01 – 12 - 2003 project: catering for individual differences— building on variation cid(v)...

01 – 12 - 2003

Project:

Catering for Individual Differences—Building on

Variation

CID(v)

2000-2003

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Members

Tripartite collaboration

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Consultant: Prof. Ference MARTON

Principal Investigators:

Dr. LO Mun Ling, HKIEd Dr. PONG Wing Yan, HKU

Co-investigators (in alphabetical order):

Dr. KO Po Yuk, HKIEd

Dr. LEUNG Yuk Lun, HKU

Ms. LO-FU Yin Wah Priscilla, HKIEd

Ms. NG Fung Ping, HKU

Dr. PANG Ming Fai, HKU

Research Team

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S.R.B.A.C. Ho Sau Ki School

St. Edward’s Catholic Primary School

Partnership schools

Curriculum Development Institute

Attachment officers

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1. Our view of “Catering for Individual Differences”

2. Project goal

3. Methodology

4. Results & Impact

5. Conclusion

5. Insights & Recommendations

Outline

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Our view of

“Catering for Individual differences”

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Trying to reduce the variation in

learning outcomes of pupils in what they

are supposed to learn, instead of to

reduce the variation in abilities.

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Learning is always the learning of

“something”.

Objects of LearningObjects of Learning

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What does it take to learn certain

object of learning?

To see the object of learning in new and

meaningful ways such that knowledge

acquired can be applied appropriately to

new situations and to illuminate new

phenomena.

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Pupils’ different ways of seeing the

object of learning will result in their

different learning outcomes.

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Why pupils fail to learn in school?

Due to incomplete ways of seeing that

they have acquired of the object of

learning, instead of their lack of ability.

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a) Some children bring with them intuitive

ways of seeing which become obstacles for

new ways of seeing as the two may be in

conflict.

What contributes to pupils’ incomplete

ways of seeing?

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Example 1:

T: Guess what happens to the short

hand when the long hand moves?

S: The short hand will jump

from one number to the

next after the long hand

moves a round.

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b) Some children fail to focus on the critical

aspects of what is to be learnt.

What contributes to pupils’ incomplete

ways of seeing?

c) Some children have not been exposed

to suitable learning experiences that

make it possible for them to learn.

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已

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已巳

己已

巳

己

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What are the critical conditions of catering for individual differences?

a) Defining the object of learning

Is the teaching of this object of learning worthwhile?

How is it related to the goal of education?

What are the difficulties that pupils will encounter when learning it?

What must they have learnt before they can acquire this particular concept/skill?

How is it related to the rest of the topic that have been taught or will be taught later in the year?

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The idea of “Building blocks”

Pupil A Pupil B

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Rotation & Revolution自轉、公轉

Rotation & Revolution自轉、公轉

Sun 太陽

Earth 地球 Moon 月球

Solar eclipse 日蝕

Seasons 四季 Lunar eclipse

月蝕

Moon waning月虧

Moon waxing 月盈

Tides 潮汐

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S1: … whether there could be 12 solar eclipses in a year. I think it is possible f

or the Moon to pass between the Sun and the Earth once a month, since it revol

ves around the Sun. Although the Moon's orbit is tilted by 5 degrees, it is possib

le for a partial eclipse of the Sun to occur. Even the umbra or the penumbra is

on the sea, we can still see it. …But it is stated on the website that solar eclipse

only occurs twice a year, and I am not convinced.

S2: But I think there should not be as many as 12 solar eclipses in a year. ...

If the Moon were to pass through the same location every time it revolves, …

say, on August 15 of the lunar calendar…it would be covered by the Earth,

no Full Moon would happen. …The Moon should revolve like this, and

sometimes, it has not yet arrived at that location, but this one. So, there

should not be as many as 12 solar eclipses.

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S3: Usually, I will not think of questions like “Is it possible for these tw

o phenomena to happen at the same place?” Like what Ms. Kwong has

raised just now, “Can we have Solar eclipse and Full Moon in the same

day?” Very often, I will not consider both at the same time. Today, I rec

ognized that it is impossible [for them to happen at the same time].

