Theoretical and Methodological Issues in Research on Teachers Beliefs

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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

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Presentation Outline

• Beliefs as a Lever for ChangeDenise
• Viewing Teachers Beliefs as Sensible
  SystemsKeith
• Inconsistencies in beliefs and practices
  Methodological artifact?Natasha
• Discussion

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Beliefs as a Lever for Change

• Denise S. Mewborn
• University of Georgia

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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.

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Carrie, 6 months later

• Teaching math is nothing more than exploring math
  with your learners. Ive 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
• structure
• and the
• content
• of a
• system of beliefs

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Green (1971)

• Primary vs. derivative

primary
primary
der
der
der
der
der
der
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• Core vs. peripheral

peripheral
core
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• Clusters
• Evidentially-held vs. nonevidentially-held

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Greens 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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Carries 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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Carries core belief

• Care ethic
• Children as people who need to be respected
• School as a safe placephysically, intellectually
  emotionally
• Celebrating children

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Carries 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
teaching
math
celebrating children
students
learning
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Explaining change

• Carrie was aware of and could articulate the
  conflicting clusters of beliefs
• Teacher education built on Carries core belief
• Teacher education challenged Carries beliefs
  about mathematics
• Beliefs about mathematics were held
  evidentiallyteacher education provided new
  evidence
• Carrie subsumed mathematics cluster into main
  cluster of beliefs

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Structure revisited
celebrating children
teaching
learning
students
math
math
math
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Content of Carries 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 Carries 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

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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
  mathematicshow 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

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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

• 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 individuals 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
belief-set 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

• Greens 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.

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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.

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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.
• Traditional beliefs about mathematics
• Primarily nontraditional beliefs about learning
  and teaching mathematics
• Primarily traditional practice

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The Case of Joanna

• Joannas 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

• Joannas 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.

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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.

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The Case of Fred through the Sensible System Lens

• Freds 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.

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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 Christophers activity was
  not mathematical learning. He was, so to speak,
  playing another game than that of teaching
  mathematics.

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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 dont
  know much about that. I dont have very much
  exposure. No matter what level Im teaching, it
  doesnt matter I would like to use
  technology. So, in that sense, it doesnt
  depend on what level Im teaching. And then,
  Are there topics where you think that it is
  necessary? I think its necessary above Algebra
  I.

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The Case of Jeremy
In my class I will consider technology
necessary, because Ive 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.
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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.

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Teachers make sense.

• Keith R. Leatham
• Brigham Young University
• kleatham_at_mathed.byu.edu

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Inconsistencies in beliefs and practices
Methodological artifact?

• Natasha Speer
• Michigan State University

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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)

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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?

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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 dont 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.

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Today

• Brief tour of some solutions to the problem
• Critique of data collection and analysis methods
• Alternative methods

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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.

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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?

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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.

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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.

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Those are fine solutions, but

• they dont explain the source(s) of the
  inconsistencies
• they dont give us a way to make progress on the
  issues from the (still quite dominant) cognitive
  perspective taken by many researchers

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Typical data collection methods

• Beliefs (professed)
• Questionnaires/surveys
• Interviews
• Practices (attributed beliefs)
• Observations
• Teacher self-reports (interviews, surveys, etc.)

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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

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problem-solving
Researchers definition
Teachers definition
Researchers ideas of evidence of enactment
Teachers enactment
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Alternative explanation

• Teachers definition of problem-solving ?
  researchers definition.
• To the teacher, what she does is problem-solving.
• ? Lack of shared understanding between teacher
  and researcher about definition of
  problem-solving.

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problem-solving
Researchers definition
Teachers definition
Researchers ideas of evidence of enactment
Teachers enactment
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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.

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Developing shared understanding
Inform/refine
Teachers definition
Researchers conception of teachers definition
test
Inform/refine
Researchers conception of teachers evidence of
enactment
Teachers enactment
test
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problem solving
Researchers conception of teachers definition
Teachers definition
Researchers ideas of evidence of enactment
Teachers 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.

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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.

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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.

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Questions Comments

• 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?

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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

77
Contact Information

• Keith R. Leatham
• Brigham Young University
• kleatham_at_mathed.byu.edu
• Denise S. Mewborn
• University of Georgia
• dmewborn_at_uga.edu
• Natasha M. Speer
• Michigan State University
• nmspeer_at_msu.edu