




Mathematical Education Cognition in Mathematics / Enseignement des
mathématiques Cognition et mathématiques (Florence Glanfield, Organizer)
 COLIN CAMPBELL, Information Systems and Technology, Pure Mathematics; and
Waterloo
The expanding role of Mathcad in mathematical courses at
Waterloo

Instructors seeking to add dynamic mathematical explorations to their
courses have turned to Mathcad in record numbers at the University of
Waterloo. From Physics and Chemistry to Engineering and Mathematics
dozens of instructors have adopted Mathcad mainly because of it's ease
of use for faculty and students alike (compared to Maple and MATLAB).
The challenge with all technology is to use it effectively. The
presenter will describe what has been done so far, particularly in
Linear Algebra courses with support from UW's Teaching and Learning
Through Technology Centre (LT3), and seek feedback from participants on
ways to improve.
 JAMIE CAMPBELL, University of Saskatchewan, Saskatoon, Saskatchewan
Cognitive architecture and numerical skills

Educated adults acquire an elaborate system of numerical skills that
has its roots in basic perceptual processes in infancy and that
ultimately involves the functional integration of a diverse set of
complex cognitive procedures. These component skills include the
ability to comprehend and produce written and spoken numbers, to count
by various increments, as well as to retrieve, calculate, or estimate
the results of both simple and complex arithmetic problems. Numerical
competence emerges through the functional and conceptual integration of
these various numerical activities. The question of how to
conceptualize the cognitive architecture underlying numerical skills
has been the focus of much theoretical debate over the last few years.
I will review research that supports an encodingcomplex view of basic
numerical cognition. This approach emphasizes representational
concreteness (i.e., number processing is based on perceptual and
linguistic codes, rather than on abstract codes), hyperspecificity
(i.e., skilled performance depends on implicit memory processes
that are specialized for codespecific input/output pathways), and
interactivity (i.e., competition and resolution of competition
among numerical cognitive operations).
 ALAN COOPER AND ERIC WOOLGAR, Department of Mathematics and Statistics, Langara College,
Vancouver, British Columbia V5Y 2Z6 and Department of
Mathematical Sciences, University of Alberta, Edmonton,
Alberta T6G 2G1
Webbased resources for teaching and learning: building a
location and retrieval service for the Canadian mathematical
community

There is a large body of webbased material intended to support the
teaching and learning of mathematics, but its quality is uneven and it
is still not easy to quickly locate the best available resources
related to any particular topic. Both users and authors will benefit
from improved indexing and review of such materials. A number of
current projects are directed towards providing such a service, and the
speakers have received an Endowment Fund Grant to support work towards
the development of a Canadian version, but it is not yet clear what
will best meet the needs of the mathematical community.
Our intent is both to review the current state of affairs, and to
initiate a discussion of what features of such a service would be most
useful for both authors and users of the material. A report and
handson lab regarding work to date will therefore be followed by a
working group of those who wish to participate in further development.
 IMPLICATIONS FOR TEACHING I
discussion of Orzech/Orzech talk

 IMPLICATIONS FOR TEACHING II
discussion of Campbell/May/Rabinowitz

 IMPLICATIONS FOR TEACHING III
discussion of Sierpinska talk

 SHERRY MAY AND MICHAEL RABINOWITZ, Memorial
To be announced

 GRACE ORZECH AND MORRIS ORZECH, Queen's
Dealing with dimension & teaching and learning issues

The two of us teach courses for students with quite different
mathematical backgrounds. It was therefore interesting to find that
students in both classes exhibit similar (and to us surprising)
misconceptions about dimension, a notion that appears as an issue in
both our courses. Observing this phenomenon has not led us to dramatic
success in overcoming student difficulties, but it has informed our own
ideas about how to promote mathematical understanding and has
influenced the conversations we have with our students. Our reflection
on what our students seem to think has influenced not only the way we
teach, but the mathematical material we select and how we present it.
 ANNA SIERPINSKA, Concordia
Is it enough to `understand' when learning mathematics? Is
it necessary?

Motto: `In mathematics, nothing is necessary, or sufficient'.a
well known saying.
This talk will look at the relations between understanding in
mathematics and other mental processes and acts such as doing
mathematics, memorising, taking another person's point of view, taking
another point of view, constructing mental schemata, theoretical
thinking, ingenuity. Underlying the discussion of these relations will
be, mainly, the question posed in the title of the talk. Two other
questions will be asked to provoke further discussion: `Can
understanding in mathematics be taught?'; `Is it possible to prevent
our teaching from becoming a complete impediment to understanding?'

