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Singapore Math at Highline Public SchoolsMarch 2013 Session 5Yeap Ban Harwww.banhar.blogspot.com The Merlion by Yeap Ken Min
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John had 1.5 m ofcopper wire. He cutsome of the wire tobend into the shapeshown in the figurebelow. In the figure,there are 6 equilateraltriangles and thelength of XY is 19 cm.How much of thecopper wire was left?
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19 cm x 5 = 95 cm150 cm – 95 cm = 55 cm55 cm was left.
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“… over-emphasising procedural skillswithout understanding the underlying mathematical principles should be avoided.” Ministry of Education 2006
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Student Achievement Average Learners Performing WellPathlight School, Singapore
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Singapore Math allows average learners perform at a high level. The following are some data from some international research on math achievement and attitude.East Coast Primary School, Singapore
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All major international tests (literacy, science and mathematics) between 1964 and2003 were placed on a common scale. Selected countries shown in the table. Score 1960-1970s 1980s 1990s 2000s 500 Japan Hong Kong Hong Kong Hong Kong Japan Japan Japan Korea Korea Korea Singapore Singapore 400 Thailand The Philippines Malaysia Malaysia Singapore Thailand Thailand Thailand 300 Indonesia Indonesia The Philippines The PhilippinesReference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
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H Gardner Multiple IntelligencesKeys Grade School, Manila
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Observing patterns andmaking generalizationsinvolves reflection.Seely Place Elementary School, New York
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Singapore National ExaminationFind the value of 12.2 ÷ 4 . Answer : 3.05 [B1] Example 1
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3 .05 12.20 4 12.20 12 12 20 hundredths 0.20 0.20Number Bond Method 0 Long Division Method
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A show started at 10.55 a.m. andended at 1.30 p.m. How long wasthe show in hours and minutes? 2 h 30 min 11 a.m. 1.30 p.m. Answer : 2 h 35 min [B1] Example 2
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Find <y in the figure below. 70 o 70 o y 70 o360o – 210o = 150o Example 3
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Cup cakes are sold at 40 cents each.What is the greatest number of cupcakes that can be bought with $95? $95 ÷ 40 cents = 237.5 Answer: 237 cupcakes Example 4
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Mr Tan rented a car for 3 days. Hewas charged $155 per day and 60cents for every km that he travelled.He paid $767.40. What was the totaldistance that he travelled for the 3days? $767.40 – 3 x $155 = $302.40$302.40 ÷ 60 cents per km = 504 km Example 5
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“Mathematical problem solving is central tomathematics learning.” Ministry of Education 2006
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“… including non-routine,open-ended and real-world problems.” Ministry of Education 2006
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Parents Up In Arms Said Mrs Vivian Weng: "I think the setters feel itll be faster for them to compute with aOver PSLE calculator. So the problems they set are much more complex; there are more values, more steps. But its unfair because this is the firstMathematics Paper time they can do so and they do not know what to expect!"TODAY’S 10 OCT 2009 … "The introduction of the use of calculators does not have any bearing on the difficulty ofSINGAPORE: The first thing her son did when he came out from paper. The use of calculators has beenthe Primary School Leaving Examination (PSLE) maths paper on introduced into the primary maths curriculumThursday this week was to gesture as if he was "slitting his so as to enhance the teaching and learning ofthroat". maths by expanding the repertoire of learning"One look at his face and I thought oh no. I could see that he felt activities, to achieve a better balance betweenhe was condemned," said Mrs Karen Sng. "When he was telling the time and effort spent developing problemme about how he couldnt answer some of the questions, he got solving skills and computation skills.very emotional and started crying. He said his hopes of getting Calculators can also help to reduce(an) A* are dashed." computational errors." …Not for the first time, parents are up in arms over the PSLE Another common gripe: There was notMathematics paper, which some have described as "unbelievably enough time for them to complete the paper.tough" this year. As recently as two years ago, the PSLE A private tutor, who declined to be named,Mathematics paper had also caused a similar uproar. told MediaCorp she concurred with parentsThe reason for Thursdays tough paper, opined the seven parents opinions. "This years paper demanded morewhom MediaCorp spoke to, was because Primary 6 students were from students. It required them to read andallowed to use calculators while solving Paper 2 for the first time. 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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Trends in InternationalMathematics and Science Study TIMSS Students in the highest international benchmark are able to apply their knowledge in a variety of situations and able to explain themselves.
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“Skill proficiencies include the ability to use technologyconfidently, where appropriate, for exploration and problem solving.” Ministry of Education 2006
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Table 1 consists of numbers from 1 to 56. Kay and Lin are given aplastic frame that covers exactly 9 squares of Table 1 with the centresquare darkened.
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Table 1 consists of numbers from 1 to 56. Kay and Lin are given aplastic frame that covers exactly 9 squares of Table 1 with the centresquare darkened.(a) Kay puts the frame on 9 squares as shown in the figure below. 3 4 5 11 13 19 20 21 What is the average of the 8 numbers that can be seen in the frame?
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Table 1 consists of numbers from 1 to 56. Kay and Lin are given aplastic frame that covers exactly 9 squares of Table 1 with the centresquare darkened.(a) Kay puts the frame on 9 squares as shown in the figure below. 3+4+5+11+13+19+20 = 96 3 4 5 96 ÷ 8 = 12 11 13 Alternate Method 4 x 24 = 96 19 20 21 96 ÷ 8 = 12 What is the average of the 8 numbers that can be seen in the frame?
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(b) Lin puts the frame on some other 9 squares. The sum of the 8 numbers that can be seen in the frame is 272. What is the largest number that can be seen in the frame? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
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Weiyang started a savings plan byputting 2 coins in a money box everyday. Each coin was either a 20-cent or50-cent coin. His mother also puts in a$1 coin in the box every 7 days. Thetotal value of the coins after 182 dayswas $133.90.(a) How many coins were there altogether?(b) How many of the coins were 50-cent coins? Example 7
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Reference: Department of Education State of New Yorkassessment
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assessment Reference: Department of Education State of Hawaii
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Teacher as a learner (professor as a model) Teacher as an observer of learning (lesson study) Teacher as reflective practitioner (professional learning community)teacher preparation
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teacher preparation National Institute of Education SingaporeSingapore teachers learn what they need to learn through anapproach that balances content and pedagogy.
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teacher preparationNational Institute of Education SingaporeThe practice component is given emphasis – micro teaching,practicum and lesson study.
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teacher preparation There is an emphasis on teachers solving the problems themselves during the course.
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teacher developmentTeachers learn from thetextbooks and teachersguide.
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teacher developmentWe learn from the Japanese method to help teachersdevelop better skills in observing students. This is lessonstudy. Princess Elizabeth Primary School Singapore
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National Institute of Education, Singapore Edgewood Elementary School, New York Fuchun Primary School, Singapore
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Bina Bangsa School, Indonesia Keys Grade School, The Philippines Kranji Secondary School, Singapore
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leadership Mayor of Newark gave an inspirational message to teachers attending professional development on Singapore Math.
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• What can I do as a teacher?• What can my school do?• What can the education schools do?• What government support should be in place? Slides are available at www.banhar.blogspot.com
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Singapore Math at Highline Public SchoolsMarch 2013 Yeap Ban Haryeapbanhar@gmail.com The Merlion by Yeap Ken Min
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