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The “same learning outcomes” mean

those important “building blocks” for

pupils to progress in schools.

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b) Identifying critical features of the object of learning

What causes pupils’ difficulties?

Where are the learning gaps?

What are the important aspects that pupils fail to attend to?

14/8 or 14/16 ?

What are the critical conditions of catering for individual differences?

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Q： Have you ever taken out a can of coke from the refrigerator? What happens on its surface?

A： There are some water droplets on its surface.

Q：Where do these water droplets come from?

A： They come from the refrigerator.

Q： You mean they are brought out from the refrigerator?

（ Pupil nodded）

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A: Ms. Wong said that water will leak out from the bag of ice when there is w

ater vapour. It really did. …

Q: Will water leak out from the bag of ice? But it was in a plastic bag!

A: … It’s like my bottle of drink I brought this morning, it was cold, and it al

so leaked.

Q: Let me ask you a question: Is there water vapour here?

A: No… Yes.

Q: Why did you say “No” in the first place?

A: Because I remembered what Ms. Wong said.

Q: Don’t try to memorise. Think on your own. …Is there water vapour in air?

A: No…. I can see none. …

Q: Now, let me ask you again. Is there… water vapour? … What do you think?

A: (Shaking head) No.

Q: You say “NO”. Why?

A: Water vapour will disappear, and will change back to air.

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A: Actually, there is no water in air, but it is transformed from water.

Q: What do you mean by “air being transformed from water” ? Do you mean water

transforming into oxygen, carbon dioxide that we breathe in?

A: Not carbon dioxide… Q: How about oxygen?

A: It’s possible… Actually, there is hydrogen in air. Hydrogen rises up to the sky,

they hit each other and turn into water. Water gathers to form a cloud and falls

down when it becomes too large a cloud …

Q: …Then, is there water vapour in air? A1: Yes.

A ： “ Yes” and “No”. …Because if water is present everywhere in air, we will be dr

own. Water and air cannot mix…

Q ： … But the teacher just said that there is water vapour in air, and you believe it!

A: Actually, … why isn’t there water in planets with no air? Why do we have water si

nce we have air? …

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The role of the teacher in catering for

individual differences is thus to consci

ously structure learning experiences th

at help pupils to discern the critical fea

tures identified for the object of learnin

g.

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Pong and Morris (2002)

The crux in having an impact on pupil

learning actually lies in how teachers

make specific content of learning available

to pupils.

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Marton and Tsui (In press)

What the teachers focused on, what aspects

were being varied and what aspects were

being kept invariant could either constrain

learning or make learning possible.

It is more likely that pupils learn when it is

possible for them to learn, than when it is not.

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Gu (1991) after observing hundreds of class

rooms in the Shanghai area for many years, a

rrived at the empirical conclusion that good cl

assroom practices are characterized by partic

ular patterns of variation in dealing with the o

bjects of learning.

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Goals of Education

Objectives

Critical Feature 1Critical

Feature 1Critical

Feature 2

Pattern of variation Pattern of variation

Strategy 1 Strategy 1, 2, 3

Object of Learning 1 Object of Learning 2

DiscernmentDiscernment

(Theory of (Theory of Learning and Learning and Awareness)Awareness)

Outcomes Outcomes

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Project Goal

We aimed at helping every child to learn what is

worthwhile, essential and reasonable for them to

learn in the school curriculum so that they can

proceed in schooling.

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Methodology

Learning Study

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What is Learning Study?

“Learning Study” draws its inspiration from the

systematic and intensive investigation by Japanese

and Chinese teachers into particular lessons

—“research lessons”.

It is a systematic process of enquiry into teaching

and learning, employing action research

methodology.

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The primary focus is on an object of learning,

not teaching methods.

It differs from a “Lesson Study” as described

by Stigler and Hiebert (1999): It is

theoretically grounded.

