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) 14 15 16 17 1 2 3 4 5 6 7 13 Math Singapore Korea, Republic of Chinese Taipei Hong Kong SAR Japan Belgium-Flemish Netherlands Australia Finland Czech Republic Malaysia Bulgaria 14 15 16 17 1 2 3 4 5 6 7 13 Science Chinese Taipei Singapore Hungary Japan Korea, Republic of Netherlands Australia Slovenia Canada Hong Kong SAR Russian Federation Bulgaria 26 27 36 37 18 19 20 21 22 23 24 25 38 Latvia-LSS United States England New Zealand Lithuania Italy Cyprus Romania Moldova Thailand Philippines Morocco South Africa 26 27 36 37 18 19 20 21 22 23 24 25 38 United States New Zealand Latvia-LSS Italy Malaysia Lithuania Thailand Romania Israel Cyprus Philippines Morocco 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 1 st 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 whole class 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 Teacher Centred Syllabus

Teacher

Dissemination of Knowledge

Instruct, discipline, assess

Students Problem-based Student Centred The Problem

(Curriculum) Team members 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: 1

st

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: 1

st

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: 2

nd

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: 2

nd

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: 3

rd

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 Fractionating column Examine and describe the heat transfer process that happens in the

condenser

.

Water out Water in Heat Miscible liquid Liebig condenser Distillate

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. Rationalism 2. Empiricism 3. Control 4. Progress 5. Openness 6. 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

[email protected]

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.

1.0

2.0

Amount of liquid added (kg)

The Graph …

1.0

2.0

Reading on weighing scale (kg)

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 vs Temperature

0.12

0.1

0.08

0.06

0.04

0.02

0 299 300 301 302

Temperature (K)

303 304 Series1

Distance vs Temperature

3.02

3 2.98

2.96

2.94

2.92

2.9

2.88

346.2 346.4 346.6 346.8

347 347.2

Temperature (K)

Series1

The Heating Process In The Condenser

Conduction is the transfer of heat through a substance from a higher to a lower temperature region Water out Water is drain out at the top to provide further conduction back to the water vapour in the inner tube.

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.