Research Projects

Bruce C., Flynn, T., Yearly, S. (in development). The Foundations of Fractions. Pearson, Canada.

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Yearley, S. & Bruce, C. (2014). A Canadian Effort to Address Fractions Teaching and Learning Challenges. Australian Primary Mathematics Classroom Journal, 19(4).

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Bruce, C., Flynn, T. & Bennett, S. (2014). Fractions Report for 2013-2014. Submitted to the Ontario Ministry of Education, Toronto, Ontario.

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Bruce, C., Flynn, T. & Bennett, S. (2014). Fractions Operations Literature Review. Submitted to the Ontario Ministry of Education, Toronto, Ontario.

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Bruce, C., Chang, D, Flynn, T & Yearley, S. (2013). Foundations to Learning and Teaching Addition and Subtraction of Fractions. Comprehensive literature review submitted to the Ontario Ministry of Education. Toronto, Ontario Canada. Posted at www.tmerc.ca and www.edugains.ca

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Bruce, C. & Flynn, T. (2011). Which is greater: One half or two fourths? An examination of how two Grade 1 students negotiate meaning. Canadian Journal for Studies in Science, Mathematics and Technology Education, 11(4), 309–327 >View Journal

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Bruce, C. & Ross, J.A. (2009). Conditions for Effective Use of Interactive On-line Learning Objects: The case of a fractions computer-based learning sequence. Journal of Education. >View Journal /Show Abstract

Conditions for Effective Use of Interactive On-line Learning Objects: The case of a fractions computer-based learning sequence 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 scaffolding teachers might have difficulty providing. A development team of teachers, researchers and educational software programmers designed five sets of fractions activities in the form of learning objects, called CLIPS. As part of a larger mixed-methods study, 36 observations as well as interviews were conducted in four classrooms, grades 7-10. Four students were selected by their teachers for CLIPS use from each of these four classrooms because the students were experiencing difficulty with fractions concepts. CLIPS use contributed to student achievement, provided the conditions enabled an effective learning environment and students experienced the full sequence of tasks in the CLIPS. In this article we describe the conditions that enabled student success. Three interacting contexts affected successful use of CLIPS: technological contexts (such as access to computers with audio), teaching contexts (such as introductory activities that prepared students for the CLIPS activities) and student contexts (such as the level of student confidence and opportunities to communicate to a peer). The study illustrates how a research-based set of learning objects can be effective and provides guidelines to consider when using learning objects to enhance mathematics programs.

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Ross, J.A., Ford, J., Bruce, C. (2009). Student Achievement Effects of Technology-Supported Remediation of Understanding of Fractions. >Download Article

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Bruce, C. Ross, J.A. & Scoffin, S. (2007). Tools to support low achievers: A mixed methods study of students learning fractions. Interim Report of Ontario Ministry of Education & Training Research Grant, Peterborough, ON: Trent U/OISE of UT

Bruce, C., Flynn, T., & Bennett, S. (2016). A focus on exploratory tasks in lesson study: The Canadian ‘Math for Young Children’ project, ZDM Mathematics Education. 48(4), 541-554. doi: 10.1007/s11858-015-0747-7

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Bruce, C., Flynn, T. & Moss, J. (2016). Early mathematics: Challenges, possibilities and new directions in the research (Mathematics for Young Children: Literature Review, 2nd ed.). Comprehensive literature review submitted to the Literacy and Numeracy Secretariat, Ontario Ministry of Education. Toronto, Ontario, Canada. Original publication date: June 25, 2012. >Download Literature Review

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Bruce, C., Moss, J. & Flynn, T. (2013). A “no-ceiling” approach to young children’s mathematics: Preliminary results of an innovative professional learning program. In Martinez, M. & Castro Superfine, A (Eds.). Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Chicago.

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Bruce, C. & Flynn, T. (2012). Integrating instruction and play in a Kindergarten to Grade 2 lesson study project. In L.R. Van Zoest, J.J. Lo, & J.L. Kratky, (Eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Kalamazoo, MI: Western Michigan University.

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Bruce, C., Flynn, T. & Bennett, S. (2014). Math for Young Children. Report for 2013-2014. Submitted to Waterloo Catholic District School Board, Kitchener, Ontario.

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Bruce, C., Flynn, T. & Bennett, S. (2014). Math for Young Children. Report for 2013-2014. Submitted to Waterloo Catholic District School Board, Kitchener, Ontario.

