Teachers in Bina Bangsa School, from Kindergarten to Junior College, had their mathematics professional development with a focus on student engagement and designing problem-based lessons.

1. BinaBangsa School professional development for mathematics teachers pedagogy for engagement and problem-based learning www.mmepdpm.pbworks.com Yeap Ban Har

2. To see examples of using problems to organize lessons so that students are engaged. To use lesson study structure to deepen our understanding of student engagement To provide platforms for learning to mastery – that means every student must have mastered the key focus of a lesson by the end of the lesson, and if not the next lesson should be designed for that To provide constant opportunities to develop 21st Century skills What are the goals of this workshop?

3. Example One

4. Primary Mathematics Standards Edition (Grade 6) problems for students to learn new ideas

8. Area > 2r2

9. Area < 4r2

10. 2r2 < Area < 4r2

16. 2r2 < Area < 4r2

17. 2r2 < r2 < 4r2

18. Primary Mathematics Standards Edition (Grade 6)

19. Primary Mathematics Standards Edition (Grade 6)

20. Primary Mathematics Standards Edition (Grade 6)

21. Primary Mathematics Standards Edition (Grade 6)

22. Learning through Inquiry

23. problems for students to apply what they learn Primary Mathematics Standards Edition (Grade 6)

24. Primary Mathematics Standards Edition (Grade 6)

25. Primary Mathematics Standards Edition (Grade 6)

26. Primary Mathematics Standards Edition (Grade 6)

27. Primary Mathematics Standards Edition (Grade 6)

28. Primary Mathematics Standards Edition (Grade 6)

29. Primary Mathematics Standards Edition (Grade 6)

30. Primary Mathematics Standards Edition (Grade 6)

31. Primary Mathematics Standards Edition (Grade 6)

32. Primary Mathematics Standards Edition (Grade 6)

33. Example Two

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

35. Learning through Collaboration Fuchun Primary School, Singapore: Lesson Study

36. Learning through Collaboration Fuchun Primary School, Singapore: Lesson Study

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

38. A teacher observing student engagement during the lesson. Fuchun Primary School, Singapore: Lesson Study

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

40. Used the relationship between circumference and circumference

41. Did not use the relationship between radius and circumference

42. Learning by Doing

43. Professional Learning 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.

44. Example Three

47. North Vista Primary School, Singapore Fuchun Primary School, Singapore Learning by Collaborating

48. Example Four

49. This problem is about a game between two players. n beans are placed between two players. They take turn to remove either 1 or 2 beans. They cannot remove any other number of beans. The winner is the one who takes the last 1 or 2 beans. If this cannot be done then the game ends in a draw. You are given about 50 beans to investigate the winning strategy for this game. Write a short essay that includes: 1. a description of how the game is played 2. a detailed description of how one can win a game 3. an opinion on the statement ‘the player who starts will win the game’. [12] Anglo Singapore International School Bangkok 2010 Lower Secondary SA1

50. Learning by Reflecting

51. Example Five

52. All whole number can be written as a sum of consecutive whole numbers. Investigate this statement.

53. Learning through Inquiry

54. Example Six

55. Problem: What is half of one half? What is half of one third? DaQiao Primary School, Singapore

56. Example Seven

57. 12 ÷ 4 = 3 1 ÷ ¾ = ?

58. 12 ÷ 4 = 3 1 ÷ ¾ = ? 1 ÷ ¾ = 2 ÷ ¾ = 3 ÷ ¾ = n ÷ ¾ =

59. 

60. 

