Transcript Sensible Systems of Beliefs

Theoretical and Methodological Issues
in Research on Teachers’ Beliefs
Keith R. Leatham
Brigham Young University
Denise S. Mewborn
University of Georgia
Natasha M. Speer
Michigan State University
2006 NCTM Research Pressession
Presentation Outline
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Beliefs as a Lever for Change—Denise
Viewing Teachers’ Beliefs as Sensible
Systems—Keith
Inconsistencies in beliefs and practices:
Methodological artifact?—Natasha
Discussion
2006 NCTM Research Pressession
Beliefs as a Lever for Change
Denise S. Mewborn
University of Georgia
2006 NCTM Research Pressession
Carrie
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I hate math. Math was invented by
someone who was very angry as a way to
get back at society. And the thought of
teaching math wakes me up in the middle
of the night in a cold sweat.
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Carrie, 6 months later

Teaching math is nothing more than
exploring math with your learners. I’ve
learned that “wrong answers” are such a gift
in the classroom because they open the
doors for so much more understanding and
exploration of math.
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Explaining change
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Abundance of studies that show no change
Few studies that explain change
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My claim
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Explain change by looking at both the
structure
and the
content
of a
system of beliefs
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Green (1971)
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Primary vs. derivative
primary
der
primary
der
der
der
der
der
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Core vs. peripheral
peripheral
core
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Clusters
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Evidentially-held vs. nonevidentially-held
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Green’s ideal belief system
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Minimum number of core beliefs
Minimum number of clusters
Maximum proportion of evidential beliefs
Primary-derivative structure is logical
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Conclusion: We have much work to do here.
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Carrie’s beliefs about mathematics
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Not creative (left brain vs. right brain)
Not coherent (mathematics vs. language
arts)
Difficult, frustrating, humiliating
Evidentially-held based on personal
experience
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Carrie’s core belief
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Care ethic
Children as people who need to be
respected
School as a safe place–physically,
intellectually & emotionally
“Celebrating children”
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Carrie’s derivative beliefs
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Students
–
–
–

Learning
–
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Value their thinking
Boost their self-confidence
Learn to be a better person
Process, not product
Teaching
–
Teacher as role model
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Structure: Preservice
teaching
math
students
celebrating
children
learning
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Explaining change
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Carrie was aware of and could articulate the conflicting clusters
of beliefs
Teacher education built on Carrie’s core belief
Teacher education challenged Carrie’s beliefs about
mathematics
Beliefs about mathematics were held evidentially–teacher
education provided new evidence
Carrie subsumed mathematics cluster into main cluster of
beliefs
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Structure revisited
celebrating children
teaching
students
learning
math
math
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math
Content of Carrie’s beliefs
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Confirms much earlier literature
No new information from a research
perspective
No viable avenues for change from a
teaching perspective
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Structure of Carrie’s beliefs
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Really not possible to look at structure alone
–
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Determining primary and derivative beliefs
requires examination of content
Again, no viable explanation of change from
looking at structure only
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Combining structure & content
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Levers for change
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Promote self-awareness of beliefs
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Determine core belief-must be affirmed
Lever for resolving apparent inconsistencies
Look at wider set of beliefs
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Determine what counts as evidence
Lever for presenting perturbations
Research inroads
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Implications/Questions
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Under what conditions are beliefs less
resistant to change?
Under what conditions can change be more
rapid?
Look at beliefs in wider context than
mathematics–how wide?
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Is Carrie a special case?
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Yes
–
–
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Aware of inconsistencies
Seeking answers
Not necessarily
–
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How many Carries have I missed because I saw
only the content of their beliefs?
Structure of beliefs made her a prime candidate
for change
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Methodological considerations
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Deliberate efforts to uncover structure
Push for connections and related ideas
Widen the focus
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Viewing Teachers’ Beliefs as
Sensible Systems
Keith R. Leatham
Brigham Young University
2006 NCTM Research Pressession
Defining Belief
It will not be possible for researchers to
come to grips with teachers’ beliefs…
without first deciding what they wish belief
to mean and how this meaning will differ
from that of similar constructs.
Pajares
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Defining Belief
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“All beliefs are predispositions to action.”
–
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Rokeach
one need not be able to articulate that belief, nor even be
consciously aware of it
A belief “speaks to an individual’s judgment of the
truth or falsity of a proposition.”
