10:05 - 10:40 am (including 15 minutes discussion).
Chris Suurtamm (University of Ottawa) and Martha Koch (University of Manitoba)
'Reconceptualizing the mathematics curriculum as a dynamic, co-created
network'

Abstract: In this presentation, we provide an overview of research on learning trajectories in mathematics and discuss the implications of this research for curriculum design. Our conception of curriculum is rooted in metaphors of emergence and growth drawn from complexity thinking. We draw on three characteristics of complex systems to envision a more effective mathematics curriculum: complex systems are comprised of many co-implicated levels or layers; complex systems have a networked structure rather than a linear one; complex systems adapt to changing circumstances and re-define themselves. We propose a view of school mathematics as multi- dimensional networks of interconnected concepts and processes. Further, we offer some innovative ideas for building and representing the curriculum as a web-enabled, co-created resource. Using digital technology we surmount the limitations of print-based curricula which have generally been structured as linear progressions of achievement outcomes organized in discrete mathematics strands. In our vision, teachers and students are key players and the curriculum develops as teachers and students explore mathematical ideas and propose new connections, representations and learning tasks. Thus, rather than a static document teachers must follow, we reconceptualize the curriculum as a dynamic resource that supports mathematics teaching and learning.

10:40 - 11:15 am (including 15 minutes discussion)
Tina Rapke (York University)
'Students and their instructor co-developing a final closed book math exam'

Abstract: In this presentation I will describe the process of my students and I co-developing the closed book final exam for a college mathematics course and detail some of the effects of assessing with and being involved in such an activity. I will draw on qualitative data to discuss how the process fostered creativity in mathematics and the growth of more generalized mathematical understandings.

11:15 - 11:45 a.m. Short Oral Communications (10 min each):

1. Ariel Wan-Hua Ho & Joanne Lee (Wilfrid Laurier University)
'Promoting purposeful play through LittleCounters program'

Abstract: We sought to examine the effectiveness of a community-based early numeracy program called LittleCounters, in promoting purposeful play and instilling numeracy concepts with young children. Thirty-four children between 16 - 34 months and their caregivers participated in a 30- minute naturalistic play session at their home. All play sessions were transcribed and coded for the following variables: types of play (i.e., play-based learning, purposeful play), types of purposeful play (reinforcing concepts, assessing and confirming, advancing concepts), numeracy talk produced by both caregivers and children (quantity words, cardinality, counting with or without objects, ordinality), and the mathematical strategies (problem solving, representing, cognitive challenge, emotional scaffolding). The present study demonstrates that the LittleCounters program was efficient in facilitating parents to engage in mathematical strategies, especially representing, with their children through purposeful play.

2. Shelley Yearley, Catherine Bruce, Tara Flynn, & Rich MacPherson (TrentUniversity)
'Exploring learning and differentiated instruction of fractions through collaborative action research'

Abstract: This project was designed to explore how students approach fractions both formally and informally. As a KNAER funded project, another key component of the study was developing and implementing innovative knowledge mobilization strategies. The Ontario project consists of three phases: Phase 1 involved cycles of collaborative, action research in three district school boards with junior teachers, board mathematics leads and researchers. Phase 2 involved, a literature review, Foundations to Learning and Teaching Fractions: Addition and Subtraction, and a draft pathway/map for learning fractions. Phase 3 is currently underway and involves a mixed-methods approach to validating the fractions learning
pathway both cell-by-cell and across cells (pathways) in three school
boards with junior and intermediate teachers. The research is on-going,
but current findings will be presented and discussed.

3. Ann Kajander & Jennifer Holm (Lakehead University)
'Reluctant gate-keepers: Outcomes and consequences of high-stakes mathematics content requirements for preservice teachers'

Abstract: The development of content knowledge in elementary mathematics teacher education remains a significant challenge to the field, particularly the development of pedagogical content knowledge as needed for effective teaching. Data collected in Northwestern Ontario illustrates over and over again the significant challenges faced by preservice elementary teachers as they strive to deepen their specialised knowledge of elementary mathematics. Last year we focused our study on PSTs who initially identified themselves as exceptionally at-risk as to our institution's high stakes mathematics program requirements. In particular, the contrasting journeys of two PSTs who struggled with the mathematics content in the methods course will be described using a narrative case study methodology. The potentially detrimental effect of program changes in the mathematics requirements which took place this year in our program will be discussed, particularly in light of these findings.

11:45 - 12:00 pm Discussion of Short Oral Communications

12:00 - 1:00 pm LUNCH BREAK
(Light refreshments provided)

1:00 - 2:00 pm
Poster Presentations (Posters will be exhibited in the hall to allow for
informal and individual discussion with poster authors)

1. Yasmine Abtahi (University of Ottawa)
'Mathematics manipulatives: Things kids think with'

2. Malcolm Cunningham (OISE, University of Toronto)
'A socio-behavioral definition for mathematics learning'

3. Jeff Irvine (Brock University)
'From description to prescription: A theoretical model of teacher
behaviour'

4. Tim Sibbald (Nipissing University), Edward Chapman (Thames Valley DSB),
& Mark Fletcher (Thames Valley DSB)
'Comparing instructional designs in grade ten applied math'

5. Diane Tepylo, Joan Moss, & Carol Stevenson (OISE, University of Toronto)
'Exploring a rigorous play-based block building program'

6. Kristina Wamboldt (Brock University)
'Are you the right type for mathematics? Personality type, mathematics
anxiety and achievement in undergraduate mathematics students'

7. Zhaoyun Wang (OISE, University of Toronto)
'Creating effective approaches to upgrade inservice teachers' knowledge'

8. Joanna Zambrzycka & Joanne Lee (Wilfred Laurier University)
'The nature of spatial talk in child care centres'

2:00 pm Adjournment

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