1. MAVI 17, Bochum 2011 THE THEORY OF CONCEPTUAL CHANGE AS A THEORY FOR CHANGING CONCEPTIONS Peter Liljedahl

2. MAVI 17, Bochum 2011 Origins research on changes in beliefs MAVI 2009, MAVI 2006*, CERME 2009, PME 2006* changes in beliefs as conceptual change CERME 2007*, PME 2007*, JMTE 13 (5) changing conceptions WoMB 2010 NOMAD 16(1-2) * with Bettina Rösken & Katrin Rolka

3. MAVI 17, Bochum 2011 Teachers’ Beliefs beliefs ↔ practice

4. MAVI 17, Bochum 2011 Teachers’ Beliefs beliefs ↔ practice ↕ contemporary notions of good practice

5. MAVI 17, Bochum 2011 Teachers’ Beliefs beliefs ↔ practice ↕ contemporary notions of good practice

6. MAVI 17, Bochum 2011 Beliefs are Difficult to Change Beliefs are “like possessions. They are like old clothes; once acquired and worn for awhile, they become comfortable. It does not make any difference if the clothes are out of style or ragged. Letting go is painful and new clothes require adjustment” (Schommer- Aikins, 2004, p. 22).

7. MAVI 17, Bochum 2011 Beliefs are Difficult to Change Beliefs are “like possessions. They are like old clothes; once acquired and worn for awhile, they become comfortable. It does not make any difference if the clothes are out of style or ragged. Letting go is painful and new clothes require adjustment” (Schommer- Aikins, 2004, p. 22).

8. MAVI 17, Bochum 2011 Beliefs are Difficult to Change Beliefs are “like possessions. They are like old clothes; once acquired and worn for awhile, they become comfortable. It does not make any difference if the clothes are out of style or ragged. Letting go is painful and new clothes require adjustment” (Schommer- Aikins, 2004, p. 22).

9. MAVI 17, Bochum 2011 Changing Beliefs

10. MAVI 17, Bochum 2011 Changing Beliefs CONCEPTUAL CHANGE emerges out of Kuhn's (1970) interpretation of changes in scientific understanding through history progress in scientific understanding is marked more by theory replacement than theory evolution

11. MAVI 17, Bochum 2011 Changing Beliefs CONCEPTUAL CHANGE emerges out of Kuhn's (1970) interpretation of changes in scientific understanding through history progress in scientific understanding is marked more by theory replacement than theory evolution

12. MAVI 17, Bochum 2011 Changing Beliefs CONCEPTUAL CHANGE emerges out of Kuhn's (1970) interpretation of changes in scientific understanding through history progress in scientific understanding is marked more by theory replacement than theory evolution

13. MAVI 17, Bochum 2011 Replacing Conceptions CONCEPTUAL CHANGE applicable only in those instances where misconceptions are formed through lived experiences and in the absence of formal instruction

14. MAVI 17, Bochum 2011 Replacing Conceptions CONCEPTUAL CHANGE applicable only in those instances where misconceptions are formed through lived experiences and in the absence of formal instruction phenomenon of theory rejection phenomenon of theory replacement cognitive conflict

15. MAVI 17, Bochum 2011 Replacing Conceptions CONCEPTUAL CHANGE applicable only in those instances where misconceptions are formed through lived experiences and in the absence of formal instruction phenomenon of theory rejection phenomenon of theory replacement synthetic model cognitive conflict

16. MAVI 17, Bochum 2011 Replacing Conceptions CONCEPTUAL CHANGE applicable only in those instances where misconceptions are formed through lived experiences and in the absence of formal instruction phenomenon of theory rejection phenomenon of theory replacement synthetic model cognitive conflict

17. MAVI 17, Bochum 2011 Replacing Conceptions CONCEPTUAL CHANGE applicable only in those instances where misconceptions are formed through lived experiences and in the absence of formal instruction phenomenon of theory rejection phenomenon of theory replacement synthetic model CAN I DO THIS? cognitive conflict

