FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
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
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
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
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
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
5. Limin Jao (OISE, University of Toronto): Teaching practices
to increase student engagement in the Grade 9 Applied mathematics
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
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
INVITATION FOR SUBMISSIONS
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,
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>brocku.ca) or Ami Mamolo (AMamolo<at>edu.yorku.ca).
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:http://fmej.fields.utoronto.ca/index.php/FMEJ,
or contact Donna Kotsopoulos (dkotsopo<at>wlu.ca) or Dragana
Martinovic (dragana<at>uwindsor.ca), the Editors.
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