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July 2014

Singapore Math Strategies National Conference Staff Development for Educators | Las Vegas

yeapbanhar@gmail.com | www.banhar.blogspot.com |

Course SE01 | The ABC’s of Singapore Math through Whole Numbers

The Singapore approach to teaching and learning mathematics was the result of

trying to find a way to help Singapore students who were mostly not performing

well prior to 1980’s.

The CPA Approach as well as the Spiral Approach are fundamental to teaching

mathematics in Singapore schools. The national standards, called syllabus in

Singapore, is designed based on Bruner’s idea of spiral curriculum. Textbooks are

written based on and teachers are trained to use the CPA Approach, based on

Bruner’s ideas of representations.

Using the tasks listed here and the observations you share during the session, we

learn some fundamentals of good mathematics instruction. These are also

elements of Singapore Math.

Task 1 |

Show 5 beans.

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Task 2 |

Use 3 tiles to make a shape.

Use 4 tiles to make a shape.

Use 5 tiles to make a shape.

Make different shapes using the same number of tiles.

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Task 3 |

Aaron has 8 cookies.

Beth has 6 cookies.

How many cookies do they have altogether?

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Task 4 |

400 – 189

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Task 5 |

David has 19 more rocks in his collection than Emily.

David has 51 rocks in his collection.

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Task 6 |

3 x 6

4 x 6

8 x 6

9 x 6

9 x 7

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Task 7 |

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Task 8 |

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Task 9 |

Frank has 10 coins more than Gary.

Together, they have 34 coins.

How many coins does Frank have?

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Task 10 |

At first, Frank had 10 coins more than Gary.

Then Gary gave Frank 6 coins.

Who had more coins in the end? How many more?

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Task 11 |

Compare these three lessons on division of whole numbers

Anchor Task A | Try putting 14 children into 3 equal groups.

Anchor Task B | Try putting 41 children into groups of threes.

Anchor Task C | Try putting 41 liters of water into 3 containers. Is it possible

to make sure each container contains the same amount of water?

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Task 12 |

There are three times as many boys as there are girls in the soccer club.

There are 96 children in the soccer club.

Is this possible?

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Task 13 |

Use 12 square tiles to make a rectangle or square.

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Task 14 |

Han arranged 110 squares and circles in a straight line. There are at least3 circles

between any 2 squares. What is the largest possible number of squares among

the 110 squares and circles?

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Task 15 |

Indra was packing a batch of cookies into some containers she had in her kitchen.

She tried to pack 11 cookies into each container but the last one contained only

6 cookies. When she packed 8 sweets into each container, there were 25 sweets

left over.

How many cookies were there altogether?

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“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

“I was struck by the fact that successful efforts to teach highly structured bodies

of knowledge like mathematics, physical sciences, and even the field of history

often took the form of metaphoric spiral in which at some simple level a set of

ideas or operations were introduced in a rather intuitive way and, once mastered

in that spirit, were then revisited and reconstrued in a more formal or operational

way, then being connected with other knowledge, the mastery at this stage then

being carried one step higher to a new level of formal or operational rigour and

to a broader level of abstraction and comprehensiveness. The end stage of this

process was eventual mastery of the connexity and structure of a large body of

knowledge.”

| Bruner 1975

Anchor Task | Bar Model | CPA Approach | Differentiation | Enrichment | Focus | Guided Practice |

Homework | Independent Practice | Journal | Kindergarten Math | Learning Theories | Mental Strategies

| Number Bonds | Operations | Problem Solving | Questioning | Remediation | Spiral Approach | Three-

Part Lesson Format | Visualization | Word Problems | ABC’s of Singapore Math |