### Math Ed Forum Meeting Minutes

### SATURDAY OCTOBER 14

HELD AT THE FIELDS INSTITUTE

The Meeting convened at 10:30 am

Present: Rina Cohen, Stewart Craven, Sandy Dilena, Gary Flewelling,
Bradd Hart, Eric Muller (Chair), Geoffrey Roulet, Tom Sutton, Chris
Suurtamm, Peter Taylor, Walter Whiteley,

Bradd Hart welcomed everyone to the Fields and indicated that the Fields
intended to have an alpha testing version of its Web pages ready for
the end of October.

Reports of the three Forum Task Forces were presented and are appended
to these Minutes.

The Forum was informed about the "Learning Partnership" by Gary Flewelling
and Stewart Craven. This partnership brings together individuals from
different interest groups, some willing to provide financial support.
Its mandate is wider than mathematics.

There appears to be some plans by the Ministry to direct funds towards
Web material development. It was suggested that there should be some
input from mathematics and that this could be coordinated by the Fields
Forum.

It would be useful for the Forum to be informed about the activities
of the various centres supported by the ESSO Educational Foundation.
The meeting was adjourned at 2:00pm.

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REPORT FROM THE TASK FORCE ONMDM 4U: MATHEMATICS OF DATA MANAGEMENT

1. Members:

Shirley Dalrymple Co-chair York Region DSB Sandy DiLena Co-chair
Toronto DSB

Eric Muller Brock University

Tom Sutton Mohawk College

Steve Brown University of Waterloo

Sunita Kossita Statistics Canada

2. Meeting #1 August 31, 2000 Field's Institute

Review of the Expectations for the course Suggestions of Potential
Software:

MINITAB, ACTIVE STATS, ESTAT, Fathom

Preliminary Discussion of the Focus of this Task Force

Meeting #2 September 22nd, 2000

Statistics Canada Review of Statistics Canada Website including ESTAT
and CANSIM

3. Concerns:

· The fourth strand - "Integration of the Techniques of Data Management"
Students are required to carry out a culminating project. What should
this project look like?

· To what depth are the expectations to be taken? (with consideration
of the intended audience)

· Contexts for topics. (ex. Matrices)

1. Foci of Task Force:

· The Culminating Project i.e. defining the project, ensuring it is
rich enough, ensuring consistency in assessment of the course

· Resource packages for teachers with strategies, integration of software,
and activities tailored to the course

1. Getting the Word Out:

· OAME 2001 - Shirley and Sandy to present a preliminary resource

· OAME 2002 - Full Presentation

· Additional Workshops through the Fields Institute

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REPORT FROM THE TASK FORCE

ON MATHEMATICS TEACHER PREPARATION

Eric Muller (Brock) co-chair

Walter Whiteley (York) co-chair

Ed Barbeau (Toronto)

Bradd Hart (Fields)

John Kezys (Mohawk)

Pat Rogers (York)

Geoffrey Roulet (Queens)

An all day meeting of Mathematics Department Chairs of Ontario Universities
was held at the Fields Institute on Saturday September 30th. Representatives
from Brock, Guelph, Laurier, McMaster, Queens Toronto, Western and York
were in attendance. Participants had received a position paper prepared
by Geoffrey Roulet. A copy can be found in the Appendix. The aim of the
meeting was to explore short term ways in which Mathematics Departments
could encourage more mathematics students to consider teaching as a career
and apply to Faculties of Education, and to review prerequisite structures
within their own mathematics department in order to open some mathematics
courses to students who are not completing a mathematics major.

The Agenda was as follows:

10:00 Opening presentation by Bradd Hart (Fields Institute) who outlined
what this Task Force has accomplished to date and presented some projections
on the Ontario mathematics teacher situation.

10:15 two discussion groups were formed and addressed the question:

"What mathematics courses would you or your undergraduate
student advisor recommend to a student who is

a) majoring in Biology and wishes to complete four mathematics courses
to present mathematics as a second teachable for her entry into a Faculty
of Education?

b) majoring in English and wishes to complete four mathematics courses
to present mathematics as a second teachable for his entry into a Faculty
of Education?"

11:30 short presentations were made by Walter Whiteley (York University),
William Ralph (Brock University) and Miroslav Lovric (McMaster University),
who reflected on "responding to the needs of the future teachers in our
mathematics courses"

12:00 lunch

13:00 the two discussion groups addressed the question

"Are there ways to encourage more students to choose teaching
and mathematics as a teaching subject?"

