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The Japanese Problem Solving Approach (PSA) In JHSM

The Japanese Problem Solving Approach (PSA) In JHSM. F adjar Shadiq, M.App.Sc Formerly as Teacher Trainer in CDEMTEP and SEAMEO QITEP in Mathematics.

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The Japanese Problem Solving Approach (PSA) In JHSM

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  1. The JapaneseProblem Solving Approach (PSA)In JHSM Fadjar Shadiq, M.App.Sc Formerly as Teacher Trainer in CDEMTEP and SEAMEO QITEP in Mathematics QiM: 2017 PSA TMTA

  2. PowerPoint Presented on TMTA Course for Junior High School Mathematics TeachersSEAMEO QITEP in Mathematics, YogyakartaApril 26 – May 9, 2017 QiM: 2017 PSA TMTA

  3. Personal Identity Name: Fadjar Shadiq, M.App.Sc The Former of the Deputy Director for Administration SEAMEO QITEP in Mathematics Place and Date of Birth: Sumenep - Indonesia, 20-4-55 Education: Unesa/IKIP Surabaya (Indonesia) and Curtin University of Technology, Perth, WA Teaching Experience: SHS Mathematics Teacher, InstructorandTeacher Trainer (+62 274)880762; +62 8156896973 fadjar_p3g@yahoo.com & www.fadjarp3g.wordpress.com QiM: 2017 PSA TMTA

  4. 2010 2013 2016 2014 2017 2011 2015 2012 QiM: 2017 PSA TMTA

  5. Introduction Task Dr. Shirakawa Hideki, Professor Emeritus. ChemistryNobelariat awardeein 2000, conductive polymers developer. Dr. Esaki Leo, Professor Emeritus, the former ofThe University of TsukubaPresident. Physics Nobelariatawardee in 1973. Dr. Tomonaga Sin-Itiro, Professor EmeritusfromTokyo University of Education.Physics Nobelariat awardeein1965. 3 Nobelariatawardee from Uni of Tsukuba. Why they can do it? How?  By Math Ed Can We? What should we learn? QiM: 2017 PSA TMTA

  6. + + + 99 1 + 2 + 3 + - - - 98 ? 100 How did GAUSS Solve this Problem? 101 101 So, the result: 50x101 Learning Math means to make better and easier. The importance of thinking, reasoning and creativity. QiM: 2017 PSA TMTA

  7. What is Mathematics? De Lange (2005) stated: “Mathematics could be seen as the language that describes patterns – both patterns in nature and patterns invented by the human mind.” QiM: 2017 PSA TMTA

  8. Should our studentsjust followers or players? How? QiM: 2017 PSA TMTA

  9. Imagine the Future. • What kinds of: • Mathematical Knowledge • Mathematical Skills • Mathematical Attitudes • Are neededby our young generation to survive in the 21st Century and beyond?  The Focus must be on our Studentsand on our Mathematics Classes. QiM: 2017 PSA TMTA

  10. QiM: 2017 PSA TMTA

  11. Explore: A three digit number is subtracted by a two digit number and the result is 3. – 3 QiM: 2017 PSA TMTA

  12. Explore: A three digit number is subtracted by a two digit number and the result is 3. 9 2 0 7 8 1 0 0 9 0 9 9 1 1 1 – – – 3 3 3 What can you learn from these results? What can you do in helping your students? How? QiM: 2017 PSA TMTA

  13. Learn From Japanese Teachers Regarding the PSA • (detik 12.00) Examples Of Mathematics Teaching QiM: 2017 PSA TMTA

  14. Objective of Math Education We should develop children who can use what they learned before without our support. If they developed, they can reply the question what do you want to do next. Human Character Formation Attitude and Values:Beautifulness, Curiosity, Reasonableness, Appreciation Skills for Learning: Learning How to Learn Mathematical Thinking: Extension, Generalization, Anticipation, Integration, Change the representation for explaining Knowledge and Skills Traditional way of calculation New way of calculation Pattern on the calculations `Source: Isoda (2015) QiM: 2017 PSA TMTA

