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Background: |
The Cartesian Coordinate System is the mathematician’s worksheet. It is where algebra and geometry are unified to create a powerful and beautiful system of relationships. |
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Objectives: |
To strengthen the background of teachers in the connection between algebra and geometry through the Cartesian Coordinate System. The class will focus on content as well as teaching techniques that are aligned with NCTM recommendations. |
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Intended Audience: |
Pre-service and in-service elementary and middle school teachers wishing to strengthen their mathematical background. |
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Prerequisite: |
Approval of the department. |
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Text: |
The Cartesian Triad: Algebra, Geometry and the Cartesian Coordinate System – Let’s Talk (On-Line) |
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Recommended Technology: |
Geometer’s Sketchpad,
WinGeom, WinPlot, Graphing Calculator and possibly Derive or Maple (computer
software is available in campus labs or is free on the Internet). |
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Hours
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Chapter 1: The
Cartesian Coordinate System A reintroduction to the Cartesian Coordinate System. |
6 |
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Chapter 2. Functions An examination of the general form or forms of functions and
deriving conclusions from computer analysis to what happens to the graph as
the parameters change. Classes of functions will include polynomials of
degree 2 and higher, rational, trigonometric, inverse, logarithmic and exponential. |
15 |
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Chapter 3. Solutions
to Equations and Inequalities An examination of techniques for solving equations both by
hand and computer analysis but with an emphasis on computer analysis. Focus
will be on the question “Why is solving f(x) = 0 so important?” |
3 |
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Chapter 4. Informal
Limit Concepts A conceptual analysis of the idea of a limit its importance and its use. Topics may include the tangent line to a curve and rates of change, investigation of function properties using the slopes of tangent lines, asymptotes and asymptotic functions, continuity, calculations of e and pi, dynamical systems and self-similar objects, area, sequences and series. |
15 |
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Chapter 5. Transformations and Matrices An examination of vectors, matrices and their operations
mainly as transformations of the Cartesian Coordinate System. |
6 45 |
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Assignments |
25 – 70% |
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Portfolio |
10 – 25% |
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Modified Lesson Plan |
10 – 25% |
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Presentation |
10 – 25% |
This course complies with the University
Policy on Writing Across the Curriculum.
The Ability to communicate mathematics effectively both orally and in
writing is very important. The
assignments and modified lesson plans in this course are designed to help
students develop and enhance that ability.
DES/lsa
8/2002