Past and Future Grade 1112 Math Curriculum Revisions

1
Past and Future Grade 11-12 Math Curriculum
Revisions

• Walter Whiteley
• York University,
• Director of Applied Mathematics
• Chair, COU Math Review Task Force
• whiteley_at_mathstat.yorku.ca

2
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.

3
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.

4
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
  

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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.

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Proposed Pathways (October)
Grade 9 Principles, Academic
Grade 9 L.D.C.C.
Grade 9 Foundations, Applied
T
Grade 10 Principles, Academic
Grade 10 Foundations, Applied
Grade 10 L.D.C.C.
Few Students
Grade 11W Work and Everyday Life
Grade 11 U/C Functions and Applications
Grade 11 C Foundations for College Math
Grade 11 U Functions
Grade 12C Foundations for College Math
Revised Grade 12 College Technology
Grade 12 Data Management
Grade 12 Advanced Functions
Grade 12 Geometry and Algebra
Grade 12W Work and Everyday Life
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Revised Pathway to University Admissions
Grade 9 Principles, Academic
Grade 10 Principles, Academic
Grade 11 U/C Functions and Applications
Grade 11 U Functions
Grade 12 Calculus and Vectors
Grade 12 Data Management
Grade 12 Advanced Functions
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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

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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 pre-calculus 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)

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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

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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.

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What to add to Grade 12 Advanced Functions ( Why)

• 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?