Dr. Yeap Ban Har Marshall Cavendish Institute Singapore firstname.lastname@example.org SINGAPORE M AT H Beyond the Basics Day One St Edward’s SchoolSlides are available at Florida, USAwww.banhar.blogspot.com Marshall Cavendish Institute www.facebook.com/MCISingapore www.mcinstitute.com.sg
IntroductionWe started the day with an overview of Singapore educationsystem. We also watched a video on the Singapore educationsystem. See http://www.youtube.com/watch?v=sEn6OKsVoMs
General Overview of Singapore and its Education System Land 270 sq miles People 4.7 million
General Overview of Singapore and its Education System GDP per capita in current U.S. dollars 1965 $510 2010 $43 300
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 School 15 Mixed-Level Schools 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.
Universities National Examination Institutes of Poly Technical technics Junior Education Colleges Integrated National Examination Programmes Secondary Schools National Examination Primary SchoolsA detailed schematic diagram of Singapore’s education system is available in Education Statistics Digesthttp://www.moe.gov.sg/education/education-statistics-digest/
Curriculum document is available at http://www.moe.gov.sg/
THINKING SCHOOLSLEARNING NATION Singapore Ministry of Education 1997
Singapore Mathematics: Focus on Thinking anexcellent vehicle for the development &improvement of a person’s intellectual competencies Ministry of Education Singapore 2006
Lesson 1We did a lesson on multiplication facts to understand theemphasis on visualization in learning basic materials. We alsosaw the use of an anchor tasks to engage students for anextended period of time.
Lesson 1 June 18, 2012 Problem 2x4=8 10 x 4 = 5 x 4 = 20 5 x 4 = 20 9x4= 2x4=8 4x4= 8x8= 7x4= 2x4=8 6x4= 5 x 4 = 20 3x4= 2x4=8This Grade 2 lesson on multiplication facts of 4 centers around using doublingstrategy and adding one row strategy in addition to previewing more advancedstrategies such as using 2 x 4 and 5 x 4 to get 7 x 4 as well as ‘subtraction’ strategy.The anchor task is to use 2 x 4 and 5 x 4 to obtain all the other facts. The anchor taskallows students to work on one task for an extended period of time.
Lesson 2We continued to see the emphasis on visualization through theuse of bar models in solving word problems. This lesson wasdone with a small group of Grade 3 students who have noexperience with Singapore Math. This session and the onesafter lunch focused on helping students who have difficultieswith reading word problems, representing complex situationsand doing computations. We also saw the use of the cut upword problems in doing differentiated instruction.
Lesson 2 June 18, 2012 Jack $3 Jack Kyla $2 Kyla gave more had than
Lesson 2 June 18, 2012 Open Lesson at Hawaii, USA
Lesson 2 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 2 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 3Question: How do we help students set up the model? Studentsare introduced to the idea of using a rectangle to representquantities – known and unknown. Paper strips are used. Later,only diagrams are used. Advanced skills like cutting andmoving are learned in Grades 4, 5 and 6. How is the idea of barmodel introduced in Grades K – 3? Listen out for this on Day 2.Lesson 3 show a basic bar model solution.
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.
Lessons 4 & 5We studied the strategies to help struggling readers as well asthose weak in representing problem situations.• Who is in the story? What is it all about?• Is the sentence easy?• Read a complex sentence as simple sentences.• Leave out numbers in reading
Lesson 4 June 18, 2012 In the end ... At first …Alice 20Betty 10Charmaine Dolly