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Bruce, C., Moss, J. & Flynn, T. (2013). A “no-ceiling” approach to young children’s mathematics: Preliminary results of an innovative professional learning program. In Martinez, M. & Castro Superfine, A (Eds.). Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Chicago.

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Bruce, C., Moss, J., Ross, J. & Flynn, T. (2012). Report on Year 1 of the Math for Young Children Lesson Study research project. Submitted to the Literacy and Numeracy Secretariat. Ontario: Toronto.

Bruce, C., Hawes, Z. & Flynn, T. (accepted). Supporting the development of young children’s spatial reasoning: Insights from the math for young children (M4YC) project. 14^th International Congress on Mathematical Education (ICME), Shanghai, July 2020.

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Woolcott, G., Chamberlain, D., Hawes, Z., Drefs, M., Bruce, C. et al. (submitted). Is Education ‘Mission Control’ for Knowledge Mobilization? Insights from Network Analyses of Spatial Reasoning Research across Disciplines, American Educational Research Journal, October 2019.

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Bruce, C., Davis, B., Sinclair, N. & the Spatial Reasoning Study Group (2016). Understanding gaps in research networks: Using “spatial reasoning” as a window into the importance of networked educational research. Educational Studies in Mathematics. 93(3). doi:10.1007/s10649-016-9743-2

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Moss, J., Bruce, C., Caswell, B., Flynn, T., & Hawes, Z. (2016). Taking Shape: Spatial Reasoning for Young Children. Pearson Canada. isbn10: 0134153499 | isbn13: 9780134153490

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Davis, B., & Spatial Reasoning Study Group. (2015). Spatial reasoning in the early years: Principles, assertions, and speculations. New York, NY: Routledge (Taylor & Francis Group). >View Article

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Bruce, C, & Hawes, Z. (2015). The role of 2D and 3D mental rotation in mathematics for young children: what is it? Why is it important? And what can we do about it? ZDM: Mathematics Education, 47(3). >View Book Information

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Sinclair, N. & Bruce, C. (Eds). (2015). Special Focus Issue of ZDM International Journal of Mathematics Education, on Geometry in the Primary School. Vol 47(3). >View Book Information

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Sinclair, N. & Bruce, C. (2015). New opportunities in geometry education at the primary school. ZDM: Mathematics Education, 47(3).

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Hawes, Z., Lefevre, J., Xui, C. & Bruce, C. (2015). Mental Rotation with Tangible Three Dimensional Objects: A new measure sensitive to developmental differences in 4-8 year old children, Mind, Brain and Education. 8(4). 10-18. DOI: 10.1111/mbe.12051 (Online first)

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Bruce, C., Sinclair, N., Moss, J., Hawes, Z. & Caswell, B. Spatializing the curriculum (2015). In Spatial Reasoning for Young Children, Brent Davis & the Spatial Reasoning Study Group. Routledge of Taylor & Francis: New York.

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Sinclair, N. & Bruce, C. (2014). Spatial reasoning for young learners. In Liljedahl, P., Nicol, C., Oesterle, S., & Allan, D. (Eds.). Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education, Vol1 (pp. 173-203). Vancouver, Canada: PME.

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Hawes, Z., & Bruce, C. (2014). A misnomer no more: Using tangible cube-figures to measure 3D mental rotation in young children. In Liljedahl, P., Nicol, C., Oesterle, S., & Allan, D. (Eds.). Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education, Vol. 1 (pp. 95-97). Vancouver, Canada: PME.

Bruce. C., & Flynn, T. (2013). Assessing the Effects of Collaborative Professional Learning: Efficacy shifts in a three-year mathematics study. Alberta Journal of Educational Research 58(4), 691-709.

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Ross, J. & Bruce, C. (2012). Quantitative inquiry into collaborative action research: Measuring teacher benefits. Teacher Development, 16(4), 537-561.

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Bruce, C., Jarvis, D., Flynn, T. & Brock, E. (2012). Lead Teachers in Collaborative Action Research: Perceptions of Role and Responsibility. Canadian Journal of Action Research 12 (3), 29-46. >View Journal

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Bruce, C., Flynn, T, & Peterson, S. (2011). Examining what we mean by collaboration in collaborative action research: a cross-case analysis. Educational Action Research, 19(4), 433-452.

