MathEd Forum

June  5, 2020


Annual Research Day

January 26, 2013 at 10 am- 2 pm
Fields Institute,
222 College Street, Toront

10:00 - 10:05 a.m.
Reports: OAME, OMCA, OCMA, CMESG, CMS, and other.

10:05 a.m. - 11: 00 a.m. Luis Radford (Université Laurentienne):
Mathematics Education: Its past, its present, its dreams, and its unresolvable tensions.

Abstract: This talk is about mathematics education and its current challenges and tensions. The main argument of my talk is that, like all educational project, mathematics education inherits the intrinsic ideational contradictions of the societal life in which it finds itself subsumed. Despite its apparent neutrality, mathematics education is part of a political, social, historical, and cultural project. It is against this background that I review some of the unresolvable tensions of mathematics education in the past and the present. At the end of the talk I speculate about some short-term problems and dreams of our discipline.

Bio: Luis Radford is full professor at Laurentian University, in Sudbury Ontario, Canada. He teaches at École des science de l'éducation, in the pre-service teachers' training program and conducts classroom research with teachers from Kindergarten to Grade 12. His research interests include the development of algebraic thinking, the relationship between culture and thought, the epistemology of mathematics, and semiotics. He has been co-editor of three special issues of Educational Studies in Mathematics. He co-edited the book Semiotics in mathematics education: epistemology, history, classroom, and culture (Sense Publishers, 2008) and co-authored the book A Cultural-Historical Perspective on Mathematics Teaching and Learning (2011, Sense Publishers). He received the Laurentian University 2004-05 Research Excellence Award and the 2011 ICMI Hans Freudenthal Medal.

11:00 a.m. - 11:30 a.m. Ruth Beatty (Lakehead University - Orillia Campus):
Two Studies of Young Students' Mathematical Thinking

Abstract: In this session I will present two current research projects that focus on children's mathematical thinking.
First, as part of a larger study of Mathematics For Young Children (Cathy Bruce, Trent University and Joan Moss, OISE/UT) I extended my previous research to study how kindergarten students can think explicitly about linear relationships, that is, use multiplicative rather than additive reasoning when working with linear growing patterns. In this study students were introduced to a number of linear growing patterns presented using visual, narrative and tabular representations. Pre/post results suggest that even very young students can make accurate predictions about the next (4th), near (10th) and far (100th) terms of a linear growing pattern, and can reason explicitly about the relationship between two data sets.
In another project I have been working with a research team to study the connections between Anishinaabe Agindaasowin and Western ways of teaching mathematics. Our goal is to support the mathematical learning of Aboriginal students through recognizing and including traditional teachings. This year we are working with Elder Stephen Kejick and members of the Obashkaandagaang Community (Washagamis Bay) and Wauzhushk Onigum Community (Rat Portage) to design and deliver culturally responsive instruction in two Grade 3 classrooms.

11:30 a.m. - 12:00 p.m. Nadia Hardy (Concordia University)
Students (non)uses of mathematical theory.

Abstract: The focus of this talk is on college mathematics; in particular Algebra and Calculus as these are taught in colleges and several universities across Canada and the US. Every year thousands of students are required to take these courses as prerequisites to enter programs in Engineering, Computer Science, Natural Sciences, etc. Many of these students won't take mathematics courses past these ones. Previous research has addressed the absence of theoretical content - or its dissociation from tasks and techniques - in college mathematics courses and have discussed among its likely consequences, students' inabilities to deal with non-routine problems. I will start this talk with a reflection, based on previous research, on what is it that students do learn in these courses and what may be the use of such knowledge in a non-mathematics student's career. I will continue by giving a characterization of the roles that mathematical theory plays in mathematics knowledge. The goal of such characterization is to serve as a framework for discussing results of an empirical study aimed at revealing college students' perceptions and uses of mathematical theory. Data collected through interviews with 55 college students show that they don't make any use of theory and perceive only one of its roles, namely 'justifying'. Furthermore, their recollection of their previous experiences with mathematical tasks involves exclusively particular examples. Thus, they don't count on experiences that can help them to decode and use 'generalizations'. I end the presentation with a reflection on how theoretical content could be incorporated to college mathematics in order to provide students with resources to deal with non-routine problems and with a foundation to advance in their learning of mathematics.

12:00 p.m. - 1:00 p.m. LUNCH BREAK and Poster Presentations (Light refreshments provided)

1. Kinga Petrovai (Harvard Graduate School of Education) and Jason Chen (College of William and Mary, Virginia, USA): In Search of Math People.

2. Kerry Kwan (OISE, University of Toronto): Reciprocal Partnership: A mathematics intervention to improve self-efficacy and academic performance of first and second year college students

3. Malcolm Cunningham (OISE, University of Toronto): Institutional Measures are not Proxies for Children's Mathematics Learning

4. Carol Carruthers (Seneca College): An Interactive Learner-Centered Classroom: Successful use of Pen-Based Tablet Computing in College Foundational Mathematics

5. Limin Jao (OISE, University of Toronto): Teaching practices to increase student engagement in the Grade 9 Applied mathematics classroom

6. Zohreh Shahbazi, Cho Kin Cheng, & Duy-Minh Dang (University of Toronto, Scarborough): Let's Get Them Ready: Examining the Effectiveness of a Summer Preparatory Mathematics Course on Students' Readiness for University Calculus Courses.

