June  5, 2020

Math Ed Forum Meeting Minutes



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.



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:
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



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.

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.



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

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

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

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