  15. Pythagoras Source: NCTM Bruner: Discovery Learning is Learning to Discover What are the role of Math Teachers? Problem Solving Exploration, Investigation and Experimentation QiM: 2017 PSA TMTA

  16. Mental calculations. In a rural school Bogdanov - Bel’skiy, 1895 What Can You Learn from the Teacher? Source: Vysotskiy (2015) QiM: 2017 PSA TMTA

  17. Learn How to Learn/Independent L In Japan the purpose of education (Isoda & Katagiri, 2012:31) is as follows. "... To develop qualifications and competencies in each individual school child, including the ability to find issues by oneself, to learn by oneself, to think by oneself, to make decisions and to act independently. So that each child or student can solve problems more skillfully, regardless of how society might change in the future." QiM: 2017 PSA TMTA

  18. QiM: 2017 PSA TMTA

  19. Our Challenge If we agree to help our students to be competence on: (1) Math knowledge, (2) Math Process and (3) Good attitude / character for Global citizenships. How to help our mathematics teachers to be competence in helping their students to be competence on : (1) Math knowledge, (2) Math Process and (3) good attitude for Global citizenships. How? QiM: 2017 PSA TMTA

  20. The Indonesian Scientific Approach (MoEC, 2013)  More on Process Skills (FS) 1. Observing 2. Questioning 3. Reasoning 4. Collecting or experimenting 5. Communicating QiM: 2017 PSA TMTA

  21. The Japanese PSA Steps 1. Problem Posing 2. Independent Solving (FS: SA) 3. Comparison and Discussion 4. Summary and Integration. Source: Masami Isoda (2011) QiM: 2017 PSA TMTA

  22. Task How many triangles are there in this diagram on the 4th, 10th, 100th and nth diagram? Math Teachers need the experience to solve it. How do you teach your students? What are the advantages? Disadvantages? How to improve the method? QiM: 2017 PSA TMTA

  23. How many triangles are there in this diagram on the 4th diagram? What can you learn from the 5thdiagram? QiM: 2017 PSA TMTA

  24. How many trianglesare there? The Preferred Method Isoda & Katagiri, 2012:31) Clarification of the task #1  All of the Triangles Clarification of the task #2  Let them to think the best way of counting (better and easier) Realizing the benefit of sorting Knowing the benefit of encoding (naming) Validating the correctness of result Coming up with a more accurate and convenient counting method QiM: 2017 PSA TMTA

  25. The PSA Includes 1. Enabling students to apply and extend the learned ideas to new problem situation by/for themselves (meaningful learning, FS). 2. Teacher must accept any ideas (anyalternative answers, FS) of children if it is originated from what they already learned but allows them to talk on their demand. Source: Masami Isoda (2011). QiM: 2017 PSA TMTA

  26. Shadiq, (2016b): “How to Help Our Students to Learn Mathematics” meaningfully  easily? joyfully? to use their heads (think)? to be an independent learner?” QiM: 2017 PSA TMTA

  27. The Four Important Questions & Answers learn meaningfully students are given opportunity to relate the new knowledge to the previous knowledge. learn joyfully novelty, pleasure and unthreatening situation. learn to use their heads (think)  start with problems (contextual, realistic or mathematics). learn to be an independent learner? students are given opportunity to solve the problem by their selves. QiM: 2017 PSA TMTA

  28. Problem SolvingAfter the knowledge has been developed QiM: 2017 PSA TMTA

  29. Look at this picture Task 1A KSM Find out the length of TU. Find out different ways/ strategies in finding out thelength of TU. QiM: 2017 PSA TMTA

  30. 2A D C TrapeziumProblem ABCD is a trapezium. Find the area of ABCD if AB : DC = 2 : 1 and the area of CDE is 10 square unit. E B A QiM: 2017 PSA TMTA

  31. Algebra Problem 3A QiM: 2017 PSA TMTA

  32. 4A The area problem (2) Divide thisABC into 5 equal area trianglewith 4 lines of BDEFG. QiM: 2017 PSA TMTA

