Math in Focus: Singapore Math Community Institute (updated)
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These are the slides for Day 1 of the institute, taught by Yeap Ban Har.
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Math in Focus: Singapore Math Community Institute (updated)
- 1. Experiencing Singapore Math Experiencing Singapore Math M AT H I N F O C U S : S I N G A P O R E M AT H C O M M U N I T Y INSTITUTE July 24, 2012 Chicago, IL Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
- 2. Experiencing Singapore Math Land 270 sq miles People introduction 4.7 million GDP per capita 1965 USD510 2010 USD43,300 in current USD Junyuan Secondary School, Singapore
- 3. General Overview of Singapore and its Education System
- 4. General Overview of Singapore and its Education System Students 500 000 Teachers 30 000 Principals & Vice-Principals 900 Schools 173 Primary Schools (Primary 1 – 6) 155 Secondary Schools (Secondary 1 – 4) 13 Junior Colleges (JC 1 – 2) Canossa Convent Primary 15 Mixed-Level Schools School, Singapore The data refers to 1-12 school system. Pre-school is not part of the formal education system. The data excludes post-secondary education system which includes institutes of technical education, polytechnics and universities.
- 5. High achievement was not a given. In 1960, among 30 615 candidates who sat for the first Primary School Leaving Examination, 45% of the candidates passed. Keon Ming Public School, Singapore
- 6. Experiencing Singapore Math All major international tests (literacy, science and mathematics) between 1964 and 2003 were placed on a common scale. Selected countries shown in the table. Score 1960-1970s 1980s 1990s 2000s 500 Japan Japan Japan Japan Korea Korea Korea Hong Kong Singapore Hong Kong Hong Kong Singapore 400 Thailand Singapore Malaysia Malaysia Thailand Thailand Thailand The Philippines 300 Indonesia Indonesia The Philippines The Philippines Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
- 8. "Solving problems is central to mathematical proficiency and is articulated to a varying degree across the international curricula. Singapore applies the highest degree of specificity to it, placing it at the centre of all mathematical learning.“ Review of the National Curriculum in England Research Report UK Department for Education
- 9. Experiencing Singapore Math 1982 Introduction of Singapore mathematics textbooks as they are known today. Mathematics is “an excellent vehicle for the development 1992 and improvement of a person’s Introduction of Problem- intellectual competence”. Solving Curriculum Ministry of Education Singapore 2006 1997 2001 Thinking Schools Introduction of textbooks published by Learning Nation private publishers and approved by Ministry of Education. 2007 New editions of textbooks are published with the introduction of the revised curriculum. 2013 Fourth version of the problem-solving curriculum will be implemented. Page 1
- 10. Experiencing Page 4 Singapore Math
- 11. Experiencing Singapore Math on Visualization Fundamentals of Singapore Math Focus Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
- 12. 110 g 290 g Page 2
- 13. 2 units = 290 g – 110 g = 180 g 1 units = 180 g 2 = 90 g 110 g 3 x 90 g = 270 g Bella puts 270 g sugar on the dish. ? ?
- 14. Experiencing Singapore Math Escuela de Guetamala, Chile
- 15. x + 2x = 12 Experiencing Singapore Math
- 16. Experiencing Singapore Math 60% of Jon’s money is $12. Find the amount of Jon’s money. King Solomon Academy, London
- 17. Box A has 20 more Edgewood Elementary School, New York books than Box B. Box C has twice as many books as Box B. The three boxes has 340 books. How many books are there in Box A.
- 18. Experiencing Singapore Math Solve 3x – 2 = 8 Globe Academy, London
- 19. Experiencing Singapore Math 3x – 2 = 8 Globe Academy, London
- 20. Experiencing Singapore Math Share 3 fourths equally among 3. 3 fourths 3 = 1 fourth Page 5
- 21. Experiencing Singapore Math Share 3 fourths equally between 2. 3 fourths 2 = 6 eighths 2 Share 3 fourths equally among 4. = 3 eighths 3 fourths 4 = 12 sixteenths 4 = 3 sixteenths
- 22. Experiencing Singapore Math 12 cookies 4 12 pieces 4 12 sixteenths 4 12 tenths 4 12 cookies 4 cookies 12 x 4 12 pieces 4 pieces 12 x 4x Page 13
- 23. Share 3 fourths equally between 2.
