Past and Future Grade Math Curriculum Revisions Walter Whiteley York University, Director of Applied Mathematics Chair, COU Math Review Task Force

Time Line of past events  Fall feedback on current K-12  Fall Spring Grade 1-10 Math Curriculum fixed  Spring further discussions of Grade  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 Ministry Task Force / Consultation:  Small group with diverse representation;  Wide Consultations with many groups and individuals;  Report and recommendations submitted;  Minister changes  June 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  Grade 12 (Advanced Functions modified) September  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.

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

Grade 9 Principles, Academic Grade 10 Principles, Academic Grade 11 U/C Functions and Applications Grade 12 Data Management Grade 12 Advanced Functions Grade 11 U Functions Probable addition of Calculus Grade 12 Calculus and Vectors Revised Pathway to University Admissions 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  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 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)

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) 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?