CI 512: Teaching and LearningThursday, 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)

Class OutlineGestaltism, 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)

Notes from Exit Cards

How to teach conceptually?Many would like to see more

international comparisonsDiffering definitions of conceptual

and procedural understanding

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

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)

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

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

Reification: the constructive aspect of perception

Reification: the constructive aspect of perception

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

More Resources

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.

Transfer

Transfer does not stand alone as a learning theory

Implications for learning theory and teaching theory

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?

“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)

Progressivism

Child-centered teaching theoryChildren should learn through

experienceEducation and learning is social and

interactive

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

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

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

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/

Modern Progressive Teaching Theories

Modern Progressive Teaching Theories

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.html

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://tsg.icme11.org/document/get/812 proceedings from 11th International Congress on Mathematics Education (2008)

Volleyball Problem

What letter comes next in this sequence?

O T T F F S S __

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

Theory Recap

Plato’s Theory of Eternal Knowledge

Locke’s “Tabla Rasa”

Behaviorism

Gestaltism

Progressivism and Realistic Education

Reading

Ch. 5 Phillips & Soltis (Constructivism)

Ch. 1 Brooks & BrooksAny extra reading on Gestaltism or

Progressivism for snapshots

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