Assessing Analytic Geometry Understanding: Van Hiele, SOLO, and Beyond


  • Michael J. Bosse Appalachian State University
  • Anass Bayaga University of ZuluLand
  • Kathleen Lynch-Davis Texas A&M University Corpus Christi
  • Ashley DeMarte Appalachian State University


In the context of analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999; Biggs & Collis, 1982); syntactic and semantic elaborations (Kaput, 1987a, 1987b, 1989); and isomorphic, transcendent, and mixed connections (Adu-Gyamfi, Bossé, & Lynch-Davis, 2019). Along with producing a fuller analysis of student work and communication, the study found that for only the students with the lowest and highest scores regarding either their understanding or actions on the analytic geometry task might there be a predictive association between knowledge and action levels. For other students, a predictive association could not be determined. This may mean that the level of understanding a student possesses regarding a particular mathematical concept may not parallel the level of actions they use when working with an associated task.

Author Biography

Michael J. Bosse, Appalachian State University

Michael. J. Bossé is the Distinguished Professor of Mathematics Education and MELT Program Director at Appalachian State University, Boone, NC. He teaches undergraduate and graduate courses and is active in providing professional development to teachers in North Carolina and around the nation. His research focuses on learning, cognition, and curriculum in K-16 mathematics.