Members of the Visualization, Interaction, & Reasoning Lab Team who work on the spatial mathematics project.
Our mission is to empower students to become mathematical authors and inquirers.
"Spatializing" Elementary Mathematics
Learning to See Space: Exploring and Supporting Students’ Spatial Reasoning
This research project aims to support and understand students’ spatial reasoning within geometry. Spatial reasoning involves seeing and imagining the orientation and movement of objects. Spatial reasoning is used when parallel parking, reading a map, or interpreting a graph. Through our research, we hope to center the voices and perspectives of students by focusing on their reasoning processes as they engage in spatial tasks in geometry.
Our main research objectives are to:
- Characterize spatial reasoning processes in geometry in grades 1-8.
- Understand how features of students’ learning environments contribute to changes in students’ spatial reasoning.
Data collection, analyses, and dissemination are ongoing.
Funding: Canadian Social Sciences and Humanities Research Council (SSHRC) Insight Grant
Previous Research Projects
Supporting Prospective Teachers to Engage Students in Constructing and Reasoning about Mathematical Definitions
This research project (2017-2022) aimed to support preservice teachers to learn to engage students in constructing and reasoning about mathematical definitions (what we term defining). This design study took place in a university mathematics teaching methods course for elementary preservice teachers. The designed supports included two components: a) activities to help preservice teachers understand the nature of mathematical definitions and defining and b) opportunities to practice engaging students in definition construction. Our study goals were to understand: a) how preservice learned about the nature of defining and definitions, b) how preservice teachers learned about engaging students in mathematical defining, and c) how engagement with designed supports and interactions with tools and others may have contributed to learning.
Funding: Fonds de Recherche Québec Société et Culture
Examining the Development of Facilitation Practices and Noticing of Coaches of Prospective Mathematics Teachers
This research project (2016-2023) aimed to understand how to support teacher educators in coaching preservice elementary mathematics teachers during rehearsals of teaching. Rehearsals are simulations of teaching in which a preservice teacher practices teaching a lesson while other preservice teachers act as students. Rehearsals provide the ability to “pause” or interject to allow teacher educators and preservice teachers to exchange questions, suggestions, and reflections about teaching. Over two studies, we examined: a) teacher educators' facilitation practices and noticing, b) teacher educators’ learning about providing rehearsal feedback, and c) how preservice teachers’ and teacher educators’ interpretations of rehearsal feedback were similar or different.
Funding: Internal McGill Development Grant (completed); Social Sciences and Humanities Research Council (SSHRC) Insight Development Grant
Our Lab Logo
Our logo emphasizes the three letters of our lab name: Visualization, Interaction, and Reasoning. In addition, the logo includes two people connected by two lines.This image reflects our focus on studying interaction and the value we place in collaboration in our research and in mathematics learning. The lines also symbolize how visualization and reasoning are not just in a person's head but occur through and are situated within interaction. We chose to keep our logo simple so that it could blend in well for different uses (e.g., posters, infographics) and to emphasize the words in our lab name.
We developed our lab logo through a collaborative process. To read more about our process, click on the link below.
Featured Publications
This article shares results from our study, "Supporting Prospective Teachers to Engage Students in Constructing and Reasoning about Mathematical Definitions."
This article describes earlier work in spatial mathematics that we're building on in our current project.
This conference proceeding comes from our project focused on teacher educator facilitation during rehearsals of teaching.