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Theoretical framework

The theoretical framework of variation is

used to achieve the object of learning.

It is guided by three types of variation.

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V1: Variation in pupils’ ways of seeing the object of learning

V2: Variation in teachers’ ways of dealing with the object of learning

V3: Variation as a pedagogical tool

Three types of variation

Conscious effort in creating patterns of variation—varying

certain aspects of the object of learning while keeping the

others invariant, to highlight its critical features.

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1) Choosing and defining the object of learning

Main steps in a Learning Study:

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2) Ascertaining pupils’ prior knowledge and understanding of the object of learning

Pre-lesson interviews

Pre-test

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3) Planning and implementing the research lessons with using variation as pedagogical tool

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4) Evaluating the lessons

Post-lesson interviews

Post-test

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Pre-test and Post-test are parallel in design,

where appropriate assessment items are use

d.

Pre-test is used to collect useful information

on pupils’ difficulties, for lesson planning.

Post-test is used to feedback on how well the

plan was implemented and how it could be

improved.

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5) Reporting and disseminating the results

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Is it feasible to use Learning Study which is

premised on the three types of variation to help

catering for individual differences in mainstream

schools?

Main research question:

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1) Can worthwhile objects of learning that serve as foundations to pupils’ learning be identified?

2) Can critical features of these intended objects of learning be found?

3) Can teachers make use of pattern(s) of variation to help pupils of different abilities to grasp the critical feature(s) identified for their learning of a particular object of learning?

4) Are the participating teachers empowered to cater for individual differences using the three types of variation through engaging in Learning Studies?

Specific research questions:

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Data collection and analysis:

1. Learning Studies

A total of 29 Learning Studies were carried out in the subjects of Mathematics (14), Chinese language (11), General Studies (3), and English language (1), resulting in 29 research lessons.

Data collected: audio recordings and notes of the regular meetings, the lesson plans and video recordings of the research lessons, and the pre- and post-test papers completed by pupils, and/or recordings of pupil interviews.

Data analysis: A case study was built from the data collected in each Learning Study to draw insights on and to address the research question.

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2. Teacher interviews

Data collected: audio recordings and the subsequent transcription of each teacher interview.

Data analysis: a source for triangulation with the data collected in each Learning Study.

Year 01/02 Year 02/03

Number of individual interviews conducted

37 31

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3. Additional sources

Data collected:

i. the written feedbacks by some of the participating teachers, the school principals and the representative of CDI; and

ii. the results of the Hong Kong Attainment Test in Chinese Language and Mathematics at Primary 4, 5 and 6 in the `academic year of 2000/2001, 2001/2002 and 2002/2003 respectively to be provided by the ID evaluation team.

Data analysis: a source for triangulation with the data collected.

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Results & Impact

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Three phases of the project: Phase 1 : Exploration and preparation, 2000-2001

Setting up an infrastructure to facilitate the project’s implementation

Phase 2: Development and consolidation, 2001-2002

Enhancing teachers’ capability in running Learning Study cycles

Phase 3: Capacity building and preparation for withdrawal, 2002-2003

Building capacity of the leaders so that Learning Study can take root in the schools

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1) Can worthwhile objects of learning that serve as

foundations to pupils’ learning be identified?

2) Can critical features of these intended objects of

learning be found?

Main Results:

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Example 1: P.2 Mathematics

Textbook: Six types of Quadrilaterals

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Object of learning: Features of a rectangle Vs parallelogram

Critical Features:

1. 4 angles are equal in a rectangle; and

2. 2 pairs of opposite angles are equal in a parallelogram.

AWhat is/are the opposite angle(s) of Angle A?

What was found to be most difficult for pupils?

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Example 2: P.3 The colour of light

Textbook:

1. A rainbow consists of 7 colours (red, orange, yellow,

green, blue, indigo and violet ).

2. The 7 colours can be focused to form white light

(sunlight).

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Example 2: P.3 General Studies What was found to be most difficult for pupils?

