PBL4C Book Project - Draft & stays incomplete.
Date: 21 July 2011
Agenda & Consensus :
1. Relooking at the objectives & proposal for grants
 Complete book is the target goal, and then later to trim down for the Guide Book
 Proposal for grant for the complete book, not the guide book, of which the fund
should come from MOE
 If book is of good quality, then we will engage an external publisher to edit,
publish & market the book
2. Reviewing the work up to the moment
 Title to include “Mathematical perspectives”
 3 contexts to be shared for reference as we write
i. Garden Design context
ii. Building New island nation in SEA
iii. Tsunami context?
(will choose one)
 Chapter 1- Constructivism/student centered/ as bullets and not as separate
headings.
3. Any new content chapters to add
 To be decided later after going through some of the existing PBL books
e.g.
i. Crafting the PBL4C context
ii. Chapter - Assessment – add portfolio
iii. Questioning techniques (LCK to help WAP)
4. Others
 Agreed on the following features when we write:
i. Target readers
– primary & secondary mathematics teachers,
– mathematics teacher educators (in teaching colleges & universities)
ii. Very reader friendly
iii. Use passive voice – exclude ‘we’, etc
 As we write references will be to refer to 1 problem context – to be decided from
either
i. Garden Design context
ii. Building New island nation in SEA
iii. Tsunami context?
 Request to resend the paper presented at EARCOME5 as guide to write this
book
Tentative titles
2 in 1 Project:
1. Book - PBL4C for the 21st Century Learning
2. A Guide Book for MOE
Problem-Based Learning the 4 Core Areas (PBL4C)
: meeting the needs and demands of Mathematics in the 21st Century Education
- mathematical perspectives
with Editable Context Modules downloadable online
A Guide Book to
Problem-Based Learning the 4 Core Areas (PBL4C)
: meeting the needs and demands of the 21st Century Education in Secondary Mathematics & Additional
Mathematics, Malaysia
with Editable Context Modules in CD
Idea for cover
Behind front cover (A5 folded)
1. CD
2. A mind-map – a chart that summaries PBL4C
Foreword
1. BPK MOE
2. RECSAM Director
Panel of Writers for Guide Book (in alphabetical order)
1. Dr. Leong Chee Kin
2. Mr. Teoh Boon Tat
3. Dr. Warabhorn Preechaporn
Module Developers
1. MOE Officers
2. RECSAM Academics
3. JPN Officers
4. Teachers …
Organisations
1. Curriculum Development Division, Ministry of Education Malaysia
2. SEAMEO RECSAM
Content
1. 21st Century needs and demands (WAP)
a. What Needs (student’s needs) and Demands (society, market, environmental
demands) in the 21st Century

Soft but essential human skills

Attitude, personality, …

Creativity, innovativeness,

Constructivism

Student-Centred learning, real life context, making sense of maths, …
b. Contextualising, Decontextualising & Recontextualising – 3-Stage Model
- Jack Holbrook, ICASE immediate past President

