The document discusses the Singapore approach to teaching mathematics, which was developed to help Singaporean students perform better in math. It is based on Bruner's ideas of a spiral curriculum and using representations. The document provides 15 sample math tasks that demonstrate fundamentals of Singapore Math instruction, such as the Concrete-Pictorial-Abstract approach. It also includes quotes from Bruner about revisiting basic ideas repeatedly to help students master structured bodies of knowledge.

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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 |