April 23, 2014

Mathematics Transition from School to College and University

Minutes of Task Force Meeting - Thursday, January 17, 2002

1. List of attendees

Ryerson PU
Peter Danziger, Chris Grandison, Ann-Marie Filip, Randall Pyke, Sophie Quigley

York U
Tom Salisbury, Margaret Sinclair

U Toronto
Ed Barbeau, Ragnar Buchweitz, Dietrich Burbulla, Christine Clement, Steve Cook, Danny Heap (CSC), Arnold Rosenbloom,
Any Wilk

Stewart Craven, Sandy DiLena, Gord Doctorow, Biyu Joseph, Maharukh Kootar, Michael McMaster, Steffi Nathan, Bob Pickering, Inga Shukla, Silvana Simone, Peter Wei

Maria Chiu

Martin Muldoon, York U
Stephen Chamberlin, York U
Walter Whiteley, York U
John Bland, U of Toronto
Abe Igelfeld, U of Toronto
Mike Lorimer, U of Toronto

2. Dissemination of Information

(a) Some websites:

(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 40-50% 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 university-bound 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, 15-16-year-olds 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.

List of Abbreviations
AFIC: MCB4U Advanced functions and introductory calculus
GDM: MGA4U Geometry and discrete mathemaatics
MDM: MDM4U Mathematics of data management
OSIS: the old curriculum
OSS: the new curriculum


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