Milton meets Einstein Inquiring Minds want to Know Drs.Mary Hynes-Berry and Gordon Berry at the University of Nebraska 9 April 2009 INQUIRY In Science and Literature Failure produces learning A paradox (a more gentle form of failure) can help learning
The incompleteness of mathematics: Godel (1933) strikes down the completeness of axiomatic set theory postulated by Whitehead and Russell in Principia Mathematica (1912) Is a parallel to The incompleteness of science Refinement of Newtonian theory (the Principia, 1702) by Einsteins theory of relativity (1905) Incompleteness in literature too! From Sorensen (2005)
G.G. Berry was one of the first individuals to produce new semantic paradoxes. Berrys paradox was first presented to Russell (1905) in the following sentence: The least integer not namable in fewer than nineteen syllables is itself a name consisting of eighteen syllables; hence the least integer not namable in fewer than nineteen syllables can be named in eighteen syllables, which is a contradiction A more recent paradox (Douglas Hofstadter) is What is the smallest uninteresting integer? What do you think it might be? Is it different from mine? As part of the answer you can note: 1 is interesting it is the smallest positive integer, 2 is interesting it is the smallest even number
3 is interesting it is the smallest prime-number, 7 is interesting it is a prime-number .. . These Inquiring Minds both want to know BUT They ask different questions! Key Concept 1 Elegant Solutions
are the highest order of what might be termed Quality Intellectual Work To produce good scientists, good humanists, good world citizens, our goal must be to support quality intellectual work in teaching and learning at all levels, i.e. from earliest childhood til death do us part.
ELEGANT SOLUTIONS Concise synthesis Deceptively simple but comprehensive in what they explain Compelling Physics/sciences Open-ended question concerning the nature of the physical universe
Poetry/arts Open-ended question concerning Human nature Uses inference, analogy, Uses causal reasoning metaphor Result is reproducible Result is unique, Solution can be validated by
irreproducible reproducing the proof and is Truth or validity resonates with verified by other/new the human experience experiments or demonstrations Imitations lose the elegance of the solution Einstein : Why the passage of Milton : How does imagery of time depends on our relative the sun shining on a manspeeds? centered universe justify Gods
ways to man? (scientists in general) (artists in general) Inquiring minds may want to know different answers to the same question: In Physics, Literature, Life The two body problem has satisfactory solutions The three body problem remains
challenging Key concept 2 Learning INQUIRY Play Quality Intellectual Work
Quality intellectual work, learning, and play are different angles in the process of INQUIRY Key Concept 3: Inquiry calls for deep engagement with the question; Misconceptions and error
are essential to the process of problem-solving Quality intellectual work Has three essential features: Construction of knowledge that actively involves the learner in developing his/her understanding Through the use of Guided/disciplined Inquiry To produce discourse, products, or performances that have Value beyond the classroom.
cf: Newman, F. and associates. (1996) Authentic achievement: Restructuring schools for intellectual quality. San Francisco: Jossey-Bass. The SIP Principle Play is Satisfying Intentional Problem solving Do you feel the same way about your work?
Learning INQUIRY Play Quality Intellectual Work Every child is a scientist at play: Wondering and problem-solving about how the world works. Every scientist was a child at play.
Goldilocks and the Three Bears Has the science in this story ever worried you? How could the porridge in the Bears bowls be too hot, too cold and just right? Working with 1 or 2 others: write an explanatory scenario in your blue book that is consistent with your scientific understanding.
Do we have any volunteers with solutions.! What Makes Guided Inquiry? Engagement Exploration Evaluation What makes Guided Inquiry
Engagement ENGAGEMENT is triggered by posing an interesting, open-ended question about a specific problem that does not have a unique solution Whatever the solution, it must be wellsupported What Makes Guided Inquiry? Exploration EXPLORATION is carried out by the learners,
Drawing on prior knowledge and experience, using methodology appropriate to the discipline (in this case, physics - the laws of thermodynamics). The Teacher facilitates by raising clarifying, probing questions. NOT full frontal lecture, cookbook science lab; fill-in-the blank worksheets What Makes Guided Inquiry? Evaluation EVALUATION is intrinsic.
Is this a sufficient answer to the problem, as far as Im concerned? Possibilities include Yes, its Goodor at least its good enough Yes, but it raises a new question/problem I now want to pursue. No, I need to decide if the question needs revising or there was a problem with the investigation (identify new variables, refine data collection, use tools better or use better tools) NOT: Is this the teachers right answer?
