# 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.

**References**

Ball, D. L., & Forzani, F. M. (2011). Building a common core for learning to teach: And connecting professional learning to practice. *American Educator,* *35*(2), 17-39.

Desimone, L. M. (2009). Improving impact studies of teachers’ professional development: Toward better conceptualizations and measures. *Educational Researcher*, *38*(3), 181–199.

Faulkner, V. N., & Cain, C. R. (2013). Improving the mathematical content knowledge of general and special educators: Evaluating a professional development module that focuses on number sense. *Teacher Education and Special Education,* *36*(2) 115-131.

Graham, S., & Harris, K. R. (2009). Almost 30 years of writing research: Making sense of it all with The Wrath of Khan. *Learning disabilities research & practice*, *24*(2), 58-68.

Hacker, D. J., Kiuhara, S. A., & Levin, J. R. (2019). A metacognitive intervention for teaching fractions to students with or at-risk for learning disabilities in mathematics.* ZDM Mathematics Education*, 1-12. https://doi.org/10.1007/s11858-019-01040-0

Harris, K., Lane, K., Graham, S., Driscoll, S., Sandmel, K., Brindle, M., & Schatschneider, C. (2012). Practice-based professional development for self-regulated strategies development in writing. *Journal of Teacher Education,* *63*(2), 103-119.

Hill, H. C., Rowan, B., & Ball, D. L. (2004) Effects of teachers' mathematical knowledge for teaching on student achievement**. ***American Educational Research Journal, 42*, 371-406.

Kiuhara, S. A., Gillespie Rouse, A., Dai, T., Witzel, B. S., Morphy, P., & Unker, B. (2019). Constructing Written Arguments to Develop Fraction Knowledge.* Journal of Educational Psychology*. Advance online publication. http://dx.doi.org/10.1037/edu0000391

National Center for Education Statistics (2017). National Assessment of Educational Progress: Mathematics 2015. Washington, DC: Institute of Education Sciences.

National Council of Teachers of Mathematics. (2014). *Principles to actions: Ensuring mathematical success for all. *Reston, VA: NCTM. National Center on Response to Intervention (March 2010). *Essential Components of RTI – A Closer Look at Response to Intervention*. Washington, DC: U.S. Department of Education, Office of Special Education Programs, National Center on Response to Intervention. Retrieved from -1 rtiessentialcomponents_042710.pdf

National Mathematics Advisory Panel. (2008). *Foundations for success: The final report of the National Mathematics Advisory Panel*. Washington, DC: U.S. Department of Education. Retrieved from www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

Rand Mathematics Study Panel. (2003). *Mathematical proficiency for all students. *Santa Monica, CA: RAND. Regional Education Laboratory [REL], 2007.

Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., . . . Chen, M. (2012). Early predictors of high school mathematics achievement. *Psychological Science,* 23, 691–697. http://dx.doi.org/10.1177/0956797612440101