Problem-based Learning: Putting the
"Why" back into Science and Math
Education
Glen O’Grady
Director
Centre for Educational Development
Crisis in Science/Math Education?
• Widespread scientific
illiteracy amongst the
general public
• Shortage of good
science teachers
• A reluctance on the part
of pupils to pursue
scientific subjects
Situation in Malaysia
“In the year 2000, there were only 28% of
the secondary school students in the
science stream. The figure is low and
greater efforts need to be put in bringing
the figure to the 60% as targeted by the
government”.
Professor Dr. Hassan bin Said (2000)
Trends in International Mathematics & Science
Study (1999)
Math
Science
18
Latvia-LSS
18
United States
1
Singapore
1
Chinese Taipei
19
United States
19
New Zealand
2
Korea, Republic of
2
Singapore
20
England
20
Latvia-LSS
3
Chinese Taipei
3
Hungary
21
New Zealand
21
Italy
4
Hong Kong SAR
4
Japan
22
Lithuania
22
Malaysia
5
Japan
5
Korea, Republic of
23
Italy
23
Lithuania
6
Belgium-Flemish
6
Netherlands
24
Cyprus
24
Thailand
7
Netherlands
7
Australia
25
Romania
25
Romania
13
Australia
13
Slovenia
26
Moldova
26
Israel
14
Finland
14
Canada
27
Thailand
27
Cyprus
15
Czech Republic
15
Hong Kong SAR
36
Philippines
36
Philippines
16
Malaysia
16
Russian Federation
37
Morocco
37
Morocco
17
Bulgaria
17
Bulgaria
38
South Africa
38
South Africa
National Center for Education Statistics
Science Proficiency in US (2000)
• Grade 4 (9-10 yr olds)
The percentage of students who performed at or
above the Proficient level was 28 percent
38% were below basic (California 62%)
• Grade 8 (13-14 yr olds)
The percentage of students who performed at or
above the Proficient level was 30 percent.
41% were below basic (California 55%)
National Center for Education Statistics
Math Proficiency in the US (2003)
So what’s the Problem?
There's a tug-of-war
between those who feel
that math and science
education should be
aimed at a clever elite,
and those who want
everyone to be able to
do the subject.
“We still force two cultures on our children
aged 16, we ask them do you stand for
Humanities or the Sciences”
Sir Peter William Chairman of the Engineering
& Technology Board, UK.
Science is taught as a collection of
(assumed-to-be) facts, in other words
dogma, which is an anathema to the
practice of Science. To unlearn the dogma of
Science is very difficult, it has been said
that: “You cannot reason a person out of a
position he did not reason himself into in the
first place.”
Is the world round rather or flat?
1150 1st year Polytechnic
students all said they believed
that the earth was round not flat,
however none of the 1150 were
able (or willing) to state what
was the scientific evidence that
supported this proposition
Most said they knew it was
round because:
• they read it in a book,
• seen pictures on TV, or
• their teachers had told them.
Teaching Math in 7 Countries (Eight- Grade Classes): Video
Study (1999): Common Findings
• In all of the countries, math was often taught through
solving problems; at least 80% of lesson time, on
average, was devoted to solving math problems.
• Math lessons were organized to include some wholeclass work and some individual or small-group work.
The most common pattern was for students to work
individually, rather than in pairs or groups.
• On average, lessons included some review of previous
content as well as some attention to new content.
• At least 90 % of lessons made use of a textbook or
worksheet of some kind.
• Teachers in all of the countries talked more than
students, at a ratio of at least 8:1 words.
National Center for Education Statistics
Types of Math Problems used in Eighth-Grade
Classes
National Center for
Education Statistics
"school science education must
reflect science as it is practiced,"
The U.S. National Committee on Science Education
Standards and Assessment (1992)
Solution?
Problem-based Learning (PBL)
an alternative model for students
to learn and teachers to teach?
