Past and Future Grade 11-12
Math Curriculum Revisions
Walter Whiteley
York University,
Director of Applied Mathematics
Chair, COU Math Review Task Force
whiteley@mathstat.yorku.ca
Time Line of past events
 Fall 2003 - 2005 feedback on current K-12
 Fall 2004 - Spring 2005 - Grade 1-10 Math Curriculum fixed
 Spring 2005 - further discussions of Grade 11-12
 Crisis with Advanced Functions and Calculus:
 Math Department consensus: students taking only Grade 12
Advanced Functions and Calculus were ill-prepared overall;
 changes needed for average (70-85%) students.
 more students need more time in math to be well prepared but …
 Crisis in Geometry and Discrete Math enrolments:
 course not required, not taken, not being offered in many
schools;
 identified gaps in 9-11 which make Geometry and Discrete
Math difficult.
Time Line of past events (continued)
 Fall 2005, official feedback to Drafts
 proposal Calculus Techniques dropped from Grade 12
Functions (20% of course),
 Concepts for rate of change kept.
 Doubt that ‘Geometry, Discrete’ will survive (rough draft).
 Nov - February. Major concerns about:
 not enough challenge to prepare strong students;
 not enough time and diversity to prepare average students;
 survival of ‘fifth course’ in most schools
February 2006:
 Decision to proceed with Grade 11 changes Fall 2006
 Decision to postpone changes to Grade 12 U till Fall 2007
 More consultations of Grade 12 U courses.
Time Line of past events (continued)
 February-April 2006. Ministry Task Force / Consultation:
 Small group with diverse representation;
 Wide Consultations with many groups and individuals;
 Report and recommendations submitted;
 Minister changes
June 2006 - now. Task Force and Ministry announcements
 Grade 11 will be ‘like’ the draft last November;
 Grade 12 U is a major revision,
 Like recommendations from last fall (COU);
 Move calculus content to ‘fifth high school math course’
 Add something richer to ‘Advanced Functions and …’
COU/Task Force Proposal
 Interim (need thorough review K-12 over next five years).
 Focus on processes and concepts, not just procedural knowledge.
 Data management mildly revised for Fall 2007.
 Grade 12 (Advanced Functions modified) September 2007.
 Some shifts in topics among 11-12;
 Remove calculus techniques from 1st course;
 add diversity of math: geometry OR discrete math OR ?;
 Keep course learnable - focus on better foundations
concepts.
 Move calculus to fifth course with Vectors
 make fifth course essential for more students;
 change university admissions requirements;
 more in line with other provinces,
 calculus and vectors focused on stronger students/ students
who will need this math.
Proposed Pathways (October)
Grade 9
Principles,
Academic
T
Grade 10
Principles,
Academic
Few Students
Grade 11 U
Functions
Grade 12
Geometry and
Algebra
Grade 12
Advanced
Functions
Grade 11 U/C
Functions and
Applications
Grade 12
Data
Management
Revised Grade 12
College
Technology
A success
Valuable for stats
Grade 9
Foundations,
Applied
Grade 9
L.D.C.C.
Grade 10
Foundations,
Applied
Grade 10
L.D.C.C.
Grade 11 C
Foundations for
College Math
Grade 11W
Work and
Everyday Life
Grade 12C
Foundations for
College Math
Grade 12W
Work and
Everyday Life
Revised Pathway to University Admissions
Grade 9
Principles,
Academic
Grade 10
Principles,
Academic
Grade 11 U
Functions
Grade 12
Calculus and
Vectors
Probable addition
of Calculus
Grade 12
Advanced
Functions
Grade 11 U/C
Functions and
Applications
Grade 12
Data
Management
Previous techniques
of Calculus
Admissions Transition Planning
 Admissions / planning timeline (now)
 Revised Admissions Requirements.
 New University requirements to schools: October 2006
 Fall 2006 students take appropriate Grade 11
 This means Grade 11 U for any students planning math
beyond stats, in university
 Fall 2007 students take appropriate Grade 12, apply to
university
 2007 - Redesign University courses to match up to new
Grade 12;
 Fall 2008 students begin revised university courses;
Comparisons with Other Provinces
 Outside Quebec:
 None have calculus in first Grade 12 course;
 Many have calculus in second Grade 12 course
 Calculus not taken by most students;
 None have vector algebra;
 All have some additional geometry, other topics beyond precalculus in core Grade 11, Grade 12.
 None have equivalent to data management.
 Quebec is a distinct system
 Students more advanced by end of Grade 8, and Grade 11;
 More if you are interested (I taught CEGEP for 20 years)
Some points to observe
 One issue: Speed at which material is done (quantity).
 Bigger issue: students’ preparation in concepts, in reasoning, in
communication, in applications, in problem solving.
 Key processes of the curriculum - achieved by 85%+ students
(level 4), but not by other students (level 3) who take math at
university.
 Second bigger issue: maturity, study skills, work habits of
entering students;
 This is key reason for failure in first semester math and science.
 Five math courses are better than four courses.
 Some material to build reasoning in Grade 12 Functions
Issues to work on now:
 Science courses are now in first year of revision cycle, major
changes are possible. Need to also track these.
 Content to be added to Grade 12 (possible leak to Grade 11 in
2007)
 Have universities adapt first year courses to content, process,
and age / study habits of students;
 Universities should support changes (not act as if students had
old curriculum);
 Consultations mean better chance that written curriculum will
be the taught curriculum;
 Make prerequisite curriculum match the written curriculum.
 Collaboration now will benefit all concerned.
What to add to Grade 12 Advanced Functions
(& Why)
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Missing pieces / moving pieces:
Geometry: conics, plane, other …
Discrete Mathematics
Rich problem solving / explorations
Assesment?
Why? Student learning? student attitudes to
mathematics? university needs? Teacher
background?