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Bruce, C., Esmonde, I., Ross, J., & Gookie, L., Beatty, R. (2010). The effects of sustained classroom-embedded teacher professional learning on teacher efficacy and related student achievement. Teaching and Teacher Education, 26 (8). >View Article

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Bruce, C. & Ross, J.A. (2008). A Model for increasing reform implementation and teacher efficacy: Teacher peer coaching in grade 3 and 6 mathematics. Canadian Journal of Education. >Download Article /Show Abstract

A Model for Increasing Reform Implementation and Teacher Efficacy: Teacher Peer Coaching in Grade 3 and 6 Mathematics This study examined the effects of peer coaching on mathematics teaching practices and teacher beliefs about their capacity to impact 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 math teaching strategies and peer coaching opportunities. Data sources included classroom observations, teacher self-assessments, interviews, and field notes. Data were analysed using a two level qualitative coding strategy with multiple interpreters. Findings showed that teachers implemented key strategies for effective math teaching, especially for facilitating student interaction and improving the quality of tasks assigned.

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Ross, J.A., & Bruce, C. (2007). Professional development effects on teacher efficacy: Results of a randomized experiment. Journal of Educational Research 101(1), 50-60.

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Ross, J.A., & Bruce, C. (2007). Teacher self-assessment: A mechanism for facilitating professional growth. Teaching and Teacher Education 23(2), 146-159. >View Article /Show Abstract

Teacher self-assessment: A mechanism for facilitating professional growth 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 explanatory case study in which use of the self-assessment tool, in combination with other elements, contributed to change in the instructional practice of a grade 8 mathematics teacher. Provision of a self-assessment tool contributed to teacher growth by: (1) influencing the teacher’s definition of excellence in teaching and increasing his ability to recognize mastery experiences; (2) helping the teacher select improvement goals by providing him with clear standards of teaching, opportunities to find gaps between desired and actual practices, and a menu of options for action; (3) facilitating communication with the teacher’s peer; and (4) increasing the influence of external change agents on teacher practice. The study argues that providing a self-assessment tool is a constructive strategy for improving the effectiveness of in-service provided it is bundled with other professional growth strategies: peer coaching, observation by external change agents, and focused input on teaching strategies.

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Ross, J. A., Bruce, C., & Hogaboam-Gray, A. (2006). The impact of a professional development program on student achievement in grade 6 mathematics. Journal of Mathematics Teacher Education, 9, 551-577. >View Journal

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Bruce, C. (2013). The relationship between collaborative action research and leadership. In Collaborative Action Research: Effects of teacher-directed research in Ontario schools. Monograph: Elementary Teachers’ Federation of Ontario Press: Toronto.

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Ross, J. & Bruce, C. (2013). Teacher efficacy effects of action research. In Collaborative Action Research: Effects of teacher-directed research in Ontario schools. Monograph: Elementary Teachers’ Federation of Ontario Press: Toronto.

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Bruce, C. & Ladky, M. (2011). What’s going on backstage? Revealing the work of lesson study. In Hart, L., Alston, A., & Murata, A. (Eds.), Learning Together: Lesson-study research and practice in mathematics education. Springer Press. >View Book Information

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Beatty, R. & Bruce, C. (2011). Assessing a research/professional development model in patterning and algebra. In Bednarz, N., Fiorentini, D. & Huang, R. (Eds.), International Approaches to Professional Development for Mathematics Teachers. University of Ottawa Press. >View Book Information

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Bruce, C., Flynn, T., Ross, J. & Moss, J. (2011). In Ubuz, B. (Ed.). Promoting teacher and student mathematics learning through lesson study: A design research approach. Proceedings of the thirty-fifth conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 193-200. Ankara, Turkey: PME.

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Ross, J. A., McDougall, D., Bruce, C., Ben Jaafar, S., & Lee, J. (2004). A multi- dimensional approach to mathematics in-service. In McDougall, D. & and Ross, J.A. (Eds.)Proceedings of the twenty-sixth Psychology of Mathematics Education – North America.

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Bruce, C., Flynn, T. & Ross, J. (2012). Assessing the effects of collaborative professional learning: Efficacy shifts in a three-year mathematics study. Submitted to the Literacy and Numeracy Secretariat. Ontario:Toronto

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Bruce, C., Flynn, T., Ross, J. & Lessard, G. (2011) External Report on Mathematics Collaborative Inquiry Initiatives of the Literacy and Numeracy Secretariat: Year 3, Ontario: Toronto.

