The aim of this paper is to discuss preservice mathematics teachers' in-the-moment noticing of mathematical opportunities and how they reflected on those opportunities both orally and in writing. A faculty-school collaboration program was set up to enable preservice teachers to work with students in a school setting throughout a year. Ten…

In this article, I explore the impact of receiving mentorship into research and theory of the field that was guided by a social constructivist learning lens. I reflect on the ways that my conception of research and research agenda were framed subconsciously by early experiences investigating my secondary mathematics teaching practice under the…

Implicit bias is an issue that all instructors must face in their classrooms; this article describes an academic development method to help instructors address it. The method centres on EQUIP (https://www.equip.ninja), a free, web-based application for performing classroom observations that provides data disaggregated by social markers.…

The impetus for this article was a university-school research project (Teaching Perimeter and Area in a Primary Classroom) and it was while working with Lani, a Year 4 teacher, that the role of reflection both 'in and on' her practice (Schön, 1983) became evident. Lani was subsequently interviewed about her reflective practices and the new…

The COVID-19 pandemic has significantly impacted on schools globally with closures and the implementation of online learning (UNESCO, 2020). This rapid shift has resulted in a significant change to traditional modes of delivery, including classroom teaching and professional learning opportunities for teachers, as well as thinking differently about…

Teachers are increasingly being called upon to teach in ways that develop 21st century learning skills in their students. Various frameworks for 21st century learning have been proposed and while they differ, all agree on four components for development--creativity, collaboration, communication and critical thinking. Both individually and…

Preservice teachers (PSTs) must be able to link content, effective teaching practices, and student learning; thus, it is critical for teacher educators to emphasize connections between research and practice in methods courses. Reflection plays an important role in this process. In this article, the authors discuss and illustrate a vignette…

Reflection and collaboration are two activities teachers can use to change and improve their practice. However, finding the time and space to do so can be challenging. The collaborative reflective teaching cycle is a structured activity teachers can use to engage in reflection and collaboration. This article describes how a seventh grade teaching…

In recent years, I have cultivated an almost pathological resistance to grading. Here I explore the reasons why and describe how I eventually recovered. In particular, I propose that although grading, or more explicitly, effective assessment of student learning, is a challenging component of a mathematics instructor's job description, reflective…

The author's teaching goal is always to make certain that his students, children and adults alike, have some reason for joining him on his mathematical journeys. The lesson he describes in this article provides him with the unusual opportunity to call attention to strategies that have had a long history and remarkable results. With careful…

The purpose of this article is to provide a deeper understanding of the natural rhythm of a typical semester, as observed in students' reflections in journals kept during the semester. Our analysis of students' writings rendered a breakdown of the semester into four distinct periods that were independent of the particular semester or section the…

Education experts argue that using rich mathematical tasks in student-centered classrooms is especially conducive to student learning (NCTM 2000). That said, they also acknowledge that using complex tasks and developing student-centered classrooms can be intimidating and challenging for teachers (Chazan and Ball 1999). One difficulty associated…

Both writing and math require purposeful teaching. This article describes how one teacher discovered that she could teach math in a way that paralleled how she taught writing by researching what students know and then nudging them ahead to the next level of understanding. Just as effective writers employ creativity, perseverance, and revising,…

Fraction division is generally introduced in sixth or seventh grade with this rule: "Invert and multiply." The authors examined current commercial curricula and found that few textbooks use context as a way to build meaning for the division of fractions. When context is used, the connection between the invert-and-multiply rule and the context is…

In this article, the authors discuss some of the dispositions that comprise students' (and teachers') relationships with mathematics--what they call a "mathematical identity." They define "mathematical identity" as an individual's "relationship" with mathematics. They present three reflective tasks that can be used with math students at all levels…