Thursday , 8/11/2011: Week 4 Critiques of r eform education Tools for reform education

1. CI 512: Teaching and Learning Thursday, 8/11/2011: Week 4 Critiques of reform education Tools for reform education

2. Class Outline: Critiques and Tools of Reform Teaching Note Taker: Laura White Observer: Mike McClellan • Logistics (9:00-9:05) • Critiques of Reform Teaching • Small Group Discussion (9:05-9:35) • Whole Class (9:35-10:05) • Break (10:05-10:15) • Tools for reform teaching (10:15-10:30) • Video Viewing (10:30-11:10) • Discussion (11:10-11:40) • Observer Observations (11:40-11:45) • Conclusions and Exit Cards (11:45-11:50)

3. Synthesis Draft Comments Citing a lecture • Internal citation: (McCaffrey, 2011) • End reference: Last, F. (July 5, 2011). Name of Talk. Title of Event. Lecture conducted from Location, City, State. Ex. McCaffrey, C. (July 5, 2011). Constructivism. CI 512 Teaching and Learning Theories. Lecture conducted from Portland State University, Portland, OR.

4. Synthesis Draft Comments • Avoid using contractions • Avoid starting sentences with conjunctions (so, and, but, …) • Be sure to include “age-appropriate application of teaching and learning theory within a cultural and community context.”

5. Critiques of Constructivism Ogborn, J. (1997). Constructivism metaphors for science learning. Science & Education. 6, p. 131.

6. Questions • What are Kirschner’s primary critiques of reform teaching? Which of his critiques are focused on constructivism? Which are focused on discovery learning? • Do you agree with Kirschner’scritiques? How might Brooks & Brooks respond to his criticisms? • What implications does the case of Mrs. Oublier have for reform teaching? • Pick out 2 strengths and 2 critiques from Ogborn’s evaluation of constructivism. Do you agree or disagree with his points? What might you add to his list that is currently missing?

7. Tools for Reform Teaching How do you honor the mathematical contributions of students while still moving the mathematical agenda forward?

8. Tools of Reform Teaching: The importance of a teaching goal The Case of Noelle (Hill et.al, 2008) • 3rd grade teacher • Strong use of mathematical language • Provided rich opportunities for students to engage in mathematics • Supported student thinking through in-depth investigations

9. Tools of Reform Teaching: The importance of a teaching goal The Case of Noelle (Hill et.al, 2008) • Complete lack of telos: an end and a purpose • Cube arrangement task • Soma cube task • Net cube task • Students were given a series of rich, engaging tasks that allowed for exploration with no explicit learning goal.

10. Hypothetical Learning TrajectorySimon (1995) Three components: • The learning goal • The learning activities • The hypothetical learning process: a prediction of how the students’ understanding will evolve

11. Hypothetical Learning TrajectorySimon (1995) Hypothetical Learning Trajectory Teacher’s learning goal Teacher’s plan for learning activities Teacher’s hypothesis of learning process Teacher’s Knowledge Assessment of students’ knowledge Interactive constitution of classroom activities

12. Tools for Reform Teaching • Sequencing • Transformational Records* • Counter examples • Selective revoicing • Scaffolding student discourse * Pedagogical Content Tools (Rassmussen & Marrongelle, 2006)

13. Sequencing Intentionally sequence student contributions in a logical order that builds toward the learning objective.

14. Sequencing Bill: And I want to go ahead and start with you guys because I know that you are kind of still in the middle- more in the process of being formed, but you have some of the idea.

15. Transformational Records “Transformational records are defined as notations, diagrams, or other graphical representions that are initially used to record student thinking and that are later used by students to solve new problems” (Rasmussen & Marrongelle, 2006, p. 389) • Teachers can intentionally select which written artifacts are preserved for the class record

16. Counter-examples • Teachers can indirectly challenge student thinking or assumptions through judicious counter-examples • Counter-examples can help redirect students away from misconceptions and toward mathematical goals

17. Bill: If a rectangle is my figure, is that a rigid motion? [Bill rotates the rectangular eraser 90.] Class: Yes. Bill: And what makes that a rigid motion? S1: It has a pivot point. Bill: It has a pivot point. What else? Ellie: It’s not changing the object itself. Bill: It’s not changing the object itself. Is this a rigid motion? [Bill moves the eraser 12 inches up and to the left.] Class: Yes. Bill: Does it have a pivot point? Class: No. Bill: Ok, so a lot of the rigid motions we have been dealing with have pivot points, it doesn’t seem to be a requirement of a rigid motion.

18. Selective Revoicing • Not all student contributions move the mathematical agenda forward • Revoicing is a tool to highlight which student contributions are particularly valuable. • Revoicing can be done by the teacher or a student • Revoicing allows the teacher the opportunity to impart emphasis on the student’s original contribution or to engage other learners

19. Selective Revoicing Bill: And so, Ellie, what again, was your way of expressing that, what a rigid motion is? I did this [moves eraser 12 inches up and to the left], and you had a great explanation just now. Ellie: Something that does not affect the object itself, from changing.

20. Scaffolding Student Discourse • Assigning roles to group members • Dictating speaking order • Providing sentence starters

21. Video Viewing • LP is a 7th grade math teacher at an Oregon middle school • Homogeneous grouping • LP has been teaching for 15 years • Participated in extensive professional development

22. Video Viewing Task: Students have been given a previous class period to work on the following question: How do you think perimeter, area and volume are affected when a figure is scaled?* Students begin by examining the effects of scaling on the perimeter of a square. “Scaling” a figure means multiplying each dimension of the figure by a “scale factor.”

23. Questions for Video Viewing • What pedagogical tools does LP use in this lesson? How were they used? Did you notice other tools? • Sequencing • Transformational Records • Counter examples • Selective revoicing • Scaffolding student discourse 2. What might LP’s hypothetical learning trajectory be? Is there evidence that LP diverts from this learning trajectory? 3. How might Brooks & Brooks analyze LP’s teaching? 4. Did LP provide evidence of telos(a directed learning goal)?

24. Presentations

25. Presentation 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)

26. Observations

27. Exit Card Reflections • Rate your level of participation today (0-3) • Name one thing that you learned today/ positive comment • Name one thing you are struggling with or would like to know more about/less positive comment