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## A Seminar on SingaporeMath @ SALT LAKE CITY, UTAH

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**A Seminar on SingaporeMath@ SALT LAKE CITY, UTAH**Yeap Ban Har, Ph.D. National Institute of Education Nanyang Technological University Singapore banhar.yeap@nie.edu.sg**Singapore**A multi-racial, multi-cultural, multi-religious and multi-lingual society. Gained independence in 1965. Population of 4 million with ½ million students in about 350 schools, all public.**Presentation Outline**• Singapore Education in a Nutshell • Singapore Mathematics Curriculum • National Tests in Singapore • Mathematics Teaching in Singapore • Mathematics Teachers & Professional Development • Achievements of Singapore Students • Questions & Discussion**Mathematics Curriculum**Development & Focus**Vision of Ministry of Education**Moulding the Future of the Nation**Columbus was searching for hardware – precious metals,**silk, and spices – the sources of wealth in his days. Thomas L. Friedman 2006 The World Is Flat**I was searching for software – brain power and knowledge**workers – the sources of wealth in our day. Thomas L. Friedman 2006 The World Is Flat**Future of the Nation**Nurturing Knowledge Workers through Ability-Driven Education**As the 21st century approaches … countries will need**citizens prepared to participate in ‘brain-power’ industries Beaton, Mullis, Martin, Gonzalez, Kelly & Smith 1996**The Singapore mathematics curriculum states that “an**emphasis on mathematics education will ensure that we have an increasingly competitive workforce to meet the challenges of the 21st century”**Impact of Globalization**Schools around the world are forced to move forward if they want to make a difference to the future of their students.**Problem-Solving Curriculum**Agenda for Action (USA) and Cockcroft Report (UK) led to the introduction of a problem-solving curriculum in 1992.**Beliefs**Interest Appreciation Confidence Perseverance Monitoring of one’s own thinking Self-regulation of learning Attitudes Metacognition Numerical calculation Algebraic manipulation Spatial visualization Data analysis Measurement Use of mathematical tools Estimation Mathematical Problem Solving Reasoning, communication & connections Thinking skills & heuristics Application & modelling Skills Processes Concepts Numerical Algebraic Geometrical Statistical Probabilistic Analytical Singapore Mathematics Curriculum Framework**Thinking SchoolsLearning Nation**This initiative was introduced in 1997. It focuses on explicit teaching of thinking through school subjects.**Problem-Solving Curriculum**It was revised in 2001 to give more emphasis on a range of heuristics.**Innovation & Enterprise**This initiative was introduced in 2003. It focuses on inculcating good habits of minds amongst students.**Teach LessLearn More**This call was made in 2004 to encourage the development of strong foundation knowledge.**Sample Test Item**3 cm 5 cm 3 cm 7 cm Find the area of the figure shown.**3 cm**5 cm 3 cm 7 cm Find the area of the figure shown.**3 cm**5 cm 3 cm 7 cm Find the area of the figure shown.**3 cm**5 cm 3 cm 7 cm Find the area of the figure shown.**Nurturing Every Child**This call has been made since 2005. Every child should be developed to maximize their potential using different approaches.**Impact of Technology**Technological advances have compelled educators to re-consider what is considered significant in school curriculum.**Otherwise, schools will be teaching students “19th-century**school mathematics concentrating on isolated skills” Kaput, Noss & Hoyles 2002**Problem-Solving Curriculum**It was revised in 2007 for this reason. It places greater emphasis on visualization and number sense. With the introduction of calculator, mental strategies are also emphasized.**PSLE: Emphasis on Visualization**The figure below is made up of 2 identical squares, 4 identical rectangles and 3 identical semi-circles. What is the area of the figure? 70 cm**PSLE: Emphasis on Number Sense**Each of the three cards shown is printed with a different whole number. The smallest number is 23. When these numbers are added two at a time, the sums are 61, 71 and 86. What is the largest number on the cards? 23**It is recognized that mathematics is “an excellent vehicle**for the development and improvement of a person’s intellectual competence in logical reasoning, spatial visualization, analysis and abstract thought” Ministry of Education Singapore 2006**National Test**Emphasis on Basics & Problem Solving**National Tests in Singapore**• Grade 6 Primary School Leaving Examination PSLE • Has always been under the control of Singapore Ministry of Education • Singapore Examinations and Assessment Board (SEAB) was set up recently to handle national tests in Singapore • Grade 10 GCE Ordinary Level • Has always been offered by Cambridge Examination Syndicate until 2008. • Grade 12 GCE Advanced Level • Has always been offered by Cambridge Examination Syndicate until 2007.**Knowledge 25%**• Recall specific • mathematical facts, • concepts, • rules, and • formulae. • Perform straight-forward computations**Comprehension 35%**• Interpret data • Use mathematical concepts, rules, and formulae • Solve routine or familiar problems**Application & Analysis 40%**• Analyse data • Apply mathematical concepts, rules and formulae in a complex situation • Solve unfamiliar problems**Basic & Routine Skills**• Example 1 • Find the value of 12.2 ÷ 4 . • Example 2 • A show started at 10.55 a.m. and ended at 1.30 p.m. • How long was the show in hours and minutes?**Basic & Routine Skills**• Example 3 • Find <y in the figure below. 70o 70o y 70o**Basic & Routine Skills**• Example 4 • Cup cakes are sold at 40 cents each. • What is the greatest number of cup cakes that can be bought with $95? • Example 5 • From January to August last year, Mr Tang sold an average of 4.5 cars per month, He did not sell any car in the next 4 months. On average, how many cars did he sell per month last year?**Novelty**Students are expected to handle novel situations i.e. those not in the textbooks or previous examinations.**Problem Solving**1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97 The first 97 whole numbers are added up. What is the ones digit in the total?**Problem Solving**Rena used stickers of four different shapes to make a pattern. The first 12 stickers are shown below. What was the shape of the 47th sticker? ………? 1st 12th 47th**Complexity**Students are expected to handle multi-step problems with some degree of complexity.**Problem Solving**In Figure 1, Tank A is completely filled with water and Tank B is empty. Water is poured from Tank A into Tank B without spilling. The heights of the water level in the two tanks are now equal as shown in Figure 2. What is the height of the water level in Tank A in Figure 2?**Problem Solving**Siti started saving some money on Monday. On each day from Tuesday to Friday, she saved 20 cents more than the amount she saved the day before. She saved a total of $6 from Monday to Friday. How much money did she save on Monday?**Problem Solving**Siti started saving some money on Monday. On each day from Tuesday to Friday, she saved 20 cents more than the amount she saved the day before. She saved a total of $6 from Monday to Friday. How much money did she save on Monday? $6**Problem Solving**Siti started saving some money on Monday. On each day from Tuesday to Friday, she saved 20 cents more than the amount she saved the day before. She saved a total of $6 from Monday to Friday. How much money did she save on Monday? $4