Nicolas Boileau

Ontario Council on Articulation and Transfer (ONCAT)

Over the last 30 years, in the field of mathematics education, there has been a growing interest in the notion of identity and much important research on the topic. This is related to the theme of this symposium, STEM engagement, in that one of the motivations for studying students’ mathematical identities—their sense of self in relation to mathema...

In this blog post, I share early findings from a longitudinal mixed-methods study of transfer student decision-making and experience in Ontario. Link to post: https://oncat.ca/en/news/why-students-transfer-early-findings-longitudinal-study-transfer-students-ontario

In an era of increasing data interoperability, researchers can now easily link many datasets to answer questions that would have been very laboursome to answer previously; however, this has not been the case with creating seamless processes and information systems for students wishing to transfer credit between post-secondary institutions (Horn & P...

In this poster, we share preliminary results of the current phase of a longitudinal mixed-methods study of transfer students’ experiences and decision-making in Ontario, Canada. We conceptualize the transfer process as consisting of three main stages: (1) a period when students choose which programs (and institutions) to apply to and which to enrol...

Transfer pathways between Ontario Colleges, Universities, and Indigenous Institutes, as well as other forms of inter-institutional partnerships that facilitate transfer, can increase access to postsecondary education for students that often face barriers. For that reason in particular, since 2011, the Ontario Council on Articulation and Transfer (O...

In this session, we report on the first stage of an ongoing longitudinal study: interviews with transfer students at the stage of intent (i.e., when they are still only considering transferring). To identify members of this population, we invited individuals visiting ONTransfer—a website with information on postsecondary student transfer in Ontario...

Des recherches antérieures ont démontré que les normes ont une influence considérable sur le comportement humain. Ils ont aussi démontré que les violations des normes sont parfois acceptées, mais qu’elles sont plus souvent sanctionnées négativement. Dans ma thèse, je discute de la possibilité d’une autre conséquence de la violation d'une norme: que...

The investigation at scale of the tensions that teachers need to manage when deciding to follow recommendations for practice has been hampered by the problem of occurrence: The conditions in which those decisions could be made need to occur during an observation in order for observers to document how teachers handle them. Simulations have been reco...

One of the main responsibilities of a mathematics teacher is to support their students in learning mathematics. It is widely accepted that teachers are most effective at this when they base their instructional decisions on their understandings of what their students know at any given point, which they infer from students’ mathematical activities (e...

To operationalize the notion that lessons are the knowledge base of the teaching profession and enable the study of teacher decision making during lessons, we provide a conceptualization of lesson as part of a multiverse of mathematics teaching. Using the case of problem-based instruction and a particular example in teaching high school geometry, w...

Prior research has demonstrated that norms have considerable influence on human behaviour. It has also demonstrated that, while breaches of norms are sometimes accepted, they are often negatively sanctioned. In my dissertation, I discuss another possible consequence of breaching a norm: that doing so may have individuals (e.g., teachers) abandon th...

Studies have demonstrated that norms have considerable influence on human behaviour, in particular, that of teachers and students in mathematics classrooms. Studies have also shown that breaches of norms are frequently sanctioned, sometimes positively, but typically negatively. The present study builds on that literature by investigating two other...

In this chapter, we contribute some insights from project SimTeach (Herbst P, Chieu VM, SIMTEACH: What can practical knowledge modeled in a teaching simulator contribute to support mathematics teacher learning? National Science Foundation Grant, EHR, DRL-1420102, 2014) concerning the role that technologically mediated teaching simulations can play...

Novel tasks are valuable, yet discussions of novel tasks are often challenging to manage. In this paper, we describe a U.S. high school geometry lesson taught by two teachers in six different classes, in which students were assigned a novel task that the teacher framed as an instance of two familiar instructional situations — constructing a diagram...

Using mixed-effects regression, we analyzed teachers’ responses to a multimedia survey of instructional practices in posing proof problems in geometry. Teachers described and rated for appropriateness three different ways of involving students in deciding what to prove, including one in which the teacher chooses the givens and the conclusion to pro...

Based on data collected from the administration of a multimedia questionnaire to a nationally-distributed sample of secondary mathematics teachers, we investigated such teachers’ stances on the norm of high school geometry instruction that the teacher is responsible for providing the propositions (‘given’ and ‘prove’ statements) that students are a...

For more than 30 years, education researchers have been trying to characterize and differentiate between the practice and thinking of expert and novice teachers (Borko, Roberts, & Shavelson, 2008). Berliner (1986) identified four challenges in studying expertise: (1) The shortcomings of (then) common methods of studying teaching expertise (e.g., th...

This paper describes how the notion of instructional situation can serve as a cornerstone for a subject specific theory of mathematics teaching. The high school geometry course in the U.S. (and some of its instructional situations — constructing a figure, exploring a figure, and doing proofs) is used to identify elements of a subject-specific langu...

For decades, mathematics educators have been interested in engaging K-12 students in the practice of creating and using mathematical models. What might this look like in the context of geometry? Inspired by claims that students come to secondary school with knowledge of three-dimensional space that can be leveraged to engage them in modeling, we wo...

We discuss affordances and liabilities of using a storyboard to depict a written case of a teacher’s dilemma that involves race, opportunity to learn, and student community. We rely on reflections by the teacher educator who authored the written case and later depicted it as a storyboard to use it with his preservice teachers (PSTs). The analysis i...

The primary goal of this paper is to investigate whether a computer-based simulation can detect the difference between novice and expert teachers’ decision-making in mathematics instruction, which is complex in nature. The design of the simulation is grounded in a sociological perspective on practical rationality of mathematics teaching. The simula...

Secondary geometry teachers have been shown to recognize norms of instructional situations such as installing a new theorem (Herbst, Nachlieli, & Chazan, 2011) or doing proofs (Herbst, Aaron, Dimmel, & Erickson, 2013). In the latter case, the diagrammatic register norm describes the customary way in which a diagram and notation are used to present...

We examine responses from a national sample of high school mathematics teachers to a questionnaire, which had been developed to study teachers’ recognition of a system of hypothesized norms that stipulate that geometry proof problems are to be posed using a diagrammatic register. We report on the psychometric properties of the questionnaire, as wel...

This paper reports on a study of two norms of an instructional situation in high school geometry - Geometric Calculation in Algebra (GCA) - that consisted of confronting practitioners with representations of practice as a way to stimulate them to relay their knowledge of practice. In the situation of GCA, students are provided with a diagram in whi...

This paper reports on a study of the instructional situation in high school Geometry that Hsu (2010) called Geometric Calculation in Algebra (GCA). In particular, we conducted a virtual breaching experiment in order to examine the extent to which high school teachers recognized breaches of two norms that we conjectured to describe geometry teachers...

The poster presents a research instrument designed to explore the existence of norms in the instructional situation of geometric calculations in algebra. The instrument was piloted with twenty-nine high school mathematics teachers. The data provides evidence that high school mathematics teachers recognize the hypothesized norms targeted by the inst...

[Draft version: http://deepblue.lib.umich.edu/bitstream/handle/2027.42/110700/SITE2015-ChieuBoileauHerbst.pdf?sequence=1&isAllowed=y] LessonSketch is an online, multimedia-based learning environment that supports practice-based teacher education. A work in progress since the development of its initial components in 2008 and its launch in 2011, Less...

The primary goal of our research was to gain a sense of the technology that secondary school mathematics teachers in Montreal, Québec are currently using, how they are using it, and some of the reasons why they use the technology that they do, in the ways that they do. The secondary goal was to test the effectiveness of our approach in obtaining th...