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Dr Yeap Ban Har<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />Seminar on Singapore Math in Chile<br />SANTIAGO CONCEPTION<br />This seminar is about mathematics teaching and learning that focuses on helping average and struggling learners do well in mathematics while maintaining a suitable challenge for advanced learners.<br />Presentation is available at www.banhar.com<br />
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Beliefs<br />Interest<br />Appreciation<br />Confidence<br />Perseverance<br />Monitoring of one’s own thinking<br />Self-regulation of learning<br />Attitudes<br />Metacognition<br />Numerical calculation<br />Algebraic manipulation<br />Spatial visualization<br />Data analysis<br />Measurement<br />Use of mathematical tools<br />Estimation<br />Mathematical Problem Solving<br />Reasoning, communication & connections<br />Thinking skills & heuristics<br />Application & modelling<br />Skills<br />Processes<br />Concepts<br />Numerical<br />Algebraic<br />Geometrical<br />Statistical<br />Probabilistic<br />Analytical<br />In Singapore, a curriculum that focuses on mathematical problem solving was introduced in 1992. <br />
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thinking schools<br />learning nation<br />The emphasis on thinking continues in the late 1990s with the introduction of Thinking School, Learning Nation philosophy to the entire education system in 1997.<br />
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The assessment reflects the focus of the curriculum. For example, the Grade 6 national examination (Primary School Leaving Examination or PSLE) includes a significant section that requires problem solving.<br />
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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.<br />How many cookies did Mrs Hoon sell?<br />
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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.<br />How many cookies did Mrs Hoon sell?<br />210<br />
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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.<br />How many cookies did Mrs Hoon sell?<br />210<br />MrsHoon sold 960 cookies.<br />
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Schools make problem solving a priority in their mathematics programme because of the demands of the PSLE.<br /> <br />Grade 3 Examination Item (Raffles Girls’ Primary School 2009)<br />Devi had some $2 notes and $5 notes.<br />She had a total of $76.<br />She had 4 more $5 notes than $2 notes.<br />How many $2 notes did she have?<br />
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Schools make problem solving a priority in their mathematics programme because of the demands of the PSLE.<br /> <br />Grade 3 Examination Item (Raffles Girls’ Primary School 2009)<br />Devi had some $2 notes and $5 notes.<br />She had a total of $76.<br />She had 4 more $5 notes than $2 notes.<br />How many $2 notes did she have?<br />$78<br />Number of $5 notes<br />4<br />$20<br />$58<br />8<br />Number of $2 notes<br />$58 ÷ 7 = 8<br />8<br />She had eight $2 notes.<br />
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Textbooks place an emphasis on problem solving and thinking.<br />2740 + 3560<br />= 6300<br />Mr Khan<br />5 units = 6300<br />1 unit = 1260<br />Mr Chen<br />4 units = 4 x 1260<br />4 units = 5040<br />In the end, Mr Chen had 5040 sacks and Mr Khan had 1260 sacks.<br />
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Textbooks place an emphasis on problem solving and thinking.<br />
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A strong foundation is necessary for the students to do well in mathematics. In the Singapore textbooks, such a strong foundation is achieved through the application of a few learning principles.<br />Singapore Math in Chile<br />
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bruner’s theory<br />concrete<br />Singapore Math in Malaysia<br />
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concrete<br />experiences<br />Singapore Math in Malaysia<br />
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The CPA Approach – the progression from concrete to pictures to abstract symbols is recommended for concept development. This is based on the work of Jerome Bruner.<br />
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For example, students learn the idea of division by sharing 12 cookies among 4 persons as well as by putting 12 eggs in groups of 4 before progressing to using drawings to solve division problems. Later they learn to use division sentence 12 ÷ 4 = 3. <br />
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The Spiral Approach – students get to revisit core ideas as they deepen their understanding of those ideas. This is also one of Jerome Bruner’s ideas.<br /> <br />Singapore Math in the Netherlands<br />
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<br />For example, students learn to do division of discrete quantities without the need to write division sentence in Grade 1. In Grade 2, the revisit this idea and use division sentences to represent the situations. In Grade 3, the idea is extended to include the idea of a remainder. They also learn to regroup before dividing for 2-digit and 3-digit numbers. <br />Singapore Math in USA<br />
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In Grade 4, 4-digit numbers are used. In Grade 5, division of continuous quantities are dealt with where 13 ÷ 4 = 3.25 rather than 3 remainder 1. <br />Singapore Math <br />in <br />The Philippines<br />
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Systematic Variation – students are presented with a variety of tasks in a systematic way. This is based on the idea of ZoltanDienes.<br />
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Students in Singapore have demonstrated high achievement and positive attitude towards mathematics. <br />In Trends in Mathematics and Science Study, more than 40% of Singapore’s 4th and 8th graders are in the Advanced International Benchmark (the international average is 5% and 2% respectively). <br />1995<br />2003<br />2007<br />International<br />5<br />Advanced<br />38<br />41<br />38<br />Grade 4<br />26<br />High<br />70<br />74<br />73<br />67<br />Intermediate<br />89<br />92<br />91<br />90<br />Low<br />96<br />98<br />97<br />
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In the PSLE, the national average for students who are capable of completing the most challenging items in the examination is between 40% and 45%. We saw one such challenging items earlier.<br />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.<br />How many cookies did Mrs Hoon sell?<br />
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The attitude index for Singapore students in TIMSS is also relatively high compared to other high-performing countries. <br />Also, the majority of students in Singapore opt to study mathematics in Grades 11 and 12 when they are no longer required to.<br />
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Dr Yeap Ban Har<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />Seminar on Singapore Math in Chile<br />SANTIAGO CONCEPTION<br />Singapore Math in Chile<br />Presentation is available at www.banhar.com<br />
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