Abstract
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.
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