Use term Mathematisation (RME) ?
c. The Challenge – PBL4C emerged to meet the needs & demands
- PBL4C can be read as Problem-based, Learning the 4 Core Areas
2. What is PBL and Why PBL4C? (TBT)
a. What is PBL?
Historical Background
Problem-Based Learning (PBL) started in the medical schools in the training of doctors during the
1960’s and a look at its historical background will be insightful to understand what this approach
is really about. This is important since much confusion has arisen about what Problem-Based
Learning is and how it is different from Project-Based Learning, which incidentally also takes the
acronym of PBL. The use of the terms ‘cases’ and ‘scenarios’ in PBL may now seem to be more
obvious reflecting on its medical origin.
We would like to give an example using a medical class, and then after understanding the
different structures and terminologies involved, we will then proceed to provide examples in
mathematics.
Figure 1: A medical model showing the use of cases and scenarios
Figure 1 shows how medical students may approach a health problem faced by a patient. From
the very start, the patient has a PROBLEM, and so Problem-Based Learning is coined! From the
physical symptoms, an initial diagnosis may point to a few possibilities of ailments, medically
called cases. When further test results are obtained in the subsequent scenarios, diagnoses may
change. This prompts for further tests or the search for additional facts. Finally the best probable
treatment is prescribed after having considered the various facts personal to the patient. A key
feature of the PBL approach is team work. And in the above example, each case can be worked
upon by a team.
Various PBL Context Models (another word to use?)
Model 1
Figure 2: A simplest model
Figure 2 shows the simplest model of PBL that consists of only the problem. An example would
be to design a game on algebra. This model borders upon project-based learning. So if one uses
this model then it is very difficult to differentiate between problem-based learning and projectbased learning. However it depends on the creativity of the implementers to incorporate the
importance of the processes rather than just looking at the end product.
Model 2
Example of Model 2
Model 3
Example of Model 3
Model 4 – Inter Team Collaborative model
Example of Model 4
Cases and Scenarios
Cases – the lessons can proceed simultaneously
Scenarios – the lessons to proceed consequently, the scenario is dependent upon the preceding
scenario/case
Common PBL Processes
Some common PBL processes that the teams may go through are: identifying the problem;
gathering the information given unique to the problem; procuring extra information in the view of
finding a solution to the problem; generating possible solutions; communicating, accommodating,
selecting and executing the best solution, and finally making a presentation of the solution.
is essential in understanding what the approach is about especially so in comparison to projectbased learning which incidentally has also the acronym of PBL and much confusion has arose
because of the overlapping of similarities between Problem–Based Learning and Project-Based
Learning.
Problem-Based learning (PBL) is a learning and teaching approach based on the principle of
using realistic context problems as a starting point for the searching and learning of new content
knowledge. It is also designed to reinforce and recall the existing or prior knowledge. And
because they will be able see the need to know the connection between what they learnt in the
classrooms and its application in their future context, this important gap filler makes learning
mathematics meaningful and applicable.
1. Problem is presented and read by group member, while another acts as scribe to mark
down FACTS as identified by group.
2. Students discuss what is known (the facts).
3. Students discuss what they think and identify the broad problem
(brainstorm their ideas and formulate their hypotheses).