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Bruce, C., Flynn, T., Ross, J. & Lessard, G. (2011) External Report on Mathematics Collaborative Inquiry Initiatives of the Literacy and Numeracy Secretariat: Year 3, Ontario: Toronto.

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Bruce, C. & Ross, J. (2010). Report for External Review of the Collaborative Inquiry and Learning-Mathematics Project: Year 2. Submitted to the Literacy and Numeracy Secretariat. Ontario: Toronto.

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Bruce, C. & Flynn, T. (2010). Collaborative Action Research in Mathematics: A three-year partnership project with the Elementary Teachers’ Federation of Ontario. Submitted to the Elementary Teachers’ Federation of Ontario: Toronto.

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Bruce, C., Ross, J., Esmonde, I., Beatty, R., Demers, S. & Duquette, C. (2009). Report on the External Review of the Collaborative Inquiry for Learning Mathematics (CIL-M) Project. Literacy and Numeracy Secretariat, Ontario: Toronto.

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Bruce, C. & Flynn, T. (2009). Collaborative Action Research in Mathematics: A partnership project with the Elementary Teachers’ Federation of Ontario. Submitted to the Elementary Teachers’ Federation of Ontario: Toronto.

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Bruce, C. & Mackenzie, J. (2008). Collaborative Action Research: A model for teacher professional development. Submitted to the Elementary Teachers’ Federation of Ontario: Toronto.

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Bruce, C., Ross, J.A. & Scoffin, S. (2006). Effects of peer coaching and professional development in mathematics literacy: One school story, Kawartha Pine Ridge District School Board. Peterborough, ON: Trent University.

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Ross, J.A., Bruce, C., Scoffin, S. (2005, November). Peer coaching in grade 3-6 mathematics: effects on teacher practice and teacher efficacy.Year2. Final Report of Ontario Ministry of Education & Training Transfer Grant. Peterborough, ON: OISE/UT Trent Valley.

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Ross, J.A., Hogaboam-Gray, A., & Bruce, C. (2004, December). Student achievement effects of professional development for grade 6 mathematics teachers in the Kawartha Pine Ridge District School Board. Peterborough, ON: OISE/UT Trent Valley.

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Bruce, C. & Ross, J. (2010). Collaborative Inquiry and Learning in Mathematics: Year 1 research review, Inspire Series: Professional On-line Publication of the Literacy and Numeracy Secretariat. >View Video

Bruce, C. & Flynn, T. (2012). Exploring interactivity between students, teachers and the interactive whiteboard: Video analysis of pedagogical-technological interactivity during mathematics lessons. RicercAzione Journal, (4)2.

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Bruce, C. (2012). Technology in the Mathematics Classroom: Harnessing the Learning Potential of Interactive Whiteboards. Research into Practice: Ontario Association of Deans of Education. Research Monograph # 38, March, 1-4. >Download Monograph

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Beatty, R. & Bruce, C. (2012). Supporting students with learning disabilities to explore linear relationships using on-line learning objects. Pensamiento Numerico y Algebraico 7(1). >Download Journal

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Bruce, C., McPherson, R. & Sabbati, M. & Flynn, T. (2011). Revealing significant learning moments with interactive whiteboards in mathematics. Journal of Educational Computing Research, 45(4), 433-454. >View Abstract

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Ross, J., Bruce, C., & Sibbald, T. (2011). Sequencing Computer-Assisted Learning of Transformations of Trigonometric Functions. Teaching Mathematics and Its Applications, Oxford Press. >View Abstract

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Bruce, C. & Ross, J.A. (2009). Conditions for Effective Use of Interactive On-line Learning Objects: The case of a fractions computer-based learning sequence. Journal of Education. >View Journal /Show Abstract

Conditions for Effective Use of Interactive On-line Learning Objects: The case of a fractions computer-based learning sequence 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 scaffolding teachers might have difficulty providing. A development team of teachers, researchers and educational software programmers designed five sets of fractions activities in the form of learning objects, called CLIPS. As part of a larger mixed-methods study, 36 observations as well as interviews were conducted in four classrooms, grades 7-10. Four students were selected by their teachers for CLIPS use from each of these four classrooms because the students were experiencing difficulty with fractions concepts. CLIPS use contributed to student achievement, provided the conditions enabled an effective learning environment and students experienced the full sequence of tasks in the CLIPS. In this article we describe the conditions that enabled student success. Three interacting contexts affected successful use of CLIPS: technological contexts (such as access to computers with audio), teaching contexts (such as introductory activities that prepared students for the CLIPS activities) and student contexts (such as the level of student confidence and opportunities to communicate to a peer). The study illustrates how a research-based set of learning objects can be effective and provides guidelines to consider when using learning objects to enhance mathematics programs.

