Cathy Bruce

• PhD
• Vice President at Trent University

This paper finds its origins in a multidisciplinary research group’s efforts to assemble a review of research in order to better appreciate how “spatial reasoning” is understood and investigated across academic disciplines. We first collaborated to create a historical map of the development of spatial reasoning across key disciplines over the last...

This paper outlines the new opportunities that that will be changing the landscape of geometry education at the primary school level. These include: the research on spatial reasoning and its connection to school mathematics in general and school geometry in particular; the function of drawing in the construction of geometric meaning; the role of di...

The ability to mentally rotate objects in space has been singled out by cognitive scientists as a central metric of spatial reasoning (see Jansen, Schmelter, Quaiser-Pohl, Neuburger, & Heil, 2013; Shepard & Metzler, 1971 for example). However, this is a particularly undeveloped area of current mathematics curricula, especially in North America. In...

In a three-year study of teacher professional learning in Canada, researchers examined the outcomes of professional collaborative inquiry in mathematics on teacher efficacy. The study applied a mixed methods approach involving over 200 teachers and 1000 students as well as case study sites in English and French. The collaborative inquiry-based prof...

Researchers examine the outcomes of professional collaborative inquiry in mathematics on teacher efficacy in a three-year study of teacher professional learning in Canada. The study applies a mixed methods approach involving over 200 teachers and 1000 students as well as case study sites in English and French. The collaborative inquiry-based profes...

Beyond 1, 2, 3 is a comprehensive collection providing an overview of important topics within the field of early childhood mathematics education in Canada. Chapters include a mix of theory and practice, a set of learning objectives, key terms, and discussion questions. In this chapter, the learning objectives are to: Engage in spatial reasoning as...

Fractions remain a challenging area of school mathematics at every stage of education, with impacts that extend far beyond the school years. For this study, researchers engaged in classroom-based design research over a 6-year period to investigate effective strategies for teaching fractions with Canadian students. Participants included 86 teachers...

What do students already understand? How can we build on these strengths? What are students ready for next? These questions were at the heart of a multi-year collaborative research project investigating how fractions understanding develops and identifying the instructional strategies that would effectively scaffold student learning. The result is t...

Knowledge mobilization is becoming increasingly important for research collaborations, but few methodologies support increased knowledge sharing. This study provides insights, using a reflective narrative, into a transdisciplinary knowledge-sharing investigation of the connectivity of educational research to that of other disciplines. As an exempla...

This is the third in a series of articles reporting on forensic epistemology. Our first two research articles presented scientific results that are based in experimental design; including quantitative and qualitative responses from forensic science practitioners to scenarios and evidence. Based on a synthesis of this research there is evidence of a...

In recent years, crime scene analysis has been transitioning from being a technical discipline to being a scientific process. This progression is shifting the forensic practitioner examining crime scenes into a deeper level of scientific reasoning. This study evaluates the use of reasoning by practitioners in the disciplines of crime scene investig...

This chapter describes how collaborative action research functions as a professional learning experience, citing three illustrative examples, and elaborating on the intersection of action research and professional learning. It focuses on three large‐scale and multi‐year research projects that involved professional learning through action research....

Society’s fascination with forensic science has been on an increase for many years. Evidence of this is supported by the development of many tertiary education forensic science programs and the continued increase in student numbers within these programs. In this project, we investigate the reasoning behind why students find forensic science an enga...

How can universities ensure that the first-year learning experiences for students are in alignment with a vision of education that is purposeful, personal and transformative? This essay presents the study of Trent University’s first- year academic experience, that aimed to uncover the problems post-secondary institutions face in the ever-changing l...

The Action Research Network of the Americas (ARNA) was founded in 2012 to support action researchers throughout the Western Hemisphere and around the world. In this chapter, we describe how the network began; its vision, values, mission, and leadership structure; major accomplishments to date; and the strategic goals that guide the network’s action...

Peter Reason and Hilary Bradbury (2006) began the introduction to the second edition of their groundbreaking Handbook of Action Research with a broad overview of the volume’s contents and a framing of action research as “inquiry and participation in search of a world worthy of human aspiration” (p. 1). The framing suggests that they were observing...

Summary: Results of Study 1 showed that students in the experimental group outperformed the control group on a comprehensive test of visual-spatial reasoning at post-test. Results also showed a medium within-group effect size (Cohen’s d) on the same measure from pre to post. Teachers in the study also reported deep learning about connections betwee...

Spatial reasoning plays vital roles in choice of and success in STEM careers; yet the topic is scarce in grade-school curricula. We conjecture that this absence may be due to limited knowledge of how spatial reasoning is discussed and engaged across STEM professions. This study aimed to address that gap by asking 19 professionals to comment on a vi...