4. Students identify their learning needs (what they need to learn in order to prove or
disprove their ideas).
5. Students share research findings with their peers, then recycle steps 2-4
6.
Problem-based learning (PBL) is a meaningful approach that fits in well in the 21 st century
learning. It is meaningful because it is context-based and the content knowledge, skills and
thinking of the individual are applied according to the case and scenario which they are
happening. Students then making decisions are these are made based on various values that
they hold and accommodated in the team.
Problem-based learning (PBL) is an approach that fits in snuggly in this 21st century learning.
Many approaches and strategies have been used to overcome the weaknesses and deficiencies
of the educational systems. However, PBL encapsulates these strategies & approaches
holistically and appropriately, and applies them when and where they are suitable in real life
context. For example, a teacher may have been using mastery learning strategies but ultimately
applying what one learns by mastery methods are tested when they are applied in real life using
the PBL approach.
has fast been adopted in many fields of education including the search of excellence in the field
of Mathematics education. As expected, diversity in forms has emerged. Whilst the main
processes of PBL can commonly be found in many of the diversed forms, one question arises in
regard to the purpose of using the PBL approach in Mathematics education in particular, and in
any other subjects of learning in general, in solving real life problems – what kind of problems?
Problem-Based Learning the 4 Core Areas (PBL4C) emerges in trying to provide solutions to this
pertinent question. The 4 core areas incorporated in this form of PBL are the core areas of
content, thinking processes, skills and values. The interconnectivity and significance between
these core areas are illustrated through a PBL activity. This paper further proposes with reasons
why these 4 core areas could be the holistic goal of education for any nation, beyond
Mathematics, in the search of excellence in lifelong education.
b. Why PBL4C?
In this paper, while still maintaining these important features and processes, the purpose of PBL
in Mathematics education, or in whatever subjects the approach is used, becomes crucial with the
asking of the following question: what kind of problems? In our search of excellence in
education generally and in Mathematics specifically, while trying to find some possible answers to
this pertinent question, Problem-Based Learning the 4 Core Areas (PBL4C) emerged. The four
core areas that we are proposing in PBL4C are the core areas of content, skills, thinking
processes, and values (Teoh & Warabhorn, 2009). We will now illustrate the 4 core areas in a
student’s learning by using the following PBL activity.
Change Management
One feature which we found to be quite unique to the PBL approach is the ability to introduce
change in student’s learning through the provided scenarios (Teoh & Preechaporn, 2009) and
thus presenting an opportunity for students to learn about change management, a lifelong
learning skill. And when changes occur, not only content knowledge and skills are reapplied but
the whole person’s standing is called up to make decisions especially those that affect the core of
one’s beliefs, habits and values. This is where the core of values in PBL4C will help introduce the
students to such important aspects of life and their application starting from young. Some of us
may think that young learners should not be exposed to these aspects since they are still young
and tender but we found it otherwise. We would like to show what we mean by an example. Take
in a normal family outing, when young children are initially taken to their favorite place of
restaurant and upon reaching there they found that it is closed because of certain unforeseen
reason. This is a new scenario, some …
Emotion Management
Conflict Management

