2006 nctm research pressession theoretical and methodological issues in research on teachers’...

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


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


Beliefs as a Lever for Change

Denise S. Mewborn

University of Georgia


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.


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.


Explaining change

Abundance of studies that show no change Few studies that explain change


My claim

Explain change by looking at both the

structureand the

contentof a

system of beliefs


Green (1971)

Primary vs. derivative

primary

der

der

der

der

der

der

primary


Core vs. peripheral

core

peripheral


Clusters

Evidentially-held vs. nonevidentially-held


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.


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


Carrie’s core belief

Care ethic Children as people who need to be respected School as a safe place–physically,

intellectually & emotionally “Celebrating children”


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


Structure: Preservice

math

teaching

students learning

celebrating children


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


Structure revisited

celebrating children

students

teachinglearning

math math

math


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


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


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


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?


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


Methodological considerations

Deliberate efforts to uncover structure Push for connections and related ideas Widen the focus


Viewing Teachers’ Beliefs as Sensible Systems

Keith R. Leatham

Brigham Young University


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


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


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


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


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.


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.


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


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.”


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.


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


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.”


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.


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


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.”


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.


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.”


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.”


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.”


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).


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


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.


Teachers make sense.

Keith R. LeathamBrigham Young [email protected]


Inconsistencies in beliefs and practices:

Methodological artifact?

Natasha SpeerMichigan State University


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)


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)


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)


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?


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?


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.


Today

Brief tour of some “solutions” to the “problem”

Critique of data collection and analysis methods

Alternative methods


Dominant theoretical perspective

Cognitive Some variation on cognitive


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.


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


What to do?

Adopt a different theoretical perspective?


“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.


“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.


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


Typical data collection methods

Beliefs (professed)– Questionnaires/surveys– Interviews

Practices (attributed beliefs)– Observations– Teacher self-reports (interviews, surveys,

etc.)


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


Claim #1

Some apparent inconsistencies between (professed) beliefs and (attributed beliefs from) practices are an artifact of data collection and analysis methods


“problem-solving”

Researcher’s definition

Teacher’s definition

Researcher’s ideas of evidence of

enactment

Teacher’s enactment


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.


“problem-solving”

Researcher’s definition



enactment



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


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.


Researcher’s conception of

teacher’s definition



teacher’s evidence of enactment


Inform/refine

test

Inform/refine

test

Developing shared understanding


“problem solving”


teacher’s definition



enactment



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.


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.


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.


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?


Theoretical and Methodological Issues in Research on Teachers’ Beliefs

Keith R. LeathamBrigham Young UniversityDenise S. MewbornUniversity of GeorgiaNatasha M. SpeerMichigan State University


Contact Information

Keith R. LeathamBrigham Young University

[email protected]

Denise S. MewbornUniversity of [email protected]

Natasha M. SpeerMichigan State University

[email protected]

2006 nctm research pressession theoretical and methodological issues in research on teachers’...

Documents

nctm research pressession

change slide

primary slide

mathematics beliefs

learning math slide

system of beliefs

derivative beliefs students

natasha discussion slide