June  5, 2020

REPORT: Ontario Mathematics Curriculum Review Meeting
Fields Institute, June 29, 2005


The Ontario Ministry of Education is currently conducting a review of the grade 11-12 mathematics curriculum. Universities provide input to that review through the Council of Ontario Universities (COU). In preparation for a set of meetings to be held in July 2005, the two COU delegates to these meetings met with representatives of many Ontario universities, at the Fields Institute on June 29, 2005, from 10am-3pm. As well as Mathematics departments, faculties of Engineering, Science, and Business were invited to send representatives. Present at the meeting were the COU delegates Walter Whiteley (York) and Peter Taylor (Queen's), as well as Anthony Azzopardi from the Ontario Ministry of Education.

The discussions concentrated on three courses, 11U, 12U Advanced Functions and Introductory Calculus and 12U Geometry and Discrete Mathematics. The 12U Mathematics of Data Management course seems to be working well and only minor changes are contemplated. The COU representatives will meet with Ministry of Education folks July 5-6 along with representative from other organizations (Colleges, Teacher Associations) to prepare a revised curriculum draft. This will be available in the Fall (late Sept. or Oct.) for a feedback process.

Anthony Azzopardi described changes currently being proposed to the existing courses and changes proposed for the pathways between the courses. These include adding a trigonometry component to the 12U AFIC course, requiring 12U AFIC students to have the 11U Functions and Relations course, changing the 11U/C Functions course so that 11U/C followed by 11U is a reasonable progression for students requiring additional study before taking Calculus, and moving conic sections and loci from 11U Functions and Relations into 12U GDM.

The points below address specific suggestions for further changes, that were raised at the meeting and received widespread support:

11U Functions and Relations

1. Remove or greatly deemphasize the financial math strand in 11U and replace it with some analytic geometry. By this we don't mean an exhaustive treatment of analytical geometry, but a few nice examples of geometry problems in 2-D and 3-D (especially 3-D) that are beautifully handled by introducing a coordinate system or with vector methods. This will naturally extend and build on the geometry topics covered in Grade 10. This is important material for students to see who would not normally take GDM in grade 12. It is also important for students taking GDM as this bridges the time gap between early and late geometry, created by the lack of geometry in grade 11.

2. The sequences and series component of the financial math strand is better covered under the expanded exponential functions strand.

3. Students at this stage need lots of practice with algebraic manipulations, but done in the context of interesting questions.

12U Advanced Functions and Introductory Calculus.

1. The course might better be called Advanced Functions and Calculus Concepts. We should remove or greatly reduce the last strand on calculating derivatives except for last section on "Calculus techniques (replaced by ideas) to analyze models of functions." This section can be expanded somewhat to provide interesting modeling examples in the physical, life and social sciences.

2. Support the inclusion of trigonometry (already in the plans). A few trig identities might be covered here, again done in the context of interesting questions. Examples: sine sum, half angle, in addition to sin^2 + cos^2 = 1 which has been in Grade 11. Working with such formulas goes beyond trig: they provide meaningful practice in algebraic manipulation.

12U Geometry and Discrete Mathematics

There was much discussion about removing counting techniques in order to give more time for an in-depth, investigative approach to geometry, proof, and vectors. This would be particularly helpful if the plan to put conic sections into this course is followed. The point is that these counting techniques are not part of the main-stream requirements for any math/science/engineering program other than computer science.

Having said this, one of the advantages of this topic is that it ties in well with notions of probability, a topic that receives too little attention in the curriculum between K-8 and Mathematics of Data Management.

Our long-term goal is a curriculum in which the basic requirements of functions, algebra and geometry required for university students are covered in 4 courses, one in each of grades 9-12. There could be an extra enriched course for those who wanted more mathematics, but perhaps the marks in this course would not count as part of the entrance average. Such a course could however be used for special purposes, e.g. a component of certain types of scholarships, entrance to special programs within the university etc. The GDM course was in fact designed as an elite course but in the present structure in which marks mean everything and the marks in this course are expected to be lower, students are warned away from taking it.

Walter Whiteley (York)
Peter Taylor (Queen's)
July 2005