nspm summer training.pdf
TRANSCRIPT
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Singapore Mathematics Model Method
Rex Bookstore Inc.s NSPM
Summer Training Program
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REVISITING SINGAPORE PRIMARY MATHEMATICS CURRICULUM
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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.
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ScopeOverview of Singapore primary mathematics curriculum, and its unique features
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What is Singapore Mathematics?
The way students learn Mathematics and way teachers teach Mathematics in Singapore.
Revisiting Singapore Primary Mathematics Curriculum
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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.
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Derived from an education
system that focuses on thinking
(1997)
Thinking Schools,
Learning Nation
Revisiting Singapore Primary Mathematics Curriculum
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Make a triangle
that is green.
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Make a triangle
that is a third
green.
Revisiting Singapore Primary Mathematics Curriculum
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Move 3 sticks to make 3 squares.
Revisiting Singapore Primary Mathematics Curriculum
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Move 3 sticks to make 2 squares.
Revisiting Singapore Primary Mathematics Curriculum
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Move 3 sticks to make 2 squares.
Revisiting Singapore Primary Mathematics Curriculum
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Its outcomes centrally assessed
through public examinations.
Revisiting Singapore Primary Mathematics Curriculum
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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?
Revisiting Singapore Primary Mathematics Curriculum
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Problem
150 cm 19 cm x 5
= 150 cm 95 cm = 55
cm
55 cm of the copper wire was left.
Revisiting Singapore Primary Mathematics Curriculum
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Source
PSLE Mathematics Singapore Examination and Assessment Board
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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.
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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.
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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.
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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.
Revisiting Singapore Primary Mathematics Curriculum
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UNIQUE FEATURES SINGAPORE PRIMARY MATHEMATICS CURRICULUM
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Spiral Approach in Learning Mathematics
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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
Revisiting Singapore Primary Mathematics Curriculum
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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.
Revisiting Singapore Primary Mathematics Curriculum
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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
Revisiting Singapore Primary Mathematics Curriculum
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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
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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
Revisiting Singapore Primary Mathematics Curriculum
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Differentiated Syllabus
Revisiting Singapore Primary Mathematics Curriculum
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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
Revisiting Singapore Primary Mathematics Curriculum
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Algebraic Thinking
Revisiting Singapore Primary Mathematics Curriculum
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Revisiting Singapore Primary Mathematics Curriculum
Number Pattern
What is the missing number?
(a) _____, 17, 18, 19, _____, 21
(b) 2, 4, 6, _____, 10, 12, _____
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Revisiting Singapore Primary Mathematics Curriculum
Number Pattern
Complete the following number pattern?
(a) 6780, 6880, _____, _____, 7180
(b) 11, 10.95, 10.9, _____, 10.8, _____, 10.7
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Assessment
Revisiting Singapore Primary Mathematics Curriculum
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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
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Which is larger in
magnitude 5+n or
5n? Explain your
answer?
Revisiting Singapore Primary Mathematics Curriculum
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Revisiting Singapore Primary Mathematics Curriculum
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Other Unique Features of Primary Mathematics Curriculum
Teaching Approaches
Role of Information and Communication Technologies (ICT)
National Education
Model Method
Revisiting Singapore Primary Mathematics Curriculum
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Singapore Math is about thinking
and problem solving
Revisiting Singapore Primary Mathematics Curriculum
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Why Teach Mathematics?
Mathematics is an excellent vehicle to develop and improve
a persons intellectual competence.
Ministry of Education, Singapore 2006
Revisiting Singapore Primary Mathematics Curriculum
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Making the Average Student on
Top
Thinking-oriented Curriculum
Theoretically-sound Pedagogy
Assessment that is coherent with the
curriculum
Revisiting Singapore Primary Mathematics Curriculum
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Children are truly the future of our nation.
Irving Harris
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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.
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PROBLEM SOLVING
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Model Method
The ability to solve problems is at the heart of mathematics.
(Cockcroft Report, 1982)
Mathematical Problem Solving
Concepts
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Heuristics
Polyas How to Solve It 4-phased Process
1. See
2. Plan
3. Do
4. Check
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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
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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?
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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
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MODEL METHOD
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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
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Part-Whole Model (Addition and Subtraction)
part part
whole
part + part = whole
whole part = part
Model Method
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Model Method
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Model Method
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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?
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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
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8
3
48 children went to the zoo. of
them were girls. How many were
boys?
Model Method
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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
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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?
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larger quantity smaller quantity = difference
smaller quantity + difference = larger quantity
larger quantity - difference = smaller quantity
Comparison Model
Model Method
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Comparison Model(Multiplication and
Division)
larger quantity smaller quantity = multiple
smaller quantity multiple = larger quantity
larger quantity multiple = smaller quantity
Model Method
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Model Method
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Model Method
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Model Method
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John sold three times as many
computers as Bob. They sold 48
computers altogether. How many
computers did Bob sell?
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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?
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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.
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Before-after Model
Model Method
Shows the relationships between thenew value of a quantity and its originalvalue after an increase or decrease.
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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?
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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?
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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?
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Model method is a synthetic-analytic process.
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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.
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Model Method and Algebra
Concrete
Pictorial
Abstract
Model Method
Algebraic Equation
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Model Method and Algebra
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.
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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.
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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)
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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.
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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
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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)
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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
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inculcate and strengthen intellectualqualities such as independent learning, thinking and inquiry; critical thinking, creative problem solving, intellectual
curiosity, skepticism, informal judgmentand articulateness.
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An EDUCATOR is a TEACHER, but NOT ALL TEACHERS are EDUCATORS
(Wang, 2001)
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THANK YOU VERY MUCH!