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Math in Focus: Singapore Math Community Institute (updated)
 

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.

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) Math in Focus: Singapore Math Community Institute (updated) Presentation Transcript

    • Experiencing Singapore MathExperiencing Singapore MathM 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
    • Experiencing Singapore Math  Land  270 sq miles  People introduction  4.7 million  GDP per capita  1965 USD510  2010 USD43,300 in current USDJunyuan SecondarySchool, Singapore
    • 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) 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.
    • High achievement was not a given. In1960, among 30 615 candidates whosat for the first Primary School LeavingExamination, 45% of the candidatespassed. Keon Ming Public School, Singapore
    • 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 PhilippinesReference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
    • "Solving problems is central to mathematical proficiencyand is articulated to a varying degree across theinternational curricula. Singapore applies the highestdegree of specificity to it, placing it at the centre of allmathematical learning.“ Review of the National Curriculum in England Research Report UK Department for Education
    • Experiencing Singapore Math 1982Introduction 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
    • ExperiencingPage 4 Singapore Math
    • Experiencing Singapore Math on Visualization Fundamentals of Singapore MathFocus Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
    • 110 g 290 g Page 2
    • 2 units = 290 g – 110 g = 180 g 1 units = 180 g 2 = 90 g110 g 3 x 90 g = 270 g Bella puts 270 g sugar on the dish. ? ?
    • Experiencing Singapore MathEscuela de Guetamala, Chile
    • x + 2x = 12 Experiencing Singapore Math
    • Experiencing Singapore Math60% of Jon’s money is $12.Find the amount of Jon’s money. King Solomon Academy, London
    • Box A has 20 more Edgewood Elementary School, New Yorkbooks than Box B. BoxC has twice as manybooks as Box B. Thethree boxes has 340books. How manybooks are there in BoxA.
    • Experiencing Singapore MathSolve 3x – 2 =8 Globe Academy, London
    • Experiencing Singapore Math3x – 2 = 8 Globe Academy, London
    • Experiencing Singapore MathShare 3 fourths equally among 3.3 fourths 3 = 1 fourth Page 5
    • Experiencing Singapore MathShare 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
    • Experiencing Singapore Math12 cookies 412 pieces 412 sixteenths 412 tenths 4 12 cookies 4 cookies12 x 4 12 pieces 4 pieces 12 x 4x Page 13
    • Share 3 fourths equally between 2.
    • =
    • ExperiencingSingapore Math
    • ExperiencingSingapore Math
    • ExperiencingSingapore Math
    • ExperiencingSingapore Math
    • ExperiencingSingapore Math
    • Experiencing Singapore MathJunyuan Secondary School, Singapore  Concrete to Visual visualization  J Bruner  Human Intelligences  H Gardner Page 11
    • King Solomon Academy, London
    • Experiencing Singapore MathKing Solomon Academy, London
    • Singapore Math ExperiencingKing Solomon Academy, London
    • Experiencing Singapore MathGlobe Academy, London
    • Experiencing Singapore MathGlobe Academy, London
    • Experiencing Singapore MathGlobe Academy, London
    • 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
    • Experiencing Singapore MathDa Qiao Primary School, Singapore
    • Experiencing Singapore MathJunyuan Secondary School, Singapore Mathematical patterns and Practices “Mathematically generalization proficient students look closely to discern a pattern or structure.”
    • Experiencing Singapore MathFundamentals 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
    • Desde los primeros años, los estudiantesaprenden a hacer conjuntos o grupos igualesutilizando materiales concretos.From the early grades, students learn to make equalgroups using concrete materials.
    • Luego, representan estas situacionesconcretas utilizando, en primer lugar, losdibujos y, …After that they represent these concretesituations using, first, drawings ..
    • … más tarde, diagramas (modelos debarras). Después de eso, escribenmultiplicaciones. Por supuesto, losprofesores volverán a las representacionesconcretas y pictóricas una y otra vez enaprendizajes posteriores.… and, later, diagrams. After that they writemultiplication sentences.
    • Multiplication involving whole numbers istaught over five years, starting in Primary 1.The focus is on one of the meanings ofmultiplication – equal sets or equal groups.La multiplicación con números enteros seimparte en cinco años, a partir de 1º básico.La atención se centra en uno de lossignificados de la multiplicación; conjuntosiguales o grupos iguales. Los estudiantesaprenden a representar 3 platos de frutascomo de 3 x 6, cuando hay 6 frutas en cadaplato. No se espera que recuerden las tablasde multiplicar.
    • conjuntos iguales o gruposiguales
    • There is a progression from equal groups toskip-counting.Hay una progresión de los grupos de igualespara 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 multiplicationfacts of 2, 3, 4, 5 and 10. In Primary 3, theylearn the multiplication facts of 6, 7, 8 and 9.En 2º básico, losalumnos aprendenlas tablas demultiplicación del2, 3, 4, 5 y 10. En3ºbásico, aprendenlas tablas demultiplicación, de6, 7, 8 y 9.