Mis-Guided Inquiry Ptolemaic vs Copernican Universe Better Poetry Vs
Better Science Representations of the Solar System A B C
Which of these three figures best represents the earth moving in orbit around the sun? Lets VOTE. How do preconceptions/misconceptions affect the ability to learn? How do Harvard Professors and students compare with Nebraska professors and students? Graduation at Harvard.. The Reasons for the Seasons Notes: 1. Why are these misconceptions so strong?
(even after taking several physics courses) 2. How do you verify prior learning or mislearning of your students? A more personal view of ones UNIVERSE Consider The science you do The science you teach IS IT WORK? or
IS IT PLAY? Do you consider Quality Intellectual Work Important? Which is a more serious concern? The students dont work hard enough. The students are only interested in the right answers, not in reasoning or playing with the ideas?
Science Daily (Feb. 1, 2009) Researchers Tested Nearly 6,000 Students Majoring In Science And Engineering At 7 Universities -- 4 In The United States And 3 In China. Chinese Students Greatly Outperformed American Students On Factual Knowledge Of Physics Averaging 90 Percent On One Test, versus The American Students 50 Percent But In A Test Of Science Reasoning, Both Groups Averaged Around 75 Percent Not A Very High Score, Especially For Students
Hoping To Major In Science Or Engineering. Does your testing of students follow this model? Experience is a better teacher than the voice of experience. We tend to
remember Inquiry Based Learning Two questions for you about this presentation 1. What surprised /interested/ delighted you? 2. What applications do you see this having to you own teaching
Please write your answers in your blue book They will help us in our research on Learning how to learn - Thank you The END References / Bibliography Newman, F. and associates. (1996) Authentic achievement: Restructuring schools for intellectual quality. San Francisco: Jossey-Bass.
Richard F. Elmore (2008) Improving the Instructional Core. Preprint form Science Media Group, Harvard-Smithsonian Center for Astrophysics A Private Universe - Minds of our own. (DVD) W. C. Kreye and F. L. Roesler, Analysis of Hollow-Cathode-Discharge-Excited Ar I, Ar II, and Au I Spectral-Line Profiles Measured with a Fabry-Perot Interferometer J. Opt. Soc. Am. 60, 1100 (1970). For preliminary observations, see also M. Hynes, Love Song to a Hollow Cathode Appl. Opt. 7, 1809 (1968) Gregory Chaitin (2005) Meta Math! Vintage Press Roy Sorensen, (2003) A Brief History of the Paradox - Philosophy of the Labyrinths of the Mind. Oxford University Press Sherry Turkle, (2008) Falling for Science: Objects in Mind. Cambridge: MIT Press
A pdf file of this presentation can be found at the website: http://www.nd.edu/~hgberry/berry1.html W. C. Kreye and F. L. Roesler, J. Opt. Soc. Am. 60, 1100 (1970). For preliminary observations, see also M. Hynes, Appl. Opt. 7, 1809 (1968) 1. Reflection (a lesson you have had before - although you may not remember the details...) - from a rough surface - from a flat mirror - from a curved mirror 2. Refraction - the lesson for today How does light change direction when passing through a transparent material?
The sketch below on the left shows a light beam passing through the flat face of a semicircular block. How do you think the beam will behave if it enters the flat face at an angle as shown in the sketch at the right? ? (A) Draw a sketch - you might want to make the sketch scientific by adding labels/short explanatory descriptions. page 2 (B) WHAT ARE YOUR GROUP'S IDEAS? Draw sketches and ideas that are different from yours. Can you come a
consensus on what happens? (C) Now your group can do the experiment with the laser provided.... Important instruction: note that the laser light should hit the surface at the CENTER of the flat side. Discuss with your group: What did you observe? Was it what you predicted? If not, how did it differ? Make a sketch of what happens to the beam of light (D) Discuss our results as a whole group (E) What general conclusions can we draw about REFRACTION?
Where do you see refraction in your life - ...?? (F) How did learning take place? Did you ever wonder why? Science word use Pierre and Marie Curie were radiating enthusiasm. Einstein thought it would be relatively easy.
Volta was electrified Archimedes was buoyant about it. Ampere was happy that it was up on current research. Ohm resisted the idea at first. Descartes said he'd think about it. Newton was moved to react. Salk said it gave him a shot in the arm Pavlov was drooling at the thought. Boyle said it would not be too much pressure. Edison thought it would be an illuminating experience.
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