I have developed an adaptation of the emerging duoethnography methodology that allows me to draw on my processes of creating mathematics, interpret these processes for what they might mean for classrooms, and explore/reconceptualize my complementary and competing perspectives as a mathematician and an educator. This article includes a…

This article discusses an activity designed to encourage writing to learn in mathematics. There were three stages of data collection. An assessment, requiring basic algebra only, was completed by 118 undergraduates from statistics and calculus courses. Students were given summaries of all participant responses, along with the correct answers.…

Following Star (2005, 2007), we continue to problematize the entangling of type and quality in the use of conceptual knowledge and procedural knowledge. Although those whose work is guided by types of knowledge and those whose work is guided by qualities of knowledge seem to be referring to the same phenomena, actually they are not. This lack of…

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 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…

This article discusses findings from a two-day teacher conference focusing on discursive authority and sociocultural positioning in mathematics classrooms. The conference was designed to study how research on classroom discourse could be transformed into effective professional development activities. We describe how the focus on discourse,…

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…

The purpose of this article is to address the lack of research on teachers' knowledge of probability. As has been the case in prior research, we asked prospective mathematics teachers to determine which of the presented sequences of coin flips was least likely to occur. However, instead of using the traditional perspectives of heuristic and…

David Burns and Stephen Norris's (2012) article entitled "Activist Environmental Education and Moral Philosophy" offers a thought-provoking response to the CJSMTE special edition. The authors would like to thank these authors for their supportive and philosophically adroit arguments. Burns and Norris provide an opportunity to continue the…

Uses the metaphor of shadows in a critical exploration of what it means to know and how the cultures of classrooms have shaped these images of knowing. Directs attention to objects that cast shadows on the learning and knowing of mathematics and science through the voices of preservice teachers. Discusses shadow casting toward textbooks, teachers,…

Describes designing, implementing, and evaluating a teaching experiment that traced the evolution of mathematical practices associated with the way Basotho students in the 4th and 5th grades grow in probabilistic thinking, especially sample space and probability of an event. Focuses on small sample experimenting and analysis of sample space…

Points out the effectiveness of student-generated examples as a teaching tool. Examines the roles played by examples constructed and generated by students, illustrates and analyzes the use of this tool, and develops a theory for the act of exemplification as an act of cognition. Introduces a framework developed for this work. (Contains 39…

Describes the history of science and its purposes in school curriculum, and the reform movements in science education. Explains confusion of "literacy" and "literate" and the use of mass media as a major source for scientific literacy. Discusses science for all and science for possible future scientists. (Contains 41 references.) (Author/YDS)

Reports on a study in which anchoring probability situations that are conceptually analogous to misconception-prone target probability situations were generated and tested with secondary mathematics students. Reports that a follow up test showed that 65% of the reconstructed knowledge was retained after six months. (Author/MM)

Focuses principally on the high school mathematics curriculum. Observes that it is, for most students, lifeless and ineffective. Proposes that the curriculum be implemented as a sequence of good examples designed to expose not content so much as method. (Author/MM)