IMPROVING TEACHERS' CONCEPTUAL KNOWLEDGE OF FRACTIONS THROUGH ONLINE SUBJECT-SPECIFIC PROFESSIONAL DEVELOPMENT

Background: Mathematics teachers must possess a thorough understanding of the mathematics content they teach. Content knowledge is particularly essential for teachers responsible for teaching fractions, a principal foundation of algebraic reasoning and structure. Research shows that students who do not grasp the conceptual understanding of fractions in elementary school continue to struggle with these concepts in middle and high school. Therefore, successful instruction of high-leverage concepts that are cardinal in developing advanced mathematics is required for overall student success. Teachers who participate in professional development (PD) opportunities grounded in Specialized-Content Knowledge (SCK) can increase their understanding of subject matter knowledge and build the conceptual fluency necessary for mathematics teaching. However, teaching methods must mirror best practices for learning fractions, such as using manipulatives rather than relying on procedural or memory-based approaches. By including PD opportunities that utilize research-based design principles for adult learners, teachers in this study received instruction on vertical alignment and conceptual fluency to effectively teach fraction concepts. Purpose: This study was prompted by the need to develop a relevant online professional development series for elementary and middle school teachers that supported their understanding and instruction of fractions through virtual manipulatives. The study describes the impact of an SCK professional development series on a group of mathematics teachers. Methods: This small-scale study included eight participants, all mathematics instructors at a private Prek-8th school in southeast Texas. The participants completed six sessions of professional development, each lasting one hour in duration. The synchronous virtual sessions followed a sequence designed to build both conceptual and procedural fraction understanding in comparison, equivalency, addition, subtraction, multiplication, and division through the use of virtual manipulatives. The evaluation study utilized quantitative methods that included a pre-test and post-test design and analysis to determine participants' change in mathematics knowledge of fractions expected for mastery in the elementary and middle school years. The pre-tests and post-tests were evaluated for participants' use of conceptual representations as justification for their responses. Additionally, descriptive analysis of participants' responses in the form of exit tickets captured participants' ability to apply their learning accurately and navigate the virtual manipulatives employed during the PD sessions. Results: The results from the pre-tests (M=61.2250, SD=19.99605) and post-tests (M=92.8750, SD=4.86819) covering fractional knowledge indicated that there was statistical significance in the findings of participants' increased scores upon completion of the PD series, t(7)=-4.668, p = .002. Furthermore, the evaluation of specific content categories confirmed that all eight participants improved their fractional knowledge. The most significant improvement was seen in the fraction division category, with a 47.95% increase in correct responses. Additionally, the combined exit tickets and evaluation of the use of representations on the pre-tests and post-tests confirmed that participants utilized virtual manipulatives to show their thinking, with an overall increase of 73.75% in the use of representations. Conclusion: The pre-test and post-test data showed an increase in fractional knowledge among the participants at the conclusion of the PD. The exit tickets and evaluation of representations used on the pre-test and post-test suggests that participants could apply the virtual manipulatives to create models that showed participants' conceptual understanding of fractions. Overall, subject-specific professional development increased the participants' understanding of fractional knowledge. Further study will serve to clarify whether the gains are sustainable and impact student learning of fractions.