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Teaching and Learning of  Mathematics in Korea Kyung  Hwa, Lee Seoul National University
[object Object],[object Object],The aim of this talk:
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
君師父一體 ,[object Object],[object Object],[object Object],[object Object],Teachers in Korean Society
學無止境 ,[object Object],[object Object],[object Object],[object Object],Students in Korean Society
[object Object],[object Object],[object Object],[object Object],Change and Challenge (1) Competitive society
[object Object],[object Object],[object Object],[object Object],Change and Challenge (2) Curriculum reform(1997, 2007)
Lee Kyeong Hwa Change and  Challenge (3) ,[object Object],[object Object],New textbooks Real-life context Student-centered Creative thinking
Typical Korean Math Teacher Orchestration of lessons Complete practice Coherent explanation Efficient imprinting Systematic instruction
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
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
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 ,[object Object],[object Object]
Efficient Imprinting Last 3-5 minute-long imprinting provides students with efficient condensation of the intended learning content in a lesson  ,[object Object],[object Object],[object Object],[object Object]
“ Good” mathematics teaching Enculturation   Focused on process  Conceptual understanding Guide to invention Positive attitude Rich context Meaningful Appropriate provocative Participation Student-centred Various contribution
Lee Kyeong Hwa ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Good mathematics teachers …
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
Problems by Students ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Task (1) ,[object Object]
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
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
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 .
S1 ,[object Object],[object Object],[object Object],[object Object],[object Object]
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
Task (2) ,[object Object],[object Object]
Task (3) ,[object Object],[object Object]
Definition by students Spherelike (All the same  for every vertex) Not spherelike (Not same  for every vertex)
Task (4) ,[object Object],[object Object],[object Object]
Task (5) ,[object Object],[object Object]
Representation   ,[object Object],(3, 4, 4, 4) (5, 3, 5, 3)
Observation & Discovery  ,[object Object],[object Object],Sphere solid (3,4,4,4) (5,6,6) (4,6,6) (3,6,6) (3,4,3,4)
Observation & Discovery ,[object Object],[object Object],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
Observation & Discovery ,[object Object],[object Object],[object Object],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
Discovery  ,[object Object],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
Observation & Conjecture  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Informal proof  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Unanswered questions Persistence Why for all solids 720°? How many spherelike? How do we know?
[object Object],Characteristics (1): S & W Complete practice Coherent explanation Efficient imprinting Systematic instruction
[object Object],Characteristics (3): S & W
Characteristics (3): S & W 師  =  父 Students Teacher  Care students  Accompanying  Act as a model   師 ≠ 君 Respect teachers imitating Act as a follower
Lee Kyung Hwa Company Logo Thank you!   [email_address]

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韓國數學教育的分享

  • 1. Teaching and Learning of Mathematics in Korea Kyung Hwa, Lee Seoul National University
  • 2.
  • 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
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  • 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
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  • 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
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  • 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
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  • 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 .
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  • 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
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  • 26. Definition by students Spherelike (All the same for every vertex) Not spherelike (Not same for every vertex)
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  • 36. Unanswered questions Persistence Why for all solids 720°? How many spherelike? How do we know?
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  • 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]

Hinweis der Redaktion

  1. 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.