


Mathematics for Future Teachers / Mathématiques pour futur(e)s profeseur(e)s Org: Leo Jonker (Queen's)
 FRANCE CARON, Université de Montréal, C.P. 6128, Succ. Centreville,
Montréal, Québec H3C 3J7
The transition from secondary to elementary: a teacher
educator's experience

If we are to look for possible bridges and articulations that would
help smooth the transition of children from elementary school
mathematics to secondary school mathematics, can we find a common
denominator to build upon in preservice math education? Or, even
more interestingly, can we use some specificities of elementary
teachers approach to mathematics to the benefit of secondary math
education? In this talk, I will address these questions, based on my
recent experience of designing and giving a new course to future
elementary teachers, after some years of teaching to future secondary
math teachers.
 VIKTOR FREIMAN, Université de Moncton, Faculté des sciences de
l'éducation, Moncton, NB E1A 3E9
Preservice teachers communicate with schoolchildren about
mathematical problems through the Internet site CAMI:
building new learning communities

A new math curriculum in New Brunswick defines a particular role of
mathematical problems as a tool for learning about mathematical
methods and building a strong understanding of mathematical concepts.
The project CAMI (Chantier d'Apprentissages Mathématiques
Interactifs,
www.umoncton.ca/cami)
was created in 2000 in order
to help schoolchildren to improve their problem solving abilities in
mathematics. Every week, schoolchildren have a choice of four new
challenging mathematical problems. Then they use an electronic form
to submit their solutions to the CAMI team. The university students
taking courses in mathematics education at the Université de Moncton
evaluate children's solutions and send them a personalised comment via
email. This project gives to all participants a chance to start a
dialogue about mathematics that they will continue in the classrooms.
In our presentation, we will analyse several examples of how this
communication contributes to a more positive attitude in mathematics
for both children and preservice teachers.
 FREDERIC GOURDEAU, Université Laval, Québec, G1K 7P4
Different mathematics for teachers

The degree program for secondary education in mathematics is a
fouryear integrated degree. As part of this degree, the department
of mathematics provides seven courses designed exclusively for
students in this program. I will give examples taken from two courses
which illustrate the type of approach we follow in those specific
courses, explaining what we are trying to achieve through various
activities.
 JOHN GRANT MCLOUGHLIN, University of New Brunswick
Developing the Number Sense of Mathematics Teachers

"Developing Numeracy" is a course designed to promote enhanced
understanding and awareness of number among prospective teachers of
mathematics. The course was initially designed to address the
mathematical weaknesses of prospective elementary teachers; however,
its role has expanded through the participation of middle school and
secondary teachers. A rich sense of number is fostered through
considering numbers and operations on several levels: historically
through algorithms and representations; conceptually through
connections and examination of (un)familiar facts/rules; and,
pedagogically through consideration of contexts, processes, and
language. An overview of the course, including snapshots of the
content and reflections from a teaching perspective, will be
considered in the presentation.
 RICHARD HILL, Michigan State
A Capstone Course for Future Secondary Math Teachers

Following the recommendations of the CBMS in "The Mathematical
Education of Teachers", we decided to jointly teach a capstone course
for future secondary teachers in the fall 2003 semester. It was
repeated this semester, teamtaught by Richard Hill and Gail Burrill.
We restricted it to students who had completed their core juniorlevel
math courses and had also been accepted into the teacher preparation
program at MSU. We ended up with 23 students in 2003 and 20 students
in 2004. For a textbook, we use "Mathematics for High School
Teachers, An Advanced Perspective" by Usiskin et al., but
supplemented it somewhat. I will present what our initial plans were,
what we ended up doing each of the two semesters, what the surprises
were, and how we would modify the course this time. I will also
discuss things we learned from having a mathematics educator and a
mathematician teamteach the course.
 BERNARD HODGSON, Département de mathématiques et de statistique,
Université Laval, Québec G1K 7P4
Formation initiale en mathématiques des enseignants du
primaire et du secondaire : l'expérience de l'Université
Laval

