Extended Analysis of Functions 2

Summer/Fall 2006


Assignments and classes will run according to this schedule. Please let me know if any of these dates conflict with a university-recognized religious holiday that you observe as a matter of faith.

All assignments must be submitted in the form of typed, word processor documents (MS Word) unless otherwise noted in the assignment schedule or the assignment itself. Upload elecronically-submitted assignments to your private page on the EAF 2 Course Forum.

You might also wish to consult lesson logics, discussions, and assignments listed in the Exended Analysis of Functions 1 website.

Please name your assignment files by the convention given below (files not following this convention will be returned unread). Name the file with:

In Class
Jun 5
  • Course Forum: Discuss why the idea of "instantaneous speed" should be problematic for students.
  • Course Forum: Discuss the definition of average rate of change that was given today.
Jun 6
Jun 7
  • Average rate of change of a function
  • Average rate of change as a function
  • Defining tangents to curves using rates of change
  • Uses of parameters in GC to show relationships within a graph
  • Introduce parametric functions
  • Introduce parametric functions in 3-d
  • Curves on a surface
Jun 8
  • Parameters vs parameters
  • Parametric functions (again)
  • Designing aids to help students "see" functions in 3-dimensions
Jun 12
  • Course Forum: Continue discussion of under what conditions and to what benefit might we include ideas of graphs and surfaces in 3d in the high school math. curriculum
  • Course Forum: Give your thoughts on the aims and purposes of the 6/12 lesson on functions that have planes as graphs.
Jun 13
  • Tangent lines to a surface
  • Tangent planes to a surface
  • Create a GC document that, given any function f(x,y) and a point on f's graph, produces tangent lines to the graph of f in the x- and y- directions and produces the plane containing those tangent lines.
  • Explain the development of your formulas. Assume you are explaining them to a student who knows how to use GC, understands that any function that has a plane as its graph is of the form f(x,y) = nx + my + K (and understands why this is so), and understands that a function g having a rate of change of m with respect to its argument implies that however much the function's argument changes, the functions value changes m times as much. (If I've omited anything that is important to your explanation, then include it and say what it is they understand about it.)
  • Post your explanation to your personal page at Course Forum
Jun 14
  • More on averate rate of change
  • Lines and curves -- linear approximations
  • "Smoothness" of a function
  • Issues of smoothness
  • Accumulations and Riemann Sums
  • Focus on why some Riemann sums are step functions and why some are not
  • More on Riemann Sums
Jun 15
  • Prepare for Fall 06
Aug 21
  • Discuss the nature of explanations (examples from analysis and from geometry)
  • Geometric constructions (compass and straightedge)
  • What makes a figure a geometric figure?
    • Activity
    • Discussion of constraints and dependencies
  • Introduction to Sketchpad 4.0
    • Points
    • Straight things
    • Circles
    • More
  • What does a proof prove?
    • Whence "the thing to be proved"?
    • Fundamental constructions
  • Constructions 1 (See discussion of difference between making a duplicate segment and making a duplicate segment given a segment, a line, a point on the line, and having that point as an endpoint)
  • Saturday Math Club
Sep 11
  • Dependencies and assumptions
  • Assumptions, conjecures, and arguments
Sep 25
  • Geomery and algebra
  • Using Sketchpad as a teaching aid in algebra and calculus
  • Examine problems from Functions 1, Modeling. Pick two problems (other than #1); create a dynamic illustration that you could use with an overhead projector to help students understand the problem.
  • Pick 3 problems from additional constructions. For construction problems, develop a goal structure for the construction and create the construction.
Oct 9
Oct 23
Nov 13
Nov 27
Dec 11

Present projects

Party at Dr. T's home, 6:00p