Math in Focus: Singapore Math Community Institute (updated)

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Experiencing Singapore MathM A T H I N F O C U S : S I N G A P O R E M A T H C O M M U N I T Y

I N S T I T U T E J u l y 2 4 , 2 0 1 2 C h i c a g o , I L

Yeap Ban HarMarshall Cavendish Institute

Singapore

[email protected]

Slides are available atwww.banhar.blogspot.com

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Land 270 sq miles

People 4.7 million

GDP per capita 1965 USD510 2010 USD43,300

in current USD

Junyuan Secondary School, Singapore

introduction

General Overview of Singapore and its Education System

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) 15 Mixed-Level Schools

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.

Canossa Convent Primary School, Singapore

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

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Score 1960-1970s 1980s 1990s 2000s

500 Japan JapanKorea

Hong Kong

JapanKorea

SingaporeHong Kong

JapanKorea

Hong KongSingapore

400 Thailand SingaporeThailand

The Philippines

MalaysiaThailand

MalaysiaThailand

300 IndonesiaThe Philippines

IndonesiaThe Philippines

Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)

All major international tests (literacy, science and mathematics) between 1964 and 2003 were placed on a common scale. Selected countries shown in the table.

"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

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1992Introduction of Problem-

Solving Curriculum

1997Thinking SchoolsLearning Nation

1982Introduction of Singapore mathematics

textbooks as they are known today.

2001Introduction of textbooks published by

private publishers and approved by Ministry of Education.

2007New editions of textbooks are

published with the introduction of the revised curriculum.

Mathematics is “an excellent vehicle for the

development and improvement of a person’s intellectual competence”.

Ministry of Education Singapore 2006

Page 1

2013Fourth version of the problem-solving

curriculum will be implemented.

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Page 4

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Fundamentals of Singapore Math

Focus on VisualizationYeap Ban Har

Marshall Cavendish InstituteSingapore

[email protected]


110 g

290 g Page 2

110 g

??

2 units = 290 g – 110 g = 180 g1 units = 180 g 2 = 90 g

3 x 90 g = 270 gBella puts 270 g sugar on the dish.

Escuela de Guetamala, Chile

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x + 2x = 12

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King Solomon Academy, London

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60% of Jon’s money is $12.Find the amount of Jon’s money.

Edgewood Elementary School, New YorkBox A has 20 more 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.

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Globe Academy, London

Solve 3x – 2 = 8

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3x – 2 = 8


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Share 3 fourths equally among 3.

3 fourths 3 = 1 fourth

Page 5

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Share 3 fourths equally between 2.

3 fourths 2 = 6 eighths 2= 3 eighths

Share 3 fourths equally among 4.

3 fourths 4 = 12 sixteenths 4= 3 sixteenths

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12 cookies 4

12 pieces 4

12 sixteenths 4

12 tenths 4

12 x 4

12 cookies 4 cookies

12 pieces 4 pieces

12 x 4 x

34

÷1434

÷12

Page 13

Share 3 fourths equally between 2.

=

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Concrete to Visual J Bruner

Human Intelligences H Gardner


visualization

Page 11



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Focus on PatternsYeap Ban Har


[email protected]


Da Qiao Primary School, Singapore

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Mathematical Practices

“Mathematically proficient students

look closely to discern a pattern or structure.”


patterns and generalization

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Case Study on Multiplication

Yeap Ban HarMarshall Cavendish Institute

Singapore

[email protected]


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.

Luego, representan estas situaciones concretas utilizando, en primer lugar, los dibujos y, …After that they represent these concrete situations using, first, drawings ..

… 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.

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.

conjuntos iguales o grupos iguales

There is a progression from equal groups to skip-counting.

Hay una progresión de los grupos de iguales para saltar de conteo.

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 30

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.

Later, the array meaning of multiplication is introduced.

Más tarde, se introduce el significado del producto vectorial.

Students apply their understanding of multiplication to solve word problems including those that include multiplicative comparison, and at the same time, deepen their understanding of multiplication.

Los estudiantes aplican sus conocimientos de la multiplicación para resolver problemas que incluyen la comparación multiplicativa, y al mismo tiempo, profundizan su comprensión de la multiplicación.

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.

In Grade 3 they learn multiplication of 2-digit with 1-digit numbers as well as multiplication of 3-digit and 1-digit numbers.

Después de completar las tablas de multiplicar, los estudiantes aprenden multiplicaciones que van más allá de la tabla de multiplicar. Ellos aprenden a multiplicar números de dos dígitos con números de 1 dígito, así como la multiplicación de números de tres dígitos y números de un dígito.

In Primary 4, the learn multiplication of 4-digit and 1-digit numbers as well as multiplication of 3-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.

42

34

4

Finally in Primary 5, students learn to use calculator to multiply larger numbers.Por último, en 5º básico los estudiantes aprenden a utilizar la calculadora para multiplicar grandes cantidades.

Pedagogical Principles of Singapore MethodConcrete Pictorial Abstract Approach

Principios pedagógicos del Método SingapurConcreto Pictórico Abstracto

10 5 = 2

Pedagogical Principles of Singapore MethodSpiral Approach

Principios pedagógicos del Método SingapurEnfoque en Espiral

10 : 5 = 2

12 : 5 = 2 restante 2

“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).

.

“A curriculum as it develops should revisit this 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).

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.

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. .

In Grade 1, the symbol ÷ or : is not used. The symbol is introduced in Grade 2. The idea of remainder is introduced in Grade 3.

La idea de reagrupar antes de dividirse se introduce al finalizar 3º básico y también se enseña en 4 º básico.

.

The idea of regrouping before dividing is introduced later in Grade 3 and is taught in Grade 4 as well.

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Challenging Word Problems using Bar

ModelsYeap Ban Har


[email protected]


110 g

??

2 units = 290 g – 110 g = 180 g

1 units = 180 g 2 = 90 g

3 x 90 g = 270 gBella puts 270 g sugar on the dish.

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Page 15

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Page 15

Math in FocusGrade 1

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Math in FocusGrade 2

Escuela de Guetamala, Chile

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

543

274

cars

buses

543 + 274 =

543 274

cars buses

Carl

Ben

$4686

Lesson July 23, 2012

Differentiated instruction for students who have difficulty with

standard algorithms. Use number bonds.

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.

Lesson June 18, 2012

Jack

Kyla

had

$2

more

than

Jack

Kyla

gave

$3


Open Lesson at Hawaii, USA


Story 1Jack had $3.Jack gave Kyla $2 more.

Jack Kyla

Before $3 $1 $5 $19

After $1 $3 $7 ?

What if Kyla had this amount before?


Story 2Kyla had $3 more than Jack.

Jack

Kyla

Jack gave Kyla $2.

$2

$3

Who had more money afterwards? How much

more?

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.


In the end ...

At first …

Alice

Betty

Charmaine

Dolly

20

10


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Concrete to Visual J Bruner

Human Intelligences H Gardner


visualizationand managing

information

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.