Object of learning: Conceptual understanding of the relationship

between white light (or sunlight) and the colours of a rainbow

Critical Features:

The prism is only a tool used to split up the white light.

There is a direct relationship between white light and the rainbow.

Prism Magnifying glass

ｘLight

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3) Can teachers make use of pattern(s) of variation

to help pupils of different abilities to grasp the

critical feature(s) identified for their learning of

a particular object of learning?

Main Results:

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Example 1: P.3 General Studies

Soap bubbles

A Prism

Spraying water

Invariant

Varying

The prism is only a tool used to split up the white light.

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There is a direct relationship between white light and the rainbow.

Tools

Varying

Invariant


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(1) When white light passes through a prism, what can be seen?(1) When white light passes through a prism, what can be seen?

(2) When a spectrum passes through a magnifying glass, what (2) When a spectrum passes through a magnifying glass, what

can be seen?can be seen?

(a) White light will split into a spectrum.

(b) A spectrum will be focused to form white light.

0%

20%

40%

60%

80%

100%

Pre-test 13% 22% 3% 68%

Post-test 64% 46% 30% 20%

Knew (a) Knew (b)Knew both (a) &

(b)Did not know (a)

nor (b)

Magnifying glass

ｘLight

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Setting up a closed circuit


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Setting up a closed circuit


1st Cycle 3rd Cycle68% 85%

Which of the following circuit(s) could successfully light up a bulb?

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Part I: Constructing and exploring the common features of prisms and cylinders


Varying

Pupils’ constructions

Correct and Incorrect

Constructions/ features

A given prismInvariant

What is discerned: characteristics of a prism

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Part II: Categorizing three-dimensional objects


Prisms Non-prismsVarying

Common features of prisms

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Pre-test Post-test ChangeAverage score of the whole level 1.8 4.3 + 2.5Average score of 10 pupils whoscored the lowerest in the pre-test

1.5 6.7 +5.2

Total score= 8

Pre-test Post-test Changescored 6 or above out of 8 2% 25% 13%scored 0 or 1 out of 8 47% 7% -40%

The number of pupils who

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Example 4: P.6 Chinese

A baby in the sun is like a seedling, can’t let you sway in wind and rain.[ 陽光中的寶寶如幼苗，難讓你在風裏搖，雨中飄。 ]

A baby in the sun is like a weed, can’t let you sway in wind and rain.[ 陽光中的寶寶如野草，難讓你在風裏搖，雨中飄。 ]

A baby in the war is like a seedling, can’t let you sway in wind and rain.[ 戰爭中的寶寶如幼苗，難讓你在風裏搖，雨中飄。 ]

Part 1

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The small boat is like the cradle of my babyhood

Gently, tenderly

Swaying in a river

……

The small boat is like a swing that I like to play

In an endless flow of water

Rocking higher and higher

小船像我幼時的搖籃

輕輕柔柔的

在河上搖晃……

小船像我愛玩的盪鞦韆

在無盡的流域裏

愈盪愈高

Part 2

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The small boat is like the cradle of my babyhood

In an endless flow of water

Rocking higher and higher

……

The small boat is like a swing that I like to play

Gently, tenderly

Swaying in a river

小船像我幼時的搖籃

在無盡的流域裏

愈盪愈高……

小船像我愛玩的盪鞦韆

輕輕柔柔的

在河上搖晃

Part 2

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Part 2

Surface meaning:

• Subject—the motions of the small boat in different places

• Post-modifier—different phases of life

• Connotation

Deep meaning:

• Subject—Different phases of life

• Post-modifier—the motions of the small boat in different places

• Connotation

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Learning Outcomes: Pre- and Post-test results

Task Pre-test Post-test

Writing a poem with proper use of simile and in proper format

39% 71%

with proper use of simile 48% 73%

in proper format 70% 85%

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Pupil B (lower ability)

Pre-test Post-test

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Pupil A (higher ability)