    • Later, the array meaningof multiplication isintroduced. Más tarde, se introduce el significado del producto vectorial.
    • Students apply their Los estudiantesunderstanding of aplican susmultiplication to conocimientos de lasolve word problems multiplicación paraincluding those that resolver problemasinclude multiplicative que incluyen lacomparison, and at comparaciónthe same time, multiplicativa, y aldeepen their mismounderstanding of tiempo, profundizanmultiplication. su comprensión de la multiplicación.
    • Multiplication is alsoapplied to find the areaof rectangles andsquare when Primary 3students learn theconcept of area.La multiplicación seaplica también paraencontrar el área derectángulos y cuadradoscuando los estudiantesde 3º básico aprendenel concepto deárea, contandounidades cuadradas alfinal de 3º básico.
    • In Grade 3 they Después de completar laslearn tablas de multiplicar, losmultiplication of estudiantes aprenden2-digit with 1- multiplicaciones que vandigit numbers as más allá de la tabla dewell as multiplicar. Ellos aprenden amultiplication of multiplicar números de dos3-digit and 1-digit dígitos con números de 1numbers. dígito, así como la multiplicación de números de tres dígitos y números de un dígito.
    • 42In Primary 4, the learnmultiplication of 4-digit 4and 1-digit numbers aswell as multiplication of 3- 34digit and 2-digit numbers.The focus is on partialproducts.En 4º básico, aprenden a multiplicar númerosde cuatro dígitos y un dígito, así comomultiplicar números de tres dígitos y dosdígitos. La atención se centra en productosparciales.
    • Finally in Primary 5,students learn to usecalculator to multiplylarger numbers. 5º básico los estudiantesPor último, enaprenden a utilizar la calculadora paramultiplicar grandes cantidades.
    • Pedagogical Principles of Singapore MethodConcrete  Pictorial  Abstract Approach 10 5 = 2Principios pedagógicos del Método SingapurConcreto  Pictórico  Abstracto
    • Pedagogical Principles of Singapore MethodSpiral Approach 10 : 5 = 2 12 : 5 = 2 restante 2Principios pedagógicos del Método SingapurEnfoque en Espiral
    • “Un plan de estudios de la manera que sedesarrolla debe revisar estas ideas básicasen varias ocasiones, construyéndose sobreellos hasta que el estudiante ha comprendidotodo el aparato formal que conllevan”.(Bruner 1960 en El Proceso de laEducación). as it develops should revisit this“A curriculumbasic ideas repeatedly, building upon themuntil the student has grasped the full formal.apparatus that goes with them.” (Bruner 1960in The Process of Education).
    • En los cursos de 1º a 4º básico, se utilizancantidades discretas, por ejemplo piedrecillasy los niños. En 5º básico se utilizancantidades continuas como las medidasestándar de 13 kg y 13 cm.In Grades 1 to 4, quantities used are discreteones e.g. pebbles and children. In Grade5, continuous quantities like standardmeasures 13 kg and 13 cm are used.
    • En 1º básico no se utiliza el símbolo ÷ o :para la división. El símbolo se introduce en 2ºbásico. La idea de resto se introduce en 3ºbásico. 1, the symbol ÷ or : is not used. TheIn Gradesymbol is introduced in Grade 2. The idea of.remainder is introduced in Grade 3.
    • The idea ofregroupingbeforedividing isintroducedlater in Grade3 and istaught inLa idea 4 asGrade de reagrupar antes de dividirse seintroduce al finalizar 3º básico y también sewell.enseña en 4 º básico.
    • Experiencing Singapore Math Fundamentals of Singapore Math Challenging WordProblems using Bar Models Yeap Ban Har  Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
    • 2 units = 290 g – 110 g = 180 g 1 units = 180 g 2 = 90 g110 g 3 x 90 g = 270 g Bella puts 270 g sugar on the dish. ? ?
    • ExperiencingPage 15 Singapore Math
    • ExperiencingPage 15 Singapore Math
    • Math in Focus Grade 1 Experiencing Singapore Math
    • Experiencing Singapore Math Math in Focus Grade 2Escuela 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 cars 543 buses 274 543 + 274 =  cars buses 543 274
    • Lesson  July 23, 2012 Carl $4686 Ben
    • Differentiated instruction for students who have difficulty with standardalgorithms. Use number bonds.
    • 2x + x = 4686 3x = 4686Students in Grade 7 may use algebra to deal with such situations. Barmodel is actual linear equations in pictorial form.
    • Lesson  June 18, 2012 Jack $3 Jack Kyla $2 Kyla gave more had than
    • Lesson  June 18, 2012 Open Lesson at Hawaii, USA
    • Lesson  June 18, 2012 What if KylaStory 1 had thisJack had $3. amount before?Jack gave Kyla $2more. Jack Kyla Before $3 $1 $5 $19 After $1 $3 $7 ?
    • Lesson  June 18, 2012Story 2Kyla had $3 more than Jack. Who had more moneyJack $2 afterwards? How muchKyla $3 more?Jack gave Kyla $2.
    • 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.
    • Lesson  July 23, 2012 In the end ... At first …Alice 20Betty 10Charmaine Dolly
    • Lesson  July 23, 2012
    • Experiencing Singapore MathJunyuan Secondary School, Singapore  Concrete to visualization Visual and managing  J Bruner  Human information Intelligences  H Gardner
    • can learn. Our students must too.Google learns from typos and spelling mistakes we all make when searching to help give youquicker and more accurate search results. So if you type ‘grizzly pears’, we can guess that youprobably meant ‘grizzly bears’.Goggle does not have a degree in English. We can do this because over the years we’vestudied how people search and learned what the most common errors are. So it’s good toknow that all those little mistakes aren’t made in vain.