Ego managing
3. Features of PBL4C
a. Content Knowledge – (FHK)
b. Skills – 21st Century Skills, Human Skills – (FHK)
Collaboration is not a 21st Century Skill, it is a 21st Century Essential.
In a recent blog post from the official google blog, Google identified the following as key traits or abilities
in 21st Century Employees:
“... communication skills. Marshalling and understanding the available evidence isn't useful unless you
can effectively communicate your conclusions.”
“... team players. Virtually every project at Google is run by a small team. People need to work well
together and perform up to the team's expectations. ”
Source: http://googleblog.blogspot.com/2008/07/our-googley-advice-to-students-major-in.html
c. Thinking processes – HOTS - (FHK)
d. Universal Harmonious Values in decision making – characteristics, newspaper
clippings (positive & negative stories clippings) - (TBT)
Values as the Foundational Core Area
Allow us to elaborate further about the core area of values. All the content knowledge, thinking
processes and skills that we usually place increasing importance in education nowadays will
become questionable when all these 3 core areas are used and applied for the wrong reasons.
We will illustrate what we mean by the following newspaper cuttings.
The interchanging of Creativity & Evaluation in the Taxonomies – Bloom & Anderson
When things are created, usually evaluation also plays an important part.
However a simple knife after being created can still be subject to various uses. These uses can
be for good or bad. Another example is nuclear power. It can be used for good or bad…an
essential criteria of evaluation.
ANY INVENTIONS, no matter how simple or complex, they can be used for good or for bad.
As a result, if evaluations come first before any invention, then no inventions will be allowed
& developed ! So from this flow of thoughts, evaluation must come after synthesis/creativity
level. All inventions should be promoted to be used for good, avoiding the bad for unscrupulous
gains. We must not discourage useful inventions. I feel we need to inculcate the use of all these
inventions for good uses rather than bad. Look at the various scams & trickeries, some very
high tech. It is their use for cheating and harm from the various inventions & innovations
already developed.
WITHOUT PROPER USE, WE ARE ALL IN TROUBLE ! Even the most cunning people in the world
will still be trouble, … from other cunning people !
Positive examples (innovations that improve, …)
1. Virtual keyboard inventions,
2.
Negative examples (war, greed, rape, scams, lies, ……… )
Austrian
electrical
engineer,
73
imprisoned his daughter in cellar for 24
years, raped 3000 times and fathered her
seven children.
Norway rampage culprit calm, held in isolation. Killings of
over 90 innocent people
Bribery RM100 jailed for 5 years ??
Chemists
with
undisputed
content
knowledge using their higher order
thinking processes and acquired skills for
the
wrong
reasons
by
unwise
considerations
Highly intelligent professor with obvious
professional and academic knowledge, with
thoughts of solving his problem by exercising his
forging skills in an unwise decision
Tens of thousands of red-shirted antigovernment protestors are converging on
Bangkok, vowing to oust the Thai
government by means of a mass
demonstration which turned violent.
Figure 1. Newspaper cuttings illustrating the interconnectivity of the 4 core areas
We hope these newspaper cuttings have helped us make our point to convince the readers on
the importance of these 3 core areas and their interconnectivity, and their cumulative importance
founded on and guided by values in the search of excellence in Mathematics education and
education as a whole, by trying to answer the question: “what kind of problems?” There are many
aspects to values, and their many interpretations. We would like to propose some of the main
characteristics of values as we see them, within the constraint of this paper.
Some of the values listed in the activity are real values while others we found to be pseudo
values. Real values are universal in nature. Examples of real values comprise all deeds, speech
and thoughts which incline towards harmlessness, belief in the sanctity of life, respect for one’s
and others’ possessions both human and non-human, truthfulness, avoidance of intoxicants like
drugs, just to mention a few. Universal here means that when they are practised they are good for
all. For example, harmlessness is good for the one who practises it and also for others.
Harmlessness does not bring harm to oneself as well as others. Furthermore when others
practise harmlessness, it is always welcomed to oneself. Universal values do not bite back. So is
the value of respect for one’s or other’s possessions. Universal security is felt. In other words,
they are universally good. One takes care of other’s possession as if one would with one’s own.
Pseudo values at first glance may look like values but they are not. Take for example cooperative
team spirit and diligence can be observably practised to excellence by members of certain
political factions but can cause untold disharmony and misery to the citizens, factional and neutral
alike, taking the political events in Bangkok for instance.
Values have a goal, that is, to nurture citizens who are wise, who are able to use wise
considerations, for universal good. If one advocates a policy of no child left behind, one
advocates nurturing a wise child irrespective of whether one has grasped a particular subject
content or otherwise. Only then can such a policy work because if the emphasis is on academic
excellence or “intelligence” then sadly many children are going to be left behind! However
achieving the understanding and grasping of the subject matters by these children would be an
icing on the cake.
4. Facilitating Skills
Facilitation and Evaluation are among other important features of PBL (Finkle & Torp, 1995;
Lambros, 2002; Wee, 2004).
a. Observation Skills (TBT)
b. Questioning Techniques (WAP/LCK)
5. Assessments for Learning (LCK)
In any learning experience, assessment plays an important role and is a pertinent component of any
teaching and learning approaches. The assessment method utilized need to be compatible and
aligned with the learning objectives of the learning processes of the approach used. With PBL this
means progress testing to determine the level of student’s knowledge and understanding. It also
means testing for competency rather than for isolated factual knowledge. (van der Vleuten, Norman,
G. R., & De Graaff E., 1991). In PBL, assessment, teaching and learning is inextricably linked, as
each informs the others.
a. Assessment for learning
Assessment for learning approaches is needed to provide the required information for the teachers to
adjust their teaching strategies, and by students to adjust their learning strategies. Assessment for
learning is a way of developing learning using the evidence of student’s learning. It uses the whole
process of assessment to help learners to improve their learning. It allows plenty of scope for learners
to input their own decisions and solutions. The better the quality of the evidence of the students’
understanding, knowledge and ability, the more accurately the learning activity can be modified to
drive and support their learning forward. However, the feedback will only be of sufficiently high quality
if:



i.
They engage in activities or response to questions that fully explore their
understanding
They have the time both to think through what they know, understand and can do,
and to fully express their thoughts
They are able to use mathematical language to communicate effectively what they
know, understand or can do.
For teachers
Teachers will have a more satisfying and enjoyable experience using assessment for
learning. They will become more aware of how their students learn and become more
engaged with students in the learning process. It results from them helping the
students to set goals and criteria, evaluate their progress, and experience the many
small learning "wins" that lead to them reaching their goals.
Assessment for learning helps teachers gather information and evidence to:



ii.
plan and modify teaching and learning programmes for individual students,
groups of students and the class as a whole
pinpoint students’ strengths and misconceptions so that both teachers and
students can build on them
identify students’ learning needs in a clear and constructive way so they can
be addressed
For students
Assessment for learning empowers and motivates learners. It is widely recognize that
ownership of the learning process is an important factor in the development of the
efficient and independent learner. Students have the opportunity to experience a
greater sense of purpose and involvement in learning. It also provides students with
information and guidance to plan and manage their next steps in their learning. It
leads them from what has been learned to what needs to be learned.
Assessment for learning provides information and evidence for students to:

know how they are progressing

understand what need improving and how to achieve the learning goals

monitor their own improvement over time

get the support they need to be motivated

be independent learners

develop deeper understanding of their learning

empowers them to assess and reflect on their work
b. Methods of assessment
Macdonald and Salvin-Baden (2004) listed some of the forms of assessment that have been used
successfully in Assessment for Learning and specifically for Problem-based Learning. Assessment for
learning can take place in teaching and learning sessions, through written and verbal feedback and
as part of review, goal setting and action planning. The following are some of these forms and its brief
description:
i.
Group presentation
Here students are asked to submit their work either orally or written. They can play a role or work
within a particular context and scenario as a collaborative product. The product should model the
process of PBL. This method posed difficulties for the teachers to mark and is time consuming. Steps
need to be taken to ensure the assessment criteria are clear of what are being assessed.
ii.
Individual presentation
Students are required to submit the component of work that they have researched as part of their
contribution to the overall solution of the problem scenario. This form of assessment does pose some
difficulties such as it requires quite a lot of preparation time. Also, if the students just present their
work that was researched there would be little synthesis with the overall problem scenario.
iii.
Tripartite assessment
This form of assessment balances the individual and group marks. The group has to submit a report
and each group member submits the component of work that they have researched. Then the
individual writes an account of the group process that is linked to the theory of group work. The
overall mark is obtained by totaling the marks of these three components. In this way, the grading
would be perceived as being fair and does not privilege students who contributed less.
iv.
Case-based individual essay
This form of assessment requires the student’s response to a case scenario in the form of an essay.
They may be given options of scenarios to choose. These scenarios vary in the level of detail and
complexity which link well with PBL.
v.
Triple Jump
Triple Jump is a three-stage assessment: hop, step and jump. In the hop stage, questions are
assigned to students. The step stage is where the students are given time to research their findings
and hypotheses that have emerged from the previous stage. Normally, they are to write an essay as
their responses to the questions. In the jump stage, the students are expected to present their
findings. This is a period of re-appraisal and then synthesis follows. This form of assessment although
was specifically developed for PBL, it is time consuming and costly. However, it is one of the few
forms of assessment that measures both specific acquired knowledge and problem solving
processes.
vi.
Self-assessment
This form of assessment involves students judging their own work. It may be essays, presentations,
reports, and reflective diaries. Self-assessment works well with PBL. It allows students to reflect on
what they already know and not know, and what other additional information to seek to complete
certain tasks. It drives self-evaluation along with self-verification and self enhancement. However, one
of the difficulties with self-assessment is the tendency to make judgments about what the students
actually meant rather than what they actually achieved
vii.
Peer Assessment
Students are involved in making judgments and comments about other students’ work. Similar to selfassessment, it also fit well with PBL and is generally used for presentations, practical work, essays,
reports and examination scripts. Ideally, the students design their own assessment criteria and use
an assessment rubric as a guide. It also emphasizes the cooperative nature of the PBL environment.
Some of the advantages derived from this form of assessment are:

Assists students to become more autonomous, responsible and involved.

Encourages students to critically analyse work done by others.

Helps clarify assessment criteria.

Provides students a wider range of feedback.
(Weaver, W. & Cotrell, H.W., 1986).
However, teachers need to be aware that:

Students may lack the skill and ability to evaluate each other.

Students may be influence by factors such as friendships and entertainment
values when making their judgment.

Students may not like peer marking because of the possibility of being
discriminated against or being misunderstood.