A number of recommendations came out of this meeting. That the Fields
prepare an information sheet to be sent to all Mathematics Departments
in Ontario Universities containing the following information:

statistics on the projected shortage of mathematics teachers; encouraging
more students with mathematics; background to consider teaching as a career;
providing a listing of appropriate mathematics courses for students looking
for mathematics as a second teachable and that this information be directed
to the undergraduate advisors. That the Fields have a section on its Web
site addressing mathematics students who are considering teaching as a
career. This section would contain information on Faculties of Education,
how to apply, what strengths they are looking for, how to build a portfolio,
etc.

APPENDIX:

Ontario Secondary School Mathematics Teacher Education:

Why It Should Be of Concern to You

Geoffrey Roulet

Faculty of Education, Queen's University

Ontario Secondary School Mathematics Teacher Supply and Demand - A Growing
Crisis

Data gathered by the Ontario College of Teachers show a growing imbalance
between teacher supply and demand. Over fifteen thousand teachers have
retired during the past two years and, with over half the profession of
age 50 years or more, this trend will continue. Teacher shortages are
expected at all grades and subjects, but high school mathematics is predicted
to be a point of major concern. Ontario mathematics classrooms have not
been left unattended, but regulations that grant school principals considerable
flexibility in creating teacher assignments are resulting in increasing
numbers of mathematics courses led by teachers lacking appropriate subject
qualifications.

At present, a solution to the growing mathematics teacher shortage is
not in sight. Twenty-seven percent of presently qualified mathematics
teachers will retire over the next 5 years, and the yearly average of
540 retirees is 175% of the present graduation rate. Recent increases
in the number of spaces in teacher education programs have not had much
impact in our subject area. The 500 extra enrolments for 1999-2000 resulted
in only 32 more mathematics teacher candidates. Mathematics qualified
graduates from university bachelors programs are not applying to Faculties
of Education, and reducing entry qualifications is not a viable option.

Ontario Secondary School Mathematics Teachers' Subject Preparation

Teacher candidates preparing for high school mathematics, many with A
and B grades in their university mathematics courses, are generally quite
confident about their mathematical abilities. In fact, they are quite
competent in mathematics if a very narrow definition of the subject is
employed. On the other hand, when one surveys the wide range of activities
presently found in mathematics, it can be argued that many of those preparing
to teach the subject suffer from a poverty of mathematical experience.

Ontario Faculties of Education set their own admission requirements, and
for mathematics candidates these range from a minimum of the equivalent
of 2 full-year courses in the subject to a maximum of 6. Applications
tend to be clustered at the lower end of this range. Students in Ontario,
preparing to teach at the secondary school level, study to become qualified
in two subjects, usually referred to as their first and second teachables.
Over half those applying to Faculties of Education for entry to mathematics
teacher preparation programs present mathematics as their second subject
where lower qualifications apply. The other teachable subjects for many
mathematics candidates come from the Sciences. This often means that they
have followed undergraduate programs that restricted mathematics experience
to multiple calculus courses, and in some cases linear algebra. Surveys
indicate that only approximately 10% of mathematics teacher candidates
have taken courses other than calculus (analysis), differential equations,
linear algebra, and introductory statistics and probability. Thus they
have had no contact with large segments of our discipline - geometry,
number theory, algebraic structures, logic, finite mathematics. In addition,
many future mathematics teachers, having experienced university level
mathematics through "service" courses designed for those majoring in other
fields, possess not only narrow subject knowledge, but also impoverished
mathematical visions and passion.

Ontario Secondary School Mathematics Teachers' Subject Vision and Passion
The question, "What is mathematics?", when presented to students beginning
their final course in preparation for teaching mathematics, elicits responses
that indicate rather limited subject images. Answers vary, but the majority
paint a picture of a discipline that involves numbers, computation, manipulation
of symbols, absolute rules, and step-by-step procedures. About two-thirds
of the students hold a "toolkit" image of our subject. Mathematics supplies
well-defined, fixed, and effective methods for addressing problems that
exist in other disciplines, occupations, or daily living. Teacher candidates'
descriptions of mathematics do not suggest that open and interesting questions
exist within the subject itself. Such images of mathematics are not likely
to generate passion for the discipline or motivate teaching in an open
investigative manner. In fact, research shows that mathematics teacher
candidates' enthusiasm for the subject declines during their years of
undergraduate study and in Canada only one-third of mathematics teachers
cite interest in the discipline as a reason for their entering or remaining
in the profession.

