
MATHEMATICS EDUCATION FORUM 

September 27, 2016  
FIELDS MATHEMATICS EDUCATION FORUM

AFIC MCB4U Advanced functions and introductory calculus  OSIS the old curriculum 
MDM MDM4U Mathematics of data management  OSS the new curriculum 
GDM MGA4U Geometry and discrete mathematics 
1. The list of attendees Ryerson PU Peter Danziger danziger@acs.ryerson.ca Chris Grandison cgrandis@acs.ryerson.ca AnnMarie Filip amfilip@acs.ryerson.ca Randall Pyke rpyke@hopper.acs.ryerson.ca Sophie Quigley quigley@acs.ryerson.ca 
York U Tom Salisbury salt@mathstat.yorku.ca Margaret Sinclair msinclair@edu.yorku.ca 
U Toronto Ed Barbeau barbeau@math.utoronto.ca Ragnar Buchweitz ragnar@math.utoronto.ca Dietrich Burbulla burbulla@math.utoronto.ca Christine Clement cclement@astro.utoronto.ca Steve Cook sacook@cs.utoronto.ca Danny Heap (CSC) heap@cs.utoronto.ca Arnold Rosenbloom arnold@cs.utoronto.ca Any Wilk awilk@utm.utoronto.ca Guest Maria Chiu maria_c900@hotmail.com 
Secondary Stewart Craven stewart.craven@tdsb.on.ca Sandy DiLena Sandy.Dilena@tdsb.on.ca Gord Doctorow doctor2@sympatico.ca Biyu Joseph bjoseph26@hotmail.com Maharukh Kootar kootar@look.ca Michael McMaster mimcm@sympatico.ca Steffi Nathan mathpi@rogers.com Bob Pickering bob.pickering@sympatico.ca Inga Shukla inge.shukla@sympatico.ca Silvana Simone silvana.simone@ntel.tdsb.on.ca Peter Wei peter.wei@etel.tdsb.on.ca 
Regrets: Martin Muldoon, York U muldoon@mathstat.yorku.ca Stephen Chamberlin, York U chamber@mathstat.yorku.ca Walter Whiteley, York U whiteley@mathstat.yorku.ca John Bland, U of Toronto bland@math.utoronto.ca Abe Igelfeld, U of Toronto igelfeld@math.utoronto.ca Mike Lorimer, U of Toronto lorimer@math.utoronto.ca 
2. Dissemination of Information
(a) Some websites:
http://www.curriculum.org/occ/occindex.html
http://www2.tvo.org/edulinks/subject_math.html
http://www.edu.gov.on.ca/eng/document/curricul/secondary/grade1112/math/math.html
http://www.oame.on.ca/
(b) It might be useful to have a website that teachers and students can go to to get test items to help them check their readiness for university study. These would test fluency and reasoning. However, it should be emphasized that they should be predicated on the OSS curriculum and not include material that students cannot be expected to master. (Someone mentioned PLAR Prior Learning Assessment R..., but I did not pick up the details of this.)
(c) It is important that final examinations be available.
3. Concerns about OSS graduates
(a) It was emphasized by many present that the OSS graduates on the whole will be less mature, and this may have at least as great an impact as any other factor.
(b) The new curriculum has trigonometry in Grade 11 but not in Grade 12. Students may come to university with a weaker background of this important area than before.
(c) Students will not have sufficient experience with proofs, or have a strong enough ability to reason step by step.
(d) Will students be able to understand and use notation?
(e) Students may be too strongly seduced by the calculator to gain other important skills for science and engineering programs.
(f) The use of technology by the students will be largely banal; the opportunity for real power does not seem to be in the curriculum.
(g) Will the students know what they must master or what will be expected of them when they enter university? Can we provide sample tests and diagnostics?
(h) While students may have understanding, they may not have algebraic fluency required.
(i) Will it be possible for all schools to mount GDM?
(j) There are lots of impending retirements, and will be lots of new teachers in the system. There is an impending shortage of qualified mathematics teachers. Will the new teachers have the background to implement the new curriculum?
(k) What will happen in the transition year? Will some schools combine OSS and OSIS courses, and what will be the result?
(l) Ontario seems to be a pioneer in the new curricular philosophy; there do not seem to be other jurisdictions we can look to for guidance.
(m) It is likely that universities for various reasons will not be able to put much effort into sorting out the problems of the double cohort.
4. Assessment
Under OSS, the final examination will be worth 30% (as compared with 4050% under OSIS), and the other 70% will be on term work. Teachers will be expected to assess along four categories: knowledge & understanding, applying procedures, problem solving, and communication. This will be boiled into a final mark. Boards will create examinations and evaluation instruments centrally. In the short term, not too much will change.
5. The technology
(a) The technology will be chiefly calculators. Students will use packages like Geometer's SketchPad, but most will not be familiar with Maple or Mathematica.
(b) The pedagogical advantage of technology will be in helping students to visualize, and be readily able to see the results of transformation.
(c) Technology will provide an additional way for students to perceive and represent mathematical ideas.
(d) Research indicates that student investigations with SketchPad lead to more secure geometric knowledge.
6. Differences between graduates of the two regimes
(a) (PW) The chief difference will be maturity.
