EMAT 3500, FALL 2004

Exploring Concepts (with Technology) in Secondary School mathematics

Outline (Subject to adjustments as needed)

Week 0: (8/19)

Thinking about being a mathematics teacher
Introduction to NCTM Principals & Standards
Setting up electronic communications (email and web page)
Week 1: (8/24 & 8/26)
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
Constructing a product of two numbers on a number line using dilation (connecting with transformational geometry)

Week 2: (8/31 & 9/02) Number and Operations

Representing arithmetic operations dynamically on a number line
Investigating arithmetic relations dynamically: Mystery Machines

Artin's Braids: contrasting approaches to mathematical learning experiences

Week 3: (9/7 & 9/9) 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 (Exploring Algebra, pp. 104-116)
Composing functions using a sequence of Dynagraphs

Week 4: (9/14 & 9/16) Exploring Functions with GSP

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

Week 5: (9/21 & 9/23) Further Explorations of Functions with GSP

Transformations of the quadratic function graph
Paper folding to produce a parabola and other conics
Using GSP to model a headlight from a parabola.

Week 6: (9/28 & 9/30) Graphing Functions with GSP

Using GSP4 as a function-grapher (Olive, 2002. Introduction to Functions with GSP4 )

Week 7 (10/05) Investigating Functions

Sorting Functions
Using multiple coordinate systems to investigate operations on functions
Conic functions using Polar Coordinates
(10/07) Generating data through GSP simulations
The Box problem -- linking GSP simulation to measurements and graphing
The Cardboard Tube Telescope

Week 8: (10/12) Midterm Review

Click here to download Dynagraphs_5.gsp

(10/14) Visit to the GCTM Annual Meeting at Rock Eagle

Week 9: (10/19) Mid-Term Exam on Functions

(10/21) Starting from Data: Linear Models

Introduction to Fathom 
Chapters 1-3 of The Model Shop© by Tim Erickson

Week 10: (10/26 & 10/28) Non-Linear Models

Chapters 4 & 5 of The Model Shop© by Tim Erickson

Week 11: (11/2 & 11/4) Exploring relations among data

Chapter 6 of The Model Shop© by Tim Erickson
Experimental Labs: Collecting, representing and analyzing data pairs

Week 12: (11/9 & 11/11) Representing relations among data

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: (11/16 & 11/18) Transforming Data

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

Week 14: (11/23) Reporting the Results

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

Week 15: (11/30 & 12/02) Modeling with GSP

Using GSP to model physical situations and generate data:

The Biggest Box Problem
The Cardboard View-Tube Problem

Week 16: (12/09) Work on final projects

Final Projects due on Monday, December 13 before 5:00 p.m.

Final Exam: Group A: Tuesday, December 14, 8:00-11:00 a.m

Group B: Thursday, December 16, 8:00-11:00 am

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