EMAT 3500, Fall 2008

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

Week 1: (08/19 & 08/21) National and State Standards for Mathematics Teaching

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

Choose two of these Excel spreadsheet activities to explore!

Week 2: (08/26 & 08/28) Number and Operations & Characteristics of Functions

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

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

Week 3: (09/02 & 09/04) Exploring Functions with GSP

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

Click here to download a starting dynagraph sketch

Exploring the behavior of functions with Dynagraphs
Composing functions using a sequence of Dynagraphs

From Dynagraphs to Rectangular Coordinates.

Investigating different functions using both Dynagraphs and Rectangular Coordinates

Operations on functions using multiple coordinate systems

Week 4: (09/09 & 09/11) 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: (09/16 & 09/18) Trigonometry of the unit circle with GSP

Chapter 8 from Transforming Mathematics with GSP
Click here to download a starter sketch for the trig functions based on a unit circle

Week 6 (09/23 & 09/25) Investigating Functions

Sorting Functions
Conic functions through paper folding
    Download Chapter 13 from
Transforming Mathematics with GSP: Conic Sections
GSP Simulation of paper folded conics

Week 7: (09/30) Midterm Practice Exam

Click here to download Dynagraphs_5.gsp

(10/02) Midterm Practice Review

Week 8: (10/07) Mid-Term Exam on Functions

(10/09) Example Data Investigations from Core-Plus, Course 1, Unit 2.
       An introduction to Fathom

Week 9: (10/14) Continue investigation from Core-Plus, Course 1, Unit 2.

(10/16) Visit to GCTM Annual Conference at Rock Eagle

Week 10: (10/21, 10/24 & 10/25)
            (10/21) Reports of Visit to GCTM Conference

Discussion of Experimental Labs

(10/24 & 10/25) TI-nSpire Workshop Training
Download Agenda for the Workshop

Week 11: (10/28 & 10/30) Using TI-nSpire and Fathom to Collect and Analyze Data

        (10/28) Experimental Labs
                Collecting data from lab experiments
                Finding function graphs to fit your data from your lab experiments

        (10/30) Representing and Analyzing Data from Experimental Labs           
                Activities from: Discovering Algebra 1 with the TI-nSpire (From Key Curriculum Press, copyright 2009)
                    Simulation of Radioactive Decay (pages 67-69 of Exponential Equations PDF)
Download the TI-nSpire file Radioactive Decay.tns
Line of best fit for a set of data pairs: Signed, Absolute and Squared deviations
                Discussion of implications of labs for teaching

Week 12: (11/04 & 11/06) Data Explorations & Probability

More Activities from Discovering Algebra 1 with the TI-nSpire
Polynomial Factoring--Maximum Area of a Folded Triangle (pages 119-121 of Quadratics and Higher Degree Polynomials PDF)  

An example Integrated Mathematical Exploration
Geometric Probability and Curve Fitting using Fathom and/or TI-nSpire
Click here to download the Fathm activity.
Click here to download the TI-nSpire document Monte Carlo.tns
Week 13: (11/11 & 11/13) Modelling with GSP

Chapter 9 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: (11/18 & 11/20) Modelling with GSP (continued)

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

Proposals for Final Projects due

Week 15: (12/02 & 12/04)  Work on final projects

Final Projects due on Monday, December 8 before 5:00 p.m.

Final Exam (Project Presentations): Tuesday, December 16, 8:00-11:00 a.m. in room 111/113
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