This article explores the integration of innovative technologies into forensic science training initiatives and their effect on student engagement and depth of learning. Novel situation-oriented teaching practices were researched and implemented with the goal of enhancing the quality of practitioner forensic science training. Specifically, a basic...

Strengthening education and training in the forensic sciences requires the implementation of new and innovative technologies into existing teaching strategies. Scientific research in the design and use of artificial substitutes can offer new and advantageous contributions to such initiatives. This article describes the relevant considerations and a...

In Taking Shape, spatial reasoning is greeted and treated as integral to and foundational of all mathematics understanding - present in every action, influenced by and influencing every movement through our structured world, and impacting the language used to make sense of experience. To that end, spatial reasoning is not presented as yet another c...

In Taking Shape, spatial reasoning is greeted and treated as integral to and foundational of all mathematics understanding - present in every action, influenced by and influencing every movement through our structured world, and impacting the language used to make sense of experience. To that end, spatial reasoning is not presented as yet another c...

Background: Accurate calculation of medication dosages can be challenging for nursing students. Specific interventions related to types of errors made by nursing students may improve the learning of this important skill. Objective: The objective of this study was to determine areas of challenge for students in performing medication dosage calcul...

In an effort to increase our understanding of what mathematics young children are capable of when provided with playful yet purposeful opportunities to learn, Canadian researchers initiated lesson study over 4 years with teams of teachers of young children (ages 4–7). The lesson study process followed a lesson study cycle of goal setting, planning,...

The ability to mentally rotate objects in space has been singled out by cognitive scientists as a central metric of spatial reasoning (see Jansen, Schmelter, Quaiser-Pohl, Neuburger, & Heil, 2013; Shepard & Metzler, 1971 for example). However, this is a particularly undeveloped area of current mathematics curricula, especially in North America. In...

There is an emerging consensus that spatial thinking is fundamental to later success in math and science. The goals of this study were to design and evaluate a novel test of three-dimensional (3D) mental rotation for 4- to 8-year-old children (N = 165) that uses tangible 3D objects. Results revealed that the measure was both valid and reliable and...

This Research Forum proposal arises from a recent focus on spatial reasoning that began with a multi-year collaborative project amongst a diverse group of researchers (mathematicians, psychologists, mathematics educators) from Canada and the US, and continues to expand with the goal of: mapping out the terrain of established research on spatial rea...

The study of linear relationships is foundational for mathematics teaching and learning. However, students’ abilities to connect different representations of linear relationships have proven to be challenging. In response, a computer-based instructional sequence was designed to support students’ understanding of the connections among representation...

Recent research demonstrates that in many countries gender differences in mathematics achievement have virtually disappeared. Expectancy-value theory and social cognition theory both predict that if gender differences in achievement have declined there should be a similar decline in gender differences in self-beliefs. Extant literature is equivocal...

In 2008-09, the Elementary Teachers’ Federation of Ontario (ETFO) sponsored a professional learning initiative entitled, Teachers Learning Together: The Math Journey. The context for teachers was one of team-based, collaborative action research (CAR) dealing with a mathematics topic of their own choosing.University researcher teams in provincial re...

This monograph is a research summary of interactive whiteboard use. It was written for K-12 educators in Canada and is widely available through the Ontario government and on the web. http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/WW_technology.pdf

From Patterns to Algebra: Lessons for Exploring Linear Relationships is an innovative professional learning resource. It is based on Canadian curricula, Canadian research, and seven years of field-testing with Canadian teachers and over 1000 students. This resource builds on students’ experience with patterning in early grades to construct algebrai...

Researchers at Trent University, Canada, have conducted a series of studies on IWB use in mathematics classrooms with two main goals: (i) to develop and test video research methods for IWB mediated classrooms; and (ii) to identify types of IWB activity and interactivity during mathematics classroom lessons. Video data of 15 lessons from two classro...

Recent research demonstrates that in many countries gender differences in mathematics achievement have virtually disappeared. Expectancy-value theory and social cognition theory both predict that if gender differences in achievement have declined there should be a similar decline in gender differences in self-beliefs. Extant literature is equivocal...

In 2008-09, the Elementary Teachers’ Federation of Ontario (ETFO) sponsored a professional learning initiative entitled, Teachers Learning Together: The Math Journey. The context for teachers was one of team-based, collaborative action research (CAR) dealing with a mathematics topic of their own choosing. University researcher teams in provincial r...

The authors extend findings from qualitative research on the effects of action research by reporting two linked quantitative studies (N = 80 and 105). They found that teachers who participated in collaborative action research experienced statistically significant improvements in attitudes to educational research and teacher efficacy. The pre–post c...

This chapter describes the ways two teachers and their students used the interactive whiteboard in mathematics learning contexts. The instances of interactive whiteboard were analysed for productive and reproductive knowledge creation and for gesture use.

