2018 Research Grant Results

Name: Malynda Tolbert, M.Ed.

Title: Practice-Based Professional Development: Building Teacher Knowledge, Skills, and Self-Efficacy for Teaching Fractions to Students with Disabilities

Proposal: Engaging teachers in quality professional development (PD) to teach mathematics (Ball & Foranzi, 2011; National Mathematics Advisory Panel, 2008) is one way to ensure that students develop their conceptual knowledge and procedural accuracy of fractions needed for higher-level mathematics (Siegler et al., 2012). Research suggests that effective PD include opportunities for teachers to deepen their content knowledge and the pedagogical skills required to teach mathematics to students, especially students with learning disabilities (Ball & Foranzi, 2011; Faulkner & Cain, 2013).

The aim of this pilot study was to examine the effects of practice-based PD following the guidelines from prior PD research (Ball & Foranzi, 2011; Desimone, 2009; Harris et al., 2012) for implementing an intervention to develop students’ mathematical reasoning about fractions by constructing written arguments (Hacker, Kiuhara, & Levin, 2019; Kiuhara et al., 2019). Teachers learned questioning strategies for engaging students in activities to make sense of problems, attend to precision, and critique the reasoning of their peers (National Council of Teachers of Mathematics, 2014). PD Activities included modeling and scaffolding instruction of fraction concepts using the self-regulated strategy development framework (Harris & Graham, 2009); sequencing learning activities using multiple representations to develop conceptual and procedural knowledge for understanding fractions; identifying common misconceptions when learning fractions; and engaging teachers in the same learning activities students were expected to do.

Research Questions: The research questions that guided this work focused on the effects that practice-based PD had on (a) teachers’ fraction knowledge, (b) teachers’ attitudes and beliefs about teaching mathematics, and (c) students’ fraction knowledge.

Summary: Four pairs of special education teachers participated in two days of PD before implementing the intervention to their 5th and 6th grade students (N = 32). A fraction knowledge test and a survey measuring attitudes and beliefs about teaching mathematics were administered to teachers before the PD and at the end of the study. Teachers were observed for frequency of open-ended questions that prompted students to express mathematical reasoning. Overall, teachers showed a 161% increase in the number of mathematical reasoning questions from baseline (M = 47 questions) to the end of the study (M = 123 questions). They reported increased confidence to teach fraction concepts using multiple representations and argument writing. Although there was not a statistically significant increase in teachers’ content knowledge, from pre-intervention (Mdn = 16.5) to post-intervention (Mdn = 17) (z = 1.44, p < .05), six teachers showed on average a percentage increase of 21% (from 6.25% to 33.33%) in their fraction knowledge at the end of the study. The students demonstrated a statistically significant and meaningful gains in their fraction knowledge from pre- (M = 8.77, SD = 2.35) to post-intervention (M = 11.87, SD = 4.19; t = (3.76), p = .001). Further research is needed to understand the effects of practice-focused PD on special education teacher’s mathematical content knowledge and pedagogical skills.


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