Conceptual Perspective & Educational Importance

This session focuses on the construction and initial implementation of the Mathematics Experiences and Conceptions Surveys (MECS), designed to understand the evolution of preservice elementary teachers' (PSTs) attitudes, beliefs, and dispositions towards mathematics teaching and learning. In particular, MECS developers sought to create a comprehensive set of instruments to investigate the relationships between these three distinct, yet overlapping constructs. Further, the MECS include extensive demographic information and address mathematics methods coursework and co-requisite field experiences. To capture experiences of learning to teach elementary school mathematics over time, there are multiple iterations of the MECS, applicable at various stages within teacher education programs. Doing so affords opportunities for analyses of factors within teacher education that influence dispositions, beliefs, and attitudes towards mathematics teaching and learning. While a number of surveys exist that measure beliefs (e.g. Perry, Wong, & Howard, 2006; Szydlik, Szydlik, & Benson, 2003) and attitudes (e.g. Fennema & Sherman, 1976; White, 2000) in mathematics, the design of these complimentary surveys has the potential to advance the field through (a) analyses that purposefully explore the interrelated relationship of attitudes, beliefs, dispositions, and identified PST characteristics (e.g. experiences as K-12 mathematics learners, native language(s), parent education level, etc.); (b) the integration of design experiments (Cobb et al., 2003) to investigate how particular experiences within teacher education programs foster positive attitudes, beliefs, and dispositions; and (c) the extension of data collection points across time and across teacher education programs.

Our efforts to improve mathematics teaching focus on conceptions of the nature of mathematics and how one teaches and learns mathematics. The term conceptions is used as an umbrella to represent three central and interrelated subconstructs: dispositions, beliefs, and attitudes. We argue that designing appropriate and comprehensive measures of teachers' conceptions of mathematics teaching and learning is critical in supporting PSTs within teacher education programs and into the teaching profession. To develop the survey, we operationalized the aforementioned subconstructs in the following way:

Dispositions: A tendency to act in a specified way, to take on a particular position (Bourdieu, 1984, 1986). We aim to understand how PSTs position themselves and their K-12 learning experiences with respect to reform recommendations in mathematics education.

Beliefs: Beliefs tend to be true/false oriented and context dependent. Further, beliefs are more cognitive, felt less intensely, and harder to change than attitudes (Philipp, 2007). Beliefs are a primary focus here as research indicates the important role beliefs play in the opportunities students have to engage in significant mathematical thinking (Staub & Stern, 2002), teachers' fidelity to curriculum materials (Remillard & Bryans, 2004), and the integration of particular instructional materials and strategies (e.g. Walen, Williams, & Garner, 2003).

Attitudes: Judgments made about particular places, events, people, or objects. Attitudes are, to some degree, either positive or negative (Breckler & Wiggins, 1992). Attitudes change more quickly and are less cognitive than beliefs (Philipp, 2007), thus evidence of change can be seen in shorter time increments than beliefs.

During the work session, we will discuss the development and initial implementation of the first three iterations of the MECS. MECS-1, administered to students at the beginning of their elementary mathematics methods courses, was designed to measure constructs related to PSTs' past K-12 experiences in mathematics and entering conceptions of mathematics. This survey contains 60 Likert-scale, four open-ended, and 17 demographic items. MECS-2, a 75-item follow-up survey, was designed to measure constructs related to mathematics methods courses and related fieldwork experiences and PSTs' conceptions of mathematics at the conclusion of their mathematics methods courses. MECS-3 is currently being designed for repeated use with pre/inservice teachers, to measure changes in teacher conceptions at various times throughout their teacher preparation programs and into their first years of teaching.