18. MAVI 17, Bochum 2011 Replacing Conceptions CONCEPTUAL CHANGE applicable only in those instances where misconceptions are formed through lived experiences and in the absence of formal instruction phenomenon of theory rejection phenomenon of theory replacement synthetic model CAN I DO THIS? cognitive conflict

19. MAVI 17, Bochum 2011 Hmmm... the theory of conceptual change is a theory of learning and NOT a theory of teaching

20. MAVI 17, Bochum 2011 Hmmm... the theory of conceptual change is a theory of learning and NOT a theory of teaching there are NO theories of teaching

21. MAVI 17, Bochum 2011 Hmmm... the theory of conceptual change is a theory of learning and NOT a theory of teaching there are NO theories of teaching While theory provides us with lenses for analysing learning (Lerman, 2001), the big theories do not seem to offer clear insights to teaching and ways in which teaching addresses the promotion of mathematics learning. (Jaworski, 2006, p. 188)

22. MAVI 17, Bochum 2011 Hmmm... the theory of conceptual change is a theory of learning and NOT a theory of teaching there are NO theories of teaching While theory provides us with lenses for analysing learning (Lerman, 2001), the big theories do not seem to offer clear insights to teaching and ways in which teaching addresses the promotion of mathematics learning. (Jaworski, 2006, p. 188) IS THIS TRUE?

23. MAVI 17, Bochum 2011 Hmmm... I propose that the source of this tension between theories of learning and theories of teaching is the assumption that theories should play the same role in teaching as they do in learning

24. MAVI 17, Bochum 2011 Hmmm... I propose that the source of this tension between theories of learning and theories of teaching is the assumption that theories should play the same role in teaching as they do in learning teaching and learning are inherently different activities

25. MAVI 17, Bochum 2011 Hmmm... I propose that the source of this tension between theories of learning and theories of teaching is the assumption that theories should play the same role in teaching as they do in learning teaching and learning are inherently different activities IN WHAT WAYS?

26. MAVI 17, Bochum 2011 Hmmm... I propose that the source of this tension between theories of learning and theories of teaching is the assumption that theories should play the same role in teaching as they do in learning teaching and learning are inherently different activities to theorize about them requires, not (necessarily) the use of different theories, but the use of theories differently

27. MAVI 17, Bochum 2011 Theories of → Theories for THEORIES OF CONCEPTUAL CHANGE ↓ THEORY FOR CHANGING CONCEPTIONS

28. MAVI 17, Bochum 2011 Theories of → Theories for NOT A NEW IDEA Van den Heuvel-Panhuizen (2003) model of → model for Streefland (1993) pre-image → post-image Simon (1995) teaching with constructivism Fried (2011) theory of / theory for / theory in

29. MAVI 17, Bochum 2011 Methodology – participants 14 inservice secondary mathematics teachers 0 - 23 years, average of 8.7 years 8 males, 6 females 6 had undergraduate degrees in mathematics 7 had a degree in one of the sciences 1 had a degree in history majority of the group had been teaching mathematics either exclusively or in conjunction with some other subject areas for the majority of their careers ALL of the participants considered themselves to be mathematics teachers

30. MAVI 17, Bochum 2011 Methodology - interventions 6 interventions – cognitive conflict the nature of mathematics the nature of mathematics teaching the nature of assessment the nature of student knowledge the nature of student learning the nature of student motivation

31. MAVI 17, Bochum 2011 Methodology - interventions 6 interventions – cognitive conflict the nature of mathematics the nature of mathematics teaching the nature of assessment the nature of student knowledge the nature of student learning the nature of student motivation

32. MAVI 17, Bochum 2011 Methodology - interventions 6 interventions – cognitive conflict the nature of mathematics the nature of mathematics teaching the nature of assessment the nature of student knowledge the nature of student learning the nature of student motivation

33. MAVI 17, Bochum 2011 Methodology - data 1.field notes 2.students’ journals 3.informal interviews 4.students’ essays

34. MAVI 17, Bochum 2011 The Nature of Mathematics - treatment Lockhart’s Lament (2008) A musician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made— all without the advice or participation of a single working musician or composer.

