EMAT 3500, FALL 2005

Exploring Concepts (with Technology) in Secondary School mathematics

Outline (Subject to adjustments as needed)

Week 0: (8/18)

Thinking about being a mathematics teacher
Introduction to NCTM Principals & Standards
Setting up electronic communications (email and web page)
Week 1: (8/23 & 8/25)
Discussion of NCTM Principals & Standards 
Introduction to GSP4, Excel and Graphing Calculators
Choose two of these Interactive Excel spreadsheets to explore!

Chapter 6 from Transforming Mathematics with GSP

The Slide Rule (download GSP slide rule)
Constructing a product of two numbers on a number line using dilation (connecting with transformational geometry)

Week 2: (8/30 & 9/01) Number and Operations

Representing arithmetic operations dynamically on a number line (download GSP sketch)
(download Numberline Tool)
Investigating arithmetic relations dynamically: Mystery Machines
 Mystery Combinations

Week 3: (9/6 & 9/8) Characteristics of Functions

Chapter 7 from Transforming Mathematics with GSP

Dynamic algebraic functions using transformations
Constructing a linear function through dilation and translation
Constructing powers of x through dilation
Comparing Functions on parallel number lines
Exploring the behavior of functions with Dynagraphs 
Composing functions using a sequence of Dynagraphs

Week 4: (9/13 & 9/15) Exploring Functions with GSP

From Dynagraphs to Rectangular Coordinates. 
Investigating different functions using both Dynagraphs and Rectangular Coordinates

Operations on functions using multiple coordinate systems

Week 5: (9/20 & 9/22) Further Explorations of Functions with GSP

Transformations of the quadratic function graph
Using GSP4 as a function-grapher (Olive, 2002. Introduction to Functions with GSP4 )

Week 6: (9/27 & 9/29) Trigonometry of the unit circle with GSP

Chapter 9 from Transforming Mathematics with GSP

Week 7 (10/04) Investigating Functions

Sorting Functions
Conic functions through paper folding
Download this GSP activity from Dr. Hatfield
(10/06) Conic functions using Polar Coordinates
  Download a polar ellipse, Download a Polar Hyperbola

Week 8: (10/11)

Midterm Practice Exam
Click here to download Dynagraphs_5.gsp

(10/13) Midterm Practice Review

Week 9: (10/18) Mid-Term Exam on Functions

(10/20) Visit to the GCTM Annual Meeting at Rock Eagle

Click here for on-line registration

Week 10: (10/25) Data Exploration and Modeling

An introduction to Fathom: activities from Exploring Algebra 1 with Fathom

Download Airplanes.ftm

Week 11: (11/1 & 11/3) Exploring relations among data

Using Scatter Plots to display associations among data
Linear Modeling (unit 2 from Exploring Algebra 1 with Fathom)
Download Oxygen.ftm 
Exponential modeling (unit 4 from Exploring Algebra 1 with Fathom)
Download 8 Countries.ftm

Week 12: (11/8 & 11/10) Representing relations among data

Experimental Labs: Collecting, representing and analyzing data pairs
Line of best fit for a set of data pairs: Signed, Absolute and Squared deviations
Finding lines of best fit for your data from your lab experiments

Week 13: (11/15 & 11/17) Transforming Data

Linearizing quadratic data (Canadian birth rates)
Linearizing exponential data (a return to the Slide Rule function)

Week 14: (11/22) Reporting the Results

Group and individual Lab reports due. Discussion of implications of labs for teaching

Week 15: (11/29 & 12/01) Modeling with GSP

Chapter 8 from Transforming Mathematics with GSP

Using GSP to model physical situations and generate data:

The Biggest Box Problem
The Cardboard View-Tube Problem

Week 16: (12/08) Work on final projects

Final Projects due on Monday, December 12 before 5:00 p.m.

Final Exam: Thursday, December 15, 8:00-11:00 am

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