EMAT 3500, Fall 2006
Exploring Concepts (with Technology) in Secondary School mathematics
Outline (Subject to adjustments as needed)

Week 1: (8/17)

Thinking about being a mathematics teacher

Setting up electronic communications (email and LiveText)

Introduction and discussion of NCTM Principals & Standards

Introduction to the new Georgia Performance Standards for Mathematics 6-12.

Week 2: (8/22 & 8/24) Number and Operations

Introduction to GSP4, Excel and Graphing Calculators
Choose two of these Excel spreadsheet activities 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) (download GSP sketch)
(Download Numberline Tool)
Investigating arithmetic relations dynamically: Mystery Machines

Mystery Combinations

Week 3: (8/29 & 8/31) 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: (9/5 & 9/7) Exploring Functions with GSP

Click on the following links to download GSP sketches for these activities:

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

Operations on functions using multiple coordinate systems

Week 5: (9/12 & 9/14) 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: (9/19 & 9/21) Trigonometry of the unit circle with GSP

Chapter 9 from Transforming Mathematics with GSP

Week 7 (9/26 & 9/28) Investigating Functions

Sorting Functions
Conic functions through paper folding
GSP Simulation of paper folded conics

Week 8: (10/3) Midterm Practice Exam

Click here to download Dynagraphs_5.gsp

(10/5) Midterm Practice Review

Introduction to Experimental Labs

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

(10/12) Experimental Labs

Collecting data from lab experiments

An introduction to Fathom

Week 10: (10/17) Representing and Analyzing Data from Experimental Labs

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

(10/19) Visit to GCTM Annual Conference at Rock Eagle

Week 11: (10/24) Reporting on GCTM and the Results of your Data Explorations

Reports of sessions attended at GCTM

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


Week 12: (10/31 & 11/02) Data Explorations & Modeling

Activities from Unit 6 of Exploring Algebra 1 with Fathom
Download the Fathom file Escape Ramp.ftm


Week 13: (11/07 & 11/09)
Exploring Probability

Activities from Unit 7 of Exploring Algebra 1 with Fathom
An example Integrated Mathematical Exploration
Geometric Probability and Curve Fitting using Fathom

Week 14: (11/14 & 11/16) 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

Weeks 15 (11/21) Modelling with GSP (continued)

Discussion of simulations from the Biggest Box and View-Tube experiments
Proposals for Final Projects due

Weeks 16 & 17 (11/28, 11/30 & 12/05) Work on final projects 

Final Projects due on Monday, December 11 before 5:00 p.m.

<>Final Exam (Project Presentations): Thursday, December 14, 8:00-11:00 am in room 111/113