Research on technology-supported mathematics instruction indicates that technology has the potential to facilitate easy translation from concrete to abstract representations of mathematical objects, can focus student attention on key dimensions of mathematical ideas, and can represent relationships among objects that are not easily displayed withou...

The purpose of this paper is to report on the nature of collaboration in a multi-year, large-scale collaborative action research project in which a teachers’ federation (in Ontario, Canada), university researchers and teachers partnered to investigate teacher-selected topics for inquiry. Over two years, 14 case studies were generated involving six...

The aim of this study was to identify when and how the interactive whiteboard (IWB) functioned as a productive tool that impacted student learning in mathematics. Using video data, field notes, and interview transcripts from 1 school year in two optimal case study classrooms, we were able to examine the unique opportunities afforded by the size of...

A developing body of research in classroom mathematics discourse indicates that teacher facilitation can be specific and supportive without interfering in productive student talk. Students, including those who are struggling in mathematics or lack confidence, can benefit from exploring challenging mathematics and engaging in math-talk. In this stud...

Studies incorporating technology into the teaching of trigonometry, although sparse, have demonstrated positive effects on student achievement. The optimal sequence for integrating technology with teacher-led mathematics instruction has not been determined. Our research investigated whether technology has a greater impact on student achievement and...

In this project twelve mathematics teachers in four Canadian schools, ranging in experience levels from novice to over twenty years, engaged in Japanese Lesson Study cycles. Their focus was on the use of interactive whiteboards and manipulatives as supports to student learning in mathematics. These teachers identified a variety of ‘backstage activi...

Interactive whiteboards (IWB) have many features that engage students in the classroom, but little is understood about how they actually impact student understanding of mathematics. Our aim in this study was to identify how and why the IWB was a productive tool that impacted student learning in mathematics. As part of this aim, we looked closely at...

This paper reports on the impact of a classroom-embedded professional learning (PL) program for mathematics teaching in two contrasting districts in Canada, and investigates the relationship between teacher efficacy and student achievement. Before the PL, District A had lower teacher efficacy and student achievement than District B, but after the P...

Abstract Previous research has examined factors influencing teacher decisions to integrate technology using between-teacher designs. This study used a within-teacher design to compare students who were assigned multi-media learning objects for learning fractions with students taught by the same teachers who were not assigned to the technology. Ther...

Students have difficulty learning fractions, and problems in understanding fractions persist into adulthood, with moderate to severe consequences for everyday and occupational decision-making. Remediation of student misconceptions is hampered by deficiencies in teachers' knowledge of the discipline and pedagogical content knowledge. We theorized th...

Students are challenged when learning fractions and problems often persist into adulthood. Teachers may find it difficult to remediate student misconceptions in the busy classroom, particularly when the concept is as challenging as fractions has proven to be. We theorized that a technology-based learning resource could provide the sequencing and sc...

This study examined the effects of peer coaching on mathematics teaching practices and teacher beliefs about their capacity to have an impact on student learning. Twelve teachers in grades 3 and 6 participated in a brief but intensive professional development program over six months. The program focused on effective mathematics teaching strategies...

In a review of 125 needs assessments conducted in educational settings, Witkin (1994) identified multiple deficiencies: mono-method bias (use of a single data source to identify needs), confusion between solutions (instructional actions) and needs (gaps in student performance), use of unsystematic procedures, and overreliance on data from a single...

We designed a professional development (PD) program to increase the teacher efficacy of mathematics teachers. We randomly assigned 106 Grade 6 teachers in 1 school district to treatment and control conditions in a delayedtreatment design. The PD explicitly addressed 4 sources of teacher-efficacy information identified in social-cognition theory (Ba...

Self-assessment is a powerful technique for improving achievement. In this article we outline a theory of teacher change that links self-assessment by teachers to their professional growth. This theory provides avenues for peers and change agents to influence teacher practice. We apply the theory to change in mathematics teaching and report an expl...

There has been a strong call for increased clarity and transparency of method in qualitative research. Although qualitative data analysis has been detailed, data management has not been made as transparent in the literature. How do data collection and analysis interact in practical terms? What constitutes sufficient data? And can research be both p...

Grade 6 teachers (N=106) in one school district were randomly assigned to early or late professional development (PD) groups. The program focused on reform communication and incorporated principles of effective PD recommended by researchers, although the duration of the treatment was modest (one full day and four after school sessions over a ten-we...

Previous research suggests that access to technology contributes to the implementation of mathematics education reform. This case study of three primary (grade 1-3) teachers investigated how access to computers and math teaching software influenced nine dimensions of reform. Teachers were selected on the basis of their commitment to math reform and...

This study reports the results of research on the effects of peer coaching on two dimensions closely linked to student achievement: teachers' instructional practice and teacher beliefs about their capacity to impact student achievement. The study tracked 12 grade 3 and 6 teachers as they participated in a professional development program over a six...