- 24. =
- 30. Experiencing Singapore Math Junyuan Secondary School, Singapore Concrete to Visual visualization J Bruner Human Intelligences H Gardner Page 11
- 31. King Solomon Academy, London
- 32. Experiencing Singapore Math King Solomon Academy, London
- 33. Singapore Math Experiencing King Solomon Academy, London
- 34. Experiencing Singapore Math Globe Academy, London
- 35. Experiencing Singapore Math Globe Academy, London
- 36. Experiencing Singapore Math Globe Academy, London
- 38. Experiencing Singapore Math on Patterns Fundamentals of Singapore Math Focus Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
- 39. Experiencing Singapore Math Da Qiao Primary School, Singapore
- 40. Experiencing Singapore Math Junyuan Secondary School, Singapore Mathematical patterns and Practices “Mathematically generalization proficient students look closely to discern a pattern or structure.”
- 41. Experiencing Singapore Math Fundamentals of Singapore Math Case Study on Multiplication Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
- 42. Desde los primeros años, los estudiantes aprenden a hacer conjuntos o grupos iguales utilizando materiales concretos. From the early grades, students learn to make equal groups using concrete materials.
- 43. Luego, representan estas situaciones concretas utilizando, en primer lugar, los dibujos y, … After that they represent these concrete situations using, first, drawings ..
- 44. … más tarde, diagramas (modelos de barras). Después de eso, escriben multiplicaciones. Por supuesto, los profesores volverán a las representaciones concretas y pictóricas una y otra vez en aprendizajes posteriores. … and, later, diagrams. After that they write multiplication sentences.
- 45. Multiplication involving whole numbers is taught over five years, starting in Primary 1. The focus is on one of the meanings of multiplication – equal sets or equal groups. La multiplicación con números enteros se imparte en cinco años, a partir de 1º básico. La atención se centra en uno de los significados de la multiplicación; conjuntos iguales o grupos iguales. Los estudiantes aprenden a representar 3 platos de frutas como de 3 x 6, cuando hay 6 frutas en cada plato. No se espera que recuerden las tablas de multiplicar.
- 46. conjuntos iguales o grupos iguales
- 48. There is a progression from equal groups to skip-counting. Hay una progresión de los grupos de iguales para saltar de conteo.
- 49. 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
- 50. In Primary 2, students learn multiplication facts of 2, 3, 4, 5 and 10. In Primary 3, they learn the multiplication facts of 6, 7, 8 and 9. En 2º básico, los alumnos aprenden las tablas de multiplicación del 2, 3, 4, 5 y 10. En 3º básico, aprenden las tablas de multiplicación, de 6, 7, 8 y 9.
- 51. Later, the array meaning of multiplication is introduced. Más tarde, se introduce el significado del producto vectorial.
- 55. Students apply their Los estudiantes understanding of aplican sus multiplication to conocimientos de la solve word problems multiplicación para including those that resolver problemas include multiplicative que incluyen la comparison, and at comparación the same time, multiplicativa, y al deepen their mismo understanding of tiempo, profundizan multiplication. su comprensión de la multiplicación.
- 57. Multiplication is also applied to find the area of rectangles and square when Primary 3 students learn the concept of area. La multiplicación se aplica también para encontrar el área de rectángulos y cuadrados cuando los estudiantes de 3º básico aprenden el concepto de área, contando unidades cuadradas al final de 3º básico.
- 58. In Grade 3 they Después de completar las learn tablas de multiplicar, los multiplication of estudiantes aprenden 2-digit with 1- multiplicaciones que van digit numbers as más allá de la tabla de well as multiplicar. Ellos aprenden a multiplication of multiplicar números de dos 3-digit and 1-digit dígitos con números de 1 numbers. dígito, así como la multiplicación de números de tres dígitos y números de un dígito.
- 59. 42 In Primary 4, the learn multiplication of 4-digit 4 and 1-digit numbers as well as multiplication of 3- 34 digit and 2-digit numbers. The focus is on partial products. En 4º básico, aprenden a multiplicar números de cuatro dígitos y un dígito, así como multiplicar números de tres dígitos y dos dígitos. La atención se centra en productos parciales.
- 60. Finally in Primary 5, students learn to use calculator to multiply larger numbers. 5º básico los estudiantes Por último, en aprenden a utilizar la calculadora para multiplicar grandes cantidades.
