Theoretical and Methodological Issues in Research on Teachers

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 l l 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 l 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 l 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. 2006 NCTM Research Pressession

Explaining change l l Abundance of studies that show no change Few studies that explain change 2006 NCTM Research Pressession

My claim l Explain change by looking at both the structure and the content of a system of beliefs 2006 NCTM Research Pressession

Green (1971) l Primary vs. derivative primary der der der 2006 NCTM Research Pressession

l Core vs. peripheral core 2006 NCTM Research Pressession

l Clusters l Evidentially-held vs. nonevidentially-held 2006 NCTM Research Pressession

Green’s ideal belief system l Minimum number of core beliefs Minimum number of clusters Maximum proportion of evidential beliefs Primary-derivative structure is logical l Conclusion: We have much work to do here. l l l 2006 NCTM Research Pressession

Carrie’s beliefs about mathematics l l Not creative (left brain vs. right brain) Not coherent (mathematics vs. language arts) Difficult, frustrating, humiliating Evidentially-held based on personal experience 2006 NCTM Research Pressession

Carrie’s core belief l l Care ethic Children as people who need to be respected School as a safe place–physically, intellectually & emotionally “Celebrating children” 2006 NCTM Research Pressession

Carrie’s derivative beliefs l Students – – – l Learning – l Value their thinking Boost their self-confidence Learn to be a better person Process, not product Teaching – Teacher as role model 2006 NCTM Research Pressession

Structure: Preservice teaching math students celebrating children learning 2006 NCTM Research Pressession

Explaining change l l l 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 2006 NCTM Research Pressession

Structure revisited celebrating children teaching students learning math 2006 NCTM Research Pressession math

Content of Carrie’s beliefs l l l Confirms much earlier literature No new information from a research perspective No viable avenues for change from a teaching perspective 2006 NCTM Research Pressession

Structure of Carrie’s beliefs l Really not possible to look at structure alone – l 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 l Levers for change – Promote self-awareness of beliefs l l – Determine core belief-must be affirmed Lever for resolving apparent inconsistencies Look at wider set of beliefs l l l Determine what counts as evidence Lever for presenting perturbations Research inroads 2006 NCTM Research Pressession

Implications/Questions l l l 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? 2006 NCTM Research Pressession

Is Carrie a special case? l Yes – – l 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 2006 NCTM Research Pressession

Methodological considerations l l l Deliberate efforts to uncover structure Push for connections and related ideas Widen the focus 2006 NCTM Research Pressession

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 l “All beliefs are predispositions to action. ” – l 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. Alcoff A belief is justified to the extent to which the beliefset of which it is a member is coherent. Dancy 2006 NCTM Research Pressession

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 2006 NCTM Research Pressession

Sensible Systems of Beliefs l Green’s Metaphor with Coherentism – Psychological strength l – Quasi-logical relationships l – 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 l Contextualization facilitates the coherence of seemingly inconsistent beliefs. 2006 NCTM Research Pressession

Sensible Systems of Beliefs l 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. l Observations of seeming contradictions are, in the language of constructivism, perturbations, and thus an opportunity to learn. l 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 2006 NCTM Research Pressession

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 2006 NCTM Research Pressession

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. ” 2006 NCTM Research Pressession

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). 2006 NCTM Research Pressession

Implications for Research l l 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 2006 NCTM Research Pressession

Implications for Teacher Education l l l 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

Teachers make sense. Keith R. Leatham Brigham Young University kleatham@mathed. byu. edu 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 l l instructional practices (Calderhead, 1996; Thompson, 1992) teacher development and change in preparation and professional development programs (Fennema & Scott Nelson, 1997; Richardson, 1996) 2006 NCTM Research Pressession

Research has demonstrated that beliefs are NOT evident in: l l instructional practices (Cohen, 1990; Thompson, 1984) teacher development and change in preparation and professional development programs (Borko & Putnam, 1996; Sykes, 1990) 2006 NCTM Research Pressession

Inconsistencies are sometimes apparent when we… l Gather data on (1) beliefs teachers state or profess (2) beliefs researchers attribute to teachers (from data on their instructional practices) l Compare and contrast findings from (1) and (2) 2006 NCTM Research Pressession

Thought experiment l How would you define “mathematical problem -solving? ” l 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 l l l 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 l l l Brief tour of some “solutions” to the “problem” Critique of data collection and analysis methods Alternative methods 2006 NCTM Research Pressession

Dominant theoretical perspective l l Cognitive Some variation on cognitive 2006 NCTM Research Pressession

Explanations given for inconsistencies l l l 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… l l l 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 2006 NCTM Research Pressession

What to do? l Adopt a different theoretical perspective? 2006 NCTM Research Pressession

“Solution” to the “problem: ” Shift the focus l 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 l 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… l l 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 l Beliefs (professed) – – l Questionnaires/surveys Interviews Practices (attributed beliefs) – – Observations Teacher self-reports (interviews, surveys, etc. ) 2006 NCTM Research Pressession

Typical data analysis methods l Beliefs – – Sort into categories (teaching, learning, students, mathematics) Create sub-categories l l l Practices – l teacher-centered vs. student-centered 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

“problem-solving” Teacher’s definition Researcher’s definition Teacher’s enactment Researcher’s ideas of evidence of enactment 2006 NCTM Research Pressession

Alternative explanation l l 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

“problem-solving” Teacher’s definition Researcher’s definition Teacher’s enactment Researcher’s ideas of evidence of enactment 2006 NCTM Research Pressession

Alternative methods l l 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: l l l 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 2006 NCTM Research Pressession Researcher’s conception of teacher’s evidence of enactment

“problem solving” Researcher’s conception of teacher’s definition Teacher’s enactment Researcher’s ideas of evidence of 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 l l 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 kleatham@mathed. byu. edu Denise S. Mewborn University of Georgia dmewborn@uga. edu Natasha M. Speer Michigan State University nmspeer@msu. edu 2006 NCTM Research Pressession