Pre-test Post-test

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Additional analysis: HKAT—Chinese 99/00

StandardizedScore

01/02Standardized

Score

Change inStandardized

Score

Whole level Average 86.30 94.28 7.98 n=118 STDEV 20.07 17.72 2.35-

00/01, A Average 106.06 109.15 3.09 n=32 STDEV 9.88 10.53 0.66

00/01, B Average 80.82 94.61 13.79 n=21 STDEV 17.14 16.57 0.57-

00/01, C Average 81.02 81.76 0.73 n=20 STDEV 16.08 13.33 2.76-

00/01, E Average 84.52 92.21 7.69 n=24 STDEV 19.86 17.80 2.07-

00/01, F Average 68.71 85.57 16.86 n=21 STDEV 14.09 16.17 2.08

*

*

*

* p < 0.01

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A sample of pupils who scored less than 80 in standardized score in 99/00

Number of pupils (among the 48) whose standardized score increased or decreased by 01/02

n=4899/00

StandardizedScore

01/02Standardized

Score

Change inStandardized

Score

Average 65.90 79.39 13.49 STDEV 8.81 11.84 3.03

Increased Decreased00/01, B 9 100/01, C 7 100/01, E 11 200/01, F 16 1

43 5

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Main Results:

4) Are the participating teachers empowered to cater

for individual differences using the three types of

variation through engaging in Learning Studies?

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a. Teachers’ views of the project’s approach to catering for individual differences

…by looking into pupils’ different ways of

understanding something... we were actually catering

for pupils of different abilities. Pupils of lower abilities

… are often weak at seeing things in a more

comprehensive way. So, if we can show them different

ways of thinking, they will be able to view things in a

comprehensive manner. (TJL TI 0203)

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b. Teachers’ understanding and use of assessments

We chose a certain topic, then we focused on that specific

topic in setting the pre-test, the purpose of which was not f

or assigning marks to pupils, but for collecting informatio

n (about pupils’ understanding of the topic)… this was

different from our practices in the past. But setting pre-

tests is quite a difficult job. (WWY TI 0203)

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9

1 2

Answers: ( )

Calculate the sum of the

three digits given in the box,

and circle the two digits that

you add up first.


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0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

Pre-test 74.57% 47.40%

Post-test 84.97% 80.35%

% of pupils who answeredcorrectly

% of pupils who inclined to usethe combinations of 10

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QuestionQuestion: Fanny places a cold drink on a table. After a : Fanny places a cold drink on a table. After a while, she notices that there are some water droplets on while, she notices that there are some water droplets on the surface of the cold drink. Where do these water the surface of the cold drink. Where do these water droplets come from? Circle the most appropriate answer.droplets come from? Circle the most appropriate answer.

A. Leaking from the cold drinkA. Leaking from the cold drinkB. Coming from airB. Coming from airC. Coming from the refrigeratorC. Coming from the refrigeratorD. Others, please specify.D. Others, please specify.

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Pre-testPre-test Post-test

A. Leaking from the cold drinkA. Leaking from the cold drink 24.27%24.27% 10.68%

B. Coming from airB. Coming from air 37.86% 37.86% 68.93%

C. Coming from the refrigeratorC. Coming from the refrigerator 31.07%31.07% 18.45%

D. Others, please specify.D. Others, please specify. 6.80%6.80% 1.94%

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c. Teachers’ understanding and use of the theoretical framework

…what we have achieved in these several research

lessons is that we were able to approach the topic in a

clear and specific way, unlike what we did in the past

while we only set the teaching objective in a broad and

general sense, for example, how to develop pupils’

generic skills, how to develop pupils’… learning. (CTF

TI 0203)

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One person’s wisdom is limited. What you can think about

would not be able to exhaust all the pupils’ problems. If

different teachers tried to find out what difficulties their

pupils’ would encounter, making use of their collective

wisdom, then finding ways to deal with it, I find that this is

very helpful from the perspectives of both pupils and

teachers. (IMK TI 0203)

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The theory of variation not only enables us to look at the

problem from different perspectives, both pupils and

teachers can make use of variation to examine a particular

topic. For example, squashing a rectangle changes it to a

parallelogram. We can compare the variations in the

diagrams: similarities and differences in properties. This

theory can be put into practice in different subjects. It’s

only a question of whether you do it consciously or

subconsciously. If you do it consciously, you will

strengthen the use of it and be able to apply it a bit more

thoroughly. (CLP TI 0203)

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d. Teachers’ professional development within the project

• They gained better knowledge of their pupils.