Organization of the Session

The overarching goal of this working session is to allow for interaction that will not only familiarize participants with the MECS, but also improve the surveys' content validity, while generating interest and discussion surrounding the conceptions the surveys purport to measure. Opening questions will be posed to the participants to initiate a group discussion on the evolution of elementary PSTs' conceptions (10 minutes). Copies of the MECS will be distributed and participants will be presented with background information regarding survey construction, including factor analyses and split-half reliability for Likert-scale items (15 minutes). Data to be reported during this discussion were collected from ~200 students over four semesters at four institutions in the Eastern United States. In brief, our exploratory factor analyses and Cronbach's α ranging from .748 to .938 indicate high reliability in seven of the eight subscales across MECS-1 and 2: attitudes toward mathematics, beliefs about mathematics, dispositions toward teaching mathematics, mathematics teaching confidence, social justice, experience as K-12 learners of mathematics, field experience, and mathematics methods course experience. The beliefs about mathematics scale was the only scale with an alpha level lower than .50. MECS-3, which will include additional subscales, will be administered for the first time during the fall of 2011. Participants will review survey items for clarity and appropriateness (10 minutes) and be given the opportunity to suggest new items and/or improvements for items that were not included in at least one of the scales (10 minutes). After the participants have shared their suggestions (10 minutes), we will conclude by discussing opportunities for participants to implement future iterations of the MECS (5 minutes). 

The following questions will be central to guiding this working session:

1.     What influence does teacher education have on preservice elementary teachers' attitudes, beliefs, and dispositions towards mathematics teaching and learning?  More specifically, what roles do individual aspects, such as methods courses, field experiences, and student teaching, play?

2.     What are effective measures of teachers' conceptions of mathematics? Can any of these track conceptions over time and across teacher education programs?

3.     In what ways can the MECS survey items be strengthened for increased clarity and appropriateness?

4.     What changes/additions would make the MECS more useful for future implementation by the session participants and other teacher educators?

References

Bourdieu, P. (1986). The forms of capital. In J. G. Richardson (Ed.), Handbook of theory and research for the sociology of education (pp. 241-258). New York: Greenwood.

Bourdieu, P., & Nice, R. (1984). Distinction: A social critique of the judgement of taste. Harvard University Press. Breckler, S. J., & Wiggins, E. C. (1992). On defining attitude and attitude theory: Once more with feeling. In A. R. Pratkanis, S. J. Breckler & A. G. Greenwald (Eds.), Attitude Structure and Function (pp. 407-427). Hillsdale, NJ: Erlbaum.

Cobb, P., Confrey, J., Disessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational researcher, 32(1), 9.

Fennema, E., & Sherman, J. A. (1976). Fennema-Sherman mathematics attitudes scales: Instruments designed to measure attitudes toward the learning of mathematics by females and males. Journal for Research in Mathematics Education, 7(5), 324-326.

Perry, B., Wong, N. Y., & Howard, P. (2006). Comparing primary and secondary mathematics teachers' beliefs about mathematics, mathematics learning and mathematics teaching in Hong Kong and Australia. Mathematics Education in Different Cultural Traditions-A Comparative Study of East Asia and the West, 435-448.

Philipp, R. A. (2007). Mathematics teachers' beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 257-315). Charlotte, NC: Information Age Publishing.

Remillard, J. T., & Bryans, M. B. (2004). Teachers' orientations toward mathematics curriculum materials: Implications for teacher learning. Journal for Research in Mathematics Education, 35(5), 352-388.

Staub, F. C., & Stern, E. (2002). The nature of teachers' pedagogical content beliefs matters for students' achievement gains: quasi-experimental evidence from elementary mathematics. Journal of Educational Psychology, 94(2), 344-355.

Szydlik, J. E., Szydlik, S. D., & Benson, S. R. (2003). Exploring changes in pre-service elementary teachers' mathematical beliefs. Journal of Mathematics Teacher Education, 6(3), 253-279.

Walen, S. B., Williams, S. R., & Garner, B. E. (2003). Pre-service teachers learning mathematics using calculators: A failure to connect current and future practice. Teaching and Teacher Education, 19(4), 445-462.

White, A. L. (2000). The use of teacher action theories in the articulation of practice: The use of stencils in the upper primary classroom. Paper presented at the 23rd annual conference of the Mathematics Education Research Group of Australasia, Sydney.