THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

FIELDS
MATHED FORUM MEETING AGENDA
Theme:
Annual
Research Day
January 21, 2012
Fields Institute, 222 College Street, Toronto



MORNING PROGRAM:
10:00 a.m.  10:10 a.m. Reports: OAME, CMS, CMESG, OCMA, OMCA, etc.
10:10 a.m.  10:30 a.m. Lindsey Shorser (University of Toronto)
Mathematical Communication: How and Where Students Learn to Write
Mathematics
ABSTRACT: The process of doing mathematics in any complete and
formal way is necessarily mediated by the act of writing. Mathematical
objects cannot be accessed directly (there is no such thing as
a perfect circle!) and are too abstract to be described in words
without including an additional symbolic system: students must
write mathematics in order to learn and do mathematics. In this
talk, I will discuss an undergraduatelevel math writing program,
the student work produced through this program, and some resultant
insights into where students are learning their mathematical writing
skills. These insights will be discussed in the context of experimental
design and implications for the teaching and learning of mathematics
at the secondary and postsecondary levels.
10:35 a.m.  10:55 a.m. Walter Whiteley (York University)
Incomplete Diagrams: A Diagrammatic Tool for Structuring Geometric
Reasoning
ABSTRACT: Working with preservice teachers in geometry, it is
clear that many have difficulty 'ignoring' visible features which
have not yet been reasoned about. This is even more true in dynamic
geometry programs such as GSP, where the accuracy of the figure
leaves little uncertainty about what is true (but gives little
clarity about why it is true in the sample drawing). One diagrammatic
tool to distinguish what is now known from what is still to be
proven is the "incomplete diagram". Through the use
of the incomplete diagram, student reasoning becomes 'visible'
in a sequence of progressively more complete diagrams. In the
process of justifying the completion steps, some of the 'extreme
case' counterexamples also are noticed. I will illustrate this
via proofs of the Isosceles Triangle Theorem and its converse,
on the plane and sphere. In this exercise, students who used incomplete
diagrams were able to give essentially correct reasoning. Conversely,
those whose reasoning was muddled were typically grabbing a 'visible
feature' of the complete diagram which had not yet been reasoned
into existence. The process points out a basic difficulty of communicating
with completed diagrams  namely, when multiple layers are condensed
into a single image which a novice cannot disentangle.
11:00 a.m.  11:20 a.m. Neil Marshall & Chantal Buteau (Brock
University)
Contextualizing the Learning Activity of Designing and Experimenting
with Interactive, Dynamic Mathematics Exploratory Objects
ABSTRACT: As part of Brock University's innovative undergraduate
mathematics program MICA, students learn to design and implement
mathematical computer environments with an interactive interface,
called Exploratory Objects, for the purpose of investigating mathematics
conjectures, concepts, and applications. In this presentation
we discuss a project that aimed at contextualizing the learning
activity, elaborating on a preliminary task analysis, as well
as providing a list of potential skills learned by students through
this activity.
11:25 a.m.  11:45 a.m. Jessica Taylor Charland & Marlene Frederick
(University of Western Ontario)
Using the Arts and New Media to Enhance Learning of Mathematics
& Disseminate Research and Practice Findings
ABSTRACT: This presentation outlines the possibilities that the
visual, dramatic, and communicative arts provide in enhancing
learning opportunities in the mathematics classroom, as well as
how using new media can help to engage students and more accessibly
disseminate research findings and classroom practices to a wider
population.
11:50 a.m.  12:00 p.m. Discussion
12:00 p.m.  1:00 p.m. LUNCH BREAK and POSTER
PRESENTATIONS
(Light refreshments provided)
AFTERNOON PROGRAM:
1:00 p.m.  1:20 p.m. Amanjot Toor (Brock University)
Undergraduate Students' Experiences of Their Mathematical Identity
ABSTRACT: Identity is central to any sociocultural learning.
