The proposed symposium will help disseminate results from our efforts to improve teacher quality through an innovative field experience approach accompanying mathematics and science methods courses for elementary preservice teachers (PSTs). We frame the symposium around two main innovations in our Iterative Model Building (IMB) approach: (1) a focus on collaboration to plan and teach lessons through Lesson Study, and (2) a focus on student’s thinking. Based on these innovations, we present findings from our research on the reflective abilities of PSTs following lesson implementation and their ability to construct models of student’s thinking. We followed these PSTs into student teaching and will discuss findings of teacher quality as related to the two main innovations. Symposium participants will be asked to critique the research methods as well as the findings from the presented studies.

Effective teachers consider how individual students think about specific content and these teachers reflect on lesson implementation to improve their quality of teaching (Akerson & Hanuscin, 2007; Carpenter & Fennema, 1992; Carpenter et al., 1988; Carpenter, Fennema, & Franke, 1996; Cochran-Smith & Lytle, 1999; Fennema et al, 1996; Lewis, 2000). Lesson Study is one professional development method for promoting collective reflection with the intention of improving practice (Lewis, 2000). As teachers reflect on lessons and teach subsequent lessons, it is important they consider how students are constructing knowledge, so they can formulate concepts of student thinking, known as models. With the IMB approach to field experience, we have emphasized these two foci with the intention of improving teacher quality. In this process, PSTs engage in Lesson Study meetings (Lewis, 2000) and learn to build models of students’ mathematical concepts based on a series of formative assessment interviews, similar to teaching experiments (Steffe & Thompson, 2000).  

After designing and implementing the IMB approach, with the support of a DR-K12 NSF grant, we were interested in understanding the nature of PSTs’ reflections and looked to examine the predictive abilities of PSTs as related to their ability to construct models of student thinking. Studies have found reflective teachers are likely to improve the mathematical achievement of their students (Nickerson & Moriarty, 2005; Lewis, 2000); however, few studies have examined the nature and process of these reflections. Likewise, as teachers reflect, they should be cognizant of the extent of students’ knowledge in mathematics to provide students with developmentally appropriate mathematical tasks. We hypothesize that effective teachers reflect on lessons with an emphasis on student thinking to construct appropriate lessons. To measure this hypothesis, we examined the reflective practice and model building abilities of PSTs during the innovative field experience. We then followed PSTs into student teaching to examine indicators of teacher quality. Subjects included approximately 380 preservice teachers who were enrolled in the field experience course for one semester each between spring 2008 and spring 2011.

The session leader and moderator will open with a 5-minute overview. This will be followed by 4 brief, 10-minute reports from the co-presenters. The discussants will have 15 minutes to react to the presentations. We will end with a 30 minute discussion to engage symposium participants and answer questions. A description of the research reports follows.

PSTs’ Nature of Reflections:

With the IMB approach, PSTs teach or observe whole-class mathematics lessons once a week. After teaching, PSTs meet with a lesson study team (Lewis, 2000) to deliberate and reflect on their teaching and to plan the following week’s lesson. In this process, the lesson study team reflects on the extent to which lesson goals were met, the degree to which the students understood the concepts of the lesson, and ways in which the lesson could be improved. We share results from a study conducted on the nature of the PSTs’ reflections during the lesson study discussions with a focus on their lessons plans and student understanding of the mathematical concepts presented.

Examining the Role of Reflection in Preservice Teachers' Mathematics Teaching:

Studies have shown that reflective teachers can have an impact on students' mathematics achievement (US Math Recovery Council, 2005; Nickerson & Moriarty, 2005; Lewis, 2000; Carpenter, Fennema, Peterson, Chiang & Loef, 1989). To examine the reflective practices of elementary mathematics PSTs, we conducted a case study of six PSTs participating in the IMB field experience. We wanted to determine the content of PST reflections and understand how they interpret students’ mathematical thinking while considering their teaching. Analysis of the nature of PST reflection in teaching will be discussed with an emphasis on the process and nature of reflection.   

PST Construction of Models of Student’s Thinking:

The purpose of this study was to gain a better understanding of PSTs’ abilities to model their students’ thinking during field experience. More specifically, this study focused on investigating whether or not relationships existed between PSTs’ considerations of student cognition when constructing models and the predictive ability of PSTs as measured by a project implemented measure, Prediction Assessments. We share the results of video, document, and interview analysis.

Examining the Effect of an Innovate Field Experience:

During the IMB field experience, PSTs focused on student thinking and collaboration to design lessons emphasizing reflection and the creation of models of student thinking. We followed PSTs from the IMB and control sections of the field experience into their student teaching, one year later, to examine teacher quality and compare the two groups. Using a lesson observation protocol, we observed student teachers, collected lesson plans, and conducted interviews to understand how student teachers made instructional decisions. We share quantitative and qualitative findings to describe differences in teaching practice. 

Questions for symposium participants include:

1. Any experience with examining the nature of PST reflections? How do your experiences compare?
2. How can teacher educators support PSTs who are struggling to create models of student thinking?
3. What experiences have you had trying to measure teacher quality?
4. Measuring PSTs’ reflective and model building abilities is a complex endeavor. Can you provide feedback on our approach?

References

Akerson, V.L., & Hanuscin, D. (2007) Teaching the nature of science through inquiry: Results of a three year professional development program. Journal of Research in Science Teaching. 44, 653‐680.

Carpenter, T., & Fennema, E. (1992). Cognitively guided instruction: Building on the knowledge of students and teachers [Special issue]. International Journal of Educational Research, 457-470.

Carpenter, T., Fennema, E., & Franke, M. (1996). Cognitively guided instruction: A knowledge of base for reform in primary mathematics instruction. Elementary School Journal, 97, 3-20.

Carpenter, T. P., Fennema, E., Peterson, P. L., & Carey, D. A. (1988). Teachers’ pedagogical content knowledge of students' problem solving in elementary arithmetic. Journal of Research in Mathematics Education, 19, 385-401.

Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26, 499-531.

Cochran-Smith, M., & Lytle, S. (1999). Relationships of knowledge and practice: Teacher learning in communities. In A. Iran-Nejad & P. D. Pearson (Eds.), Review of research in education (Vol. 24, pp. 249–305). Washington, DC: American Educational Research Association.

Fennema, E., Carpenter, T.P., Franke, M.L., Levi, L., Jacobs, V.R., & Empson, S.B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction. Journal for Research in Mathematics Education, 27, 403-434.

Lewis, C. C. (2000, April). Lesson study: The core of Japanese professional development. Invited presentation to the Special Interest Group on Research in Mathematics Education at the annual meeting of the American Educational Research Association, New Orleans, LA.

Nickerson, S. D., & Moriarty, G. (2005). Professional communities in the context of teachers’ professional lives: A case of mathematics specialists. Journal of Mathematics Teacher Education, 8, 113-140.

Steffe, L., & Thompson, P. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E. Kelley & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267-306). Mahwah, NJ: Lawrence Erlbaum Associates.

US Math Recovery Council. (2005, July). Math recovery overview: An elementary school implementation of an early intervention program to identify and service "at risk" mathematics students. Retrieved June 2, 2005, from Math Recovery Web site: http://www.saine.com/mathrecovery/itree/uploads/MR%20Overview%20White%20Paper.pdf