NSPM Summer Training.pdf

Singapore Mathematics Model Method

Rex Bookstore Inc.s NSPM

Summer Training Program

REVISITING SINGAPORE PRIMARY MATHEMATICS CURRICULUM

Knowledge Rating Chart

Encircle the number that represents your learning experience on spiral approach.

1. Ive never heard of this before.

2. Ive heard of this, but am not sure how it works.

3. I know about this and how to use it.

ScopeOverview of Singapore primary mathematics curriculum, and its unique features

What is Singapore Mathematics?

The way students learn Mathematics and way teachers teach Mathematics in Singapore.

Revisiting Singapore Primary Mathematics Curriculum


Singapore mathematics curriculum

has its focus mathematical

problem solving and it is set within an education system that

emphasizes thinking.

Derived from an education

system that focuses on thinking

(1997)

Thinking Schools,

Learning Nation


Make a triangle

that is green.

Make a triangle

that is a third

green.


Move 3 sticks to make 3 squares.


Move 3 sticks to make 2 squares.


Its outcomes centrally assessed

through public examinations.


Problem

John had 1.5 m of copper

wire. He cut some of the

wire to bend into the

shape shown in the

figure below. In the

figure, there are 6

equilateral triangles and

the length of XY is 19 cm.

How much of the copper

wire was left?


Problem

150 cm 19 cm x 5

= 150 cm 95 cm = 55

cm

55 cm of the copper wire was left.


Source

PSLE Mathematics Singapore Examination and Assessment Board

In the diagram below,

ABCD is a square and

QM = QP = QN. MN is

parallel to AB and it is

perpendicular to PQ.

Find MPN.

UNIQUE FEATURES SINGAPORE PRIMARY MATHEMATICS CURRICULUM

Spiral Approach in Learning Mathematics

Singapore Mathematics Curriculum: Spiral Curriculum

The topics are

arranged in a way that

makes learning

progressive and

systematic this is part

of the idea of a spiral curriculum

Spiral Approach in Learning Mathematics:

Bruners Theory


In the learning from one lesson to the next lesson there

will be an increase in the level ofabstractness and complexity of theone mathematical idea, including an increase informality of the notation system is used.


Level Ideas of fractions

P2: Equal parts of a whole

What fraction of the circle is shaded?

P4: Equal subsets of a set

Shade of the smiley faces.

P5: Fraction as division 3 pizzas were shared equally among 4 friends. What fraction of the pizza did each person eat?

P6: Relationship between fractions and ratios

John, Keith and Hans collected some cards in the ratio of 2: 3: 4. What fraction of the cards belongs to Hans?

Ideas of fractions and the primary level at which they are introduced


While Count On and Count

All are used in Numbers to

10, Make Ten is given

emphasis in Numbers to 20.

Addition Facts & Number Sense

.

Spiral Within GradeGrade 2 Lesson 1: 347 + 129 Lesson 2: 182 + 93 Lesson 3: 278 + 86

Spiral Between Grade Grade 1 Adding up to 100 Grade 2 Adding up to 1000 Grade 3 Adding up to 10000


Differentiated Syllabus


Levels Number of Hours Per Week

Common Syllabus:

P1 3.5

P2 4.5

P3 and P4 5.5

Differentiated Syllabus (P5 & P6)

Standard Mathematics 5

Foundation Mathematics 6.5

Curriculum time according to levels and streams

Overall curriculum time across subjects average 24 hours per week1 period = 30 minutes


Algebraic Thinking



Number Pattern

What is the missing number?

(a) _____, 17, 18, 19, _____, 21

(b) 2, 4, 6, _____, 10, 12, _____


Number Pattern

Complete the following number pattern?

(a) 6780, 6880, _____, _____, 7180

(b) 11, 10.95, 10.9, _____, 10.8, _____, 10.7

Assessment


The Singapore mathematics curriculum calls for thefollowing to be incorporated into assessment wheneverand wherever appropriate:

Mental Calculations

Mathematical Communication

Practical Application of Mathematics

Investigations and Problem Solving

Application of ICTRevisiting Singapore Primary Mathematics Curriculum

Which is larger in

magnitude 5+n or

5n? Explain your

answer?


Other Unique Features of Primary Mathematics Curriculum

Teaching Approaches

Role of Information and Communication Technologies (ICT)

National Education

Model Method


Singapore Math is about thinking

and problem solving


Why Teach Mathematics?

Mathematics is an excellent vehicle to develop and improve

a persons intellectual competence.

Ministry of Education, Singapore 2006


Making the Average Student on

Top

Thinking-oriented Curriculum

Theoretically-sound Pedagogy

Assessment that is coherent with the

curriculum


Children are truly the future of our nation.

Irving Harris

Salute!One person acts as a captainand deals one card to eachplayer. Without looking at thecard, players hold the card upto their foreheads and saysalute.

The captain says the sum,difference or product of thetwo cards. The player to guessthe number on their card firstwins both cards. The playerwith the most cards at the endof the session or deck wins.

PROBLEM SOLVING

Model Method

The ability to solve problems is at the heart of mathematics.