In mathematics, identity  what I am  is essential to students'
beliefs about themselves as capable mathematics learners and as
potential mathematicians. In this presentation, I will examine
how undergraduate mathematics students identify themselves as
capable mathematics learners at the undergraduate level. My study
used three approaches of understanding identity: selfefficacy,
environment and four faces of learner's identity  engagement,
imagination/relativity, alignment, and nature. My findings suggest
that these approaches of understanding identity can provide a
useful lens for understanding a full picture of how undergraduate
mathematics students see themselves as capable mathematics learners.
1:25 p.m.  1:45 p.m. Ami Mamolo (York University) & Rina Zazkis
(Simon Fraser University)
Appreciating Mathematical Structure via Exploring the Unconventional
ABSTRACT: This presentation explores part of a broader study
which examined the influences of prior experience and aesthetic
sensibilities on university mathematics students' appreciation
of mathematical structure. We focus here on participants' responses
to tasks that deal with areas, perimeters, volumes and derivatives,
and their abilities to transfer appropriate knowledge to a novel
and unconventional situation. We recognize an important component
in considering the unconventional: we consider the flexibility
in accepting the unconventional and acknowledging the analogy
with the conventional as part of an individual's appreciation
of the overarching structure of mathematical concepts and relationships.
1:50 p.m.  2:00 p.m. Discussion
2:00 p.m. Adjournment
Poster Presentations
12:00p.m.  1:00p.m.
1. Alexander Antropov (University of Toronto):
Interaction Among Student Teachers' Knowledge of Content, Pedagogy
and Research in Their Practice Teaching Intermediate/Senior Mathematics
2. Alexander Antropov (University of Toronto):
Conditions Affecting the Level of Grade 9 Mathematics Assessment
Test Performance
3. Anne Mather & Bryan Karney (University of Toronto):
Math Education for Undergraduate Engineering Students
4. Jill Lazarus & Geoffrey Roulet (Queen's University ):
Blended Mathematical Collaboration using a Wiki, GeoGebra and Jing
5. Patrick Russell (York University):
Gaming and Linear Relations
6. Julia Burke, Lily Ivkovic, Hira Siddiqi, & Judy Tse (York
University):
Exploring and Designing Escherlike Tesselations  A Classroom Project
7. Sean Beaudette & Alexandra Penn (Queen's University):
Preservice Elementary Teachers' Beliefs toward Mathematics and Mathematics
Teaching
8. Zohreh Shahbazi (University of Toronto, Scarborough):
Educational Programming in Support of University Math Courses
CALL FOR PRESENTATIONS
We invite submissions of proposals for presentations at the annual
Research Day. We welcome submissions of two types:
(i) Research Report  a 3 page proposal detailing completed or
preliminary research results. Proposal guidelines are included below;
(ii) Poster Presentation  a 250 word abstract that describes the
context, research questions, goals, and findings of your research.
We especially encourage submissions from researchers affiliated
with any of Canada's universities or colleges, including graduate
students.
The deadline for submission is December 9, 2011.
Please send your proposals to either John Kezys
(john.kezys<at>mohawkcollege.ca)
or Ami Mamolo (AMamolo<at>edu.yorku.ca).
Research Report  Proposal Guidelines
Proposals should be submitted as Microsoft Word or RTF files. The
maximum length is 3 pages, including references and abstract. Formatting
should be single spaced, in 12 point Times (or Timeslike) font,
with oneinch margins. An additional page of tables or figures may
also be included. We recommend that proposals include as many of
the following considerations as
possible:
 an explicit statement of the research questions and goals
 connection of this work to the research literature
 theoretical or conceptual framework
 research methodology
 results of the research
 implications for further research or teaching
 a list of references
Participants who present at the Research Day may also wish to submit
an extended paper (815 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.
For more information regarding the journal, please contact Dragana
Martinovic (dragana<at>uwindsor.ca)
or Donna Kotsopoulos (dkotsopo<at>wlu.ca),
or check the journal web site:
http://fmej.fields.utoronto.ca/index.php/FMEJ.