CI 512: Teaching and Learning
Thursday, 8/4/2011: Week 3
Constructivism Part II
Class Outline:
Constructivism
Note Taker: Mike Povosky
Observer: Greg Richard
 Logistics (9:00-9:05)
 Constructivist Theory (9:05-9:15)
 Small Group Discussion (9:15-9:45)
 Whole Class (9:45-10:15)
 Break (10:15-10:25)
 Principles of Group Participation (10:25-10:45)
 Project Work Time
 Small Group (10:45-11:30)
 Share Out (11:30-11:40)
 Observer Observations (11:40-11:45)
 Conclusions and Exit Cards (11:45-11:50)
Snap Shots Reflections
 Many snap shots could be strengthened by
adding more specific descriptions of
theory
 Specify who’s version of constructivism
you are using for your analysis
 Please ask if you have questions about my
comments
APA Internal Citations
 When making reference to an author’s name, cite the
date after the name:
Ex. According to Labato (2003) actor-oriented transfer has
advantages over traditional views of transfer.
 When making reference to a source without using the
author’s name, cite the author’s name and date at the
end of the paragraph:
Ex. Paiget describes 4 stages of cognitive development
(Phillips & Soltis, 2009).
 When quoting directly, include author’s name, date, and
page number. Put the quotation marks before the
citation and a period after:
Ex. As Paiget explains, “It is probably possible to accelerate,
but maximal acceleration is not desirable” (Resnick & Ford,
1981, p. 178)
Exit Card Reflections
 One student asked for a shorted break–
another asked for a longer break. Vote?
 Today’s class will focus on Brooks &
Brooks
 Clarity on the connection between Piaget
and Constructivism
 Some are starting to feel the pressure of 3
classes
Constructivist Theories
(Ernst, 1996)
 A plurality of theories: occasionally in
opposition with one another
 Basic premise that learning is a
constructive process
Vocabulary
 Ontology- theory of existence
 Epistemology- theory of learning and the nature
of knowledge
 Pedagogy- theory of teaching, the means to
facilitate knowledge
Weak Constructivism
 All individual human knowledge is individually
constructed
 The mind is a data-processing computer, however all
data is self constructed
 There exists a realm of objective knowledge
 Local paradigm: only accounts for the knowledge
representations of individuals
Weak Constructivism
“Learning is then characterized as a process in which
students gradually construct mental representations that
accurately mirror the mathematical features of external
representations.”
Cobb, Yackel & Wood (1992). A constructivist alternative to
the representational view of the mind in mathematics
education. Journal for Research in Mathematics
Education 23(1) p. 3.
Social Constructivism
 Individuals are “the realm of the social” as inextricably
interconnected
 No metaphor for the isolated individual mind: must be
viewed in terms of its interactions
 Meaning is socially constructed and constrained by the
shared experiences of the underlying physical reality
 Socially constructed meaning seeks to represent the
ontological reality, which will never be fully attained
 Modified relativist ontology: “There is a world out there
supporting the appearances we have shared access to,
but we have no certain knowledge of it” (pg. 343)
Radical Constructivism
 von Glasersfeld (1917-2010)
 Cognition is adaptive
 Only concerned with the experiential world and not an
ontological reality
 Experiencers of the world construct understanding based
upon perception as opposed to inaccessible reality
 Neutral in ontology: not concerned with the existence of
objective world
 Language serves as an imperfect mediator between
unknowable minds
Fish is Fish
Leo Lionni
Small Group Discussion
 How does Fish is Fish story relate to the constructivist
paradigm?
 What are the limitations of language for understanding
the mental constructs of others? What are ways to
resolve the problems of language?
 Discuss the merits of Brooks & Brooks’ argument for a
constructivist classroom. What are some critiques?
 Pick 4 (or more) principles of “constructivist teaching”
outlined in chapter 9.
 Discuss the strengths and weaknesses of each of the
principles?
 How might you see them enacted in your future
classrooms?
Break
Group Presentations
 4-5 people (next slide)
 20-30 minute teaching/learning activity on a topic of the
groups’ choice
 Draw upon at least two different learning theories
 YOUR CHANCE TO SHOW THEORY IN ACTION!
 Feel free to draw upon pre-existing curriculum and
resources
 Illuminations.nctm.org
 Metropolitan Instructional Support Lab (3rd floor)
 Math Resource Lab Neuberger 305
Group Presentation Write-up
It is a GROUP presentation and an INDIVIDUAL write-up
1. A description of how the lesson relates to
teaching/learning theories (1-2 pages)
2. A personal reflection on what you learned and how this
project will impact your future teaching (1-2 pages)
3. An evaluation of every group member (including
yourself) based upon the principles of group
participation created by the class community.
Group Presentation
 Individual write-ups are due the date of
your presentation
 20 points are based on the presentation
 50 points based on the write-ups
 10 points based on group member
evaluations
Principles of Group Participation
 In groups of 3 or 4, brainstorm a list of principles of
group participation that you wish to be evaluated against
 Each principle should be ratable on a scale from 1 to 5
(1 means I don’t agree, 5 means I agree strongly)
Example: This group member was always happy 1 2 3 4 5
 Decide upon your top three principles and list them on
this sheet.
 Remember, these are the criteria that both you and your
group mates will be held accountable to.
Group Presentation Groups
Present Tues. 8/16
Present Thurs. 8/18
Group 1
Group 2
Group 3
Group 4
Group 5
Mike P.
Mike T.
Carlos
Westie
Greg
Nick
Michael
Casey
Laura
Kyle
Colin
Arielle
Martin
Mike M.
Chai
Teale
Iman
Sean
Chad
Karen
Derek
Group Projects
Goals:
 Topic
 Concrete sources
 PLEASE WRITE DOWN YOUR SOURCES!!
Resources:
 Illuminations.nctm.org
 Metropolitan Instructional Support Lab (3rd floor)
 Math Resource Lab Neuberger 305
Observations
Exit Card Reflections
Rate your level of participation
today (0-3)
Name one thing that you learned
today
Name one thing you are struggling
with or would like to know more
about