Teacher Practices, Beliefs, and Conceptual Understanding of Mathematics: A Phenomenological Case Study of Teachers Instructing Mathematically Gifted and Promising Students

Students in the United States are not achieving in mathematics as indicated on the NAEP (2019) exams and other measurements of student achievement (OECD, 2019; O’Dwyer, Wang, & Shields, 2015; NCES, 2019). Mathematically gifted and promising students are especially impacted by this phenomenon, though it is not exactly known what factors contribute to successful teachers of these students. This phenomenological case study focused on the beliefs, instructional practices, and conceptual understanding of mathematics of five teachers in a public charter school for gifted students. Data sources collected included semi-structured interviews, classroom observations, and questionnaires based on Swan’s (2006) practices and beliefs research with effective mathematics teachers. Two theories of giftedness served as the theoretical lens for this study: Renzulli’s Three-Ring Model (1978) and Gagné’s Differentiated Model of Giftedness and Talent (1985) to better understand these phenomena. Using an interpretive phenomenological analysis several themes emerged in response to each research question. Findings for instructional practices indicated that teachers used both student-centered and teacher-centered practices and consistently utilized differentiated groupings. Additionally, teacher participants believe that gifted students possess both positive traits and challenges and specifically for math, believe that sense-making is key, and math is a subject students should enjoy. Teachers’ conceptual understanding of mathematics is guided by their ongoing practice, the curriculum, and math experiences prior to teaching. These findings indicate the importance of ongoing training and professional development in mathematics and gifted education, as well as the recruitment and retention of teachers who possess a strong conceptual understanding of mathematics, a passion for the subject, and a student-centered approach to teaching.
Keywords: mathematically gifted, instructional practices, beliefs, teachers’ conceptual understanding of mathematics