening Suspending Respecting Voicing2.Scharmer differ in terms of (1) the presence or absence of self-reflection and (2) the primacy of wholeness or parts Self-reflectiveNon-reflectivePartsWhole / / / / This teaching learning group developed their dialogue behavior based on Isaacs four basic dialoguing behaviors: listening, suspending, respecting, and voicing (Isaacs, 1999), and Scharmers four developmental stages of professional dialogues:Politeness,Breakdown, Inquiry, Flow (Scharmer, 1998). (Isaacs1999ListeningSuspendingRespectingVoicingScharmer1998/politenessTalking nice/breakdownTalking tough/inquiryReflective dialogue/flowGenerative dialogue )
*Theoretical Side--Reading Discussion Videos
Practical Side/ Actual Teaching Problems--Classroom Teaching Textbook
ReflectingSharing
Professional GrowthImproving Teaching**