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an introduction to Lesson Study in mathematics www.mmepdpm.pbworks.com Yeap Ban Har www.lessonstudyinsingapore.blogspot.com

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Part I Introduction Research Lesson in an In-service Course on Problem-Solving Heuristics. Photo: Princess Elizabeth Primary School

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At greatest risk are jobs that can be expressed in programmable rules – blue collar, clerical, and similar work that requires moderate skills and used to pay middle-class wages. Source: Levy & Murnane 2005

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Teachers as critical factors in an education system Source: BBC News 2004

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A good education system depends on high quality teachers who constantly seek to improve their practice, supported by school leaders and administrators, and resources from departments and agencies within MOE. Minister of Education Singapore 2009

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We need to build capacity for teachers themselves to take the lead in professional upgrading. Minister of Education Singapore 2009 Photo: Fuchun Primary School

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Part II Stages in Lesson Study Lesson Study adapted for Micro-Teaching in Pre-service Course Photo: National Institute of Education

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Stage 0 Research Theme

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Research Theme gives the lesson study effort focus and direction. Research Theme identifies the area of study the lesson study team has as its learning goal. Example 1 To engage pupils in the learning of mathematics. Fuchun Primary School Example 2 To help pupils develop reasoning and communication skills North Vista Primary School research theme

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The research theme can be formulated by considering: Schools Vision research theme Curriculum Focus Students Characteristics – actual and ideal Teachers Interest

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Stage 1 Lesson Planning

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Primary Mathematics Standards Edition (Grade 6)

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problems for students are required to solve

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Primary Mathematics Standards Edition (Grade 6)

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Area > 2r 2

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Area < 4r 2

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2r 2 < Area < 4r 2

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2r 2 < r 2 < 4r 2

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Questions What are the differences between AR and LS? Do we need to do literature review? Do we need to do pre-test and post-test?

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The lesson-planning process includes Materials Study lesson planning Formulate Key Problems Anticipate Students Responses Teacher Reactions to Students Responses

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Primary Mathematics Standards Edition Grade 6

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Change the square into an equilateral triangle of the same area. Suggestion 1

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Suggestion 2

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Suggestion 3

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Stage 2 Research Lesson

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Example To engage pupils in the learning of mathematics. Fuchun Primary School

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Task 1 Find the longest distance between two points on a circle. Fuchun Primary School, Singapore: Lesson Study

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Learning through Collaboration Fuchun Primary School, Singapore: Lesson Study

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Learning through Collaboration Fuchun Primary School, Singapore: Lesson Study

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Task 2 Measure circumference and diameter of four circles. Fuchun Primary School, Singapore: Lesson Study

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Task 3 Draw a circle given that its circumference is 6 metres. Fuchun Primary School, Singapore: Lesson Study

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Used the relationship between circumference and diameter

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Did not use the relationship between circumference and diameter

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Stage 3 Post Lesson Discussion

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Post Lesson Discussion Ratio 2.83.03.13.23.33.53.8 Frequency 13571841 In the post-lesson discussion teachers talked about the nature of student engagement, catalyst and obstacles to engagement, using their observation notes. They also talked about the mathematics content – relationship between diameter and circumference.

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Stage 4 Lesson Revision

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Post Lesson Discussion Teachers discussed what ifs – how students can be taught to appreciate the significance of π and that its value is approximately 22/7. The circles were of radii 4 cm, 6 cm, 8 cm and 10 cm. Why if a circle of radius 7 cm be included?

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Identify Research Theme Plan Lesson Research Lesson Post-Lesson Discussion Lesson Plan Revision

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Part III Workshop Activity Photo: National Institute of Education

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Research Theme Example: To inculcate a spirit for lifelong learning and to strive for quality and excellence in the learning of mathematics. Kuo Chuan Presbyterian Primary School

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Research Theme Example: To develop critical thinking in mathematics through questioning. Haig Girls School

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Research Theme Example: To develop enthusiastic and creative problem solvers through effective lessons Ang Mo Kio Primary School

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Research Theme Example: To help pupils develop conceptual understanding North Vista Primary School

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Example

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Problem: Find the distance between points A (2, 3) and B (10, 9). Students working collaboratively on a problem to learn the coordinate geometry topic on distance between points. Traditionally, students were given a formulae to do this.

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Every group was able to use their previous learning (Pythagoras Theorem) to solve the main problem)

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Later they were asked to find the distance between the points (5, 1) and (9, 4). They were also asked to find points where the distance is a whole number.

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5 3 4 10 6 8 15 12

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Problem-Based Lesson Find the distance between points A (2, 3) and B (10, 9). Find the distance between points C (-2, -2) and D (2, 1). Find the distance between points E (2, 5) and F (x, 2). Find two points where the distance is a whole number.