35. MAVI 17, Bochum 2011 The Nature of Mathematics - results Interviewer:A few weeks ago I had you read Lockhart's Lament in class. Tell me what you thought about that. Grant:It made things pretty clear, didn't it?[laughs] I mean, the way that he described music and art sure made you think about what we are doing to kids in math. Interviewer:And? Grant:And we sure as hell shouldn't be doing it? Interviewer:So, what should we be doing? Grant:I'm not sure. Problem solving for sure. And probably more group work. But I haven't figured it all out yet. Interviewer:So, what made you come away from your initial ideas about mathematics? Grant:To be honest, I had never really thought about it before... I hadn't really looked at what I was teaching in such a stark way. Lockhart paints a picture that is hard to ignore.

36. MAVI 17, Bochum 2011 The Nature of Mathematics - results Interviewer:A few weeks ago I had you read Lockhart's Lament in class. Tell me what you thought about that. Grant:It made things pretty clear, didn't it?[laughs] I mean, the way that he described music and art sure made you think about what we are doing to kids in math. Interviewer:And? Grant:And we sure as hell shouldn't be doing it? Interviewer:So, what should we be doing? Grant:I'm not sure. Problem solving for sure. And probably more group work. But I haven't figured it all out yet. Interviewer:So, what made you come away from your initial ideas about mathematics? Grant:To be honest, I had never really thought about it before... I hadn't really looked at what I was teaching in such a stark way. Lockhart paints a picture that is hard to ignore.

37. MAVI 17, Bochum 2011 The Nature of M. Teaching - treatment Experiencing School Mathematics (Boaler, 2002). It can be said that when we read a book we read ourselves into the text. In what ways do you read yourself into Boaler's book? Speak about your own teaching practice (past, present, and future) in relation to the book.

38. MAVI 17, Bochum 2011 The Nature of M. Teaching - results It was as though I was looking at my own teaching. I couldn't help but think that Boaler was describing my classroom. Nicholas:I certainly would fit in well with the teachers at Amber Hill, especially with the focus on testing. But I'm not exactly the same. I tend to make more use of group work especially during project work. Chad:It was good... it was eye-opening. As I was reading it I kept trying to identify myself with Jim at Phoenix Park but I kept coming back to Amber Hill. It was really troubling when I finally realized that I was an Amber Hill teacher.

39. MAVI 17, Bochum 2011 The Nature of M. Teaching - results It was as though I was looking at my own teaching. I couldn't help but think that Boaler was describing my classroom. Nicholas:I certainly would fit in well with the teachers at Amber Hill, especially with the focus on testing. But I'm not exactly the same. I tend to make more use of group work especially during project work. Chad:It was good... it was eye-opening. As I was reading it I kept trying to identify myself with Jim at Phoenix Park but I kept coming back to Amber Hill. It was really troubling when I finally realized that I was an Amber Hill teacher.

40. MAVI 17, Bochum 2011 The Nature of M. Teaching - results If the students are not going remember the stuff we teach them then have they really learned? And if not, then what was the point in the first place? (Ingrid) If the students are not engaging with the lesson then there is no way that they can learn. (Eric). Math needs to be fun. Sitting in rows and listening to the teacher is not fun. (Alicia).

41. MAVI 17, Bochum 2011 The Nature of M. Teaching - results If the students are not going remember the stuff we teach them then have they really learned? And if not, then what was the point in the first place? (Ingrid) If the students are not engaging with the lesson then there is no way that they can learn. (Eric). Math needs to be fun. Sitting in rows and listening to the teacher is not fun. (Alicia).

42. MAVI 17, Bochum 2011 Conclusions 1.the theory of conceptual change is a viable theory for designing interventions for the purpose of changing conceptions 2.implementation of these interventions resulted in cognitive conflict and eventually rejection of the participants’ a priori beliefs 3.the cognitive conflict that precipitates this belief rejection seems to be greatly affected by the starkness of the images presented – especially when those images are both troubling and undeniably reflective of the participant's practice 4.the data is replete with evidence that the participants not only rejected beliefs pertaining to their current practices, but that often they did so without an immediate replacement at hand

43. MAVI 17, Bochum 2011 THANK YOU! liljedahl@sfu.ca