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SIMON FRASER UNIVERSITY
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SUMMER SEMESTER 2006
EDUC 411-3
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INVESTIGATIONS IN SECONDARY MATHEMATICS
(D01.00)
Dr. Peter Liliedahl
Office: EDB 8662
Phone: 291-5643
email: liljedahl@sfu.ca
TUESDAY 1:00-4:50 IN EDB 7600F
Prerequisite(s)/ Corequisite(s)
It is recommended that this course is taken concurrently with EDUC 415 Designs for Learning
Mathematics: Secondary.
Schedule
This 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 10 weeks during the semester.
Course Description
The goal of the course is to examine secondary mathematics from an advanced standpoint. More
specifically, the goal is to extend the understanding of key topics from high school mathematics by
situating them in the broader mathematical and historical contexts, and by drawing connections between
key topics. Though the course content comes from mathematics, the approach is a pedagogical one,
which draws on the knowledge and practices from education rather than applying the lecture/tutorial
format most commonly seen in undergraduate mathematics courses. Students will engage in problem
solving, investigate conjectures, and reflection on both the content and the process. The following is a
possible list of topics to be addressed. The list is not exhaustive, nor is it sequential:
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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), and relevance of their
historical development to the curriculum.
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Functions
Examination of various definitions for a function, representation of functions in different coordinate
systems (afine, focus-directrix), and transformation of functions.
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Geometry
Axiomatic systems (Euclidean, finite), geometry on a sphere and implications for the plane, taxicab
geometry, and investigations in Euclidean Geometry with Geometer's Sketchpad
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Conic Sections
Examination of various definitions and proving their equivalence.
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Probability and Statistics
Examination of popular games and winning chances, Monty's Dilemma, bingo, slot machines, and how
to lie with statistics - a critical look.
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EDUC Outline
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(Some) Fascinating theorems and formulas of mathematics
Where do they come from? Why do they "work"? What is fascinating about them?
Readings
Reading materials will be provided by the instructor.
There may also be a textbook - but it will cost under $20.
Requirements
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.
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