FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
MATHED FORUM MEETING AGENDA
Institute, 222 College Street, Toronto
10:00 - 10:10am
Reports: OAME, OMCA, OCMA, CMESG, CMS, and other.
10:05 - 10:40 am (including 15 minutes discussion).
Chris Suurtamm (University of Ottawa) and Martha Koch (University
'Reconceptualizing the mathematics curriculum as a dynamic, co-created
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
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
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
2. Shelley Yearley, Catherine Bruce, Tara Flynn, & Rich
'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
boards with junior and intermediate teachers. The research is
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
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
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
4. Tim Sibbald (Nipissing University), Edward Chapman (Thames
& Mark Fletcher (Thames Valley DSB)
'Comparing instructional designs in grade ten applied math'
5. Diane Tepylo, Joan Moss, & Carol Stevenson (OISE, University
'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'
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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