•MON FRASER UNIVERSITY
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Summer Semester 2002
LLUL 411
-11
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Dr. RinaZazkis
Investigations in Secondary Mathematics
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Office: EDB 8661
Phone: 291-3662
E-mail: zazkis@sfu.ca
PREREQUISITE
Wednesday 8:30-12:20 in EDB 7600
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D01.00
Co-req EDUC 415 or appropriate Math background & permission of Instructor.
SCHEDULE
It is a 3-credit course. To fulfill the requirement of 39 instructional hours (3 x13) we will meet in a scheduled
4-hour slot for the first 10 weeks of the semester.
OUTLINE
The goal of the course is to examine secondary mathematics from an advanced standpoint, to broaden
the understanding of key topics by drawing connections among various topics and representations and by
situating them in a broader context, both mathematical and historical. The means towards this goal is intensive
problem solving experience, followed by reflection.
The course will involve lecture, seminar and workshop format, without explicit distinction between the
different formats.
The following is the list of topics to be addressed. The list is not sequential, as the connections among
various topics are of interest in this course:
Numbers and Number systems
Number systems from different civilization
Number representations in different bases
Computation in different bases, fractions in different bases, divisibility rules in different
bases -- implications for base-ten
Critical Number sets (natural, whole, integer, rational, irrational, real)
Relevance of their historical development to the curriculum
Functions
Examination of various definitions for a function
Representation of functions in different coordinate systems (afine, focus-directrix)
Transformation of functions
Geometry
Axiomatic systems (Euclidean, finite)
Geometry on a sphere, implications for the plane
Taxicab Geometry, implications
Investigations in Euclidean Geometry with Geometers Sketchpad
Conic Sections
Examination of various definitions, proving their equivalence
Probability and Statistics
Examination of popular games and winning chances
Monty's Dilemma
Bingo
Slot Machines
How to lie with Statistics - a critical look
Calculus
(Some) Fascinating theorems and formulas of mathematics
Where do they come from?
Why do they "work"?
What is fascinating about them?
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REQUIRED READING
There is no textbook for this course. Materials will be provided by the instructor.
Duplicating fee: Approx. $15.
GRADING: The course will be graded pass /withdrawal. Students must get a passing grade on each
assignment in order to pass the course. Assignments include:
Weekly homework
Problem solving portfolio
Project and presentation
