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)
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)
Notes from Exit Cards
How to teach conceptually?
Many would like to see more
international comparisons
Differing 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.lifecirclesinc.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 theory
Children should learn through
experience
Education 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
Modern Progressive Teaching
Theories
 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
 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://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 & Brooks
Any 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