Challenges in Supporting Teachers in Rational Numbers Instruction: Contextualizing the Results of an Experimental Study of Teacher Professional Development

• In Event: Improving Instruction About Fractions: Different Approaches to Supporting Teachers and Students in the Classroom

Abstract

This paper uses an embedded case study design to contextualize the results of the Middle School Mathematics Professional Development Impact Study, a large-scale randomized controlled trial that examined the impact of content-focused professional development (PD) on teacher knowledge, instruction, and student achievement in rational numbers (Garet et al., 2011, 2010). The larger study found that the PD had no impact on teachers’ knowledge in rational numbers or their students’ achievement, but found a significant impact on instruction (eliciting student thinking). The case study (Walters, 2009) utilized interview, observation and assessment data from subset of study teachers who were highly receptive to the study’s PD program—a “critical case” (Flyvberg, 2001; Yin, 2003)—and addressed the following questions:

1. How deeply did the case study teachers understand the core content and pedagogical content of the PD program? What explained variation among the teachers?

2. How effectively did the case study teachers integrate into their instructional routines new content, pedagogical content and pedagogical knowledge? What explained variation among teachers?

3. Do any of the sources of variation among case study teachers suggest why the PD had a limited impact overall and suggest ways in which future, similar PD programs might be strengthened?

The theoretical framework that guided the larger study was that intensive, sustained, content-focused and classroom-connected PD would improve teachers’ knowledge, instructional practices and their students’ achievement in the area of rational numbers. The study’s 68-hour PD program was significantly more intensive than the amount of content-focused PD mathematics teachers typically receive in a single year (Birman et. al, 2007), yet it produced limited results. The framework that guided the embedded case study was that in-depth analyses of the extent to which a select group of teachers comprehended and made use of the core content of the PD program could be used to contextualize the results of the larger study.

The larger study was conducted in 77 middle schools in 12 districts with 195 seventh-grade teachers and included a test that measured teachers’ content and pedagogical content knowledge in rational numbers, and (2) a classroom observation instrument that measured practices emphasized in the PD. The case study was conducted with three teachers in one of the study’s middle schools and also included an in-depth knowledge assessment and observation rubric, as well as measures to assess teachers’ attitudes towards learning and implementing the PD.

The results of the case study suggest that the complexity of the mathematical content and the complexity of the instructional practices emphasized in the PD were key sources of variation among the case study teachers. Other sources of variation included teachers’ attitudes and beliefs towards learning the content and their attitudes towards teaching rational numbers conceptually.

The results of both studies point to the need for additional research on the mechanisms by which teachers learn complex content and instructional practices, including the role of teachers’ attitudes and beliefs in what they learn and what they are likely to implement in the classroom.

Author

• Kirk Walters, American Institutes for Research