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Example

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A whole number that is equal to the sum of all its factors except itself is a perfect number. Find perfect numbers.

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The ancient Christian scholar Augustine explained that God could have created the world in an instant but chose to do it in a perfect number of days, 6. Early Jewish commentators felt that the perfection of the universe was shown by the Moon's period of 28 days.

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The next in line are 496, 8128 and 33 550 336. As René Descartes pointed out perfect numbers like perfect men are very rare.

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Example Eleven

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Problem: How is the circumference and diameter of a circle related? Fuchun Primary School, Singapore: Lesson Study

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Professional Learning Ratio 2.83.03.13.23.33.53.8 Frequency 13571841 Teachers discussing what they saw in the lesson, talking about how students can be taught to appreciate the significance of π and that its value is approximately 22/7. The circles were of radii 4 cm, 6 cm, 8 cm and 10 cm. Why would a circle of radius 7 cm be included? Singapore teachers doing PLC spend 2 hours a week on such activities to deepen their learning from workshops they have attended.

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Example Twelve

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Rectangle 1 Rectangle 2

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Problem: Make Rectangle 10.

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Problem-Based Lesson Find the number of square tiles in Rectangle 10. Find the number of square tiles in Rectangle n where n is any large number. Which rectangle has 63 square tiles?

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Example 13 Find the area bounded by the curve the x -axis and lines x = 1 and x = 4. Problem to teach trapezium rule.

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Example 14 Two forces 3 N and 4 N are applied on an object. Find the resultant force on the object. Problem to teach vector addition.

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Example 15 Problem to teach measurement of volume of liquids.

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PCF Kindergarten Pasir Ris West, Singapore

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How many non- congruent quadrilaterals can be made? Each quadrilateral is made using all the tangram pieces.

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(a) 420 g x 3 = 1200 g + 60 g = 1260 g (b) The tin of beans is 341g because the ones digits must add to 10. * The tin of sardines is 493 g because the tens digits must add to 16 tens.

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Parents Up In Arms Over PSLE Mathematics Paper TODAYS 10 OCT 2009 SINGAPORE: The first thing her son did when he came out from the Primary School Leaving Examination (PSLE) maths paper on Thursday this week was to gesture as if he was "slitting his throat". "One look at his face and I thought 'oh no'. I could see that he felt he was condemned," said Mrs Karen Sng. "When he was telling me about how he couldn't answer some of the questions, he got very emotional and started crying. He said his hopes of getting (an) A* are dashed." Not for the first time, parents are up in arms over the PSLE Mathematics paper, which some have described as "unbelievably tough" this year. As recently as two years ago, the PSLE Mathematics paper had also caused a similar uproar. The reason for Thursday's tough paper, opined the seven parents whom MediaCorp spoke to, was because Primary 6 students were allowed to use calculators while solving Paper 2 for the first time. … Said Mrs Vivian Weng: "I think the setters feel it'll be faster for them to compute with a calculator. So the problems they set are much more complex; there are more values, more steps. But it's unfair because this is the first time they can do so and they do not know what to expect!" … "The introduction of the use of calculators does not have any bearing on the difficulty of paper. The use of calculators has been introduced into the primary maths curriculum so as to enhance the teaching and learning of maths by expanding the repertoire of learning activities, to achieve a better balance between the time and effort spent developing problem solving skills and computation skills. Calculators can also help to reduce computational errors." … Another common gripe: There was not enough time for them to complete the paper. A private tutor, who declined to be named, told MediaCorp she concurred with parents' opinions. "This year's paper demanded more from students. It required them to read and understand more complex questions, and go through more steps, so time constraints would have been a concern," the 28-year-old said.

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chocolates Jim Ken sweets 1212 1212 3 parts 12 + 12 + 12 + 12 + 18 = 66 1 part 22 Half of the sweets Ken bought = 22 + 12 = 34 So Ken bought 68 sweets. 1818 1212 1212 1212 1212 1818

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The ability to monitor thinking as students read – metacognition as well as the ability to show working – communication are the other important competencies.

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Ann, Beng and Siti each had some money at first. Ann gave Beng $0.50. Beng then gave Siti $0.75. Siti spent $0.25 on a ruler. At the end, they had $3 each. What is the difference between the amount of money that Ann and Siti had at first? (1)$1.00 (2)$0.50 (3)$0.75 (4)$1.25 Ann $3 Beng $3 Siti $3 $3.25$2.50 $3.75$3.25 $3.50

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Visualization – an intellectual competence - is one of the most important ability in solving problems

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My Pals Are Here! Mathematics 4A

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Shaping Maths 2A

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Shaping Maths 4B

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Mathematical problem solving is central to mathematics learning. Ministry of Education 2006

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Children are truly the future of our nation. Irving Harris

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