• They developed better understanding of the subjects they taught.

• They were willing to exercise professional judgment to adjust (or even to modify) the intended lesson plan in order to accommodate pupils’ variation in understanding during the lesson.

• They gained confidence in tailoring the curriculum

• They gained experience in being action researchers.

• They shared their experience and knowledge gained in public seminars.

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Impact on School Development:

Schools’ development within the project

[The project] help to enhance our teachers’ confidence

and professionalism. At the same time, our school has

also developed into a learning organisation which is

vibrant with the culture of innovation and peer

collaboration. (ISB Sch1 0203)

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This project widened the view of our teachers in seeing

“individual differences” not only in terms of ability, but

also in terms of pupils’ different ways of experiencing and

understanding the world. This gives teachers a sense of

success and satisfaction. On the other hand, …this has led

to the narrowing of the differences in pupils’ learning

outcomes, and pupils’ various potentials being maximised.

(LKH Sch2 0203)

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Impact on School Development:

Schools’ future adoption of Learning Study

School 1: A QEF project supporting Learning Study

School 2: A major tool for school internal development

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It is often remarked that “education reform” could bring

about school development. But I would say it is “lesson

study” that nurtures the school’s culture, helps teachers to

design curriculum, offers an opportunity for teachers’

professional development, and provides a blueprint for the

school’s curriculum reform. …We will continue to treat this

as a major item for school development. (NWL Sch2 0203)

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Conclusion

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1) Can worthwhile objects of learning that serve as

foundations to pupils’ learning be identified?

2) Can critical features of these intended objects of

learning be found?

3) Can teachers make use of pattern(s) of variation to help

pupils of different abilities to grasp the critical feature(s)

identified for their learning of a particular object of

learning?

4) Are the participating teachers empowered to cater for

individual differences using the three types of variation

through engaging in Learning Studies?

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Can it be sustainable

and transferable?

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Dissemination activities and their impact:

42 primary schools (PIPS, 2002-2003)

50 secondary schools (STEM, 2003-2004)

30 self-funding schools (e.g. QEF, 2003-2004)

10 seminars / workshops given to the partnership schools

33 public seminars / workshops

6 local / international conferences

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Insights & Recommendations

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Learning Study

Build capacity for collegial learning Provide a context

for peer review and classroom

observation and conferencing

1. Sensitize teachers to good lesson

2. Learn subject matter better

3. Develop “the eyes to see pupils”

Bridge the gapbetween the reform goals and practice

Empower teachers

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Major Recommendations:

Curriculum development to be based on research

which takes into consideration how pupils learn

An evolutionary approach to schools’ curriculum

making

Bridge the gap between the reform goals and practice

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Learning Study as a model for building a learning

community for staff development purposes.

Build capacity for collegial learning


Provide a context for peer review and classroom observation and conferencing

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Assessment for learning via the conceptual

framework based on variation

Learning study as a core component of any

teacher education programmes, e.g. engaging in

Learning Study at least once a year, and sharing

their experience with other teachers.

Empower teachers


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More Learning Studies should be done to discover

effective patterns of variations and how they can be

applied in different subject areas.

The tripartite partnership between the schools, the

Curriculum Development Institute and the research

team was considered a win-win option for all parties

involved. This mode of operation is recommendation

for future endeavours.

What is more…

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~ End ~

01 – 12 - 2003 project: catering for individual differences— building on variation cid(v)...

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