Teachers’ inquiry-based mathematics teaching (IBMT) competence is often acquired and developed through participation in professional development programs (PDPs), but researchers have not established an effective method of assessing teachers’ performance in this area. Moreover, the definition of IBMT, and the relationship between teachers’ mathematics inquiry knowledge and practice, both remain unclear. Therefore, this study first proposes a sophisticated definition of mathematics inquiry-based teaching, and goes on to use this definition as the basis of a systematic, integrated method for assessing teachers’ knowledge and practice of such teaching. Changes in four cases of teachers’ knowledge and practice of IBMT during their participation in a 1-year PDP in Taiwan are reported and analyzed. The data sources included classroom observations as well as interviews and teachers’ concept maps. Data were analyzed using an analytic framework of concept-map structure; essential constructs of knowledge regarding mathematics inquiry; and an analytic framework of inquiry-based teaching practice. The research revealed (1) that all four case teachers made positive progress in both their knowledge of mathematics inquiry and their related teaching practices; (2) that the two sets of gains described in point (1) above did not appear to have any causal relationship; and (3) that although all four teachers’ knowledge and practices were found to have changed, radical changes in their teaching practices were still rare in the short term.
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