Instruction-based
Problem-based
Teacher Centred
Student Centred
Syllabus
Subject Z
Subject X
Subject X
Subject X
Teacher
Dissemination
of Knowledge
Instruct, discipline,
assess
Students
The Problem
Team members
(Curriculum)
Student
Construction
of Knowledge
Facilitator
Prior Knowledge
The Process of PBL
• Problem (to triggers learning)
• Students specify:
– what they know about the problem,
– what they don’t know
– what they need to find out
• Student work together in teams to do research
• Presentation of findings
• Assessment & Reflection
Example of PBL in Action
Problem Based
Learning at the
Republic Polytechnic
One Day, One
Problem Approach
RP-PBL: 1st meeting
• Class of 25, 5 teams of
5 students
• Presented a problem
• Students under the
guidance of the
facilitator work on
defining the problem
and identify issues they
will do research on.
• Approximately 1 hour
RP-PBL: 1st Breakout
Student work individually
and in their teams to:
– Find and review
resources
– Begin to develop
tentative solutions for the
problem
– Refine their definition of
the problem
RP-PBL: 2nd Meeting
• Meet with the facilitator
who checks on their
progress
• Focus on any difficulties
students may be having
• Helps students to
develop learning
strategies
RP-PBL: 2nd Breakout
• Student continue to
work in their teams
• Review resources
• Develop a solution/
explanation based upon
their shared
understanding
• Produce a presentation
• 2-3 hours
RP-PBL: 3rd Meeting
• Meet with the facilitator
• Students present their
solutions/explanations
• Students observe how others
have solved the problem
• Facilitators probes and critique
these solutions giving
additional information where
necessary
• Students further check their
understanding by doing a quiz
focussed on the key issues
Assessment
•
•
•
•
•
•
Presentations Artefacts
Self Evaluation
Peer Evaluation
Reflection journal
Quiz
Feedback everyday
– Written feedback
– Daily grade derived in a
holistically
• Response to
understanding test
Examples of Triggers for Learning in Science
• There is no authentic investigation or
meaningful learning if there is no inquiry,
or seeking an answer, solution,
explanation, or decision.
• Share how it plays out
– What students did
– How it demonstrated a better understanding
of Science
– What the facilitator/teacher did
Is the world round or flat?
• What did students do?
– Responded to the question specifying at first what they believed
– Recognised that they lacked necessary information to develop a
more credible (scientific) explanation Students work
• How does this demonstrate a better understanding of
Science?
– Importance of Evidence in Science in explaining the validity of
facts
• What the facilitator/teacher did
– Question whether their “ordinary explanations” were sufficient to
accept as scientific explanations
– Provide help with resources
Hang Float Sink
Hang Float Sink
• What did students do?
– Respond to the curiousness of the activity they observed
– Search for the relevant concept/idea
– They used a scaffolding worksheet, a series of smaller
research questions that helped facilitate students thinking
through the process that leads to an understanding of
Archimedes principle
– Students work
• How does this demonstrate a better understanding
of Science?
– Meaning is derived from making sense of an observation
(concrete experience)
• What the facilitator/teacher did
– Questioning why they think what they do?
– Expecting them to qualify their answers
– Correcting students work after they had attempted the task
of understanding for themselves
– Expect a mathematical explanation
Fractional distillation is
a common process
adopted in the
petrochemical industry
and other industrial
processes. The
following diagram
shows a setup for
fractional distillation
Water out
Fractionating
column
Liebig condenser
Examine and describe
the heat transfer
process that happens
in the condenser.
Water in
Distillate
Miscible liquid
Heat
Condenser
• What did students do?
– Specify their ideas about the process
– Presumed that heat…. Students work
• How does this demonstrate a better
understanding of Science?
– Discover the complexity of the processes
• What the facilitator/teacher did
– Challenge them with an unexpected answer
– Expect students to reason out their conclusions
– Help them reconcile their common sense with a more
scientific explanation
Other tools for facilitating understanding
Other tools for facilitating understanding
Mathematics is more than just numeracy
"Affective issues play a central role in
mathematics learning and instruction. When
teachers talk about their mathematics
classes, they seem just as likely to mention
their students' enthusiasm or hostility
towards mathematics as to report their
cognitive achievements."
(McLeod 1992)
“school mathematics is structured and
delivered in such a way as to portray the
values of the society in which it is delivered”.
(Seah & Bishop 2002)
Proposed Values for Mathematics Education
1.
2.
3.
4.
5.
6.
Rationalism
Empiricism
Control
Progress
Openness
Mystery
Centre for Science, Mathematics and Technology Education,
Monash Uni
Students learn mathematics when they construct their own
mathematical understanding
• Emphasizing communications in mathematics teaching
and learning in order to increase student discourse and
promote student-teacher interactions
• Using topics such as estimation, statistics, probability,
and measurement in ways that are rich in connections to
a variety of cultures.
