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韓國數學教育的分享
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韓國數學教育的分享

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  • Add that the study was not about a particular teaching method either. It was no a development followed by evaluation. The topic has been taught more or less the way it is being taught in Israeli schools, except for one thing: The teacher, out of conviction but also to have a better insight into students’ thinking, made then puzzle over what some things might be before actually presenting these things to them.

Transcript

  • 1. Teaching and Learning of Mathematics in Korea Kyung Hwa, Lee Seoul National University
  • 2.
    • To give an overall picture of Korean mathematics education
    • To identify characteristics, strengths, and weaknesses of Korean mathematics education practice
    The aim of this talk:
  • 3. Contents Lee Kyeong Hwa 1. Teachers & Students in Korean Society 2. Challenges to Korean Math teachers 3. “Typical” & “Good” Mathematics Teaching 4. Characteristics, strengths, and weaknesses
  • 4. 君師父一體
      • Everyone can learn and become human if he/she finds a teacher
      • Students must obey teachers
      • Teacher is the last profession that is and should be respected by society
      • Teacher is future maker
    Teachers in Korean Society
  • 5. 學無止境
      • Studying is difficult and needs a lot of efforts
      • Students should study continuously
      • Students should make every endeavour to tackle hard tasks
      • Diligence and perseverance are important values that students should have
    Students in Korean Society
  • 6.
    • Exam-oriented education
    • Parents and students try to find ( better? ) teachers out of school
      • Teachers of private institutes
      • Teachers of on-line learning programs, etc.
    Change and Challenge (1) Competitive society
  • 7.
    • To improve efficiency and significance of students' mathematical learning
    • Joy of discovery and maintain students’ interest
    • Positive attitude toward mathematics
    • Mathematical communication
    Change and Challenge (2) Curriculum reform(1997, 2007)
  • 8. Lee Kyeong Hwa Change and Challenge (3)
      • Not teacher-friendly
      • Cartoon, story, game, puzzle, etc
    New textbooks Real-life context Student-centered Creative thinking
  • 9. Typical Korean Math Teacher Orchestration of lessons Complete practice Coherent explanation Efficient imprinting Systematic instruction
  • 10. Systematic instruction There is a pattern in their lessons Teacher initiates and leads learning Focuses primarily on procedures Gives priority to efficient delivery o f content Conclusion ? Introduction Development
  • 11. Coherent explanation Learn by imitation Fundamental Guide to Math an obligation to make students Learn the intended content Within a given time limit Kind Easy Intuitive Insightful Model
  • 12. Complete practice Long period of time to establish fundamental Hard for students to understand in the beginning Duty Persuade and cheer up students to practice as much as possible
      • Emotional
      • Parent-like
  • 13. Efficient Imprinting Last 3-5 minute-long imprinting provides students with efficient condensation of the intended learning content in a lesson
    • What students should keep in mind
    • How to memorize definitions, algorithms, etc
    • Why some specific knowledge is prior to others
    • Special order, context, map, relationship, etc
  • 14. “ Good” mathematics teaching Enculturation Focused on process Conceptual understanding Guide to invention Positive attitude Rich context Meaningful Appropriate provocative Participation Student-centred Various contribution
  • 15. Lee Kyeong Hwa
    • Design a lesson creatively and appropriately
    • Lead students to explore and understand content
    • Have enough PCK and CK
    • Promote students’ creativity and thinking
    • Extend and synthesis students’ thinking
    • Ask adequate and diverse level of questions
    • Use instructional materials timely
    Good mathematics teachers …
  • 16. T: A soccer ball is made of black and white pieces of leather as you can see in the picture. What kind of problems do you want to explore with a soccer ball? One example
  • 17. Problems by Students
    • How can we make it?
    • How many white pieces?
    • _________ vertices?
    • _________ edges? etc
    • Why the manufacturer chose that shape?
    • Different ways to make?
  • 18. Task (1)