(b) (PW) The old textbooks have short problems. In the new, the problems will be more extensive, "like a story". Chapters will tend to be organized around a main problem. Then the tools will be developed in the chapter to tackle the problem.
(c) (GD) The technology will make a difference. Students will have used graphing calculators since Grade 9. Students will be able to communicate more readily and use the technology, but there will be no more depth than before.
(d) (GD) The main attention to proof will be in the GDM. In the old curriculum, proof was addressed before Grade 12, but this was not effective for most students. The difference between old and new may not be as great as might be expected, and students with GDM may be in better shape.
(e) (PW) There are three broad groups of students. Many universitybound students will be enriched and do quite well in university. A lot of students will be struggling, and a third group, who may find themselves in U courses, may not be fit for university.
(f) (MS) Students will have more experience in modelling, dealing with data and representing data.
(g) (SC) The goal of the OSS is to bind students and teachers into a "community of learners".
(h) (SN) Students should be more skilful at looking at problems.
7. Caveats
(a) One should not judge the new curriculum on the basis of the first cohorts to reach university, as they will not have had the revised curriculum at the elementary level to prepare them for high school. The current elementary curriculum puts a lot of emphasis on communicating and justifying, and this will lead to better performance in high school. [It was noted that in Eastern Europe, 1516yearolds are good at reasoning because of their earlier exposure to solving problems.]
(b) The implementation of the new curriculum will be uneven, according to the competence or resistance of the teacher.
(c) Students are having to make choices quite early, and may do so unwisely. There is a lot of responsibility on the individual teacher.
(d) Already there is a wide variation in incoming students to university. Students tend to sort themselves according to intended destination, which may not correspond to their preparation. Departments cannot check or enforce high school prerequisite for first year entrants.
(e) The pace of instruction is like to continue to be a problem with students.
(f) Only in Ontario is calculus the fourth high school mathematics credit. In other jurisdictions, students have four courses before they get to calculus.
(g) High school is more than preparation for university.
(h) There will be permanent changes in the students, and the universities must be prepared to make changes to the first year courses to accomodate these. Otherwise, there will be an invidious gap between what students come with and what they will be expected to know at university. However, universities should not simply reteach what students should be expected to pick up in high school.
(i) Professional schools, such as engineering, have to worry about accreditation, and this crimps their ability to make substantial modifications to the curriculum.
(j) University people should examine the texts for OSS when they appear.
8. Reports from Associations and other Groups
a. OMCA
 resources for grade 12 courses: college/tech. courses as high priority,
and gr. 12 workplace course (no text for these)
 involved in profiling course material
 all dependent on Ministry funding
b. OAME
 annual Leadership Conference is fully booked February 21, 22, 23,
2002 at the Four Points Hotel
 registration brochures for the annual Spring Conference: May 2 to
4, 2002 at Georgian College, have been sent to members and school 
registration online as well
 next board meeting: Friday February 8, Saturday February 9, 2002
 forum discussion topics: "Issues related to becoming a service
provider for teacher recertification" and " Developing professional
portfolios for teachers"
 strong discussion on who will be service providers and who will not
(boycotting) "all universities should refuse to be service providers!!!"
 alternate models of growth and professional models
c. OCMA
The Ontario Colleges Mathematics Association will be holding a PD dinner
meeting March 4 at 5:45 to 9 pm; George Brown College where Dr. Georges
Monette will present "Paradoxes of Regression: Some Elliptical
Insights"
The 22nd Annual OCMA Conference will be held at the Georgian College
Kempenfelt Conference Centre, Barrie Ontario, May 29 to 31 2002. This
event attracts college mathematics educators from across Ontario. We
are looking for presenters and if you wish to address our group, let's
talk.
All are welcome to participate and for further information contact John
Kezys
d. CMESG
December 9, 2001  speaker David Kim (Alberta)
 exchange between teachers in universities and other math educators
Aside discussion of EQAO math testing results
 results coming out soon
 Junior High schools scored highest percentile
 some boards counting marks toward courses, others not
 inconsistent administration of test, marking, student confidence and
test taking
 difference between semester and nonsemester school
 there needs to be strong communication between university math teachers
and elementary and high school math teachers
e. CMS
f. Other
9. Other matters
10. Forum discussion organized and led by Ed Barbeau 
. how much change can we really expect from the OSS matriculants?
. how will tertiary institutions be able to interpret the new assessment
and make comparisons between the OSS and OSIS applicants?
To inform the discussion, I would like to make the following observation.
It appears that with OSIS there is considerable variation among schools
in preparing students for higher education, and one might expect a similar
variation with OSS. Indeed, one might argue that some of the attributes
that lead to success in university mathematics (clear thought, ability
to reason and analyze, flexibility of expression and thinking) are promoted
by good teachers in any regime, although the new curriculum if properly
handled might make such things more explicit and lead to a higher probability
of success. The question of fairness in admitting students in the double
cohort is a serious one, and one wonders to what extent the secondary
sector can be helpful in allowing tertiary institutions to properly
interpret the results. (see 7c for more detail).
The meeting will adjourn at 2:00pm
Reminder: Dates of Future Meetings
March 2, 2002
April 6, 2002
May 11, 2002
June 8, 2002