Without facilitator intervention, students may misinform each other.
viii.
Facilitator/tutor assessment
Here the feedback is provided by the facilitator/tutor. The feedback provided should encourage and
drive the students to explore various ideas. This form of assessment may consist of feedback on how
successful the individuals communicated and reacted with their group. Information on the individual’s
cognitive growth may also be provided. However, it is important that the facilitators do not try to
control or influence the group. They should only facilitate exploration and learning.
ix.
Collaborative assessment
In this form of assessment, learners and facilitators/tutors collaborate in order to clarify objectives and
standards/criteria. They also collaborate to negotiate details of the assessment and discuss any
misunderstandings that exist.
x.
Reports
Written communication is a vital skill for the students to acquire. Through writing reports
students can practice this form of communication. It also promotes succinct and critical
pieces of work.
c.
Development of Rubrics
The most common assessment tool and an important key concept in PBL assessment is rubric. A
rubric is a scoring tool that can be used by students (for self assessment), peers (peer assessment),
teachers, and others to make reliable judgments. It lists important criteria applicable to a particular
type or piece of task. It describes the important components of the task being planned or evaluated. A
given criterion is then stated in several different levels of completion or competence. Each level is
assigned with a weighted score.
A rubric should give clear guidelines to a reviewer on how to evaluate or "grade" a student’s product
or performance. Since the criteria for assessment are clearly defined in gradations from poor to
excellent, different reviewers can arrive at similar conclusions when comparing a given product,
performance or presentation to each of the graduated criteria on a rubric.
As a guide for planning, a rubric gives students clear targets of proficiency to aim for. With a rubric in
hand, they know what constitutes a good product, performance or presentation. A rubric can be a
handy tool as a gauge for measuring progress while the project is under way to help keep students on
target. They can compare their progress with where they want to be on the rubric's proficiency scale,
and refer to it in order to remind themselves of their goal.
a. Self, Peer, Leader, Teacher Assessment
6. Key Processes of PBL4C
i.
ii.
Noting the facts – Student Learning Template as guide
Searching for Data
iii.
Team work
o The best gives the best
Story
Tortoise And Hare Inspirational Teamwork Story
This is an age old fable of the tortoise and hare race. Everyone knows who won the race or do
you? Well, recently I heard a new version of this story with a new twist. Read this inspirational
teamwork story with lessons in teamwork from an age old fable.
1. Once upon a time a tortoise and a hare had an argument about who was faster. They decided
to settle the argument with a race. The tortoise and hare both agreed on a route and started off
the race. The hare shot ahead and ran briskly for some time. Then seeing that he was far ahead
of the tortoise, he thought he'd sit under a tree for some time and relax before continuing the
race. He sat under the tree and soon fell asleep. The tortoise plodding on overtook him and
soon finished the race, emerging as the undisputed champ. The hare woke up and realised that
he'd lost the race.
The moral of the story is that slow and steady wins the race. This is the version of the story that
we've all grown up with.
2. But then recently, someone told me a more interesting version of this tortoise and hare story.
It continues.
The hare was disappointed at losing the race and he did some soul-searching. He realised that
he'd lost the race only because he had been overconfident, careless and lax. If he had not taken
things for granted, there's no way the tortoise could have beaten him. So he challenged the
tortoise to another race. The tortoise agreed.
This time, the hare went all out and ran without stopping from start to finish. He won by several
miles.
The moral of the story? Fast and consistent will always beat the slow and steady. If you have
two people in your organisation, one slow, methodical and reliable, and the other fast and still
reliable at what he does, the fast and reliable chap will consistently climb the organisational
ladder faster than the slow, methodical chap.
It's good to be slow and steady; but it's better to be fast and reliable.
3. But the story doesn't end here. The tortoise did some thinking this time, and realised that
there's no way he can beat the hare in a race the way it was currently formatted. He thought for
a while, and then challenged the hare to another race, but on a slightly different route. The hare
agreed. The tortoise and hare started off. In keeping with his self-made commitment to be
consistently fast, the hare took off and ran at top speed until he came to a broad river. The
finishing line was a couple of kilometres on the other side of the river.
The hare sat there wondering what to do. In the meantime the tortoise trundled along, got into
the river, swam to the opposite bank, continued walking and finished the race.
The moral of the story? First identify your core competency and then change the playing field to
suit your core competency.
In an organisation, if you are a good speaker, make sure you create opportunities to give
presentations that enable the senior management to notice you.
If your strength is analysis, make sure you do some sort of research, make a report and send it
upstairs. Working to your strengths will not only get you noticed, but will also create
opportunities for growth and advancement.
The story still hasn't ended.
4. The tortoise and hare, by this time, had become pretty good friends and they did some
thinking together. Both realised that the last race could have been run much better. So the
tortoise and hare decided to do the last race again, but to run as a team this time.
They started off, and this time the hare carried the tortoise till the riverbank. There, the tortoise
took over and swam across with the hare on his back. On the opposite bank, the hare again
carried the tortoise and they reached the finishing line together. Both the tortoise and hare felt
a greater sense of satisfaction than they'd felt earlier.
The moral of the story? It's good to be individually brilliant and to have strong core
competencies; but unless you're able to work in a team and harness each other's core
competencies, you'll always perform below par because there will always be situations at which
you'll do poorly and someone else does well.
Teamwork is mainly about situational leadership, letting the person with the relevant core
competency for a situation take leadership.
The fundamental underpinning of the situational leadership theory is there is no single "best"
style of leadership. Effective leadership is task-relevant and that the most successful leaders are
those that adapt their leadership style to the maturity ("the capacity to set high but attainable
goals, willingness and ability to take responsibility for the task, and relevant education and/or
experience of an individual or a group for the task) of the individual or group they are
attempting to lead/influence. That effective leadership varies, not only with the person or group
that is being influenced, but it will also depend on the task, job or function that needs to be
accomplished.
o
Story
The interested to develop to be the best
iv.
7. UNESCO
If we look at UNESCO's publication “The four pillars of Education, Learning: The Treasure within”
Collaboration is a key element of each of the four pillars.
UNESCO’s 4 Pillars




