the theory of conceptual change as a theory for changing conceptions n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
The theory of conceptual change as a theory for changing CONCEPTIONS PowerPoint Presentation
Download Presentation
The theory of conceptual change as a theory for changing CONCEPTIONS

Loading in 2 Seconds...

play fullscreen
1 / 43

The theory of conceptual change as a theory for changing CONCEPTIONS - PowerPoint PPT Presentation


  • 146 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'The theory of conceptual change as a theory for changing CONCEPTIONS' - debbie


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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 & KatrinRolka

Origins
teachers beliefs1

beliefs ↔ practice

contemporary notions

of good practice

Teachers’ Beliefs
teachers beliefs2

beliefs ↔ practice

contemporary notions

of good practice

CHANGE

Teachers’ Beliefs
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
beliefs are difficult to change1

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
beliefs are difficult to change2

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
changing beliefs1

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
changing beliefs2

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
changing beliefs3

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

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
replacing conceptions1

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
replacing conceptions2

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
replacing conceptions3

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
replacing conceptions4

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
replacing conceptions5

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
slide20

the theory of conceptual change is a theory of learning and NOT a theory of teaching

  • there are NO theories of teaching
Hmmm ...
slide21

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 ...
slide22

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 ...
slide23

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 ...
slide24

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 ...
slide25

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 ...
slide26

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 ...
theories of theories for1

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
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
Methodology – participants
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
methodology interventions1

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
methodology interventions2

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
methodology data

field notes

  • students’ journals
  • informal interviews
  • students’ essays
Methodology - data
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
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
the nature of mathematics results1

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
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
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
the nature of m teaching results1

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
the nature of m teaching results2

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
the nature of m teaching results3

If the studentsare 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 studentsare 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
conclusions

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
slide43

THANK YOU!

liljedahl@sfu.ca