Le Département de mathématiques et de statistique de
l'Université Laval est responsable de divers cours de
mathématiques offerts, à l'intérieur de programmes de formation
initiale des maîtres, spécifiquement à l'intention de futurs
enseignants du primaire ou du secondaire. Le but de cet exposé est
de présenter brièvement le cadre général de ces cours ainsi
que les thèmes autour desquels les contenus de cours sont
articulés. Je chercherai aussi à faire ressortir certains aspects
de la démarche départementale sur laquelle ces activités
pédagogiques s'appuient.
 LEO JONKER, Queen's University
What can a mathematics department do to improve the
preparation of elementary school teachers?

The presentation will reflect on some of the weaknesses in the
mathematical preparation of elementary school teachers at a fairly
typical Ontario university. It will reflect on the ingredients
necessary for a more effective program; it will describe attempts at
Queen's University to remedy the problem; and it will discuss
obstacles in the way of a solution.
 CATHY KESSEL, Consultant, Berkeley, CA
Toward a solid school mathematics

In her book Knowing and Teaching Elementary Mathematics,
Liping Ma says,
Reflecting on Chinese mathematics education one may notice that the
upward spiral is not there by itself but is cultivated and supported
by the solid substance of school mathematics in China. If the subject
they taught did not have depth and breadth, how Chinese teachers
develop a profound understanding of it? (p. 146)
Refocusing teacher preparation [in the United States], however,
creates another important task ... rebuilding a solid and
substantial school mathematics for teachers and students to learn
... unless such a school mathematics is developed, the mutual
reinforcement of lowlevel content and teaching will not be
undone. (p. 149)
Crossnational research and history of mathematics suggest
characteristics of "a solid school mathematics". Cognitive science
suggests why an elementary mathematics with these characteristics
might serve as a good foundation for learning of more advanced
mathematics.
 MORRIS ORZECH, Queen's University
Reexamining the real numbers with prospective teachers

A course I teach ("Our numbers systems: an advanced perspective") is
taken by mathematics students with various career goals, but its
advertised intent is to be particularly suited to prospective high
school teachersand most students in the course have that interest.
The mathematical core of the course is the real number system and its
extensions. Although the course follows a secondyear introductory
analysis course taken by our mathematics majors, it is separate from
our thirdyear Real Analysis offering, which some of my students also
take. A goal and challenge I have set myself is to have students
grapple with mathematics appropriate to the thirdyear level without
duplicating our Real Analysis course, introducing new mathematical
ideas while keeping an orientation more for prospective high school
teachers than for prospective graduate students.
To meet my objectives I have been experimenting with intertwined
mathematical and pedagogical approaches. I introduce material that
is accessible to high school students yet new to my class, and is a
vehicle for mathematical surprise that leads to reflection by
students on their mathematical knowledge and beliefs from previous
courses and earlier experience. The material that prompts students
to reexamine their understanding includes continued fractions and
Egyptian fractions, and the unfamiliar ways in which they can be used
to represent rational and real numbers. The way this material is
introduced is also part of my strategy in teaching prospective
teachers. For example, proof is an important element in the course,
but is used to highlight interesting things that are often omitted in
formal presentations. And much of what happens in class involves
student contributions, sometimes planned, sometimes
opportunistic. Some of the planned events have led to unexpected, and
even somewhat scary, learning and teaching encounters.
 CHRISTIANE ROUSSEAU, Université de Montréal
A course "Mathematics and technology" for preservice
teachers

At the Université de Montréal we have created a course
"Mathematics and technology" for preservice secondary school
teachers. The purpose of the course is to introduce the students to
modern applications of mathematics in technology: cryptography, error
correcting codes, robots, image compression, etc. The students
have to make a project. I will present the goals of the course, how
it is organized, some of the main subjects that are covered in the
course and some of the projects realized by students.

