The structure of observed learning outcomes (SOLO) taxonomy is a model that assesses student progress toward understanding a subject. In this study, we adopted SOLO for teachers and created a structure of observed teaching outcomes (SOTO) taxonomy. We used SOTO to evaluate the mathematics teaching knowledge (MTK) of four high school mathematics teachers. We executed this through a quality-oriented and quantity-supplemented case study method by implementing the mathematical quality of instruction teaching observation system proposed by the Learning Mathematics for Teaching (LMT) project in the classrooms of four high school mathematics teachers. The four teachers were observed in their teaching of four units on polynomials from the first volume of general high school mathematics of the 12-year Taiwan National Basic Education Mathematics Curriculum. The four teachers in the case study demonstrated five different cognition levels of MTK: unistructural, multistructural, relational, equivalence, and crystalline. Several U–M–R loops appeared in the cognitive development paths of the four case teachers’ MTK. The differing SOTO cognition levels and knowledge dimensions of the four case teachers reveal different progressions of MTK mastery, which in turn lead to different styles of MTK. The higher the four teachers’ SOTO cognition levels, the better their teaching knowledge quality. The SOTO taxonomy can be used to qualitatively evaluate the MTK of high school mathematics teachers.
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Constructing a Structure of Observed Teaching Outcomes Taxonomy to Evaluate the Teaching Knowledge Quality of High School Mathematics Teachers
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