10:10 - 10:30, plus 10 minutes for questions and discussion
Lyndon Martin, York University, Jo Towers, University of Calgary
Nature of mathematical understanding

In this session we will focus on the nature of mathematical understanding, and on how this can usefully be characterised and theorised. More specifically, we will talk about our ongoing work, using ideas drawn from the field of improvisation, which focuses on the growth of collective and shared mathematical understandings. Over the last few years we have been developing a framework of improvisational characteristics which can be used to identify and describe particular kinds of shared mathematical actions. In this session we will briefly present our work to date and also describe the preliminary phase of our current SSHRC-funded project which focuses on using and refining our framework through a focus on the teaching of mathematics in the high school.

10:40 - 11:00, plus 10 minutes for questions and discussion
Shannon Kennedy, MSc Candidate, McMaster University
First Year Calculus: The Student Experience!

The first year of university is filled with many changes and challenges, including first year calculus! What is it about these introductory calculus courses that makes them so challenging? In order to answer this question and help our students we need to be able to understand what they are going through. This is difficult for a typical mathematics professor or TA, having never experienced such challenges first hand! Therefore the goal of my master's thesis has been to gain some understanding of the issues first year students' face and share them with the other members of the mathematics department. To do this I have held a series of in-depth interviews with students, during which I asked them about their experiences in first year calculus. In this presentation I will be discussing some of my preliminary findings, and how we might use this information to improve the teaching of mathematics.

11:10 - 11:30, plus 10 minutes for questions and discussion
Ami Mamolo, Queen's University, Peter Taylor, Queen's University
Reconceptualising teaching and learning in a large first-year Calculus course

Engagement, investigation, discovery, participation, community--these are: (1) key aspects of mathematical learning, (2) socio-cultural rhetoric in theories of learning, (3) popular buzzwords around math education circles that are supposed to indicate how teachers ought to conduct their classes. Although social aspects of learning have been widely acknowledged within the education literature, there is yet a need for instructional design which attends to these aspects while also meeting the reality of most classroom settings within Canada. This presentation looks at some of the challenges and possibilities of implementing a 'learning through participation' metaphor in a very large, very real first-year Calculus course.

11:40 - 12:00, plus 10 minutes for questions and discussion
Asia Matthews, Department of Math and Stats, Queen's University
Teaching mathematicians how to teach

One of the difficulties that educators face in conducting research is the influential random variable: the teacher. Mathematics instructors are enormously influential both at the lower levels and at the post-secondary level. As mathematicians we sort-of love the stereotypical math professor. As math educators we recognize that it takes knowledge of mathematics AND an understanding of teaching and learning to teach well. My interest is in mathematics pedagogy instruction for post-secondary mathematics instructors. I am doing a review of existing programs as well as conducting interviews with mathematics graduates and instructors. I will
then design two courses - an overview seminar and a full-term course - that can be tailored to fit the needs of individual mathematics departments and can be easily implemented. I will present an existing course outline and I will solicit suggestions from participants.

LUNCH: 12:10 - 1:00PM

Afternoon program:

1:00 - 1:20, plus 10 minutes for questions and discussion
Nirmala Niresh, University of Miami Ohio
(Via Skype)
The significance of ethnomathematics research and its implications for teacher education

Sociocultural dimensions of mathematical knowledge have greatly influenced research in the field of mathematics education in the past few decades, resulting in the rise of different areas of research that include ethnomathematics, everyday mathematics, situated cognition, and workplace mathematics.
The term ethnomathematics was coined by Ubiratan D Ambrosio and denotes the mathematics which is practiced among distinct cultural groups. Examples of ethnomathematics include mathematics used by different groups of people such as Kpelle and Tshokwe tribe of Africa, Mayans of South America, Maori and Warlpiri of Oceania, Inuit, Iroquois, and Navajo of North America, and the Oksapmin of Papua New Guinea. Ethnomathematics could also refer to the mathematical practices that adults and children engage in outside the school settings. Examples include mathematics used by adults outside the school settings or at work places - mathematical practices of bus conductors, nurses, pilots, candy sellers, and best buy shoppers, and carpet layers.
In this session, I will provide a brief overview of research on ethnomathematics and everyday mathematics. In particular I will address the following questions:
" What is ethnomathematics? Why is it an important field of study?
" In what ways can we incorporate ethnomathematics in teacher education?
" What are the implications of ethnomathematics research on the teaching and learning of mathematics?

1:30 - 1:50, plus 10 minutes for questions and discussion
Richard Barwell, University of Ottawa
How mathematicians talk about mathematics

While much has been written about the nature of written mathematics, both from a linguistic perspective and from an educational perspective, there is little analysis of how mathematicians talk about mathematics. In this seminar, I will present some findings from discourse analysis of a corpus of 5 radio broadcasts, in which mathematicians engage in unscripted discussion and explanation of advanced mathematical ideas for a general audience. The mathematics treated includes symmetry, prime numbers and higher dimensional geometry. My analysis draws on discursive psychology to explore how the participants construct mathematics and mathematical thinking. For this seminar, I will particularly focus on the role of indexicality in these constructions. I conclude by discussing some implications for mathematics education.

2:00 P.M.CONCLUSION

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