61.  12 ÷ 4 = 3 making connections 3 ÷ ¾ = 4

62. Primary Mathematics Standards Edition Grade 6

63. How to make sure the butterfly cannot flyHow do you get a butterfly?First there is the egg which hatches into a caterpillar. The caterpillar eats and grows. At the right time, it makes a cocoon out of its own body. While in the cocoon, the caterpillar changes into a butterfly.When the butterfly is ready, it starts to break through the cocoon. First a hole appears. Then the butterfly struggles to come out through the hole. This can take a few hours.If you try to "help" the butterfly by cutting the cocoon, the butterfly will come out easily but it will never fly. Your "help" has destroyed the butterfly.The butterfly can fly because it has to struggle to come out. The pushing forces lots of enzymes from the body to the wing tips. This strengthens the muscles, and reduces the body weight. In this way, the butterfly will be able to fly the moment it comes out of the cocoon. Otherwise it will simply fall to the ground, crawl around with a swollen body and shrunken wings, and soon die.If the butterfly is not left to struggle to come out of the cocoon, it will never fly.We can learn an important lesson from the butterfly.Lim Siong GuanHead, Civil Service

64. Example Eight

65. 

69. Example Nine

70. The newspaper report stated that a draw would have sent Singapore to the Asian Cup Final. A team needed to finish first or second in their group to qualify for the Asian Cup Finals. Figure 1

71. The table shows the number of each team had played (P), won (W), drew (D), lost (L) as well as the numbers of goals it scored (F) and the numbers of goals it conceded (A). A team got 3 points for a win, 1 point for a draw and no point for a loss. The total number of points is shown in the last column (Pts). Figure 1 The results of the last two matches in each group are shown in Figure 3. Use only the information available to explain why ”a draw would have sent Singapore to the Asian Cup Finals”.

73. Figure 3

74. Learning in and about the Real World

75. Example Ten

76. Best Chance to Score A soccer player is on a breakaway, dribbling the ball downfield, parallel to a sideline. From where should he shoot to have the best chance to score a goal?

77. PSLE2010 Problems

78. Cup cakes are sold at 40 cents each. What is the greatest number of cup cakes that can be bought with $95? $95 ÷ 40 cents = 237.5 Answer: 237 cupcakes Basic Skill Item

79. Basic Application Item 4 puffs for $2.80 $50 ÷ $2.80 = 17.86 (to 2 decimal places) 17 x $2.80 = $47.60 $50 - $47.60 = $2.40  3 puffs (17 x 4 + 3) puffs = 71 puffs

80. Learning in and about the Real World

81. Engaging Students Learning through Inquiry Learning by Doing Leaning through Collaboration Learning through Reflection Learning in and about the Real World

82. Student Engagement in Research Lessons at BBS

83. Student Engagement in Research Lessons at BBS

84. PSLE2010 Problems

85. Application Item 

87.  210

88. 210 MrsHoon sold 960 cookies.

89. BinaBangsa School professional development for mathematics teachers problem-based learning

90. Primary Mathematics Standards Edition (Grade 6)

91. Example Eleven

92. 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.

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

94. 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.

95. 10 5 6 3 4 8 15 12 12

96. 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.

97. Group Task Design one double-period lesson based on a single problem with colleagues teaching the same level. Present your lesson to include The Problem Expected Solutions from Students Is the problem-based lesson to teach a new topic, for drill-and-practice or for applying knowledge? Please submit your problems via email banhar.yeap@nie.edu.sg or upload on www.mmepdpm.pbworks

99. Doing

100. Collaboration

101. Reflection

102. Real World

103. Content

104. Process

105. Skills 21Problem What is the topic or learning outcome?

106. Example Twelve

107. Teachers solved the problem of converting a square into an equilateral triangle of the same area. Three suggestions were forwarded.

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

109. Suggestion 2

110. Suggestion 3

111. Example Thirteen

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

113. 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.

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

115. Example Fourteen

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

117. Professional Learning 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.

118. Example Fifteen

119. Rectangle 1 Rectangle 2

120. Problem: Make Rectangle 10.

124. 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?

127. Find the area bounded by the curve the x-axis and lines x = 1 and x = 4. Problem to teach trapezium rule. Example 16

128. Two forces 3 N and 4 N are applied on an object. Find the resultant force on the object. Problem to teach vector addition. Example 17

129. Problem to teach measurement of volume of liquids. Example 18

130. PCF Kindergarten PasirRis West, Singapore

140. Example 19

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

142. “Children are trulythe future of our nation. “ Irving Harris