Teachers’ inquiry-based mathematics teaching(IBMT) competence is often acquired and developedthrough participation in professional development pro-grams (PDPs), but researchers have not established aneffective method of assessing teachers’ performance in thisarea. Moreover, the definition of IBMT, and the relation-ship between teachers’ mathematics inquiry knowledgeand practice, both remain unclear. Therefore, this studyfirst proposes a sophisticated definition of mathematicsinquiry-based teaching, and goes on to use this definition asthe basis of a systematic, integrated method for assessingteachers’ knowledge and practice of such teaching. Chan-ges in four case teachers’ knowledge and practice of IBMTduring their participation in a 1-year PDP in Taiwan arereported and analyzed. The data sources included class-room observations as well as interviews and teachers’concept maps. Data were analyzed using an analyticframework of concept-map structure; essential constructsof knowledge regarding mathematics inquiry; and an ana-lytic framework of inquiry-based teaching practice. Theresearch revealed (1) that all four case teachers madepositive progress in both their knowledge of mathematicsinquiry and their related teaching practices; (2) that the twosets of gains described in point (1) above did not appear tohave any causal relationship; and (3) that although all fourteachers’ knowledge and practices were found to havechanged, radical changes in their teaching practices werestill rare in the short term

• Analyzing Changes in Four Teachers’ Knowledge and Practiceof Inquiry-Based Mathematics Teaching