Instruments to Measure Elementary Preservice Teachers' Conceptions: An Application of the Rasch Rating Scale Model.

AbstractThis article reports on the development of the Mathematics Experiences and Conceptions Surveys (MECS), a pair of comprehensive instruments designed to measure elementary preservice teachers' dispositions, attitudes, and beliefs about mathematics teaching and learning. In addition to conceptions, MECS aim to capture elementary preservice teachers' related mathematical experiences at various benchmark stages in teacher education programs. The Rasch Rating Scale Model is used to examine the psychometric properties of MECS instruments and to establish six scales that are capable of producing reliable and valid measures. Finally, we present an illustration of how MECS might be used within elementary mathematics teacher preparation. (ProQuest: . denotes formulae omitted.) IntroductionDecades of mathematics education research suggests the strong role conceptions play in influencing the instructional practices teachers use within the classroom (Ball & Cohen, 1999; Ernest, 1989; Richardson, 1996; Wilkins, 2008), and students' opportunities to engage in significant mathematical thinking (Fennema et al., 1996; Staub & Stem, 2002). Researchers and teacher educators often look for opportunities to bring into focus conceptions of mathematics within methods courses and other important experiences within the continuum of teacher education (e.g. Charalambous, Panaoura, & Philippou, 2009; Quinn, 1997). Despite varying definitions in the literature, we follow Thompson's (1992, p. 130) umbrella description of conceptions as "a general notion or mental structure encompassing beliefs, meanings, concepts, propositions, rules mental images, and preferences. " In particular, we focus attention of three specific sub-constructs: attitudes toward mathematics, beliefs about mathematics, and dispositions toward reform practices in mathematics education. In this way of thinking, more positive conceptions of mathematics entail a combination of more positive attitudes, beliefs, and dispositions. Mathematics education literature (e.g. Philipp, 2007) also suggests that while these sub-constructs are related, they not synonymous. In fact, growth in certain subconstructs may lead to growth in others.Consensus exists on the critical importance of aligning attitudes, beliefs, and dispositions, with effective mathematics teaching practices within the multidimensional preparation of preservice teachers (Metzger & Wu, 2008). Consequently, the work described here provides an important step towards understanding the development of conceptions within teacher education programs. The importance of such work is two-fold: (a) to quantitatively measure outcomes on conceptions over time, which helps shape learning opportunities for preservice teachers, and (b) to illustrate how the combined efforts of teacher education researchers and psychometricians can produce meaningful measures of critical constructs in teacher education that are missing from teacher quality narratives.Conceptions for Teaching MathematicsBroadly, our work is situated within the conceptual framework for assessment teacher education developed by Cochran-Smith and Boston College Evidence Team (2009), which was later adapted to describe the interwoven relationship between aspects of teacher learning and related teacher education experiences. This framework highlights the complex, non- linear process for learning to teach, beginning as K-12 students, continuing into the teaching profession, and influenced by classroom, school, community, and university contexts and experiences. Research in mathematics education suggests that efforts to improve teacher quality should focus on transformative learning experiences that influence teaching practices within varying contexts (Ball & Cohen, 1999). In part, this work focuses on conceptions of the nature of mathematics and how one teaches and learns mathematics (Ball, Lubienski, & Mewborn, 2001). …