1. CI 512: Teaching and Learning Thursday, 8/4/2011: Week 3 Constructivism Part II

2. Class Outline: Constructivism Note Taker: Mike PovoskyObserver: 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)

3. 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

4. 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)

5. 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

6. Constructivist Theories (Ernst, 1996)  A plurality of theories: occasionally in opposition with one another  Basic premise that learning is a constructive process

7. Vocabulary  Ontology- theory of existence  Epistemology- theory of learning and the nature of knowledge  Pedagogy- theory of teaching, the means to facilitate knowledge

8. 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

9. 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.

10. 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)

11. 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

12. Fish is Fish Leo Lionni

13. 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?

14. Break

15. 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 (3 rd floor)  Math Resource Lab Neuberger 305

16. 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.

17. 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

18. 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.

19. Group Presentation Groups Present Tues. 8/16Present Thurs. 8/18 Group 1Group 2Group 3Group 4Group 5 Mike P.Mike T.CarlosWestieGreg NickMichaelCaseyLauraKyle ColinArielleMartinMike M.Chai TealeImanSeanChadKaren Derek

20. Group Projects Goals:  Topic  Concrete sources  PLEASE WRITE DOWN YOUR SOURCES!! Resources:  Illuminations.nctm.org  Metropolitan Instructional Support Lab (3 rd floor)  Math Resource Lab Neuberger 305

21. Observations

22. 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