This seminar for parents discussed the five key competencies in mathematical problem solving. Parental involvement is an important aspect of helping kids do well in school.

1. PSLE Mathematics Seminar for Parents Henry Park Primary School Organised by Henry Park Alumni Association May 2010 Yeap Ban Har National Institute of Education Nanyang Technological University banhar.yeap@nie.edu.sg

2. Introduction This seminar focuses on the key competencies required to handle challenging mathematics problems at primary school level.

3. Part 1 This section explains the PSLE format.

4. PSLE Mathematics Paper 1 (50 min) Paper 2 (1 hr 40 min)

6. Part 2 This section explains the curriculum that the PSLE is based on.

7. PSLE Mathematics is Based on a Problem-Solving Curriculum

9. rationale of the curriculum The rationale of teaching mathematics is that it is “a good vehicle for the development and improvement of a person’s intellectual competence”.

10. Part 3 This section explains that problem solving is a basic ability in the PSLE.

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

12. Ali paid for a 85-cent pen with a $5 note. How much change should he get? Answer: $__________ Example 1

13. A show started at 10.55 a.m. and ended at 1.30 p.m. How long was the show in hours and minutes? Example 2

14. Prawns are sold at $1.35 per 100 g at a market. What is the price of 1.5 kg of prawns? $13.50 + $6.75 = $20.25 Example 3

15. During a sale, mugs are sold in sets of 3 for $1.45. How much must Bala pay for buying 15 mugs during the sale? $1.45 x 5 = $14.50 ÷ 2 = $7.25 Example 4

16. Sam had 295 eggs. He packed all the eggs into boxes of 9 with some left over. How many eggs are left over? 295 270 25 295 ÷ 9 = (30 + 2) remainder 7 7 eggs are left over Example 5

17. Mr Tan rented a car for 3 days. He was charged $155 per day and 60 cents for every km that he travelled. He paid $767.40. What was the total distance that he travelled for the 3 days? $767.40 – 3 x $155 = $302.40 $302.40 ÷ 60 cents per km = 504 km Example 5

18. Mr Tan rented a car for 3 days. He was charged $155 per day and 60 cents for every km that he travelled. He paid $767.40. What was the total distance that he travelled for the 3 days? 767.40 – 3 x 155 = 302.40 302.40 ÷ 0.60 = 504 He travelled 504 km. Example 5

19. Find <y in the figure below. 360o – 210o = 150o 70 o 70 o y 70 o Example 6

20. Part 4 This section explains that there are other competencies in mathematics learning e.g. practical skills.

21. Basic Skillscomputation and procedures is not everything

22. The height of the classroom door is about __. (1) 1 m (2) 2 m (3) 10 m (4) 20 m Example 7

23. Part 5 This section explains the key competencies in solving challenging problems.

24. ““… including non-routine, open-ended and real-world problems.” Ministry of Education 2006

25. MN = AB AB = BC (ABCD is a square) BC = PQ PQ = MQ = NQ So, MN = MQ = NQ Triangle MNQ is equilateral. Angle MNQ is 60o. Example 8

26. MN = Triangle AQP is isosceles. Angle MQP is 30o. Angles QMP is (180o – 30o) ÷ 2 = 75o Angles MPN is 2 x 75o = … Example 8

27. Part 6 The ability to monitor thinking as students read – metacognition as well as the ability to show working – communication are the other important competencies.

28. Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left. How many cookies did Mrs Hoon sell? almond cookies 5/8 3/8 210 chocolate cookies 1/5 3/8 – 1/5 = 7/40  210 1/40  30 Example 10 32/40  960 She sold 960 cookies.

29. Example 11

30. Parents Up In Arms Over PSLE Mathematics Paper TODAY’S 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.

32. chocolates sweets 12 Jim 12 18 12 12 12 12 18 Ken 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.

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

34. Part 7 Students have been given opportunities to develop visualization in the six years in primary school.

35. Learning Basic Skillsemphasis on visualization in the learning process

37. My Pals Are Here! Mathematics 4A

38. Shaping Maths 2A

39.   

40.    

41.            

42. Shaping Maths 4B

43. Catholic High School (Primary)

44. Part 8 This section summarizes the five key competencies in mathematics.

45. 9 cm2 6 cm2 With visualization, one does not need to know a formula to calculate the area of a trapezium.

46. Keys Grade School Manila

47. P S L E 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

48. Five Key Competencies Visualization Number Sense Metacognition Communication Patterns – this was shown in the opening problem (see Beads Problem)