General Information
All EHS courses have the same goal. When the class is complete teachers should be empowered to expand their mathematics classrooms. At their most basic level the courses are designed to guide teachers to become proficient with available tools. But, this is only the beginning. As experience is gained with the tools, teachers will have the opportunity to create their own interactive activities and projects. The focus is on student learning and what might invite passive watchers to become active participants. Everything is hands-on, self-paced, and open for discussion.

Classroom
The EHS classroom looks very much like your living room, kitchen, or den. These professional development courses have been constructed to fit your schedule.

• Teachers install a computer algebra system (CAS) on their computer.
• Teachers interact with the course material via the CAS.
• Teachers and course instructors exchange the materials via web browser.
• Along with course materials, email and instant messenger support constant communication.
• There are no lectures or clocks. The course is open all day every day.
• The course material provides a general guide with flexibility to entertain any and all questions or interests that might come up.

• Focus: What would help, motivate, and support your students' understanding of mathematics?

Syllabus
Each course has a syllabus of its own, but they all follow the same basic blueprint.

• Gain experience with the computer algebra system.
• Discuss functionality, operation, and interface.
• Try it yourself, get feedback, and develop specific skills.
• Ask Questions.
• Discuss your classroom, brain storm, design activities and projects, then build the interactive materials and bring your project to life.
• Summarize, review, and evaluate.

Course Material
The course material is written in LiveMath notebooks to make it interactive and hands-on. Educators will learn by doing. Of course there are PDF versions for consideration away from the computer. Here is a sample notebook from the first lesson of EHS 825 (LiveMath Version, PDF version). You can download the LiveMath version and view it locally with LiveMath Viewer.

Thinking Ahead
Expanding your classroom begins inside your own head. The EHS courses are intended to help teachers discover new possibilities. Attention is given to classroom activities or projects, communication modes and mediums, and moving beyond the physical walls to make the classroom available to students at home. Start thinking now. What would help your students?

EHS 825: Introduction to Computer Algebra in Mathematics Education This course will introduce the usage of a computer algebra system in mathematics education. Applications will focus on completing a range of basic mathematical operations and computations, including arithmetic and calculator type functions, basic graphing, and basic algebraic manipulations. This course is appropriate for the computer novice, with minimal prerequisite computer skills required, or for the more experienced computer user. Tracks Track 1: Novice Computer User Track 2: Accelerated: More Experienced Computer User Credit: 3 credits Prerequisite: Math 121 (Precalculus) or equivalent 1: Mousercises 2: Installing and Launching LiveMath 3: Opening and Saving a Notebook 4: Exploring the Starter Library 5: Inputting Math 6: Simple Computations 7: Simple Graphs 8: Text Comments 9: Simple Animation 10: 3D Graph 11: Algebraic Substitution 12: Factoring and Solving 13: Tables 14: Case Theories 15: Functions 16: Making a LiveMath Webpage 17: Using LiveMath Plug-In/ActiveX

EHS 826: Developing Mathematics Curriculum for the Web Using Computer Algebra Applications This course will develop and expand upon the usage of a computer algebra system in mathematics education. Applications will include development of complex graphing systems, expanded algebraic and numerical computations, and mathematics curriculum development using a computer algebra system. This course is appropriate for all teachers. The computer novice, with minimal prerequisite computer skills will find support to get up and running while the more experienced computer user can expand on the design and construction part of the course. The idea is to equip teachers with tools with which they can enhance the learning environment of their students. Tracks Track 1: General Usage Track 2: Teaching Beginning Algebra Focus Track 3: Teaching Precalculus Focus Track 4: Teaching Calculus Focus Credit: 3 credits Prerequisite: EHS 825 or approval ofinstructor Track 1 1: Customizing Algebra: Transform Rules 2: Local Variables: Case Theories 3: Utilizing Working Statements 4: Functions and Wildcards 5: Collapsars and Password Protection 6: Matrices 7: Differential Equations 8: Computational Applets 9: Graphical Applets 10: Graph Tags 11: Using MathEQ and LiveMath via LiveMath Plug-In/ActiveX 12: Tables 13: Developing LiveMath-based Websites 14: Customizing Setup Track 2 1: Basic Arithmetic via Computer Algebra 2: Solving Equations 3: Factoring Quadratics 4: Graphing Linear Equations 5: Graphing Quadratic Equations 6: Rational Expressions 7: Roots 8: Working with Data Points 9: Algebraic and Graphical Connections 10: Animations 11: Making a LiveMath Webpage 12: Creating Projects and Experiments Track 3 1: Basic Arithmetic via Computer Algebra 2: Solving Equations 3: Factoring Polynomials 4: Substitution 5: Functions 6: Graphing Linear Equations 7: Roots and Equations 8: Working with Data Points 9: Algebraic and Graphical Connections 10: Animations 11: Summations and Sequences 12: Making a LiveMath Webpage 13: Creating Projects and Experiments Track 4 1: Basic Arithmetic via Computer Algebra 2: Solving Equations 3: Factoring and Solving 4: Functions 5: Limits 6: Graphing Functions 7: Animations 8: Derivatives: Algebraic 9: Derivatives: Numerical and Graphical 10: Implicit Derivatives 11: Differentials 12: Riemann Sums 13: Integration: Algebraic 14: Integration: Numerical and Graphical 15: Integration Rules 16: 3D Graphing 17: Partial Derivatives 18: Multiple Integrals 19: Making a LiveMath Webpage 20: Creating Projects and Experiments This course is a continuation of the previous course. Participants can expect to expand their familiarity and proficiency of subject skills visitied in EHS 825. Algebra is a huge field of study and will continue as a thread throughout all the courses. The course material will continue to investigate linear equations, quadratic equations, polynomials, graphing, solving equations, rational expressions, roots, and interconnections between any and all of these. In addition, all of these tools, skills, and concepts are employed in the study of functions. Functions will be taken up in more depth in this course. Functions are an important tool for studying information. Gaining experience with functions is paramount for students intent on any scientific work. Interactive activities and projects allow students to aquire this experience in a way that they feel best suits them. Projects in this course will focus on functions, their operation, and modeling applications.

EHS 827 - Advanced Computer Algebra Applications in Mathematics Education This course will further develop the usage of a computer algebra system in mathematics education to the expert level. Topics include advanced computer algebra development, interaction with curriculum, and advanced website development skills. Credits: 3 credits Prerequisite: EHS 826 or approval of instructor 1: Drawing Fractals: Hidden Secrets of Graphing 2: Phase Planes: Advanced Computational Techniques 3: Multivariable Functions 4: Loops 5: Text Comment Design 6: Advanced Animations 7: Designing and Using Macros 8: Custom Coordinate Transformations 9: Conditionals 10: Advanced Tables 11: 3D Graph Lighting and Shading 12: Contour Plots

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