Pajares
–
the proposition is often implicit
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Coherence Theory
Coherentism signifies the view that would seek to
explain meaning, knowledge, and even truth by
reference to the interrelationships between
assorted epistemically salient elements.
Alcoff
A belief is justified to the extent to which the beliefset of which it is a member is coherent.
Dancy
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Coherence Theory
Our knowledge is not like a house that sits on a
foundation of bricks that have to be solid, but
more like a raft that floats on the sea with all the
pieces of the raft fitting together and supporting
each other. A belief is justified not because it is
indubitable or is derived from some other
indubitable beliefs, but because it coheres with
other beliefs that jointly support each other.
Thagard
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Sensible Systems of Beliefs
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Green’s Metaphor with Coherentism
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Psychological strength
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Quasi-logical relationships
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The strength of a belief depends on how that belief coheres
with the rest of the belief system.
One reason we may posit the existence of a quasi-logical
relationship is a desire (often subconscious) to make two
beliefs more coherent when considered in tandem.
Isolated clusters
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Contextualization facilitates the coherence of seemingly
inconsistent beliefs.
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Sensible Systems of Beliefs
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As researchers it is often difficult to look beyond the beliefs
we assume must have been (or should have been) the
predisposition for a given action.

Observations of seeming contradictions are, in the language
of constructivism, perturbations, and thus an opportunity to
learn.

Teacher actions neither prove nor disprove our belief
inferences.
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The Case of Joanna
Raymond, A. M. (1997). Inconsistency between
a beginning elementary school teacher's
mathematics beliefs and teaching practice.
Journal for Research in Mathematics
Education, 28, 550-576.
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Traditional beliefs about mathematics
Primarily nontraditional beliefs about learning and
teaching mathematics
Primarily traditional practice
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The Case of Joanna
“Joanna’s model shows factors, such as time,
constraints, scarcity of resources, concerns
over standardized testing, and students’
behavior, as potential causes of inconsistency.
These represent competing influences on
practice that are likely to interrupt the
relationship between beliefs and practice.”
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The Case of Joanna through the
Sensible System Lens
Joanna’s beliefs about the importance of
standardized testing and about the need to
control students’ behavior were more centrally
held and thus had greater influence on her
mathematics teaching than her beliefs about
learning mathematics.
2006 NCTM Research Pressession
The Case of Fred
Cooney, T. J. (1985). A beginning teacher's view of
problem solving. Journal for Research in Mathematics
Education, 16, 324-336.
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Mathematics is problem solving
Mathematics teaching should focus on problem solving
Practice was fairly procedural
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The Case of Fred
“His classroom practice was faithful to his
previously espoused views, but the meaning he
held for problem solving was limited, as was
the means by which he could translate belief
into practice.”
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The Case of Fred through the Sensible
System Lens
Fred’s core belief about mathematics was that
mathematics is interesting in its own right. It appears
that Fred used “problem solving” as a catchword
associated with what he enjoyed about doing
mathematics. Motivating students to engage in
mathematics was getting them to “problem solve.” This
belief about “problem solving” significantly influenced
his teaching practice.
2006 NCTM Research Pressession
The Case of Christopher
Skott, J. (2001). The emerging practices of a novice
teacher: The roles of his school mathematics
images. Journal of Mathematics Teacher
Education, 4, 3-28.
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Mathematics is about experimenting and investigating
Teaching mathematics should be about inspiring
independent student learning
Action: Mathematics-depleting questioning
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The Case of Christopher
“[This action] should not be seen as a situation
that established new and contradictory
priorities, but rather as one in which the
energising element of Christopher’s activity
was not mathematical learning. He was, so to
speak, playing another game than that of
teaching mathematics.”
2006 NCTM Research Pressession
The Case of Christopher through the
Sensible System Lens
When time began to be an issue, the more
centrally held belief for Christopher was his
belief in the importance of individuals and their
need to feel successful. The importance of this
belief meant mathematical beliefs sometimes
took a back seat.
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The Case of Jeremy
“I plan to involve all students in technology.”
“It is necessary to use technology in all
mathematics above and including at least
Algebra I.”
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The Case of Jeremy
“Like pre-algebra and the general math, I don’t know
much about that. I don’t have very much exposure….
