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Theoretical Underpinnings of Singapore Math Seminar at Harvard Graduate School of Education Yeap Ban-Har, Ph.D. National Institute of Education Nanyang Technological University Singapore banhar.yeap@nie.edu.sg
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A Problem from Singapore Grade 6 National Test Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. How many sweets did Ken buy?
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Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. How many sweets did Ken buy? chocolates sweets Assuming that both boys did not have any sweet or chocolate before they bought the chocolates and sweets. 12 Jim 12 18 12 12 12 12 Ken 3 parts ïƒ 12 + 12 + 12 + 12 + 18 = 66 1 part ïƒ 22 Half of the sweets Ken bought = 22 + 12 = 34 So Ken bought 68 sweets.`
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88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. How many girls wore swimming goggles on that day? A Problem from a Singapore Classroom Fairfield Methodist Primary School
88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles.
88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles.
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3 x 7 = 21 21 girls wear goggles. A Curriculum That Helps Average Students Reach High Achievement
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TIMSS 2007 Trends in International Mathematics and Science Studies 1995 2003 2007 Grade 4 Advanced 38 41 38 High 70 74 73 Intermediate 89 92 91 Low 96 98 97 North Vista Primary School
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TIMSS 2007 Trends in International Mathematics and Science Studies Average Indonesia Thailand Malaysia Singapore Grade 8 Advanced 2 3 0 40 2 High 15 12 4 70 18 Intermediate 46 44 14 88 50 Low 75 66 48 97 82 Method Used in Singapore Textbooks
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Beliefs Interest Appreciation Confidence Perseverance Monitoring of oneâ€™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 Mathematics Curriculum Framework
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Bruner The concrete ïƒ pictorial ïƒ abstract approach is used to help the majority of learners to develop strong foundation in mathematics. Division National Institute of Education
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mathz4kidz Learning Centre, Penang, Malaysia brunerâ€™s theory concrete A lesson from Earlybird Kindergarten Mathematics
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mathz4kidz Learning Centre, Penang, Malaysia concrete experiences
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from concrete to pictorial mathz4kidz Learning Centre, Penang, Malaysia
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from pictorial to abstract All Kids Are Intelligent Series
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mathz4kidz Learning Centre, Penang, Malaysia symbols
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using concrete materials Professional Development in AteneoGrade School, Manila, The Philippines Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile
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Primary Mathematics (Standards Edition) 2A Pictorial Before Abstract
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bruner Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile
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skempâ€™s theory conceptual understanding BinaBangsa School, Semarang, Indonesia
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Mathematics is an excellent vehicle for the development and improvement of a personâ€™s intellectual competence .. Ministry of Education 2006 DaQiao Primary School
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