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. <ul><li>To give an overall picture of Korean mathematics education </li></ul><ul><li>To identify characteristics, strengths, and weaknesses of Korean mathematics education practice </li></ul>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 <ul><ul><li>Everyone can learn and become human if he/she finds a teacher </li></ul></ul><ul><ul><li>Students must obey teachers </li></ul></ul><ul><ul><li>Teacher is the last profession that is and should be respected by society </li></ul></ul><ul><ul><li>Teacher is future maker </li></ul></ul>Teachers in Korean Society
5. 學無止境 <ul><ul><li>Studying is difficult and needs a lot of efforts </li></ul></ul><ul><ul><li>Students should study continuously </li></ul></ul><ul><ul><li>Students should make every endeavour to tackle hard tasks </li></ul></ul><ul><ul><li>Diligence and perseverance are important values that students should have </li></ul></ul>Students in Korean Society
6. <ul><li>Exam-oriented education </li></ul><ul><li>Parents and students try to find ( better? ) teachers out of school </li></ul><ul><ul><li>Teachers of private institutes </li></ul></ul><ul><ul><li>Teachers of on-line learning programs, etc. </li></ul></ul>Change and Challenge (1) Competitive society
7. <ul><li>To improve efficiency and significance of students' mathematical learning </li></ul><ul><li>Joy of discovery and maintain students’ interest </li></ul><ul><li>Positive attitude toward mathematics </li></ul><ul><li>Mathematical communication </li></ul>Change and Challenge (2) Curriculum reform(1997, 2007)
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 <ul><ul><li>Emotional </li></ul></ul><ul><ul><li>Parent-like </li></ul></ul>
13. Efficient Imprinting Last 3-5 minute-long imprinting provides students with efficient condensation of the intended learning content in a lesson <ul><li>What students should keep in mind </li></ul><ul><li>How to memorize definitions, algorithms, etc </li></ul><ul><li>Why some specific knowledge is prior to others </li></ul><ul><li>Special order, context, map, relationship, etc </li></ul>
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 <ul><li>Design a lesson creatively and appropriately </li></ul><ul><li>Lead students to explore and understand content </li></ul><ul><li>Have enough PCK and CK </li></ul><ul><li>Promote students’ creativity and thinking </li></ul><ul><li>Extend and synthesis students’ thinking </li></ul><ul><li>Ask adequate and diverse level of questions </li></ul><ul><li>Use instructional materials timely </li></ul>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 <ul><li>How can we make it? </li></ul><ul><li>How many white pieces? </li></ul><ul><li> _________ vertices? </li></ul><ul><li> _________ edges? etc </li></ul><ul><li>Why the manufacturer chose that shape? </li></ul><ul><li>Different ways to make? </li></ul>
18. Task (1) <ul><li>How many pentagons are on the whole soccer ball? How many hexagons are on the whole soccer ball? </li></ul>
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 <ul><li>reasoned semantically </li></ul><ul><li>proved not by direct counting or mathematical calculation but by systematic counting </li></ul><ul><li>5 directions </li></ul><ul><li>4 hexagons for each direction </li></ul><ul><li>5 ×4=20 </li></ul>
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) <ul><li>How many vertices are there? Explain how you found it. </li></ul><ul><li>How many edges are there? Explain how you found it. </li></ul>
25. Task (3) <ul><li>Looking at every vertex, what do you see? </li></ul><ul><li>For every vertex, there are 1 pentagon and 2 hexagons </li></ul>
26. Definition by students Spherelike (All the same for every vertex) Not spherelike (Not same for every vertex)
27. Task (4) <ul><li>How many spherelike solids can be made if we use regular triangles? </li></ul><ul><li>How many spherelike solids can be made if we use squares? </li></ul><ul><li>How many spherelike solids can be made if we use regular pentagons? </li></ul>
28. Task (5) <ul><li>How many spherelike solids can be made if we use regular hexagons? </li></ul><ul><li>How many spherelike solids can be made if we use two kinds of regular polygons such as a soccer ball? </li></ul>
29. Representation <ul><li>“ Looking at one vertex, we know what kinds of polygons there are, are able to name it” </li></ul>(3, 4, 4, 4) (5, 3, 5, 3)
30. Observation & Discovery <ul><li>Students made many kinds of spherelike solids </li></ul><ul><li>Described each solid from their own perspective </li></ul>Sphere solid (3,4,4,4) (5,6,6) (4,6,6) (3,6,6) (3,4,3,4)
31. Observation & Discovery <ul><li>Calculated the sum of interior angles collected at one vertex </li></ul><ul><li>Discussed the meaning of the value </li></ul>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 <ul><li>Difference between the sum and 360 ° </li></ul><ul><li>Discussed the meaning </li></ul><ul><li>Semantic reasoning was often used </li></ul>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 <ul><li>Consistently observed particular cases to gain insight into generalization </li></ul>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
35. Informal proof <ul><li>The best spherelike solid </li></ul><ul><li>for the manufacturer is (5,6,6) </li></ul><ul><li>Since </li></ul><ul><li>Closed to sphere enough (348°) </li></ul><ul><li>Small number of faces (32 faces) </li></ul><ul><li>the areas of two polygons are similar, etc. </li></ul>
36. Unanswered questions Persistence Why for all solids 720°? How many spherelike? How do we know?
37. <ul><li>Korean math teachers focus on rather procedural teaching which does not necessarily imply rote learning or learning without understanding </li></ul>Characteristics (1): S & W Complete practice Coherent explanation Efficient imprinting Systematic instruction
38. <ul><li>“ Good” mathematics teaching includes discussion, students’ active participation, good questioning skills based on teachers’ solid PCK, CK, and enthusiasm </li></ul>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]
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