    • How many pentagons are on the whole soccer ball? How many hexagons are on the whole soccer ball?
  • 19. S1: So what is your answer? Mine is 12. S2: Regular pentagon? 12. I counted the regular hexagon first. It ’ s 19. S3: So did I, but in my case, it ’ s different, it ’ s 20. S1: How did you count? S2: Well, I started at this face, let ’ s count again , one, two, … , twenty. Oh, it ’ s strange, what ’ s happening here! [Pragmatic] Conversation (1) 1
  • 20. S 4 : I think 20 is correct because there were no mistakes before. Maybe you ’ ve missed one. S 2 : I need to count once again. By the way, all of you got 20? S1, S 5 : Yeah. S1 : Why don ’ t you count by following different direction s ? I t might be helpful. Conversation (2) 2
  • 21. S 5 : [speaking to S1] Directions? Why do we consider directions? S 2 : If we collect lots of evidence, then we can believe a lot. Is it correct? S1 : In addition to that, there would not be mistakes if we insist on direction while counting. S 5 : Oh! That ’ s a good idea. Then we had better investigate how many directions are there .
  • 22. S1
    • reasoned semantically
    • proved not by direct counting or mathematical calculation but by systematic counting
    • 5 directions
    • 4 hexagons for each direction
    • 5 ×4=20
  • 23. S12: We know there are 12 pentagons. For each pentagon there are 5 hexagons, for each hexagon there are 3 pentagons. Thus ( 12 ×5)/3 = 20. Conversation (3) 3
  • 24. Task (2)
    • How many vertices are there? Explain how you found it.
    • How many edges are there? Explain how you found it.
  • 25. Task (3)
    • Looking at every vertex, what do you see?
    • For every vertex, there are 1 pentagon and 2 hexagons
  • 26. Definition by students Spherelike (All the same for every vertex) Not spherelike (Not same for every vertex)
  • 27. Task (4)
    • How many spherelike solids can be made if we use regular triangles?
    • How many spherelike solids can be made if we use squares?
    • How many spherelike solids can be made if we use regular pentagons?
  • 28. Task (5)
    • How many spherelike solids can be made if we use regular hexagons?
    • How many spherelike solids can be made if we use two kinds of regular polygons such as a soccer ball?  
  • 29. Representation
    • “ Looking at one vertex, we know what kinds of polygons there are, are able to name it”
    (3, 4, 4, 4) (5, 3, 5, 3)
  • 30. Observation & Discovery
    • Students made many kinds of spherelike solids
    • Described each solid from their own perspective
    Sphere solid (3,4,4,4) (5,6,6) (4,6,6) (3,6,6) (3,4,3,4)
  • 31. Observation & Discovery
    • Calculated the sum of interior angles collected at one vertex
    • Discussed the meaning of the value
    A Sphere solid Each ver. (3,4,4,4) 330 (5,6,6) 348 (4,6,6) 330 (3,6,6) 300 (3,4,3,4) 300
  • 32. Observation & Discovery
    • Difference between the sum and 360 °
    • Discussed the meaning
    • Semantic reasoning was often used
    A B Sphere solid Each ver. 360-A (3,4,4,4) 330 30 (5,6,6) 348 12 (4,6,6) 330 30 (3,6,6) 300 60 (3,4,3,4) 300 60
  • 33. Discovery
    • Consistently observed particular cases to gain insight into generalization
    A B C Sphere solid Each ver. 360-A number of ver. B x C (3,4,4,4) 330 30 24 720 (5,6,6) 348 12 60 720 (4,6,6) 330 30 24 720 (3,6,6) 300 60 12 720 (3,4,3,4) 300 60 12 720
  • 34. Observation & Conjecture
    • (3,3,3,3,5)
    • 348°
    • 92 faces
    • (5,6,6)
    • 348°
    • 32 faces
  • 35. Informal proof
    • The best spherelike solid
    • for the manufacturer is (5,6,6)
    • Since
    • Closed to sphere enough (348°)
    • Small number of faces (32 faces)
    • the areas of two polygons are similar, etc.
  • 36. Unanswered questions Persistence Why for all solids 720°? How many spherelike? How do we know?
  • 37.
    • Korean math teachers focus on rather procedural teaching which does not necessarily imply rote learning or learning without understanding
    Characteristics (1): S & W Complete practice Coherent explanation Efficient imprinting Systematic instruction
  • 38.
    • “ Good” mathematics teaching includes discussion, students’ active participation, good questioning skills based on teachers’ solid PCK, CK, and enthusiasm
    Characteristics (3): S & W
  • 39. Characteristics (3): S & W 師 = 父 Students Teacher Care students Accompanying Act as a model 師 ≠ 君 Respect teachers imitating Act as a follower
  • 40. Lee Kyung Hwa Company Logo Thank you! [email_address]