Teacher Learning System

Oklahoma State University, Stillwater, OK

The Teacher Learning System for the TI-85 graphing calculator (TI-85 TLS) has been developed to assist the secondary mathematics teacher with learning about this technology as well as designing and managing instruction using it

The components of the TI-85 TLS are:

- Independent Study Written Materials
- Graphing Calculator Programs and Functions for Algebra, Trigonometry, and Calculus
- Video Supplements: Learning to Use the TI-85; Using Algebra, Trigonometry, and Calculus Programs; Programming the TI-85; Suggestions for Designing and Managing Instruction
- Listings of Calculator Programs

Numerous papers have been written documenting the advantages of using graphing calculators to teach and learn mathematics. Many of these papers have even described specific methods for integrating graphing calculators into the secondary mathematics curriculum. Two different positions seem to be common among practicing mathematics teachers. Some regard integrating graphing calculators into the mathematics curriculum as a sort of panacea for teaching mathematics in the next century. In an idealistic way, they believe students will be able to easily learn the procedural manipulations of the graphing calculator when they are introduced (after all, graphing calculators are "user-friendly!?"). And, students will be enthusiastically looking forward to their next opportunity to use them!

Other teachers maintain a more cautious posture. To them, perhaps a more realistic scenario would be the following. Because calculators are so powerful and offer so many options, it is likely that many students will push the wrong key at the wrong time thereby finding themselves locked into a mode from which they have no earthly idea how to recover. Since the teacher may not know how the students entered these modes, he or she may not be immediately able to return them to the proper format to continue the lesson. By the end of the class, most students will have their hands in the air begging for help! The class has the potential to end in disaster where students and teacher alike are frustrated and convinced that the graphing calculator is more trouble than it is worth! There is also the very real question of whether students are learning mathematics or learning a sequence of procedural steps required to obtain an answer.

The TI-85 TLS has been developed to help you learn about the TI-85 graphing calculator using written materials, programs, and a video supplement.

The initial portion of the video supplement sets the stage for learning how to use the TI-85. It assumes you know nothing about the TI-85 and introduces you to its organizational setup. If you are not familiar with the TI-85, we suggest you view this segment without your calculator; then, watch it again with your calculator in hand. Knowing how the TI-85 is organized will prove essential to your continued learning.

The initial chapter of the written materials builds upon the video by introducing you to some of the fundamental programs. A brief explanation of each program is given together with some examples. You should work through each of the programs in this chapter using your calculator. As you continue, you will undoubtedly feel more confident in your own abilities and begin to understand the simplicity (or "friendliness") of this powerful learning tool.

The second portion of the video supplement introduces and explains how to use some of the host of algebra and statistics, trigonometry, and calculus programs that have been written explicitly for your classroom use. The companion chapters in the written materials are arranged according to algebra and statistics, trigonometry, and calculus. The introduction to each of these chapters describes the programs and functions included in it. A concise explanation for each program or function shows how to execute it and is followed by examples and exercises; try them! Because the programs and functions relate directly to the topics in the secondary mathematics curriculum, integration of the TI-82 should be relatively simple. A brief introduction to programming the TI-82 is also included in this portion of the video supplement.

The final portion of the video supplement discusses various aspects of designing and managing instruction that integrates the TI-82 and includes suggestions for gaining school and district acceptance and support.

The final chapter of the written materials includes the statements of the programs developed. This is a valuable resource for teachers desiring to do their own programming, i.e., extending existing programs or developing new programs.

The content of the TI-85 TLS written materials is listed below. Clicking on the desired topic will work. The page references for the topics in the TI-85 TLS book are also given in parenthesis, e.g., (G-4), if you have access to this source.

- Getting Started (G-1)
- Entering Functions for Graphing (G-2,3)
- Using the "Set-Up" Programs (G-4)
- Description of "Set-Up" Programs (G-5,6)
- Running a Program Stored in the Calculator (G-7)
- Transferring Programs Using "Memory Backup" (G-8)
- Passing Programs Between Calculators (G-9)
- Using the "Catalog" (G-10)
- Using the "Custom" Menu (G-11)
- Initial "Custom" Menu Commands (G-12)

