This dissertation case study examines how teachers' levels of units coordination afford their ability to reason multiplicatively and fractionally, as well as use their mathematics knowledge for teaching to analyze student multiplicative and fractional reasoning, when a two-year intervention is put into place to evoke new mathematical reasoning.…

Teacher knowledge, especially of proportional reasoning, is important, particularly in middle school grades in the United States. In this instrumental case study, one teacher's understanding of constant as it relates to proportions and how that understanding shifted over the course of a six hour professional development experience is discussed.…

Inflation rates are often reported in the media and interpreted differently by various people. The purpose of the study was to explore mathematical literacy teachers' written responses to questions based on the concept of percentage increase and inflation. The participants were a group of 59 in-service South African teachers who were enrolled on a…

In order to provide a transforming way of knowing for teachers' professional learning, this paper uses narrative to present the knowledge emerging from teachers as participants in a concept study derived from complexity science. There are three components in the narrative: what knowledge emerged from concept study; what has been changed for the…

This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and…

These proceedings are a written record of the research presented at the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in St. Louis, Missouri, November 14-17, 2019. This year's conference theme is "...against a new horizon." The papers comprise 67…

This paper describes seven in-service teachers' interpretations of student statements about slope. The teachers interpreted sample student work, conjectured about student contributions, assessed the students' understanding, and positioned the students' statements in the mathematics curriculum. The teachers' responses provide insight into their…

As a result of the increased focus on data literacy and data science across the world, there has been a large demand for professional development in statistics. However, exactly how these professional development opportunities should be structured remains an open question. The purpose of this paper is to describe the first iteration of a design…

The paper reports an investigation into how a group of elementary and middle school teachers collectively attempted to solve and understand a fraction division problem using an area model. Solving the word problem required that teachers determine how many two-thirds fit into three-fourths. The teachers struggled to conceptualise fraction division,…

This study reports teachers' insights and challenges after one year of adopting a curricular material designed to move students through carefully engineered, small steps and encourage learners through success and accessible challenges. The analysis of interviews showed that teachers 'followed' the material in different ways, not necessary in-line…

Math Teachers' Circles (MTCs) are an innovative, problem-solving focused approach to professional development. This model provides teachers opportunities to develop their problem solving skills as well as help them to communicate with others on classroom implementation of problem-solving activities. As with any professional development with…

Although the importance of mathematical problem solving is now widely recognised, relatively little attention has been given to the conceptualisation of mathematical processes such as representing, analysing, interpreting and communicating. The construct of Mathematical Knowledge for Teaching (Hill, Ball & Schilling, 2008) is generally…

In an age when reform is based on standards and instruction is based on research, this article gives practical advice for how mathematics teachers can analyze errors in student problems to create interventions that aid not only the individual's development, but the entire class's as well. By learning how to correct mathematics students'…

The theme of the 39th proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) conference was "Synergy at the Crossroads: Future Directions for Theory, Research, and Practice." The metaphor of crossroads was inspired by the conference venue--the historic Indianapolis Union…

The theme of this year's conference is "Sin Fronteras: Questioning Borders with(in) Mathematics Education." This theme is intended to encourage research presentations, discussion, and reflection on the variety of borders within mathematics education, as well as those that might be probed, challenged, explained, enhanced and/or…