mci in chile

Dr Yeap Ban [email protected]

Marshall Cavendish Institute Singapore

Presentation slides are available at www.banhar.blogspot.com

Seminario Internacional de EducaciónConocer el método Singapur

para la enseñanza de matemáticas

4 January 2012



8:30 a 9:00 Acreditación9:00 a 9:15 Inauguración: Presentación Dr. Ban Har9:15 a 10:30 Plenaria 1:

Teorías básicas en la enseñanza de matemáticas10:45 Preguntas11:00 a 11:30 Café11:30 a 13:00 Continuación Plenaria 113:00 a 14:00 Almuerzo14:00 a 16:00 Plenaria 2:

El modelo de las barras en la enseñanza de resolución de problemas

16:00 Café16:30 a 18:00 Continuación Plenaria 218:00 Cierre MAP101 & MAP111

What to teach in

mathematics so

that it is useful

to students. How to teach it

so that all

children can

learn it well.

is singaporewhat

mathematics

Singapore Mathematics: Focus on Thinking

excellentvehicle

an

for the development&improvement ofa person’s intellectual

competenciesMinistry of Education Singapore 2006

See Page 4

110 g

290 g

110 g180 g

Bella puts 180 g brown sugar on the dish.

110 g

290 g

110 g180 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

See also Page 70

There was a discussionabout the fact that thetotal weight isambiguous. In the casewhere we take the totalweight to be the total ofthe dish and Bella’ssugar, the solution is ashown in.

Singapore Mathematicsfocuses on the ability tovisualize. Forexample, bar models areused extensively.

Fundamental of Singapore Method

Singapore Mathematicsfocuses on the ability tohandle information.Hence the emphasis onword problems.

Singapore Math

Visualization

See Page 5

C H E R Y L

C H E R Y L1

C H E R Y L2

C H E R Y L3

C H E R Y L4

C H E R Y L5

C H E R Y L6

C H E R Y L7

C H E R Y L8

C H E R Y L9

C H E R Y L

C H E R Y L

Which letter is 99?

D A V I D

Methods

Method 1: Look at the ones digit. 99 has 9 as the ones digit. So it is at E.

Method 2: Use division. One method divides 99 by 6 but this was found to be a coincidence. Later, it was found that dividing by 10 works.Another method subtracts 6 before dividing by 10.

Method 3: Look at the first column – 1, 11, 21, 31, 41 – hence 101 is at C. 99 can then be found by working backwards.

Can the three methodsbe used for DAVID?

Two new methods weregiven for DAVID

Method 4See the pattern asDAVIDIVA. This is confirmby difference of 8between 1 and 9, 9 and17 etc.

Method 5Notice 4n – 1 (1 less thanmultiple of 4) under theletter V.

Singapore Mathematicsfocuses on the ability tosee patterns and makegeneralizations.


Singapore Math

Patterns & Generalization

Singapore Mathematics: Focus on Problem Solving

See Page 6

See Page 7

CPA Approach based on

Jerome Bruner was

used to learn division offractions – using paperfolding and subsequentdrawing.

See Page 10

Singapore Math

Learn New Concept Through

Problem Solving

How many 4s are there in 12? 12 ÷ 4 = 3

Dr Yeap Ban [email protected]

Marshall Cavendish Institute Singapore

Presentation slides are available at www.banhar.blogspot.com



4 January 2012

Singapore Mathematicsfocuses on the ability tovisualize. Forexample, bar models areused extensively.


What is the Bar Model Method?

Number of women

Number of men

Number of children

5 units = 601 units = 60 : 5 = 12

8 units = 8 x 12 = 80 + 16 = 96There are 96 people at the party.

Correction: In the Spanish coursebook, it should be “1/6 del resto sonhombres.”

Bar Model MethodIn Early Grades

Jack

Kyla

3 units = $3001 units = $300 : 3 = $100Kyla gets $100.

Correction: In the Spanish coursebook, it should be “el doble de Kyla”.

Larry

Maria

4 units = $3001 units = $300 : 4 = $753 units = 3 x $75 = $300 - $75 = $225Maria gets $225.

1st Number

2nd Number

58 + 12 = 70The larger number is 70.

12

What if the larger number is 58?

Then the smaller number is 58 – 12 = 46.

What if the sum of the numbers is 58?

58 – 12 = 4646 : 2 = 23Then the smaller number is 23 and the larger number is 23 + 12 = 35.

Peter

Natalia 12

58 – 12 = 4646 : 2 = 23

Peter’s bag weighs 23 kg.Natalia’s bag weighs 23 kg + 12 kg = 35 kg.

Basic Models include Part-Whole Model and Comparison Model

Mathematics to develop visualization through bar models, number sense

through mental calculation, and ability to manage information through word

problems.

1st Day

2nd Day 4

3rd Day 4 4

4th Day 4 4 4

5th Day 4 4 4 4

6th Day 4 4 4 4 4

7th Day 4 4 4 4 4 4

8th Day 4 4 4 4 4 4 4

250

1st Day

2nd Day 4

3rd Day 4 4

4th Day 4 4 4

5th Day 4 4 4 4

6th Day 4 4 4 4 4

7th Day 4 4 4 4 4 4

8th Day 4 4 4 4 4 4 4

250

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = ?

There are 45 fours.45 x 4 = 180

10 units = 250 – 180 = 7001 units = 70 : 10 = 7

She made (7 + 9 x 4) = 43 paper cranes on the last day.

Sam

Terry

Vanessa

72

Pablo

Wynn

Zena

100

?

Advanced Techniques

110

270

110

270

2 units = 160 g1 units = 160 g : 2 = 80 gThe container weighs 110 g – 80 g = 30 g

Using algebrax+ 3y = 270x + y = 110

So, 2y = 160y = 160 : 2 = 80x + y = 110So, x = 30The container weighs 30 g.

y y

y

110

x

270

yx

boys

girls

34

boys

girls

68

boys

girls

88 – 68 = 20

boys

girls

boys

girls

34

34 – 20

2 girls units = 14

1 girls unit = 7

3 girls units = 21

21 girls wear spectacles.

Homework

cookies cake 3,6 kg

cookies

cookies

cookies

basketball

soccer

basketball

soccer

Answer: 60

Answer: 100

basketball

soccer

Answer: 84