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Mathematics for Future Teachers / Mathématiques pour futur(e)s profeseur(e)s
Org: Leo Jonker (Queen's)

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FRANCE CARON, Université de Montréal, C.P. 6128, Succ. Centre-ville, 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 pre-service 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
Pre-service 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 e-mail. 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 pre-service teachers.

FREDERIC GOURDEAU, Université Laval, Québec, G1K 7P4
Different mathematics for teachers

The degree program for secondary education in mathematics is a four-year 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, team-taught by Richard Hill and Gail Burrill. We restricted it to students who had completed their core junior-level 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 team-teach 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 low-level content and teaching will not be undone. (p. 149)

Cross-national 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 teachers-and 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 second-year introductory analysis course taken by our mathematics majors, it is separate from our third-year 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 third-year 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.