1. The theory of conceptual change as a theory for changing CONCEPTIONS
Peter Liljedahl

2. 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
Origins

3. beliefs ↔ practice
Teachers’ Beliefs

4. beliefs ↔ practice ↕ contemporary notions of good practice
Teachers’ Beliefs

5. beliefs ↔ practice ↕ contemporary notions of good practice
CHANGE
Teachers’ Beliefs

6. 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).
Beliefs are Difficult to Change

7. 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).
Beliefs are Difficult to Change

8. 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).
REPLACE
Beliefs are Difficult to Change

9. REPLACING
Changing Beliefs

10. REPLACING 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
REPLACING
Changing Beliefs

11. REPLACING 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
REPLACING
Changing Beliefs

12. REPLACING CONCEPTIONS
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
REPLACING
Changing Beliefs
CONCEPTIONS

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

14. 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
Replacing Conceptions

15. 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
Replacing Conceptions

16. 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
Replacing Conceptions

17. 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
Replacing Conceptions

18. 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?
PROBLEM
cognitive
conflict
Replacing Conceptions

19. the theory of conceptual change is a theory of learning and NOT a theory of teaching
Hmmm ...

20. the theory of conceptual change is a theory of learning and NOT a theory of teaching
there are NO theories of teaching
Hmmm ...

21. 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)
Hmmm ...

22. 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?
Hmmm ...

23. 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
Hmmm ...

24. 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
Hmmm ...

25. 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?
Hmmm ...

26. 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
Hmmm ...

27. Theories of → Theories for
THEORIES OF CONCEPTUAL CHANGE ↓
THEORY FOR CHANGING CONCEPTIONS
Theories of → Theories for

28. 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
Theories of → Theories for

29. Methodology – participants
14 inservice secondary mathematics teachers
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
Methodology – participants

30. 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
Methodology - interventions

31. 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
Methodology - interventions

32. 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
Methodology - interventions

33. Methodology - data field notes students’ journals informal interviews
students’ essays
Methodology - data

34. 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.
The Nature of Mathematics - treatment

35. 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.
The Nature of Mathematics - results

36. 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.
The Nature of Mathematics - results

37. 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.
The Nature of M. Teaching - treatment

38. 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.
The Nature of M. Teaching - results

39. 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.
The Nature of M. Teaching - results

40. 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).
The Nature of M. Teaching - results

41. 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).
The Nature of M. Teaching - results

42. the theory of conceptual change is a viable theory for designing interventions for the purpose of changing conceptions
implementation of these interventions resulted in cognitive conflict and eventually rejection of the participants’ a priori beliefs
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
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
Conclusions

43. THANK YOU!