2006 NCTM Research Pressession
Theoretical and Methodological Issues in Research on Teachers’ Beliefs
Keith R. LeathamBrigham Young UniversityDenise S. MewbornUniversity of GeorgiaNatasha M. SpeerMichigan State University
2006 NCTM Research Pressession
Presentation Outline
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
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.
2006 NCTM Research Pressession
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
Abundance of studies that show no change Few studies that explain change
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My claim
Explain change by looking at both the
structureand the
contentof a
system of beliefs
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Green (1971)
Primary vs. derivative
primary
der
der
der
der
der
der
primary
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Core vs. peripheral
core
peripheral
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Clusters
Evidentially-held vs. nonevidentially-held
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Green’s ideal belief system
Minimum number of core beliefs Minimum number of clusters Maximum proportion of evidential beliefs Primary-derivative structure is logical
Conclusion: We have much work to do here.
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Carrie’s beliefs about mathematics
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
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
Students– Value their thinking– Boost their self-confidence– Learn to be a better person
Learning– Process, not product
Teaching– Teacher as role model
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Structure: Preservice
math
teaching
students learning
celebrating children
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Explaining change
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
students
teachinglearning
math math
math
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Content of Carrie’s beliefs
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
Really not possible to look at structure alone– Determining primary and derivative beliefs
requires examination of content
Again, no viable explanation of change from looking at structure only
2006 NCTM Research Pressession
Combining structure & content
Levers for change– Promote self-awareness of beliefs
Determine core belief-must be affirmed Lever for resolving apparent inconsistencies
– Look at wider set of beliefs Determine what counts as evidence Lever for presenting perturbations Research inroads
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Implications/Questions
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?
Yes– Aware of inconsistencies– Seeking answers
Not necessarily– 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
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
2006 NCTM Research Pressession
Defining Belief
“All beliefs are predispositions to action.”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
2006 NCTM Research Pressession
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.
AlcoffA belief is justified to the extent to which the belief-set of which it is a member is coherent.
Dancy
2006 NCTM Research Pressession
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
Coherence Theory
2006 NCTM Research Pressession
Sensible Systems of Beliefs
Green’s Metaphor with Coherentism– Psychological strength
The strength of a belief depends on how that belief coheres with the rest of the belief system.
– Quasi-logical relationships 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 Contextualization facilitates the coherence of seemingly
inconsistent beliefs.
2006 NCTM Research Pressession
Sensible Systems of Beliefs
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.
2006 NCTM Research Pressession
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.
– Traditional beliefs about mathematics– Primarily nontraditional beliefs about learning and
teaching mathematics– Primarily traditional practice
2006 NCTM Research Pressession
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.”
2006 NCTM Research Pressession
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.
– 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.”
2006 NCTM Research Pressession
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.
– 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.
2006 NCTM Research Pressession
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.”
2006 NCTM Research Pressession
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
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
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.
2006 NCTM Research Pressession
Inconsistencies in beliefs and practices:
Methodological artifact?
Natasha SpeerMichigan State University
2006 NCTM Research Pressession
Research has demonstrated that beliefs ARE evident in
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:
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…
Gather data on
(1) beliefs teachers state or profess(2) beliefs researchers attribute to teachers
(from data on their instructional practices)
Compare and contrast findings from (1) and (2)
2006 NCTM Research Pressession
Thought experiment
How would you define “mathematical problem-solving?”
If you were watching a teacher, what would you look for as evidence that the class was designed to support problem-solving?
2006 NCTM Research Pressession
Issues
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?
2006 NCTM Research Pressession
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
Brief tour of some “solutions” to the “problem”
Critique of data collection and analysis methods
Alternative methods
2006 NCTM Research Pressession
Dominant theoretical perspective
Cognitive Some variation on cognitive
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Explanations given for inconsistencies
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…
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?
Adopt a different theoretical perspective?
2006 NCTM Research Pressession
“Solution” to the “problem:” Shift the focus
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
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…
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
Beliefs (professed)– Questionnaires/surveys– Interviews
Practices (attributed beliefs)– Observations– Teacher self-reports (interviews, surveys,
etc.)
2006 NCTM Research Pressession
Typical data analysis methods
Beliefs– Sort into categories (teaching, learning, students,
mathematics)– Create sub-categories
teacher-centered vs. student-centered problem solving-focused vs. skill-focused
Practices– Categorized in similar fashion
Belief-practice connection– Look for correlations between categorizations of beliefs
and categorizations of practices
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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
“problem-solving”
Researcher’s definition
Teacher’s definition
Researcher’s ideas of evidence of
enactment
Teacher’s enactment
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Alternative explanation
Teacher’s definition of “problem-solving” ≠ researcher’s definition.
To the teacher, what she does is problem-solving.
Lack of shared understanding between teacher and researcher about definition of problem-solving.
2006 NCTM Research Pressession
“problem-solving”
Researcher’s definition
Teacher’s definition
Researcher’s ideas of evidence of
enactment
Teacher’s enactment
2006 NCTM Research Pressession
Alternative methods
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
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These methods permit:
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
Researcher’s conception of
teacher’s definition
Teacher’s definition
Researcher’s conception of
teacher’s evidence of enactment
Teacher’s enactment
Inform/refine
test
Inform/refine
test
Developing shared understanding
2006 NCTM Research Pressession
“problem solving”
Researcher’s conception of
teacher’s definition
Teacher’s definition
Researcher’s ideas of evidence of
enactment
Teacher’s enactment
2006 NCTM Research Pressession
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
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) 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?
2) 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?
3) In what ways should research on teachers’ beliefs be used to inform teacher education?
4) 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. LeathamBrigham Young UniversityDenise S. MewbornUniversity of GeorgiaNatasha M. SpeerMichigan State University
2006 NCTM Research Pressession
Contact Information
Keith R. LeathamBrigham Young University
Denise S. MewbornUniversity of [email protected]
Natasha M. SpeerMichigan State University
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