A Study of Teachers Engaged in Sustained Professional Development

      Our goal is to share results of a multiyear large-scale study of K–3 elementary school teachers engaged in varying amounts of sustained professional development focused on children's mathematical thinking.  Not only will we provide evidence that professional development is valuable and that the extent of professional development is important, but we will also share which kinds of expertise develop earlier and which later in professional development. 

Background

      While teachers evolve throughout their careers, their professional development needs also change.  Unfortunately, the field of mathematics education lacks a research base from which to make coherent sense of these changing needs.  The broad goal of our project is to map a trajectory for the changing needs and perspectives of teachers engaged in sustained professional development focused on children's mathematical thinking, and in this session, we will highlight major findings and engage audience members in discussion of their instructional and methodological contributions.

Methodology

      In this cross-sectional study, we worked with 129 participants: three groups of practicing K–3 teachers and one group of prospective teachers. The three groups of practicing teachers had similar amounts of teaching experience (at least 4 years and an average of 14–16 years) but differed in their amount of professional development:  (a) 0 years but about to begin; (b) 2 years; and (c) 4 or more years with engagement in at least a few informal leadership activities.  The professional development was voluntary, consisted of about 5 days of workshops per year, and drew heavily from the research and professional development project Cognitively Guided Instruction [CGI] (Carpenter, Fennema, Franke, Levi, & Empson, 1999).  The overarching goals were to help teachers learn (a) how children think about and develop understandings in particular mathematical domains and (b) how teachers can use this knowledge to inform their instruction.

Constructs

      We assessed each participant on four constructs: knowledge, beliefs, noticing, and responsiveness.  All data were blinded and double coded, and differences among participant groups were tested using a variety of statistical techniques. 

      Knowledge.  We set out to assess common and specialized mathematical content knowledge (Ball, Hill, & Bass, 2005) but not pedagogical content knowledge.  We developed eight free-response (vs. multiple-choice) items so that participants could demonstrate their levels of expertise; thus, in addition to finding whether groups differed in content knowledge, we could learn in what ways they differed. 

      Beliefs.  Beliefs about mathematics, teaching, and learning affect the ways teachers think about and teach mathematics, for example, whether they focus on developing sense making or teaching rules without meaning.  Using a web-based survey with open-ended prompts, we assessed seven beliefs related to teaching for mathematical proficiency (National Research Council [NRC], 2001).

      Noticing.  Instruction that builds on children's ways of thinking is promoted in national reform documents (NRC, 2001) and has been linked to benefits for both students and teachers (see, e.g., Franke, Carpenter, Levi, & Fennema, 2001; Sowder, 2007).  We used a written assessment, based on student work and video, to assess teachers' expertise in professional noticing of children's mathematical thinking, which we conceptualized as a set of three interrelated skills: attending to children's strategies, interpreting children's understandings, and deciding how to respond on the basis of children's understandings.  

      Responsiveness.  Building on work that has identified the importance of teachers' responsiveness to individual children's thinking (vs. the thinking of students as a group) (see, e.g., Fennema et al., 1996), we examined teachers' expertise in eliciting and responding to children's mathematical thinking in problem-solving interviews. We argue that the expertise needed for these one-on-one conversations is foundational to the expertise needed for creating rich mathematical discussions in classrooms. Using a framework to identify patterns of interaction in interviews (and by proxy, in classrooms), we analyzed videotaped problem-solving interviews in which teachers each worked one-on-one with three students.

Results and Implications

      We recognize the importance of teaching experience but, in this cross-sectional study, we identified important components of teaching expertise that did not develop from teaching experience alone but did develop with 2 years of professional development.  We also found that continuing professional development beyond 2 years continued to make a difference.  Thus, we provide evidence of the power of sustained professional development focused on children's mathematical thinking as well as information on the development of expertise that takes place earlier and later in professional development.  Generally, we found that teachers' beliefs developed before their skills at noticing children's mathematical thinking, and their noticing skills developed before their responsiveness skills in one-on-one conversations.  Development of teachers' mathematical content knowledge did not fit as clearly on this trajectory.  Details about these findings will be shared as well as implications for customizing professional development to account for teachers' changing needs and perspectives.

Session Outline

(5 minutes)      Overview of study

(40 minutes)    Presentation of findings

We intend to structure the presentation around three cases of prototypical teachers—one from each of our practicing-teacher groups—to illustrate common profiles across our four constructs of knowledge, beliefs, noticing, and responsiveness.

(15 minutes)    Audience discussion of cases

(15 minutes)    Discussant comments (Discussant has agreed to participate.)

(15 minutes)    Audience comments/questions

Questions to Focus Audience Participation

1)  We will engage the audience with a few tasks to highlight our constructs.  For example, to illustrate the construct of noticing, we will pose questions about the Grade 2 student work in Appendix A:  (a) What were the students' strategies? (b) What did you learn about the students' understandings? and (c) What problem(s) might you pose next?

2)   We will engage the audience in considering our developmental trajectory across constructs.  For example, why do beliefs develop before skill in noticing and responsiveness?  Must they?  Why might the role of content knowledge be more variable across individuals?

3)   We will engage the audience in discussion about how professional development focused on children's mathematical thinking leads to powerful changes in instruction.  What are the key characteristics and how can our results further enhance this promising form of professional development?

References

Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching:  Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 14–17; 20–22; 43–46.

Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. (1999). Children's mathematics: Cognitively Guided Instruction. Portsmouth, NH: Heinemann.

Fennema, E., Carpenter, T., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). Mathematics instruction and teachers' beliefs: A longitudinal study of using children's thinking. Journal for Research in Mathematics Education, 27, 403–434.

Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers' generative change: A follow-up study of professional development in mathematics. American Educational Research Journal, 38, 653–689.

National Research Council (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.

Sowder, J. T. (2007). The mathematics education and development of teachers. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 157–223). Charlotte, NC: Information Age.

Appendix A

M&Ms Written Student Work

(Three examples will be shared, but only 2 may be uploaded with this proposal.)