No matter what level I’m teaching,… it doesn’t matter; I
would like to use [technology]…. So, in that sense, it
doesn’t depend on what level… I’m teaching. And then,
“Are there topics where you think that it is necessary?” I
think it’s necessary above Algebra I.”
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The Case of Jeremy
“In my class I will consider [technology]
necessary, because I’ve seen how it can help
you learn and I think that anything that can be
used to help students learn is necessary for
good learning.”
2006 NCTM Research Pressession
The Case of Jeremy through the
Sensible System Lens
Quasilogical relationship:
As a teacher, it is necessary that I use any method I know to be
effective to help students learn mathematics.
I know technology is an effective way to help students learn (from
Algebra I on up).
Therefore, it is necessary that I use technology in my teaching
(from Algebra I on up).
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Implications for Research
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Search for meaning through search for
coherence. Seek to develop models of
sensible systems.
The broader our scope, the more likely we
are to find critical, centrally held beliefs
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Implications for Teacher Education
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Goal of teacher education?
Need to connect mathematics specific and
general beliefs about education. Seek for
connection
rather
than
isolation
in
mathematics education.
Move
reform-oriented
beliefs
about
mathematics, its teaching and learning to a
more centrally located position in teachers’
belief systems.
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Teachers make sense.
Keith R. Leatham
Brigham Young University
[email protected]
2006 NCTM Research Pressession
Inconsistencies in beliefs and
practices:
Methodological artifact?
Natasha Speer
Michigan State University
2006 NCTM Research Pressession
Research has demonstrated that
beliefs ARE evident in
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instructional practices (Calderhead, 1996;
Thompson, 1992)
teacher development and change in preparation
and professional development programs
(Fennema & Scott Nelson, 1997; Richardson,
1996)
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Research has demonstrated that beliefs
are NOT evident in:
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instructional practices (Cohen, 1990; Thompson,
1984)
teacher development and change in preparation
and professional development programs (Borko &
Putnam, 1996; Sykes, 1990)
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Inconsistencies are sometimes
apparent when we…
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Gather data on
(1) beliefs teachers state or profess
(2) beliefs researchers attribute to teachers (from
data on their instructional practices)
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Compare and contrast findings from (1) and (2)
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Thought experiment
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How would you define “mathematical
problem-solving?”
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If you were watching a teacher, what would
you look for as evidence that the class was
designed to support problem-solving?
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Issues
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Examining “professed” and “attributed” beliefs
separately is relatively common in research on
teachers.
Researchers search for explanations for
inconsistencies between professed and attributed
beliefs.
But: Theories have not provided insights into why
such inconsistencies exist.
–
–
Could we just don’t know enough yet?
Could we be chasing a methodological artifact?
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Claims
1. Some apparent inconsistencies between
(professed) beliefs and (attributed beliefs from)
practices may be artifacts of data collection and
analysis methods
2. It is inappropriate to classify any belief as purely
“professed.” All beliefs are, to some extent, attributed
to the teacher by the researcher.
2006 NCTM Research Pressession
Today
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Brief tour of some “solutions” to the “problem”
Critique of data collection and analysis
methods
Alternative methods
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Dominant theoretical perspective
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Cognitive
Some variation on cognitive
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Explanations given for
inconsistencies
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Teachers are inconsistent (e.g., “They can talk the
talk, but not walk the walk”)
Beliefs function in cognition in ways that make it
possible for groups of beliefs to remain
disconnected.
Beliefs are inherently unstable and different ones are
apparent in different contexts.
2006 NCTM Research Pressession
But…
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Little theory/research to substantiate the
explanations
No unifying perspective
In some fields, this would be seen as a sign
that something is lacking in
–
–
theory, or
methods
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What to do?
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Adopt a different theoretical
perspective?
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“Solution” to the “problem:”
Shift the focus
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Interactionist perspective (Skott)
– There are no inconsistencies.
– Beliefs are continually developing, changing.
– Beliefs are not the only influence on teachers’
practices
– Other factors create perceived inconsistencies.
2006 NCTM Research Pressession
“Solution” to the “problem:”
Do not seek relationships between beliefs
and practices
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Discursive psychology perspective (Barwell,
Gellert)
–
–
Only use teachers’ statements as data.
