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 undergraduate-level 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 post-secondary 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 pre-service 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' counter-examples 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 socio-cultural 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: self-efficacy, 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 Escher-like 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 Times-like) font, with one-inch 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 (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.

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.

MathEd Forum

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

FIELDS MATHED FORUM MEETING AGENDA
Theme: Annual Research Day

January 21, 2012
Fields Institute, 222 College Street, Toronto