Why Should This Interest Departments of Mathematics?

There is a growing body of research showing that teachers' images of the
disciplines influence their instructional decisions. Those who picture
mathematics as a set of fixed rules and routines tend to employ teacher-centred
transmissive teaching styles. Research also reveals that in turn, the
manner in which a subject is presented effects students' images of the
discipline. Pupils who receive careful direct instruction in rules learn
that, while mathematics is certainly useful it is also not very interesting.
Many of these high school students will continue to study mathematics
while they pursue university science, engineering, computer science, and
business programs, but they are not likely to sign up for mathematics
majors and look toward graduate programs in the mathematical sciences.

What can be Done to Address these Issues? There are signs that the cycle
reproducing the rule-image of mathematics can be broken. Teacher candidates
who are graduates of honours mathematics programs generally hold rich
images of the subject along with their increased knowledge. Certain courses,
such as non-Euclidean geometry, history and philosophy of mathematics,
mathematical modelling, and senior undergraduate and graduate level courses
where foundational issues are raised, appear to help future teachers see
mathematics as an open, growing subject. The number of teacher candidates
with these experiences is too small and some way must be found to encourage
more students to major in mathematics with the intention of secondary
school teaching. These is also a need to ensure that there exist honours
mathematics programs that do not send future teachers down narrow tracks,
but open to them the wide field that is today the discipline of mathematics.

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REPORT OF THE SECONDARY-TERTIARY TRANSITION COMMITTEE

Membership:

Ed Barbeau Co.Chair University of Toronto

Hans Bastel Mohawk College

Stewart Craven Co-Chair Toronto District School Board

Peter Crippin University of Waterloo

Judy Crompton Niagara District School Board

Bradd Hart Field's Institute

Conference Call #1, Friday, August 18, 2000

Participants:

Ed Barbeau Co.Chair University of Toronto

Hans Bastel Mohawk College

Stewart Craven Co-Chair Toronto District School Board

Bradd Hart Field's Institute

Regrets: Judy Crompton Niagara District School Board

Item #1 Further Membership on the Committee

* Stewart Craven will invite Peter Crippin to join the committee.

* Ed Barbeau will approach Bill Higginson or Peter Taylor to see if there
is a Queen's University faculty member who would be interested in participating.

Item #2 Mandate of the Committee

* try to foster conditions so that there is good integration between programs
and courses of secondary schools and colleges and secondary schools and
universities

* ensure that colleges and universities are aware of the differences in
the new curriculum (content) so that they can set appropriate prerequisites

* ensure that colleges and universities are aware of the differences in
the new curriculum in terms of assessment, evaluation, and use of technology

* the issue of the double cohort will be deferred

Conference Call #2, Monday, September 11, 2000

Participants:

Ed Barbeau Co.Chair University of Toronto

Hans Bastel Mohawk College

Stewart Craven Co-Chair Toronto District School Board

Peter Crippin University of Waterloo

Judy Crompton Niagara District School Board

Regrets: Bradd Hart Field's Institute

Item #1 The Final Product - A Committee Report

* the audience for the report should include Secondary School guidance
and administrative personnel, board consultants, key college and university
personnel in the mathematics, pure and applied sciences, business, and
social sciences

* the report will be comprised of a comparison between the old and new
curricula, new approaches to assessment and evaluation, and the impact
of technology in the mathematics classroom

* the report will also include a description of the developer's "vision"
(i.e. explaining the "intent" of the curriculum)

* the report should include many examples of what students "do"

Item #2 Time Lines

* Phase #1 - complete curriculum comparisons

write assessment and evaluation description

describe the impact of technology in the math classroom

write the "intent" of the curriculum piece

January 31, 2001 completion

* Phase #2 - compile a database of both college and university course
requirements (i.e. listing all courses which require a mathematics prerequisite)

June 30, 2001 - First Draft

Item #3 Next Meeting - Face to Face - Mohawk College - November 2

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Eric Muller, Professor of Mathematics and Education

Chair, Department of Mathematics

Director, Concurrent BSc/BEd Program

Brock University

St Catharines, ON phone:- 905 688 5550 ext. 3297

L2S 3A1 fax:- 905 682 9020

email:- emuller@spartan.ac.brocku.ca

url:- http://www.brocku.ca/mathematics/people/muller/