No attribution of beliefs by researchers.
2006 NCTM Research Pressession
Those are fine “solutions,” but…
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they don’t explain the source(s) of the
inconsistencies
they don’t give us a way to make progress on
the issues from the (still quite dominant)
cognitive perspective taken by many
researchers
2006 NCTM Research Pressession
Typical data collection methods
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Beliefs (professed)
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Questionnaires/surveys
Interviews
Practices (attributed beliefs)
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Observations
Teacher self-reports (interviews, surveys, etc.)
2006 NCTM Research Pressession
Typical data analysis methods
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Beliefs
–
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Sort into categories (teaching, learning, students,
mathematics)
Create sub-categories
 teacher-centered vs. student-centered
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Practices
–
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problem solving-focused vs. skill-focused
Categorized in similar fashion
Belief-practice connection
–
Look for correlations between categorizations of beliefs and
categorizations of practices
2006 NCTM Research Pressession
Claim #1
Some apparent inconsistencies between
(professed) beliefs and (attributed beliefs
from) practices are an artifact of data
collection and analysis methods
2006 NCTM Research Pressession
“problemsolving”
Teacher’s definition
Researcher’s
definition
Teacher’s enactment
Researcher’s ideas
of evidence of
enactment
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Alternative explanation
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Teacher’s definition of “problem-solving” ≠
researcher’s definition.
To the teacher, what she does is problemsolving.
 Lack of shared understanding between
teacher and researcher about definition of
problem-solving.
2006 NCTM Research Pressession
“problemsolving”
Teacher’s definition
Researcher’s
definition
Teacher’s enactment
Researcher’s ideas
of evidence of
enactment
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Pressession
Alternative methods
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Data collection: Videoclip interviews
– Videotape class
– Select videoclips
– Use videoclips as context for interview with
teacher
Data analysis
– Emergent categories
– Tied to examples of instructional practice
– Consistency across multiple episodes
2006 NCTM Research Pressession
These methods permit:
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Descriptive vocabulary to emerge during
discussion of instructional practices.
Development of shared understanding of
terms and descriptions used.
Capture data closely related to belief-practice
connection.
2006 NCTM Research Pressession
Developing shared understanding
Inform/refine
Teacher’s definition
Researcher’s
conception of
teacher’s definition
test
Inform/refine
Teacher’s enactment
test
Researcher’s
conception of
teacher’s evidence of
enactment
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“problem solving”
Researcher’s
conception of
teacher’s definition
Teacher’s definition
Researcher’s ideas
of evidence of
enactment
Teacher’s enactment
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Claim #2
It is inappropriate to classify any belief as
purely “professed.” All beliefs are, to some
extent, attributed to the teacher by the
researcher.
2006 NCTM Research Pressession
Conclusions
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In some cases, distinction between professed
and attributed beliefs may be a methodological
artifact.
In particular, some findings may be the
consequence of a lack of shared
understanding.
No belief can be classified as entirely
professed.
Focus research design efforts on devising
methods to generate the most accurate
attributions of belief possible.
2006 NCTM Research Pressession
For more details and data
examples
Speer, N. (2005). Issues of methods and theory
in the study of mathematics teachers'
professed and attributed beliefs. Educational
Studies in Mathematics, 58(3), 361-391.
2006 NCTM Research Pressession
Questions & Comments
1)
2)
3)
4)
Are there aspects of educational theory that are not currently
represented in the study of beliefs that might help us advance
our understanding of the role of beliefs and their relationship to
practice?
How might new data collection and/or analysis methods (such
as those resulting from advances in technology)
shape/change/augment research on teachers’ beliefs and
practices?
In what ways should research on teachers’ beliefs be used to
inform teacher education?
Where are other gaps and potentially fruitful directions for
research on teacher beliefs?
2006 NCTM Research Pressession
Theoretical and Methodological Issues
in Research on Teachers’ Beliefs
Keith R. Leatham
Brigham Young University
Denise S. Mewborn
University of Georgia
Natasha M. Speer
Michigan State University
2006 NCTM Research Pressession
Contact Information
Keith R. Leatham
Brigham Young University
[email protected]
Denise S. Mewborn
University of Georgia
[email protected]
Natasha M. Speer
Michigan State University
[email protected]
2006 NCTM Research Pressession