7. Priscilla Bengo & Douglas E. McDougall (OISE, University of Toronto): Teacher emotions and the implementation of mathematics education reform initiatives

8. Taras Gula & Carolyn Hoessler (George Brown College): Using Randomized Field Trial to assess the effectiveness of the JUMP Math Approach in Teaching Foundations Mathematics to First Year College Students: A Tale of Potentiality (or a practitioner's journey)

1:00 p.m. to 2:00 p.m. Short Oral Communications (10min each):

1. Zachary Hawes, Diana Chang, Ashley Olver, & Joan Moss (OISE, University of Toronto):
Part 1: Investigating Spatial Reasoning in Young Children: Developing a New Measure to Inform Curriculum Design

Abstract: Studies have demonstrated an intimate link between spatial reasoning and mathematics. The extant literature has focused mostly on the spatial reasoning ability of older children and adults, largely ignoring the early years. Numerous studies have shown the importance of early years mathematics to later academic achievement. In particular, NCTM has recommended that at least half of the early years mathematics curriculum be focused on geometry, measurement, and spatial reasoning. To examine young children's spatial reasoning ability, we have developed a 3D mental rotation assessment for children aged 4-7. Preliminary results indicate that young children are far more capable of 3D mental rotation than previously reported. The development of tasks such as this one is a necessary first step to advance our understanding of the connection between spatial reasoning and mathematics in the early years. Furthermore, information derived from this task can be used support curriculum development.

2. Joan Moss, Zachary Hawes, Diana Chang, & Diane Tepylo (OISE, University of Toronto):
Part 2: From Mental Rotation Task Design to Lesson Planning: The Case of the Polyomino Challenge

Abstract: In this second paper, we show how the results of the 3D mental rotation task administered by teachers to their young students led to the design of an innovative and challenging series of lessons on spatial reasoning. Specifically, we present a case study of one of the early years lesson study teams, The Blantyre Team, from our Math for Young Children (M4YC) project. In our presentation we use the structure of Japanese Lesson Study to follow the team from first meetings and topic selection through clinical interviews with the mental rotation task to the design process and implementation of a public lesson focused on polyominoes. We highlight how the process of using the newly designed mental rotation task ultimately supported teacher change in content knowledge in geometry and in beliefs about math teaching for young children.

3. Jamie Pyper, Allison Chapman, Stefanie Sebok, & Mandy Lam (Queen's University)
Understanding Geometry in Preservice Teachers' "Mathematics for Teaching" Context

Abstract: Teacher candidates in Intermediate/Senior (I/S) mathematics education come to Bachelor of Education programs with diverse mathematics' backgrounds and experiences, which can impact how they articulate the mathematics of the curriculum to the students they teach. The importance of particular content area knowledge appropriate for teaching in the secondary school classroom was developed from Shulman's (1986, 1987) work on pedagogical content knowledge (PCK). This work became focused on mathematics using Deborah Ball's (Ball & Hill, 2008; Ball & Sleep, 2007) development of mathematics knowledge for teaching (MKFT), which is currently refined as mathematics for teaching (Adler & Davis, 2006; Davis & Simmt, 2006; Simmt, 2011). Mathematics for teaching incorporates a contextual sense to PCK and MKFT by situating the concept within mathematics classrooms and practices. The purpose of this study was to inquire into preservice teachers' mathematical understandings and learn how they use such knowledge in their early teaching practice by considering the following questions: (a) What is the nature of preservice mathematics teachers' discourse? and (b) What is the relevance of this mathematics' understanding to the teaching and learning of high school mathematics? This paper focuses on the analysis of the verbal language used during a mathematics workshop, in particular, the portion of the discussion on the geometry of three dimensional right prisms, cones and pyramids.

1:30 p.m. - 2:00 p.m. General Discussion

2:00 p.m. Adjournment


The Mathematics Education Forum of the Fields Institute for Research in Mathematical Sciences, Toronto, is inviting submissions of abstracts for presentations for its annual Research Day.

We are seeking abstracts of up to 500 words that describe the context, research questions, goals, and findings of your research in mathematics education. We especially encourage submissions from researchers affiliated with Canadian institutions, including graduate students. Accepted proposals will have a format of short presentations or poster sessions. The deadline for submission is December 16, 2012.

The MathEd Forum Research Day will be held on January 26, 2013, at the Fields Institute. Please send your abstracts to either Joyce Mgombelo (jmgombelo<at> or Ami Mamolo (AMamolo<at>

Participants who present at the Research Day may also wish to submit an extended paper (8-15 pages) for consideration for publication in the Fields Mathematics Education Journal (FMEJ). Submission of a long paper from the Research Day participants is not required, but is encouraged. The FMEJ is open for a variety of viewpoints and submissions in the areas of: Education research, teaching practice, and public forum. For more information regarding the journal, please check the journal Web site:, or contact Donna Kotsopoulos (dkotsopo<at> or Dragana Martinovic (dragana<at>, the Editors.


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