- 61. Pedagogical Principles of Singapore Method Concrete Pictorial Abstract Approach 10 5 = 2 Principios pedagógicos del Método Singapur Concreto Pictórico Abstracto
- 64. Pedagogical Principles of Singapore Method Spiral Approach 10 : 5 = 2 12 : 5 = 2 restante 2 Principios pedagógicos del Método Singapur Enfoque en Espiral
- 65. “Un plan de estudios de la manera que se desarrolla debe revisar estas ideas básicas en varias ocasiones, construyéndose sobre ellos hasta que el estudiante ha comprendido todo el aparato formal que conllevan”. (Bruner 1960 en El Proceso de la Educación). as it develops should revisit this “A curriculum basic ideas repeatedly, building upon them until the student has grasped the full formal . apparatus that goes with them.” (Bruner 1960 in The Process of Education).
- 66. En los cursos de 1º a 4º básico, se utilizan cantidades discretas, por ejemplo piedrecillas y los niños. En 5º básico se utilizan cantidades continuas como las medidas estándar de 13 kg y 13 cm. In Grades 1 to 4, quantities used are discrete ones e.g. pebbles and children. In Grade 5, continuous quantities like standard measures 13 kg and 13 cm are used.
- 67. En 1º básico no se utiliza el símbolo ÷ o : para la división. El símbolo se introduce en 2º básico. La idea de resto se introduce en 3º básico. 1, the symbol ÷ or : is not used. The In Grade symbol is introduced in Grade 2. The idea of . remainder is introduced in Grade 3.
- 68. The idea of regrouping before dividing is introduced later in Grade 3 and is taught in La idea 4 as Grade de reagrupar antes de dividirse se introduce al finalizar 3º básico y también se well. enseña en 4 º básico.
- 69. Experiencing Singapore Math Fundamentals of Singapore Math Challenging Word Problems using Bar Models Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
- 70. 2 units = 290 g – 110 g = 180 g 1 units = 180 g 2 = 90 g 110 g 3 x 90 g = 270 g Bella puts 270 g sugar on the dish. ? ?
- 71. Experiencing Page 15 Singapore Math
- 72. Experiencing Page 15 Singapore Math
- 73. Math in Focus Grade 1 Experiencing Singapore Math
- 74. Experiencing Singapore Math Math in Focus Grade 2 Escuela de Guetamala, Chile
- 76. One day, 543 cars and 274 buses pass through a toll booth. How many cars and buses pass through the toll booth? Math in Focus Grade 2 cars 543 buses 274 543 + 274 = cars buses 543 274
- 77. Lesson July 23, 2012 Carl $4686 Ben
- 79. Differentiated instruction for students who have difficulty with standard algorithms. Use number bonds.
- 80. 2x + x = 4686 3x = 4686 Students in Grade 7 may use algebra to deal with such situations. Bar model is actual linear equations in pictorial form.
- 81. Lesson June 18, 2012 Jack $3 Jack Kyla $2 Kyla gave more had than
- 82. Lesson June 18, 2012 Open Lesson at Hawaii, USA
- 87. Lesson June 18, 2012 What if Kyla Story 1 had this Jack had $3. amount before? Jack gave Kyla $2 more. Jack Kyla Before $3 $1 $5 $19 After $1 $3 $7 ?
- 89. Lesson June 18, 2012 Story 2 Kyla had $3 more than Jack. Who had more money Jack $2 afterwards? How much Kyla $3 more? Jack gave Kyla $2.
- 90. Kyla had $3 more than Jack. Jack gave Kyla $2. How much more did Kyla have than Jack? Students in Grade 6 may use algebra to deal with Story 2. Kyla had $(x + 3) Jack had $x Then, Jack had $(x – 2) And Kyla had $(x + 5) Kyla had $(x + 5) – $(x – 2) or $7 more than Jack.
- 91. Lesson July 23, 2012 In the end ... At first … Alice 20 Betty 10 Charmaine Dolly
- 92. Lesson July 23, 2012
- 93. Experiencing Singapore Math Junyuan Secondary School, Singapore Concrete to visualization Visual and managing J Bruner Human information Intelligences H Gardner
- 95. can learn. Our students must too. Google learns from typos and spelling mistakes we all make when searching to help give you quicker and more accurate search results. So if you type ‘grizzly pears’, we can guess that you probably meant ‘grizzly bears’. Goggle does not have a degree in English. We can do this because over the years we’ve studied how people search and learned what the most common errors are. So it’s good to know that all those little mistakes aren’t made in vain.