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Ross, J.A., Ford, J., Bruce, C. (2009). Student Achievement Effects of Technology-Supported Remediation of Understanding of Fractions. >Download Article /Show Abstract

Student Achievement Effects of Technology-Supported Remediation of Understanding of Fractions 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 that a technology resource could provide the sequencing and scaffolding that teachers might have difficulty providing. Five sets of learning objects, called CLIPS, were developed to provide remediation on fraction concepts. In this article we describe one stage in a research program to develop, implement and evaluate CLIPS. Two studies were conducted. In the first, 14 grade 7-10 classrooms were randomly assigned, within schools, to early and late treatment conditions. A pre-post, delayed treatment design found that that CLIPS had no effect on achievement for the Early Treatment group due to unforeseen implementation problems. These hardware and software issues were mitigated in the late treatment in which CLIPS contributed to student achievement (Cohen’s d=.30). Study 2 was a pre-post, single group replication involving 18 grade 7 classrooms. The independent variable was the number of CLIPS completed. Completion of all five CLIPS contributed to higher student achievement: Cohen’s d=.53, compared to students who completed none (d=.00)or 1-4 CLIPS (d=.02). The two studies indicate that a research-based set of learning objects is effective when the full program is implemented. Incomplete sequences deprive students of instruction in one or more constructs linked to other key ideas in the conceptual map and reduce the amount of practice required to remediate student misconceptions.

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Ross, J.A., Hogaboam-Gray, A., McDougall, D., & Bruce, C. (2002). The contribution of technology to the implementation of mathematics education reform: Case studies of grade 1-3 teachers. Journal of Educational Computing Research, 26(1), 123-140. >View Journal

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Bruce, C., Flynn, T., McPherson, R., & Sabeti, M. (2012). Understanding interactivity in an interactive whiteboard mediated classroom. In Martinovic, D., McDougall, D., & and Karadag, Z. (Eds), Technology in Mathematics Education: Contemporary Issues. Informing Science Institute.

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Ross, J. & Bruce, C. (2011). Technology-supported Instruction in the Mathematics Classroom. In Robyn Gillies (Ed.) Pedagogy: New Developments in the Learning Sciences. New York: Nova Science Publishing. >View Book Online

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Beatty, R., Bruce, C., & McPherson, R. (2011). Using computer-based instruction to support students with learning disabilities: Understanding linear relationships. In Ubuz, B. (Ed.). Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 129-136. Ankara, Turkey: PME.

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Bruce, C., Ross, J., Beatty, R., & Flynn, T. (2011). CLIPS Partnership Research Report: 2010-2011. Submitted to the Ministry of Education, Ontario: Toronto.

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Bruce, C. & Ross, J. (2010). Report on the field tests of CLIPS: Trigonometry and Algebra. Submitted to the Ministry of Education, Ontario: Toronto.

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Bruce, C., Ladky, M., Ross, J.A., Mackenzie, J. & Flynn, T. (2008). Building Capacity in Technology Use through Research in Lesson Study – A Partnership Project with KPRDSB, Trent University, the University of Toronto, and the Ontario Ministry of Education. Submitted to the Ministry of Education. Ontario: Toronto.

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Ross, J.A., Bruce, C., Scoffin, S. & Sibbald, T. (2008). Connecting practice and research: CLIPS project final report to the Ontario Ministry of Education, Peterborough, ON: Trent U/OISE of UT

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Bruce, C., Flynn, T., Ladky, M. (2009). Interactive whiteboard use in math classrooms: Grounding theory in practice. >Download Poster

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Sibbald, T., Ross, J., Bruce, C., (2009). Using a technology-based learning tool to differentiate instruction Factors influencing student assignment to multi-media learning objects in mathematics. >Download Article /Show Abstract

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Ross, J. Sibbald, T. & Bruce, C. (2009). Characteristics of students assigned to technology-based instruction. Journal of Computer Assisted Learning 25, 562-573. >View Journal

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Ross, J.A., Ford, J. & Bruce, C. (2007). Needs assessment for the development of learning objects. Alberta Journal of Educational Research 53(4). >View Journal