moanalua complex - hawaii

Hawaii Publ ic Schools Moanalua Complex Area

Dr. Yeap Ban Har Marshall Cavendish Institute

Singapore

[email protected]

Slides are available at

www.banhar.blogspot.com

www.facebook.com/MCISingapore

Marshall Cavendish Institute www.mcinstitute.com.sg

P r o f e s s i o n a l D e v e l o p m e n t o n S i n g a p o r e M a t h

Teaching Through Problem Solving

Assessing

Differentiating

Remediation

Enrichment

Acceleration

www.banhar.blogspot.com

www.facebook.com/MCISingapore

This seminar focuses on issues on pacing and differentiated

instruction. Assessment and teaching through problem solving are

secondary themes in this customized course.

This professional development is equivalent to MAP114

Differentiated Instruction in Primary Mathematics incorporating

Enrichment and Remediation in Primary Mathematics.

Improving Low Student Achievement

“Upon separation from Malaysia in 1965, Singapore

was faced with … high levels of unemployment and

poverty. 70% of Singapore’s households lived in badly

overcrowded conditions, and a third of its people

squatted in slums on the city fringes. Unemployment

averaged 14%, GDP per capita was less than $2,700,

and half of the population was illiterate. “

| Hanusek, Jamison, Jamison & Woessmann 2008

Score 1960-1970s 1980s 1990s 2000s

500’s Japan Hong Kong Japan Korea

Hong Kong Japan Korea

Singapore


Singapore

400’s Thailand Philippines Singapore Thailand

Malaysia Thailand

Malaysia Thailand

300’s Indonesia Philippines

Indonesia Philippines

Country

GDP per capita in

current USD

2012

Singapore 60,800

Malaysia 16,800

Thailand 9,500

Indonesia 4,900

Philippines 4,400

Source | IMF


Score 1960-1970s 1980s 1990s 2000s

500’s Japan Hong Kong Japan Korea


Singapore


Singapore

400’s Thailand Philippines Singapore Thailand

Malaysia Thailand

Malaysia Thailand

300’s Indonesia Philippines

Indonesia Philippines

| PISA 2012

Country % of Low Performers

% of High Performers

Mean

Singapore 8.3 40.0 573

Vietnam 14.2 13.3 511

Thailand 49.7 2.6 427

Malaysia 51.8 1.3 421

Indonesia 75.7 0.3 375

OECD 23.1 12.6 494

| PISA 2012

Country % of Low Performers

% of High Performers

Mean

Shanghai 3.8 55.4 613

Singapore 8.3 40.0 573

Hong Kong 8.5 33.7 561

South Korea 9.1 30.9 554

Japan 11.1 23.7 536

Finland 12.3 15.3 519

OECD 23.1 12.6 494

What is Essential in Mathematics Literacy What should students be learning in mathematics and what are the implications for classroom practices?

What is Essential in Mathematics Literacy What should students be learning in mathematics and what are the implications for classroom practices?

communication

metacognition

number sense

visualization

patterns

What is Essential in Mathematics Literacy Let’s look at what international assessment (PISA) for 15-year-olds and Smarter Balanced Assessment for Hawaii State test suggest.

Source | PISA2012

| Smarter Balanced Assessment

What is Basics? The state standards (in this case Common Core State Standards) outline what the basics are. In the next three examples, the standards suggest that (Kindergarten) knowing that 12 is 10 and 2 is basic, (Grade 5) being able to add and subtract mixed numbers with different denominators is basic and (High School Algebra) being able to solve simple equations is basic.

| Common Core State Standards

What Does Teaching for Relational / Conceptual Understand Look Like?

Teaching for Meaning Making

Concrete Materials

Students are given

bags of 6 beans

each

Anchor Task

How many beans in

4 such bags?

Students Talking

Multiple Responses

Count all

Repeated addition

Multiplication

Board Writing

Student Journal

Meaning Making

4 x 6 is the same as 4 bags of

6 beans. Also linking new

materials (multiplication) to old

materials (addition).


How do I know if I

have taught in a

meaningful way?

• Link to previous

knowledge

• Link to a

concrete

scenario

• Students can

extend their

thinking.


Use of Textbooks

Suggest the kind of

anticipated

responses (add

another six, double,

associative

property and

subtraction

strategy)

As a reflection tool

for students at the

end of the

discussion (“Let’s see

how they do it.”)

Four Critical Questions in Planning Lesson

What do I want students to learn

How do I know they have learned it

What if

they cannot learn it

they already learned it

| DuFour 2004

What’s My Anchor Task?

Anticipated Responses

Differentiating

Remediation

Enrichment

Acceleration

What’s My Anchor Task?

the anchor task is modified

Ming made 4 trays of Christmas cookies.

There were 24 cookies on each tray.

anticipated responses

Level Response

Low • Count all

Average • 24 + 24 + 24 + 24

• 4 x 20 + 4 x 4

High • Use 4 x 25

• Use doubling strategy

The changes are not structural but

superficial to make the context

current (Christmas) and relevant

(rolls of films, seriously?)

4 and 24 allows advanced learners

to use 4 x 25 to do 4 x 24.

Another differentiated

strategy for advanced learners

is to ask students to pose

another word problem for 4 x

24

Struggling learners

may use repeated

addition.

Alternatively they

should be able to

figure out 4 x 4 and

20 x 4.

Use of concrete

materials helps

them.

4 allows advanced learners to use

doubling strategy (mental strategy). advanced learners

struggling learners

Anchor Task

Make a play zoo using some animal

figurines. Talk about the animals. “There

are five ducks. Four ducks in the pond and

one not in the pond.” “Two big lions and

three small ones make five lions.” “Three

blue birds and four red ones make seven

birds.” Do the same with the animals on this

page.

Anticipated Responses

Expected

Find total by counting all.

Exceeded

Find total by counting on.

Find total using other sophisticated methods.

Find total suing number facts

For Advanced Learners

Is there another way to find the total

number of ducks? Can you write it down?

Five parrots and four cats is …?

For Struggling Learners

They may need to see how it is done

through teacher modeling or peer

modeling.

Differentiating for Struggling Learners


351 is renamed as 300 + 30 + 21 before

the partial division is done. This helps

students who lack metacognition and cannot

manage switching between renaming and

dividing in the standard algorithm.

Differentiating for Struggling Learners


Using childlike, informal

representation instead

of the long division

format.

Three Part Lesson

Anchor Task

Three-Part Lesson Anchor Task Guided Practice Independent Practice

Do you recall why the denominator was spelt out?

Do you recall what are some strategies to differentiate

instruction both struggling as well as advanced

learners?

Do you recall how word problems were read to help

students develop metacognition?

moanalua complex - hawaii

Education