Learning to know
Learning to do
Learning to live together
Learning to be
(http://www.unesco.org/delors/fourpil.htm) [10]
PBL4C’S 4 Core Areas
Content, Skills
Content, Skills, Thoughts (???)
Using Content, Skills, Thoughts, Values
Becoming the Core Areas
7.1
The connection between the 4 core areas and UNESCO’s 4 pillars
7.2
Learning to live together
Learning to live together entails 2 aspects: what kind of people do we want to live with? And
what kind of people do we want to be when we live with others? Fundamentally we all desire to
live with caring, thoughtful and harmonious neighbours. However, to actualize this basic human
requires everyone in the neighborhood, including we ourselves, to learn how to be. Good
relationships need fostering and effort, with all our neighbours: next door, locally, regionally
and globally.
In these ever tumultuous and challenging modern times, persistent and consistent efforts need
to be exerted and synchronised to achieve one important goal in education – harmonious
productive living. Education will be meaningless if the goal is otherwise. When the citizens of
the world especially in the immediate Southeast Asian region are living in vaporous situations
arising at various times in modern history, we are acknowledging efforts being mediated, many
times unnoticeably, to contain and ease the usually tensed moments. Needless to say, without
such mediations for peaceful reconciliations, the outcomes may become more aggravating and
sometimes devastating. And these mediations need special knowledge, skills, universal
harmonious thoughts and values. And these can be learnt through education catered towards
international and intranational understanding.
PBL4C proposes ……….. the goal is to nurture citizens, from young, to cultivate a mind that
inclines towards peace and harmony, within and without. This goal has a two-pronged effect: a
greater resource of humans who endeavour towards peaceful means and ends, and a reduction
in humans indulging in unproductive activities that need constant reconciliations. This effect
enables a SEAMEO country nation to focus on productivity and development, and thus bringing
a more accelerated and sustainable prosperity, happiness and peaceful living within that
nation, region and beyond. It is learning to live with our neighbours. This is outer peace. A vital
inherent part which is frequently being neglected is learning to live harmoniously with
ourselves. This is inner peace. This includes inculcating a sense of tolerance for outer peace to a
sense of acceptance for inner peace. Tolerance is good but not good enough because of the
tremor or turbulence felt inside. When the human mind matures this unsettling feeling within
calms and accepts.
These concepts can best be achieved through modeling by the SEAMEO-CEIU specialists,
assisted by Peace laureates, who themselves are realistically involved in such societal work and
inclined towards peaceful intentions and living. The rippling effects of those educators trained
in this new SEAMEO centre will most meaningfully be felt and internalised by their own
students through their exhibition of skills and conduct through their experience. These students
will learn to integrate whatever multi-subject knowledge in schools using harmonious means
and ends.
Fundamental Characteristics
1. Peace cultures
2. Non violence
3. Disarmament – 3 types of arms: physical, verbal and mental arms
4. Fundamental human rights
5. Sustainable and responsible development
6. Universal harmonious values & practices
7. Inner and outer peace
Affiliate Agencies
1. UNESCO – Building Peace in the Minds of Men and Women
2. APCEIU – Towards a Culture of Peace
*EIU = refers not only to Education for International Understanding but currently also includes
intranational understanding. With the incorporation of universal harmonious values, EIU will be
more encompassing to include micro to macro peace, a spectrum spanning from individual
inner peace, harmonious family living, cohesive working environment to global peaceful and
responsible living with nature.
PBL4C Context Modules
1. Module design structure – (in soft & editable copies)
a. Context Problem
b. Student learning template
c. Folder: for students – printouts, empty worksheets, empty student learning
template,
d. Folder: for teachers – PowerPoint, filled worksheets, filled student learning
template, assessment forms,
2. How to use the context modules?
3. List of Module Titles & Synopses
4. Resource Content in CD





