In a real sense, PISA 2003 has touched the mathematics education community by stealth rather than by storm. Although PISA brings "baggage" commonly associated with international assessments, it takes some refreshing perspectives especially in the way that it envisions and assesses mathematical literacy. In this panel discussion we focus…

This paper argues that discussions of diversity often avoid the issue of race. Further, it maintains that diversity and structural backlashes to it in the United States in social and economic life shape and are shaped by crises in mathematics education. Attention is paid to the lack of instructional diversity in mathematical problem types and to…

This paper provides a glimpse into the positive effect on student learning as a result of empowering a classroom teacher of 20 years (Andrea) with subject matter knowledge relevant to developing fraction understanding. Having a facility with fractions is essential for life skills in any society, whether metricated or non-metricated, and yet…

The relationship between mathematicians and researchers in mathematics education has often been fragile. Yet it is crucial. We conducted a series of themed Focus Group interviews with mathematicians from six UK universities. Pre-distributed samples of mathematical problems, typical written student responses, observation protocols, interview…

We explore the nature and consequences of teachers' problem solving through an example of a teacher's mathematical problem solving as it was occasioned by a student's mathematics. This illustration demonstrates the value of an interpretive framework that points to the mathematics of the classroom as a collective. Arising from this exploration is…

This study is to explore the potential of Fauconnier's mental space theory in understanding the teaching and learning processes of mathematics. Notions from cognitive linguistics have been introduced to research in mathematics education recently, but there have been little studies about what potential the framework of mental space has in…

Interviewing students, though a common and popular activity in teacher education programs has been scarcely researched as a strategy to prepare prospective teachers for mathematics teaching. This study explores the role of interviews as occasions for prospective elementary school teachers to learn three essential practices in the teaching of…

In contrast to the traditional top-down approach, a bottom-up approach is proposed by current reform in mathematics education. According to this alternative proposal, algorithmizing is the activity in which students should be involved. What can we do when we want to enact such an algorithmizing approach in a classroom and our students have already…