(Cockcroft Report, 1982)

Mathematical Problem Solving

Concepts

Heuristics

Polyas How to Solve It 4-phased Process

1. See

2. Plan

3. Do

4. Check

Problem Solving Strategies

Draw a diagram or picture

Make a systematic list

Look for patterns

Guess and Check

Simplify the problem

Work backwards

Model Method

Farmer Ting was counting his ducks and sheep. He counted 10 heads and 26 feet altogether. How many ducks and sheep does he have?

HOW MANY DIFFERENT STRATEGIES ARE THERE TO SOLVE THIS PROBLEM?

Experiences in problem solving should consist

of solving different problems by the same

strategy as well as the application of different

strategies to the same problem

MODEL METHOD

Model Method

Model Method stem from the use of real objects to model or represent situations in story problems.

Part-Whole Model

Comparison Model

Before-After Model

Part-Whole Model (Addition and Subtraction)

part part

whole

part + part = whole

whole part = part

Model Method

Model Method

Model Method

John bought some candies. He ate

half of them and gave 5 candies to his

best friend. Then he had 7 candies

left. How many candies did John buy?

The Part-Whole Model(Multiplication and

Division)

one part number of parts = whole

whole number of parts = one part

whole one part = number of partsModel Method

8

3

48 children went to the zoo. of

them were girls. How many were

boys?

Model Method

5

3of the beads in a box are yellow

beads. The rest are red beads and

blue beads. There are twice as many

yellow beads as red beads. There are

30 more red beads than blue beads.

Find the total number of yellow beads

and red beads.

Model Method

6 bottles of water can fill 4/7 of a

container. Another 3 bottles and 5

cups of water are needed to fill the

container completely. How many

cups of water can the container

hold?

larger quantity smaller quantity = difference

smaller quantity + difference = larger quantity

larger quantity - difference = smaller quantity

Comparison Model

Model Method

Comparison Model(Multiplication and

Division)

larger quantity smaller quantity = multiple

smaller quantity multiple = larger quantity

larger quantity multiple = smaller quantity

Model Method

Model Method

John sold three times as many

computers as Bob. They sold 48

computers altogether. How many

computers did Bob sell?

Peter collected a total of 1170

stamps. He collected 4 times as

many as Philippine stamps as

foreign stamps. How many

Philippine stamps he collected?

Two staples, two pens and a pencil

box cost P33.60. A pen cost twice as

much as a staple. A pencil box costs

P8 more than a pen. Find the cost of

a pencil.

Before-after Model

Model Method

Shows the relationships between thenew value of a quantity and its originalvalue after an increase or decrease.

A box of sweet was shared between

Milly and Sally in the ratio 3:2. After

Milly gave of her share to Sally,

Sally had 20 sweets more than Milly.

How many sweets did Milly give to

Sally?

Mike had 3 times as much money as

Gerard. After Mike had spent P60

and Gerard had spent P10, they

each had an equal amount of money

left. How much money did Mike

have at first?

A factory had 1200 workers. 40% of

them were males. Some new males

were employed until the total

number of males had increased to

70% of the total workforce. How

many new male workers were

employed?

Model method is a synthetic-analytic process.

Model Method and Algebra

Two aspects of the primary school mathematics curriculum that facilitate algebraic thinking

1. The use of model method in solving word problems

2. The inclusion of pattern recognition.


Concrete

Pictorial

Abstract

Model Method

Algebraic Equation


Problem Using Model

Method

Using Algebraic Equations

Mr. Viri is four timesas old as his son. Tenyears ago, the sum oftheir ages was 60.Find their presentage.

There are 50 children in a dance group. If

there are 10 more boys than girls, how

many girls are there?

Show different variations depicting the integration of Model Method and Algebra.

Conclusion

The integration of model drawing

method and algebraic method provides

an enriching opportunity for students to

engage in construction and interpretation

of algebraic equations through

meaningful and active learning. (Yeap,

2009)

Four Reasons Why Use the Model Method (Kho, 1987)

It help students gain a better insight into mathematical concepts such as fraction, ratio, and percentage.

It helps the pupil plan for solution for solving an arithmetic problem.

Four Reasons Why Use the Model Method (Kho, 1987)

It is comparable to, but is less abstract than, the algebraic method.

It can stimulate the pupils to solve challenging problems

The education system of Singapore isdynamic and constantly evolving. Initiativesand policies are guided by researchevidence, scans of other systems in the worldand careful deliberations of leaders ineducation. Whatever the new initiatives orpolicy may be the one thing that always keepthe house in order is the TEACHER.Therefore it is vital that the development ofteachers keep abreast of changes in thesystem.

(Kaur, 2011)

A teacher is one who helps students to learn something and an educator is

one who helps students more educated. To be an educator the

teacher must possess the ability to

inculcate and strengthen intellectualqualities such as independent learning, thinking and inquiry; critical thinking, creative problem solving, intellectual

curiosity, skepticism, informal judgmentand articulateness.

An EDUCATOR is a TEACHER, but NOT ALL TEACHERS are EDUCATORS

(Wang, 2001)

THANK YOU VERY MUCH!

NSPM Summer Training.pdf

Documents

Transcript of NSPM Summer Training.pdf