Seoul Foreign School Plenary Session
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Transcript of Seoul Foreign School Plenary Session
Dr Yeap Ban Har [email protected]
Marshall Cavendish Institute Singapore
Presentation slides are available at
www.banhar.blogspot.com
Professional Development Singapore Mathematics
Seoul 9 – 11 July 2012
www.mcinstitute.com.sg www.facebook.com/MCISingapore
MAP101
FUNDAMENTALS
of singapore
m a t h
Slides are available at
www.banhar.blogspot.com
Mayflo
wer P
rima
ry S
chool, S
inga
pore
Introduction
This course is an overview of Singapore
Math. It includes the what and how of
teaching mathematics.
Curriculum document is available at http://www.moe.gov.sg/
Singapore Ministry of Education 1997
THINKING SCHOOLS
LEARNING NATION
is singapore what
mathematics
key focus singapore
mathematics of
problem solving
thinking
excellent vehicle
an
for the development & improvement of a person’s intellectual
competencies Ministry of Education Singapore 2006
conceptual understanding
FUNDAMENTALS
of singapore
m a t h
Slides are available at
www.banhar.blogspot.com
Mayflo
wer P
rima
ry S
chool, S
inga
pore
Singapore Math
Visualization
110 g
290 g
110 g 180 g
Bella puts 180 g brown sugar on the dish.
110 g
290 g
110 g 180 g
2 units = 180 g
1 unit = 90 g
3 units = 270 g
Bella puts 270 g brown sugar on the dish.
on an identical dish
Singapore Math is based on the CPA Apporach.
Pictorial representations can be more concrete
(pictures) or more abstract (diagrams such as bar
model).
An alternate way to solve the brown sugar
problem:
Singapore Mathematics focuses on the ability to visualize. For example, bar models are used extensively.
Bar models were introduced to overcome the pervasive problems students had with word problems – even the basic ones.
Such word problems are used to help
students
Deal with information
Handle and clarify ambiguity – one
dish or two
Develop visualization – bar models
are used extensively
Practice mental strategies – numbers
used are not difficult to compute
Singapore Math
Visualization
Procedural & Conceptual
Understanding Singapore Math places an emphasis on
both. Procedures are explained in a
conceptual way. For example, long
division is seen simply as breaking
large numbers into smaller ones before
dividing.
Using number bonds to make
sense of long division
Over-emphasizing
procedural knowledge
Balancing procedural knowledge with conceptual understanding
Differentiated Instruction for advanced learners – how does one get the result
of 51 3 from 60 3.
Singapore Math
Patterns & Generalization
Task Extension for
Advanced Learners
C H E R Y L
C H E R Y L 1
C H E R Y L 2
C H E R Y L 3
C H E R Y L 4
C H E R Y L 5
C H E R Y L 6
C H E R Y L 7
C H E R Y L 8
C H E R Y L 9
C H E R Y L
C H E R Y L
C H E R Y L
C H E R Y L
C H E R Y L
C H E R Y L
Which letter is 99?
Method 1 The positions of 11, 22, 33 are at C, H, E respectively. Positions of multiples of 11 can be located.
Method 2 The positions of numbers ending with 1 and 6 can be located ta either ends. Thus 91 or 96 can be located. Subsequently, 99 can be located.
Method 3 Numbers ending with 9 are at E. So, 99 is at E too.
Method 4 The position for 99 can be found by writing out all the numbers but this is not efficient method.
D A V I D
Method 1 The letters under A and I are even. So 99 cannot be there.
Method 2 The positions of numbers ending with 9 form a diagonal pattern.
Method 3 The numbers under first D increases by 8. Thus 17 + 80 = 97 is under first D. The position for 99 can be worked out.
Method 4 The positions of multiples of 8 I is definitely under A. 8 x 12 = 96 is under A. The position of 99 can be worked out.
Method 5 Numbers under V is 1 less than multiples of 4. So, 2011 (1 less than 2012) is under V. 99 is less than 100.
Method 2 The positions of numbers ending with 9 form a diagonal pattern. The methods were the ones that participants in Chile came up with.
Another Method In a course done in December 2010 with a group of Chilean teachers, there was a method that involves division. For Cheryl, it was 99 10. For David, it was 99 8. Are you able to figure out that method?
Singapore Math
Patterns & Generalization
Singapore Mathematics: Focus on Problem Solving
CPA Approach based on Jerome Bruner was used to learn division of fractions – using paper folding and subsequent drawing.
Singapore Mathematics: Focus on Conceptual Understanding
Singapore Math
Learn New Concept Through
Problem Solving
Textbook Study
Observe the various meanings of
multiplication from Grade 1 to Grade
3.
Multiplication Facts
We do a case study on multiplication
facts. We will see the use of an anchor
task to engage students for an
extended period of time.
Strategy 1
Get 3 x 4 from 2 x 4
Strategy 2
Doubling
Strategy 3
Get 7 x 4 from 2 x 4 and 5 x 4
Strategy 4
Get 9 x 4 from 10 x 4
Strategy 1
Get 3 x 4 from 2 x 4
Strategy 3
Get 9 x 4 from 4 x 4 and 5 x 4
This is essentially the distributive
property. Do we introduce the
phrase at this point?
Strategy 2
Doubling
Strategy 4
Get 9 x 4 from 10 x 4
Unusual Response
Get 4 x 8 from 4 x 2. Can it be done? Does the number
of cups change? Does the number of counters per cup
change?
Differentiated Instruction
These are examples of how the lesson can be
differentiated for advanced learners.
Prior to learning multiplication, students
learn to make equal groups using concrete
materials. Marbles is the suggested
materials.
After that they represent these concrete
situations using, first, drawings ..
Open Lesson in Chile
… and, later, diagrams. Students also
write multiplication sentences in
conventional symbols.
First, equal groups –
three groups of four.
Second, array –
Three rows of four
Third, four multiplied three
times ….
Textbook Study
Observe how equal group
representation evolves into array and
area models. Also observe how the
multiplication tables of 3 and 6 are
related on the flights of stairs.
They begin with equal group representation.
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
In Primary 2, students learn
multiplication facts of 2, 5, 10 and 3
and 4. In Primary 3, they learn the
multiplication facts of 6, 7, 8 and 9.
Later, the array meaning of
multiplication is introduced.
Square tiles are subsequently used to lead to
the area representation of multiplication.
Open Lesson at Broomfield, Colorado
Students who were already good in the skill of multiplying two-digit number
with a single-digit number were asked to make observations. They were
asked “What do you notice? Are there some digits that cannot be used ta
all?”
Singapore Math
Drill-and-Practice Through
Problem Solving
Singapore Math
Three-Part Lesson
Singapore Math
Three-Part Lesson
Singapore Math
Three-Part Lesson
FUNDAMENTALS
of singapore
m a t h
Slides are available at
www.banhar.blogspot.com
Mayflo
wer P
rima
ry S
chool, S
inga
pore
The following slides are for additional
tasks that are discussed on the second
day for Grades 5 – 8
Marcus gave ¼ of his coin collection to his sister
and ½ of the remainder to his brother.
As a result, Marcus had 18 coins.
Find the number of coins in his collection at first.
3 units = 18
8 units = ???
Marcus had 48 coins at first.