Problem-based Learning: Putting the "Why" back into Science and Math Education

1. Problem-based Learning: Putting the "Why" back into Science and Math Education Glen O’Grady Director Centre for Educational Development

2. 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

3. 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)

4. Trends in International Mathematics & Science Study (1999) National Center for Education Statistics

5. 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

6. Math Proficiency in the US (2003)

7. 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.

8. “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.

9. 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.”

10. 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.

11. 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

12. Types of Math Problems used in Eighth-Grade Classes National Center for Education Statistics

13. "school science education must reflect science as it is practiced," The U.S. National Committee on Science Education Standards and Assessment (1992)

14. Solution? Problem-based Learning (PBL) an alternative model for students to learn and teachers to teach?

15. Subject X Subject X Subject X Subject Z Syllabus The Problem Team members (Curriculum) Prior Knowledge Students Instruction-based Teacher Centred Problem-based Student Centred Teacher Student Construction of Knowledge Dissemination of Knowledge Instruct, discipline, assess Facilitator

16. 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

17. Example of PBL in Action Problem Based Learning at the Republic Polytechnic One Day, One Problem Approach

18. 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

19. 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

20. 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

21. 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

22. 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

23. Assessment • Presentations Artefacts • Self Evaluation • Peer Evaluation • Reflection journal • Quiz • Feedback everyday • Written feedback • Daily grade derived in a holistically • Response to understanding test

24. 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

25. 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

26. Hang Float Sink 

27. 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

28. Water out Fractionating column Liebig condenser Water in Distillate Miscible liquid Heat Fractional distillation is a common process adopted in the petrochemical industry and other industrial processes. The following diagram shows a setup for fractional distillation Examine and describe the heat transfer process that happens in the condenser.

29. 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

30. Other tools for facilitating understanding

31. Other tools for facilitating understanding

32. 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)

33. “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)

34. Proposed Values for Mathematics Education • Rationalism  • Empiricism  • Control • Progress  • Openness  • Mystery Centre for Science, Mathematics and Technology Education, Monash Uni

35. 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)

36. 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

37. 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

38. Thanks glen_ogrady@rp.edu.sg http://discovery.rp.edu.sg/home/ced/research/papers.htm

40. Everywhere on Earth, objects falling towards the center of the Earth always fall straight down (can only be true on a sphere).

41. 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.  

42. 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

43. 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

44. 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.

45. Amount of liquid added (kg) 2.0 1.0 Reading on weighing scale (kg) 1.0 2.0 The Graph …

46. 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

47. Condenser Examine and describe the heat transfer process that happens in the condenser. Team 3

48. 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.

49. 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

50. The Graph