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Teacher Training in Japanese Mathematics Education

Teacher Training in Japanese Mathematics Education. Toshikazu Ikeda Yokohama National University Yoshiaki Kuwahara Shinmei Junior High School. Outline. States and issues in Japanese teacher training Pre-service education : Example in Yokohama National University

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Teacher Training in Japanese Mathematics Education

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  1. Teacher Training in Japanese Mathematics Education Toshikazu Ikeda Yokohama National University Yoshiaki Kuwahara Shinmei Junior High School

  2. Outline • States and issues in Japanese teacher training • Pre-service education : Example in Yokohama National University • In-service education • Lesson Study PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  3. First Report by the Education Personnel Training Council (1997) • Improvement of the teacher training curriculum①　Wide understanding of liberal arts　　　 ②　Problem Solving Ability, Humanity 　　　　③　Knowledge and skills of subject matters • The number of credits for subjects concerning teaching methods of mathematics →From about 2 credits to 8 credits PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  4. Second Report by the Education Personnel Training Council (1998) • Promotion of reeducation of currently employed teachers through master course • System of night master course for teachers is gradually introduced in teacher training university PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  5. University Board of education School Third Report by the Education Personnel Training Council (1999) • Facilitation of cooperation in the cultivation, appointment and training of teachers Deeper cooperation is expected PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  6. Pre-Service Education All Nothing Issue in teacher training university • In 2001 Ministry of Education, Culture, Sports, Science and Technology is planning to integrate teacher training university, keeping the quota of 10,000 students. PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  7. Example in Yokohama National University Quota of students 15000 → 10000 In 1997: Faculty of Education 　　　　　　　　　　　 →　Faculty of Education and Human Sciences 　　◇Pre-service education: 230 studentsFocus on Elementary School Education　◇Establishment of New Courses: 230 students In 2000: Introduction of a New Curriculum based on first report by the Education Personnel Training Council PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  8. Aims in mathematics educationin Yokohama National University [Mathematical points of view] ①　To foster students’ ability to think mathematically ②To enable students to understand mathematical concepts and ideas existing behind elementary and secondary mathematics. 　③　To foster students’ ability to represent mathematically ④ 　 To foster students’ ability to utilize technology PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  9. Aims in mathematics educationin Yokohama National University [Educational points of view] 　⑤　To enable students to understand the objectives and contents of mathematics 　⑥　To enable students to understand Teaching methods including assessment of mathematics 　⑦　To foster students’ ability to construct and analyze a classroom teaching 　⑧　To foster students’ ability to utilize the textbook of mathematics PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  10. Curriculum of mathematics education in YNU Introduction to Math. Observation of Classroom teaching 1 Teaching methods of elementary math. Lesson plan & observation 2 Calculus Ⅰ-Ⅳ Algebra Ⅰ-Ⅳ Geometry Ⅰ-Ⅳ Probability & StatisticⅠ-Ⅳ Problem solving and mathematical thinking Analysis of Classroom teaching Teaching Practice [elementary level] (4 weeks) 3 Contents taught in Secondary math. Development of Teaching material Assessment Teaching Practice [secondary level] (2 weeks) 4 Report to graduate PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  11. Mathematical concepts and ideas existing behind elementary mathematics １．Number and operation　２．Quantity and measurement　３．Figures ４．Relation between number and quantity　５．Way of mathematical thinking Core technology Option １．Mathematics for teachers ２．Mathematics for a real world ３．Mathematics for a joy In Case of Yokohama National University (For Elementary School Teacher) Introduction to Mathematics for elementary school teachers Presentation PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  12. Selection of problem in each group 12 groups composed of 5 members Problem Solving Preparation of Presentation Presentation, Assessing each other Mathematical points of view: 5points Presentation: 5points Option:Mathematics for a real world PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  13. ＴＲＹ Goal Post It is possible for player to kick in any place on the blue line. GOAL KICKS IN RUGBY In rugby, a chance to score a goal is given after a try. The probability of a successful goal is influenced by the position where the goal kick is made. How should you decide the position with the largest probability when attempting to make a goal kick. PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  14. “How many years does it take to make money double?” ５％　→　７２÷５＝１４．４　　　１５ years ３％　→　７２÷３＝２４　　　　　２４ years １％　→　７２÷１＝７２　　　　　７２ years Law of 72 PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  15. Eyesight • I heard that Eyesight of Inuit ismore than 5.0. If it is true, howcan Inuit see far away comparedwith us. PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  16. Mirror Problem Problem What size of mirror do we need at least in order to see the whole body? PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  17. Reflector of bicycle • Reflector of bicycle is shining even though light flood into it from any angles. What is the structure of reflector? PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  18. In-service teacher training in Japan PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  19. Classification of Teacher Training • Public Training (National,Prefecture,City/Town/Ward, School) • Private training (Individual research,society,Other Training & research circle) PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  20. Public Training for in-service Teachers • New teachers Training • Experienced Teachers Training (After 5 years & After 10 years ） • Dispatched Training (Master course in teacher training university, Company, Abroad） PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  21. New teachers Training ・About 9０ times training during first year 60 times in School , 30 times out of School ・Leading Teacher in charge guide New Teacher one by one. ・Extensive training Lecture,Lesson study,Management PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  22. Experienced Teacher Training • After 5 years ５~６ times training in 6th years Group Training in each theme (Class Management , Students Guidance, Problems to be solved (Bullying etc) • After 15 years 3~5 times training in 15th years Optional Course Training each interest (Subject ,Class Management , Students Guidance, Problem to be solved） PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  23. An example in mathematics education • In case of Junior High School Teachers • Contents: ・Explanation of the National Curriculum ・Developing New teaching materials for Team Teaching or Optional Course ・Collaboration by Experienced Teachers PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  24. Dispatched Training • To a Company • To Abroad Language TrainingJapanese SchoolInspection of various countries • To a Master Course in teacher training university (Study & Research) PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  25. Collaboration on the Daily work • Daily discussion in the Teachers’ Room • Regarding to mathematics teaching Progress of classroom teaching The way of Assessment Teaching Materials Exchange views PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  26. ② Observation of an actual classroom teaching ① Discussion about a lesson plan ③ Analytical discussion about the classroom teaching Lesson Study as teacher training • Pre-service education: One of the tools to assess a classroom teaching • Examinations to become a teacher: Demonstration of classroom teaching PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  27. Lesson plan – it’s history Before world war Ⅱ After world war Ⅱ PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  28. Five styles of a Lesson Study in Japan (in-service education) PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  29. Five styles of a Lesson Study in Japan (in-service education) PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  30. Relation between children and material Relation between children and teacher children teacher material Relation between teacher and material Lesson Study Triangle Strong Relation Between two components PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  31. Effectiveness of Lesson Study • Lesson study might be effective for teacher in the following points in particular. ① learn to see material 　 ・Can teacher identify mathematical essential points of materials? 　 ・Does teacher deprive of students’opportunity to think mathematically? PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  32. Effectiveness of Lesson Study ② learn to see students ・Can teacher understand what students understand? ・Can students understand teacher’s asking questions? ・Does teacher ignore of students’ ideas by his/her selfish reason? ・ Can teacher accept and evaluate students’ ideas appropriately? ・ Can students discuss cooperatively? PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  33. Effectiveness of Lesson Study ① learn to see material+ ② learn to see students ・Can teacher develop the material by considering both mathematical essential points and students’ interest? ・Can students find out their own problems from the original problem that teacher presents at first? ・Can teacher assist students’ cooperative discussion and summarize the mathematical essential ideas derived from their discussion? PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  34. Check 3 in the following figure ! Students’ own problem What do you consider important when introducing a mathematics lesson? • To make students clarify an ambiguous situation. Answers of students Why did we derive a variety of ideas ? PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  35. No, your idea is not good. Learn to see materialIdentifying mathematical essential points To identify essential and a wide range of mathematical ideas Ex: Division with a remainder “13÷5 = “ If I had two more, the quotient would become 3 The quotient is 3 with a lack of 2 [ Aim of teacher ] The quotient is 2 and the remainder is 3 PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  36. [ Aim of teacher ] The quotient varies based on the situation Learn to see materialIdentifying mathematical essential points Wide and deep mathematical insights are required for a teacher. Ex: Division with a remainder “13÷5 = “ Mathematical essential points Teacher can pick up students’ mutter as well as focus on mathematically essential points. PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  37. Which animal do you think is the biggest among a lion, a frog and a turtle made by the clay ? Is there any students’ ideas ignored by teacher’s selfish judgment? Focus of teacher: Measuring Volume Let’s measure the weight of three animals to compare the volume Um… Are there other ideas ? It is not appropriate for teacher to ignore student’s idea in this situation. PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  38. 15, July Summary S = (a+b)×ｈ÷２ a h b Are mathematical essential ideas elicited from students’ collaborative discussion summarized at the end of lesson? Students developed the formula to calculate the area of trapezoid. At the end of lesson, teacher put the panel on the blackboard. If you have the panel, please show us at the beginning. PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  39. Future Issues to be discussed in Japan • It is necessary for teachers to discuss the issues that are useful in a future teaching. Namely, it is expected for teachers to discuss the following questions for instance． If you have a chance to teach the same topic next time, how do you want to treat them? Is there any alternative teaching methods? What is the points that is useful in a future teaching? PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  40. Future Issues to be discussed in Japan • We often observed the stereotyped classroom teaching. (ex. Understand a problem - solving individually -Presentation by students - Negotiation) • The most important thing for teacher is to accept students’ ideas and evaluate them flexibility. If a teacher couldn’t do so, students might not come to life. PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  41. PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

  42. Elementary:407,000 (Male):(Female) =2:3 Junior High: 255,000 (Male):(Female) =3:2 Senior High: 266,000 (Male):(Female) =5:2 The number of new teachers & the number of teachers Total 31,000 Total 12,000 Number of Teachers in 2002 PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara

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