- Description of Algebra Programs (A-1)
- Displaying Results in Fractional Form (A-2,3)
- Storing Definitions in the Calculator (A-4)
- Evaluating a Function at a Given Value of x: Function evalF (A-5)
- Evaluating a Function at a Given Value of x: Program PLPTS (A-6)
- Linear Interpolation (A-7)
- Performing Linear Regression (A-8,9)
- Graphing an Inequality (A-10)
- Graphing Two Inequalities (A-11)
- Finding the Distance Between Two Points (A-12)
- Finding the Midpoint Between Two Points (A-13)
- Changing Repeating Decimals to Fractions (A-14)
- Solving Simultaneous Equations (A-15)
- Representing Matrices (A-16)
- Loading Matrices (A-17)
- Multiplying a Matrix by a Scalar (A-18)
- Adding and Subtracting Matrices (A-19)
- Multiplying Two Matrices (A-20)
- Finding the Inverse of a Matrix (A-21)
- Finding the Determinant of a Square Matrix (A-22)
- Finding the Transpose of a Square Matrix (A-23)
- Solving Simultaneous Equations Using Augmented Matrices (A-24,25)
- "Graphically" Finding the Roots of Polynomial Equations (A-26)
- Factoring Polynomials (A-27,28,29,30)
- Representing Complex Numbers (A-31)
- Adding, Subtracting, Multiplying, and Dividing Complex Numbers (A-32,33)
- Graphing Parabolas in Standard Form (A-34)
- Graphing Circles in Standard Form (A-35)
- Graphing Conic Sections in General Form (no xy term) (A-36,37)
- Graphing Ellipses in Standard Form (A-38)
- Graphing Hyperbolas in Standard Form (A-39)
- Graphing Conic Sections in General Form (with xy term) (A-40)
- Graphing "Piecewise" Defined Functions (A-41)
- Exploring Inverses of Functions (A-42)
- Calculating Logs and Antilogs (A-43)
- Solving Exponential Equations (A-44)
- Solving Financial Equations with the "Solver" Key (A-45,46)
- Using Scientific Notation in Science Classes (A-47)
- Using the "Conversion Factor" Menu in Science Classes (A-48)
- Using the "Built-in" Constants in Science Classes (A-49)
- Storing "User-Defined" Constants for Science Classes (A-50)
- Storing and Solving Equations for Science Classes (A-51,52,53)
- Evaluating Factorials (A-54)
- Finding Permutations and Combinations (A-55)
- Exploring Seven Regression Models (A-56,57)

- Description of Trigonometry Programs (T-1)
- Evaluating Trigonometric Functions (T-2,3)
- Finding Trigonometric Function Values (T-4)
- Finding Inverse Trigonometric Function Values (T-5,6)
- Graphing Trigonometric Functions (T-7)
- Graphing Inverse Trigonometric Functions (T-8)
- Using the Unit Circle for the Sine and Cosine Functions (T-9)
- Using the Law of Cosines (T-10,11)
- Using Heron's Formula (T-12,13)
- Graphically Solving Trigonometric Equations (T-14)
- Graphing Polar Equations (in Degree Mode) (T-15)
- Changing the Range in Polar Graphing (T-16)
- Graphing Parametric Equations (T-17)
- Changing Complex Numbers in Polar Form to Degree Mode (T-18,19)
- Changing Complex Numbers in Polar Form to Radian Mode (T-20)
- Vector Operations (T-21,22,23)
- Finding the Dot Product and Cross Product of Vectors (T-24)
- Finding the Angle Between Two Vectors (T-25)

- Description of Calculus Programs (C-1)
- Evaluating Summation Notation (C-2)
- Graphing a Function and its First and Second Derivative (C-3)
- Using Newton's Method to Find the Zeros of a Function (C-4)
- Using Differentials to Estimate Change and Measurement Errors (C-5)
- Using the Midpoint Rule for Integration (C-6)
- Using Simpson's Rule for Integration (C-7)
- Using Inscribed Rectangles for Integration (C-8)
- Using Circumscribed Rectangles for Integration (C-9)
- Using the Trapezoid Rule for Integration (C-10)
- Finding the Area Between Two Functions (C-11)
- Finding the Volume of Revolution Using One Function (C-12)
- Finding the Volume of Revolution Using Two Functions (C-13)
- Finding the Arc Length of a Function (C-14)
- Finding the Surface Area of Revolution (C-15)
- Finding the Center of Mass Using Integration (C-16)

This page is maintained by Doug Aichele (aichele@math.okstate.edu).