Transforming Mathematics for the 21st Century: What Teachers Need to Know

1. Transforming Mathematics for the 21st Century: What Teachers Need to Know Yeap Ban Har, Ph.D. <banhar.yeap@nie.edu.sg> National Institute of Education Nanyang Technological University Singapore Presented at 2010 ASCD Annual Conference & Exhibit Show Critical Transformations  San Antonio, Texas, USA

2. one introduction

3. What is the role of mathematics in educating children? TelokBlangah PCF Kindergarten, Singapore

4. What are the key competencies in elementary school mathematics? Princess Elizabeth Primary School, Singapore

5. What are the essential big ideas that children should develop in mathematics and the role teachers play in the formation of these big ideas? TelokBlangah PCF Kindergarten, Singapore

6. How to help teachers understand their role in helping children develop big ideas in mathematics? BinaBangsa School in Bandung, Indonesia

7. In one of the major sessions at ASCD2010, Carol Tomlinson said that it is important for teachers to be able to identify big ideas in a given content area and teach these big ideas in ways that every child gets them.This presentation is about big ideas in elementary school mathematics. Princess Elizabeth Primary School, Singapore

8. two A Big idea

9. ACTIVITY Mind ReadingThink of two digits. Do three operations.

10. Activity • Think of two digits, say, 1 and 2. • Find their sum – 3 in this case. • Use the first digit as the tens digit and the other as the ones digit to make a number. In this case the number is 12. • Find the difference between the two numbers. Write this difference on a piece of paper. In this case, 12 – 9.

11. Lesson: Mind Reading Date: 7 March 2010 18 2 ? 9 81 ? xx 3 27 1 9 ?

12. BIG Idea 1Observing Patterns & Relationships Keys Grade School in Manila, The Philippines

13. Critical Transformation Professional Development of Teachers:Lesson Study as a form of authentic professional learning.Lesson study helps teachers learn content. Keys Grade School in Manila, The Philippines

14. Lesson Study as Part of Professional Development in SingaporeLesson study helps teachers learn pedagogy. Princess Elizabeth Primary School

15. Open Lesson in Scarsdale as part of teachers’ professional development Lesson study helps shift teachers’ mindset. Edgewood Elementary School in Scarsdale, New York in USA

16. Edgewood Elementary School, New York

17. Edgewood Elementary School, New York in USA

18. BIG Idea 1Observing Patterns & Relationships Keys Grade School in Manila, The Philippines

20. three Another Big idea

21. NATIONAL EXAMINATION ITEM

22. NATIONAL EXAMINATION ITEM

23. BIG Idea 2Visualization TelokKurau Primary School, Singapore

24. Emphasis on Visuals in Word Problems A lion weighs 135 kg. A cow weighs 87 kg more than the lion. An elephant weighs 139 kg more than the cow. How heavy is the elephant? 135 kg Weight of lion Weight of cow 135 kg 87 kg Weight of elephant 135 kg 87 kg 139 kg TelokKurau Primary School, Singapore

25. 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? 3/8 210 3/8 – 1/5  210 1/5 15/40 – 8/40  210 7/40  210 1/40 30 32/40  960 MrsHoon sold 960 cookies.

26. 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.

27. Primary Mathematics Standards Edition 2009

28. Primary Mathematics Standards Edition 2009

29. 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.Lim Siong GuanHead, Civil Service

30. Emphasis on Visuals in Learning Basic Skills My Pals Are Here! Mathematics 4A 2007

31. 231 x 3 Photos: National Institute of Education, Singapore

32. Photos: National Institute of Education, Singapore

33. Pre-service teachers learn and practice to apply the CPA Approach, one of the fundamentals in mathematics learning. Photos: National Institute of Education, Singapore

34. Critical Transformation Teacher education for pre-service teachers must prepare teachers to teach so that every child learns National Institute of Education, Singapore

35. four A Third Big idea

36. “an excellent vehicle to develop and improve a person’s intellectual competence” Princess Elizabeth Primary School, Singapore

37. BIG Idea 3Number Sense Catholic High School (Primary), Singapore

38. Open Lesson in Chile Place numbers 1 to 5 in the five spaces so that the vertical sum is equal to the horizontal sum.

40. the inclusion of challenging mathematics in high-stakes testing Princess Elizabeth Primary School, Singapore

41. Fuchun Primary School Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence .. Ministry of Education 2006

42. five CONCLUSION

43. In Singapore, the emphasis of high-stakes examination on big ideas has brought about critical transformations in the classrooms. This however, must be supported by teacher education and professional development. Authentic professional development is essential to transform competent teachers into expert ones.