Guide Book for PBL4C
Folder – F1, F2 & F4 Modules developed
Folder – Literature on PBL
Folder – Training of Trainers & Implementers (for State or National Training, In-House
Training)
Folder – resources – GSP Malaysian Edition, GeoGebra, Assessment Forms,
5. Student Learning Template
6. Recommendations for the Successful Implementation of PBL4C in the Classrooms

Use of Flexibility – adopt or customize to adapt to student’s local culture

Teachers to grow together with students as in life-long learning
7. Dos & Don’ts in PBL4C
a. Teacher & Student Roles
Others
1. ICT tools – GSP, GeoGebra, web-camera & visualiser,
2. Non-ICT tool
References:
1. Holbrook, J.
2. Silver-Homes
3. Ann Lambros
4. PBL4C workshops with BPK, MOE
1) van der Vleuten CPM, Norman G. R., De & Graaff E. (1991) Pitfalls in the pursuit of objectivity:
issues of reliability. Medical Education. 25(2):110-8.
2) Macdonald, R. & Savin-Baden, M. (2004). A briefing on assessment in problem-based learning.
LTSN Generic Centre assessment series; 13. York: Learning and Teaching Support Network
(LTSN).
3) Weaver, W. & Cotrell, H.W. (1986). Peer evaluation: a case study. Innovative Higher Education,
11, 25-39.)
GENERAL NOTE
A. Guide Book
1. This Guide Book will be in soft & hard copies.
2. The hard copy will come with a CD containing the editable context modules developed with MOE,
PBL literature, tools, GeoGebra programme, resources, etc
3. The soft copy may be published online on MOE website together with the modules (however
restricted by the file size)
Timeline
Tentative target output : September 2011
First meeting
: 14 June 2011
Second meeting
:
Next meeting
: 3rd week of July 2011
B. Complete Book
1. This book is more thorough, more complete…geared for mathematics educators generally
2. It will include about 6-10 context modules
i.
New Island Nation in SEA – TBT – plan view
ii.
New Island Nation in SEA – TBT – elevation
iii.
Japan Tsunami – WAP
iv.
Garden design
v.
Web Quest through PBL4C – Back to the Future
vi.
vii.
3. CD – also ?
Quotes:
In classrooms and lectures we learn not only about academic topics but also
about ourselves, our peers and how people and ideas interact.
A sage on the stage. A guide by the side.
Critical thinking
Unkind criticism is never part of a meaningful critique of you. Its purpose is not to
teach or to help, its purpose is to punish.
-- Barbara Sher
"Japanese teachers say that the most powerful part of lesson study is that you
develop the eyes to see children." --Catherine Lewis