I.C.A.N.

Improving Confidence and Achievement in Numeracy

for 2015 Parents Symposium

Presented by Mrs Pauline Ng (School Math Mentor, Yu Neng Primary School)

Core Belief

All students can ______

Learning Issues

Learning gaps, language,

motivation and ________

learn

retention

Making the Case Focus on number sense!

Research indicates that early number sense predicts school success more than other

measures of cognition like verbal, spatial or

memory skills or reading ability.

Jordoan, Kaplan, Locuniak, and Ramineni,

2007

Number sense:

Ability to use numbers, appreciation of numbers

(knowledgeable about what a number means) and

number relationship

Factual Fluency

Ability to recall the answers to basic math facts

automatically and without hesitation.

Achieve mastery in

Primary 1

Basic addition and subtraction facts within 20

Primary 2

Multiplication and division facts (within multiplication tables of 2, 3, 4, 5 & 10)

Primary 3

Multiplication and division facts (within multiplication tables of 6, 7, 8 & 9)

Factual Fluency Targets

Factual Fluency makes it easier

to learn Math

Developmental Nature of Basic Fact Mastery

Counting Reasoning Mastery

Phase 1:

Counting strategies-

using concrete objects

Counting up

Counting down

Example includes:

5 + 1 = ?

5 + 2 = ?

5 1 = ?

5 2 = ?

Counting Strategies

Phase 2:

Reasoning Strategy:

using known information to logically determine an unknown combination

4 + 7 =?

5 x 8 is 40

Reasoning Strategy

Phase 3:

Producing answers efficiently

- Use strategy learnt to provide the correct answer within 5 seconds

e.g. 4 + 7 = 11

Mastery

Knowing Facts from Memory-

Passive Storage View

Thinking that students will learn

their facts if they just practise

enough

What does this mean

Learning isolated number facts

Memorizing many facts

Keep practising to memorize

Effects of not knowing number facts fluently

Lack of basic fact automaticity has been associated with

Limited participation in math class discussions

Unsuccessful problem solving

Weak development of skills in multiple-digit addition and subtraction, long division and fractions

Misapplication of facts and providing unreasonable answers

Inflexible thinking skills

Learning Facts: Addition

Addition

How many strategies?

Addition

Count On

Use Doubles

Bridge to 10

6 x 5 = 30

30 + 6 + 6 = 42

(Connection of Ideas)

Significance (Meaning)

Multiplication as

repeated addition

Commutative

Property of

multiplication:

the two

numbers can

be multiplied in

either order.

(equivalence)

Spiral nature of Learning Multiplication

Concrete-Pictorial-Abstract Approach

Multiple Representations

4 x 6 = ?

4 groups

of 6 cubes

4 rows

of 6 boxes

4 pots of 6 flowers each

More examples of Multiple Representations

13 x 3 = ?

(3 groups of 13 ones)

(3 rows of 13 boxes)

Place Value

Sharing Tip:

1. String 10 buttons together to represent 1 ten.

2. Egg cartons which are available in 10s or 30s may also be used.

Give Examples and Non examples

Communicate, Reason and Reflect

form relationships

make connections

integrate learning

Probe understanding and stimulate thinking

How do you know?

Why is it so?,

Explain how you..

Can you give me an example?

Promote Reasoning 16 x 5 = ?

Scaffold Learning

Mary has five stickers. Ali has three times as many stickers as Mary.

Pictorial

Use of Model:

actual number

Concrete

Use of cubes

Pictorial

Use of Model:

representation

Suggest Activiites to Achieve Factual Fluency in

Multiplication Facts

Please see notes provided.

How to teach Multiplication using cubes

REGROUP

the ones

23 x 4 = ?

4 groups of 23 (use cubes)

9 tens and 2 ones

92

Ways to Connect Conceptual Knowledge with

Procedure Knowledge

23 x 4 = ?

3 x 4 = ?

20 x 4 = ? ?

23

3 20

Thank you for your kind attention

Question & Answer Session