  33. B Task 5A Open Ended Problem 4 D 3 A C ABC is a right angled triangle in C. AC = 3 and BC = 4. CD is perpendicular to AB. Can you find the length of CD in several ways/strategies. QiM: 2017 PSA TMTA

  34. D C F H G E B A 6A Geometry Problem ABCD is a square. F is a mid point of BC. If the area of CDEF is 45, then the area of BEF is .... a. 7,5 b. 9 c. 10,5 d. 12 e. 13,5 QiM: 2017 PSA TMTA

  35. The Problem of Algebra 7A Find all of the set of consecutive naturalnumbers whose sum is 1000. QiM: 2017 PSA TMTA

  36. 8A The Problem of Geometry (8) E D C F A B QiM: 2017 PSA TMTA

  37. J F A 1 D R 3 × A F D J R 1 9A The Problem of Multiplication (9) Replace every letter with digit. Each different letter represents a different digit. QiM: 2017 PSA TMTA

  38. 10 A The Problem of Geometry How many cubes are needed in building number 4, 10, and 100? QiM: 2017 PSA TMTA

  39. 11 A The Problem of Multiplication It is known that: A = 201720172017 x 2018201820182018 B = 201820182018 x 2017201720172017 Find A – B. QiM: 2017 PSA TMTA

  40. Problem SolvingApproachWhen students start to learn the mathematical knowledge Start with problem QiM: 2017 PSA TMTA

  41. The Importance of Management of Learning “ …that the business of education is not learning, but the management of learning, that is, instruction. The teacher organizes the experiencesof learners in a way that helps them change their performance in a meaningful way.” QiM: 2017 PSA TMTA

  42. The Japanese PSA Steps 1. Problem Posing 2. Independent Solving (FS: SA) 3. Comparison and Discussion 4. Summary and Integration. Source: Masami Isoda (2011) QiM: 2017 PSA TMTA

  43. It is known that the area of the biggest and smallest squares are respectively x2and 1.Find the area of this rectangles, at least in two ways.What can you learn from the result? 1B Multiplication of two terms x2 1 QiM: 2017 PSA TMTA

  44. You are given:A square of x2 unit area, 7 rectangles of x unit area, and 10 square of 1 unit area, Design a rectangle with those shapes.What can you learn from the result? x2 2B Factorisation x 1 QiM: 2017 PSA TMTA

  45. Task If the shadow of 1 m stick is 72 cm, what is the height of the flagpole if the shadow of the flagpole is 144 cm? How do you find the answer? Why?What can you learn? Similarity 3B Can you find the height of the flagpole by using 1 m stick and the shadow principle?How? Why? 1 m ? m 144 cm 72 cm QiM: 2017 PSA TMTA

  46. R M K B P A L Q 4B Learning about the Gradient Look at this picture and answer the questions. The ‘gradient’ or ‘slope’ of a line means the slant of that line. • Do you think that the ‘gradients’ or the ‘slopes’ of those three lines are different? Why? • What factors can affect the value of the gradient or slope? Please explain. • How do you find the ‘gradient’ or ‘slope’ of the line? QiM: 2017 PSA TMTA

  47. Task 5B Open Ended Problem You will be given 12 match sticks. With all of those 12 match sticks, without bend it, please design all of the triangles that can be or cannot be constructed as triangles. What can you learn from the measure of the sides of the tiangles? QiM: 2017 PSA TMTA

  48. 6B Open Ended Problem How many squares on Diagram A? Please describe in answeringthat question at least in two ways. How many squares on Diagram B? Please describe in answeringthat question at least in three ways. A B What can you learn? QiM: 2017 PSA TMTA

  49. 7B Open Ended Problem Fahmiwas asked to find the representative of these data: 4, 3, 4, 5, 6, 4, 2 Can you help Fahmi? How? QiM: 2017 PSA TMTA

  50. 8B Open Ended Problem Amir, Budi and Charlie respectively has 10, 10 and 7marbles each. Those three children would like to share equally those marbles? Can you help them? How? 7 10 10 QiM: 2017 PSA TMTA

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