EMAT 3500, Fall 2007

Exploring Concepts (with Technology) in Secondary School mathematics
Outline (Subject to adjustments as needed)

Week 0: (08/16)

Thinking about being a mathematics teacher

Setting up electronic communications (email and network)

Introduction and discussion of NCTM Principals & Standards

Introduction to the new Georgia Performance Standards for Mathematics 6-12.
Georgia Department of Education Resource page for GPS Mathematics

Georgia DOE On-Line training Materials for HS Mathematics GPS

Week 1: (08/21 & 08/23) Number and Operations

Sharing e-Examples from the NCTM Principles & Standards
Introduction to GSP4 and Excel

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 2: (08/28 & 08/30) 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 3: (09/04 & 09/06) Exploring Functions with GSP

Click on the following links to download GSP sketches for these activities:
Click here to download a starting dynagraph sketch
From Dynagraphs to Rectangular Coordinates.

Investigating different functions using both Dynagraphs and Rectangular Coordinates

Operations on functions using multiple coordinate systems

Week 4: (09/11 &09/13) Further Explorations of Functions with GSP

Download Classwork from 9/11/07
Activity 7.4 from
Transforming Mathematics with GSP:
Transformations of the quadratic function
Using GSP4 as a function-grapher 

Week 5: (09/18 & 09/20) Trigonometry of the unit circle with GSP

Chapter 9 from Transforming Mathematics with GSP
Click here to download a starter sketch for the trig functions based on a unit circle

Week 6 (09/25 & 09/27) Investigating Functions

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

Week 7: (10/02) Midterm Practice Exam

Click here to download Dynagraphs_5.gsp

(10/04) Midterm Practice Review
               

Week 8: (10/09) Mid-Term Exam on Functions

(10/11) Example Data Investigations from Core-Plus, Course 1, Unit 2.
       An introduction to Fathom

Week 9: (10/16) Continue investigation from Core-Plus, Course 1, Unit 2.


(10/18) Visit to GCTM Annual Conference at Rock Eagle



Week 10: (10/23) Reports of Visit to GCTM Conference

Discussion of Experimental Labs

(10/25) Fall Break

Week 11: (10/30)
Experimental Labs

        Collecting data from lab experiments
                Finding lines of best fit for your data from your lab experiments

(11/01) Representing and Analyzing Data from Experimental Labs           
                Activities from:
                    Learning to Teach Mathematics with Technology: An Integrated Approach
We shall be using activities from Chapter 4: Analyzing Bivariate Data with Fathom of a new curriculum resource being developed by Hollylynne Lee & Karen Hollebrands
Download the PDF document for Chapter 4 here.
Download the Fathom data set: 2006_Vehicles.ftm here.

                Line of best fit for a set of data pairs: Signed, Absolute and Squared deviations
               
Discussion of implications of labs for teaching

Week 12: (11/06 & 11/08) Data Explorations & Probability

More Activities from
 
Learning to Teach Mathematics with Technology: An Integrated Approach
Click here to download Correlation Fathom file.

An example Integrated Mathematical Exploration
Geometric Probability and Curve Fitting using Fathom
Click here to download the activity.
Week 13: (11/13 & 11/15) Modelling with GSP

Chapter 8 from Transforming Mathematics with GSP

Using GSP to model physical situations and generate data:

The Biggest Box Problem (click here to download a sophisticated sketch of the problem)

The Cardboard View-Tube Problem (Click here to download a starter sketch)

Week 14: (11/20) Modelling with GSP (continued)

Discussion of simulations from the Biggest Box and View-Tube experiments

Proposals for Final Projects due

Week 15: (11/27 & 11/29)  Work on final projects
Week 16: (12/06)  Work on final projects  

Final Projects due on Monday, December 10 before 5:00 p.m.

Final Exam (Project Presentations): Thursday, December 13, 8:00-11:00 am in room 111/113
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