• Providing numerous opportunities for critical thinking,
problem solving, and reasoning, which many students do
not experience in school.
• Building connections between learning in school and
learning outside of school - in students' families and
communities
The U.S. National Council of Teachers of Mathematics' Curriculum
and Evaluation Standards for School Mathematics (1989)
The Debate rages on…
The equivalence of learning paths in
early science instruction: effects of direct
instruction and discovery learning
(To appear in Psychological Science, 2004)
David Klahr
Department of
Psychology
Carnegie Mellon
University
Milena Nigam
Center for Biomedical
Informatics
University of
Pittsburgh
What is the affect of asking “Why”?
• Emancipation of the learner from the constraints
of learning in a way that encompasses how we
really learn
• Students access and consider claims of a variety
of disciplines
• Critical reflection including a philosophical and
sociological critique of what is being learnt
• The fostering of student independence and
responsibility for learning
Thanks
glen_ogrady@rp.edu.sg
http://discovery.rp.edu.sg/home/ced/research/papers.htm
Everywhere on Earth, objects falling towards the
center of the Earth always fall straight down (can only
be true on a sphere).
If you watch the Sun set,
and at the very moment
when the Sun is just below
the horizon you climb
quickly up a hundred feet,
you will see the Sun again. It
is hard to explain why you
can see further when you
climb higher, unless the
Earth's surface curves
downward away from you
wherever you stand.
The Earth casts a shadow
on the Moon during a lunar
eclipse. The shadow is
round.
What we know …
 Density has a part to play in the problem.
 Weight and height will increase when water is
added into the jar
 Water will be displaced when water is in contact
with the object
 Formula for density is D = M/V
What We Don’t Know …
 What is buoyancy ?
Does the weight increase because
of the suspended bottle?
Formula for pressure
What affects the height of water
level
The Problem …
Peter placed a large jar on a weighing
scale and hung a heavy object from
above so that it does not touch the jar
but is inside the jar. Then he added
water in steps of small measured equal
quantities. After each step of adding
water he took the reading on the
weighing scale. He then plotted a graph
of the weight of total water added
versus the weighing scale reading.
Predict the graph he will get and explain
your answer.
The Graph …
Amount of liquid
added (kg)
2.0
1.0
Reading on
weighing scale
(kg)
1.0
2.0
What we discovered
Formula
• Pressure = density x height
buoyancy force cancel each other out.
This means that the boat is displacing an
amount of liquid that weight as much as
the boat does ...
Pressure = force / area
http://van.hep.uiuc.edu/van/qa/section/Underwater_and
_in_the_Air/Pressure/20030103154058.htm
Condenser
Examine and describe the heat transfer
process that happens in the condenser.
Team 3
Heat Transfer



Heat, a form of kinetic energy, is transferred
in three ways: conduction, convection, and
radiation.
Heat can be transferred only if a
temperature difference exists
Only in the direction of decreasing
temperature.
Question 3
Q/t=kA( T/d)
Difference in temp ( reason for heat transfer):
308K – 296K = 12K
Amount of energy able to transfer by glass in a
hour:
Difference in temp/the thickness X thermal
conductivity (heat lost per sec ) X area X 60 X 60
=
12/0.004 x 0.9 x (1.5 x .0.5 )x (60 x 60) = 7290000W
=7290kW
The Graph
Distance Travelled (m)
Distance vs Temperature
0.12
0.1
0.08
Series1
0.06
0.04
0.02
0
299
300
301
302
303
Temperature (K)
304
Distance travelled (m)
Distance vs Temperature
3.02
3
2.98
2.96
Series1
2.94
2.92
2.9
2.88
346.2 346.4 346.6 346.8
347 347.2
Temperature (K)
The Heating Process In The Condenser
Conduction is the transfer of heat through a substance from a higher to a lower
temperature region
Water is drain out at the top to provide
further conduction back to the water
vapour in the inner tube.
Water out
Liebig condenser
Water in
Distillate
When steam touches the inner tube of the condenser, conduction occurs.
Heat is transferred to the wall of the inner tube by the steam then to the
water in the outer tube.