1. CI 512: Teaching and Learning Thursday, 7/28: Week 2 Gestaltism Transfer and Realistic Education Warm-up: What letter comes next in this sequence? O T T F F S S __ (don’t speak if you find a solution)

2. Class Outline Gestaltism, Transfer and Realistic Education Note Taker: Colin Douglas Observer: Chai Young Kim  Logistics (9:00-9:05)  Gestaltism (9:05-9:15)  Transfer  Small Group Discussion (9:15-9:45)  Whole Class (9:45-10:15)  Progressivism and Realistic Education  Whole Class (10:15-10:35)  Small Group and Break (10:35-11:10)  Whole Class (11:10-11:40)  Observer Observations (11:40-11:45)  Conclusions and Exit Cards (11:45-11:50)

3. Notes from Exit Cards  How to teach conceptually?  Many would like to see more international comparisons  Differing definitions of conceptual and procedural understanding

4. Strands of Mathematical Proficiency  Conceptual understanding—comprehension of mathematical concepts, operations, and relations  Procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately  Strategic competence—ability to formulate, represent, and solve mathematical problems  Adaptive reasoning—capacity for logical thought, reflection, explanation, and justification  Productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding It Up: Helping Children Learn Mathematics. download.nap.edu/catalog.php?record_id=9822

5. Gestaltism: Origins  Christian von Ehenfels (1859-1932) is credited with founding the theory of gestaltism in his work Über Gestaltqualitäten (On the Qualities of Form, 1890)  Other significant contributors:  Max Wertheimer (1880-1943)  Graham Wallas (1898-1932)  Wolfgang Köhler (1887-1967)

6. Gestaltism: Primary Philosophy  “Gestalt” means “figure” or “form” in German  Reject the conception that an object could be satisfactorily studied by breaking it up into components  Maintains that objects are “more than the sum of their parts”  Conscious experience must be considered globally

7. Gestaltism: Perception  Perceiving objects typically does not take place by recognizing individual features of the object (such as the feet, nose and ears of a dog), but wholistically  Reification: the constructive aspect of perception

8. Reification: the constructive aspect of perception

11. Gestaltism: Applications to Learning  Learning does not take place in linear fashion with the accumulation of small improvements over time  Learning is characterized by an “Aha!” moment in which the pieces come together  The steps leading up to such insights may yield little external results  Something learned is not easily forgotten

12. More Resources  http://www.lifecircles- inc.com/Learningtheories/gestalt/gestalttheory.html http://www.lifecircles- inc.com/Learningtheories/gestalt/gestalttheory.html  Rock, I. & Palmer, J. (1990). The legacy of gestalt psychology. Scientific American 263(10), 48-61.

13. Transfer  Transfer does not stand alone as a learning theory  Implications for learning theory and teaching theory

14. Small Group Questions  What is transfer?  What is the difference between actor oriented transfer and traditional models of transfer?  How does context affect transfer?  What implications does transfer have for high school learning?

15. “My biggest concern about American education is that even our better students in our better schools are just going through the motions of education. There is ample evidence that suggests an absence of understanding--the inability of students to take skills, and other apparent attainments and apply them successfully in new situations. In the absence of flexibility and adaptability, the education that the students receive is worth little.” Howard Gardner, Chair of Education at Harvard (1994)

16. Progressivism  Child-centered teaching theory  Children should learn through experience  Education and learning is social and interactive

17. Progressivism Principles (1919) 1.Freedom to develop naturally 2.Interest the motive of all work 3.The teacher as a guide, not a taskmaster 4.Scientific study of pupil development 5.Greater attention to all that affects the child’s physical development 6.Cooperation between school and home to meet the needs of child life 7.The progressive school as leader in educational movements Progressive Education Association

18. Progressivism John Dewey (1859-1952)  Educational philosopher  Education as a means to reach one’s full potential  School as a primary means for social reform  Proponent of hands-on learning

19. Modern Progressive Teaching Theories  Realistic Mathematics Education (RME)  Hans Freudenthal (1973, 1991) and Keono Gravenmeijer (1999, 2003)  Focuses on guided reinvention of mathematics through experientially realistic situations  Allows students opportunities to develop and formalize informal solution strategies  Reinvention is both a collective and individual activity

20.  Project-Based Science Education (PBS)  Major initiative from University of Michigan (1991)  Science instruction centered around authentic inquiry based on meaningful questions  Allow students to construct research questions and formulate hypotheses  http://www.umich.edu/~pbsgroup/ http://www.umich.edu/~pbsgroup/ Modern Progressive Teaching Theories

21.  Mathematical Modeling  Investigating problems within a “real life” context  Focus on utilization of technology, inclusion of extra information and non-quantifiable data http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.htm l Lesh, R., & English, L. D. (2005). Trends in the evolution of models and modelling perspectives on mathematical learning and problem solving. In H. Chick & J. Vincent (Eds.), Proceedings of the 29th Annual Conference of the International Group for the Psychology of Mathematics Education. (pp. 192-196). University of Melbourne. http://eprints.qut.edu.au/3520/1/3520.pdf http://eprints.qut.edu.au/3520/1/3520.pdf http://tsg.icme11.org/document/get/812http://tsg.icme11.org/document/get/812 proceedings from 11th International Congress on Mathematics Education (2008)

22. Volleyball Problem

23. What letter comes next in this sequence? O T T F F S S __

24. Homework: Snapshot Draft 2 For 2 different learning experiences: 1. Describe the learning experience in a well written paragraph 2. Interpret that experience through the lens of at least two different learning theories

25. Theory Recap  Plato’s Theory of Eternal Knowledge  Locke’s “Tabla Rasa”  Behaviorism  Gestaltism  Progressivism and Realistic Education

26. Reading  Ch. 5 Phillips & Soltis (Constructivism)  Ch. 1 Brooks & Brooks  Any extra reading on Gestaltism or Progressivism for snapshots

27. Exit Card Reflections  Rate your level of participation today (0-3)  Name one aspect of today’s class that was beneficial for you  Name one aspect of today’s class that could be improved