We describe and analyze three episodes from mathematics classrooms. In each case, the teacher was confronted by a "contingent" situation that they had not anticipated or planned for yet that offered interesting and fruitful learning possibilities if pursued. In two cases, we analyze the teacher's response; in the third, we speculate how they might…

Some of mathematics teaching is routine, like an exercise from a textbook for which you have received instruction and already know what to do. On other occasions, however, teaching mathematics is challenging, involving problems of teaching for which the solutions may not be readily apparent. These situations require the application of mathematical…

We propose that what teachers can say or write about their views of mathematics and about a range of pedagogic strategies and didactic tactics that they use is of minor importance compared to what comes to mind moment by moment when they are planning or leading a lesson. Beginning with a quote from a teacher that provoked a focus on the role and…

We investigate whether and how personal mathematical knowledge at an advanced level impacts on teaching at a lower school level. We study this in the context of functions because understanding them permeates secondary and advanced mathematics. Textbook treatment of these can be patchy, implying a need for knowledgeable teachers to rectify…

As part of a 5-year project that examined teachers' knowledge and beliefs about mathematics and teaching mathematics, interviews were conducted with preservice elementary teachers during their certification year. The transcripts of five of these sets of pretest/posttest interviews were chosen as illustrative of the significant challenges that…

Reports on the third of a line of investigations that examine pre-service teachers' conceptions of nature of science (NOS) and the translation of those conceptions into classroom practice. Delineates the effectiveness of an intervention designed to facilitate pre-service teachers' inclusion of NOS in their classroom teaching. (Author/MM)

Explores some of the complexity of the influences that shape teacher practice in relation to teachers' theories, knowledge, and beliefs about the teaching of mathematics. Focuses on the relationships that exist between teachers' espoused theories and their theories-in-use. (Author/MM)