Best Ways to Use Algebra Course Material

"The essence of mathematics is not to make simple things complicated, but to make complicated things simple." -- S. Gudder

Our Online Algebra Course

Our web site algebra course is actually two self-contained courses. The first is Algebra By Example (text and study guide). The second (The Game of Algebra) course consists of animated Powerpoint and video presentations. Because different students will likely use different textbooks, the algebra videos are not linked to any one textbook but do match the slide show presentations. There is a suggested mapping from video to text sections

(1) Algebra By Example

The format of the text is very similar to the format of our “Gateways to Mathematics” arithmetic text. Each chapter begins with one or two introductory expository paragraphs followed by an Illustrative Example that applies the exposition to solving a specific problem followed by a solution with commentary. At the end of each section in the chapter there are exercises and at the end of each chapter there is a more extensive set of exercises. The solution manual contains the solution plus additional commentary for many of the exercises.

TOC

Short Table of Contents - Algebra By Example

Unit 1

Lesson 1 - Using Arithmetic

Lesson 2 - An Introduction to Algebraic Equations

Lesson 3 - Signed Numbers

Unit 2

Lesson 4 - The Structure of Arithmetic

Lesson 5 - An Introduction to Linearity

Lesson 6 - An Introduction to Word Problems

Unit 3

Lesson 7 - An Introduction to Graphs of Linear Equations

Lesson 8 - Simultaneous Linear Equations

Lesson 9 - An Introduction to Inequalities

Unit 4

Lesson 10 - Integral Exponents

Lesson 11 - Introduction to Polynomials

Lesson 12 - Division of Polynomials

Unit 5

Lesson 13 - An Introduction to Quadratic Equations

Lesson 14 - The General Solution of a Quadratic Equation

Lesson 15 - Algebraic Fractions

Appendix

Arithmetic Review

Arithmetic Glossary

Squares and Square Roots

Metric Conversions

Index

(2 “The Game of Algebra” (Our PowerPoint presentations)

The course is divided into 24 lessons and each lesson is accompanied by four PowerPoint presentations. (link).

TOC to be added.

You are now ready to begin your study of algebra -- Good luck!!

Our Online Algebra Course - Part 1

Our web site algebra course is actually two self-contained courses that are linked together by our algebra video lectures. Development of Herb's Classic “Algebra
by Example” program began in 1978 when D.C. Heath and Company published Herb's “Algebra by Example” work . The program consisted of a textbook, a student solution manual and an instructors guide. Both the textbook and the solution manual are posted on the web site. Herb also produced algebra video tapes similar to his earlier arithmetic videos, to provide help to any student who was having problems understanding basic algebra. Because different students would likely be using different textbooks, it was important that the algebra videos were not linked to any one textbook. So, although the videos did not exactly match the presentation in

his “Algebra by Example” textbook, they can be used as a supplement to the text by using the title of the video lectures to match the videos to the appropriate text material. There is a suggested mapping from video to text sections below and a link to the page on which the videos are provided.

How to Use Our “Algebra by Example” Program

If you elect to study our algebra course by using the "Algebra by Example” text and study guide, you should begin by reading the textbook. The format of the text is very similar to the format of our “Gateways to Mathematics” arithmetic text.

Each chapter begins with one or two introductory expository paragraphs followed by an Illustrative Example that applies the exposition to solving a specific problem.

Because mathematics is not a “spectator sport”, we suggest that you should try to do each such example on your own prior to reading our solution and commentary.

However, whether or not you follow our suggestion, you should then read our solution and commentary on the solution.

The text has a two-column format where the second column contains various types of information that might have been a distraction had the information been incorporated directly into the text.

At the end of each section in the chapter there are exercises for you to do in order to ensure that you have internalized the information in the section.

At the end of each chapter there is a more extensive set of exercises for you to try. The solution manual contains the solution plus additional commentary for many of the exercises.¹ Up to this point, what you will have done is the same thing you would have done if you had been using “Algebra by Example” as the textbook for any self-study or traditional classroom course.
What distinguishes our present course different is that the videotaped lectures that were made in 1992-93 have been added in the hope of our improving your chances for success in this course.

Unfortunately, the videos are not aligned with the textbook, As a result, whenever you feel the need for additional reinforcement, look at the titles of the video presentations and view the videos that seem to be connected with the chapter or section you are studying in the text. A suggested mapping is below along with a link to the page that contains all the video presentations.

Our Online Algebra Course - Part 2

In 2004 Herb was doing an intensive sixteen-lesson math workshop for elementary and middle school teachers in New Bedford, MA. One of the participants in
the work shop was Richard (Rick) Medeiros who had been a middle school teacher for more than 30 years. Some of the supplementary material that Rick used when he taught math to his students were PowerPoint presentations (some of them are posted on this website). Herb was extremely impressed by how much more effective animated PowerPoint presentations are when compared with the static and rather rigid format of traditional textbook presentations. As a result, Herb

invited Rick to help him by converting the written modules that he was using in the workshops into animated PowerPoint presentations. Rick was very
receptive to this idea and thus was born the present PowerPoint version of what we call “The Game of Algebra”.

Then in 2009 Judith (Judy) Bender became aware of the work Rick and Herb were doing and she immediately saw the importance of what they were trying to accomplish. In fact, she was so enthusiastic that she began to develop this website to make our material easily accessible and enabling any viewer to benefit from our approach to algebra. Thus was born the second version of the algebra course that is presented on the present website - The PowerPoint Program.

How to Use Our PowerPoint Program

If you elect to study our algebra course by using the PowerPoint slide show presentations, you will notice that the course is divided into 24 lessons and each lesson is accompanied by four PowerPoint presentations. Your should proceed in the following way:

Start by looking at the “Preface” video which explains our philosophy in greater detail. Then, starting with Lesson 1, proceed through the course lesson-by-lesson in the following order:

Watch the power point slide show presentation of the lesson's content. Simply left-click anywhere on the screen whenever the word “next” appears.² Note: Text appears word-by-word. This format was chosen to help ensure that you don't scan too quickly. Very often even one word in a mathematical explanation can have a great affect on the meaning.¹ When you come to an Illustrative Example of Problem in the presentation, we suggest that you pause and try to do the example before continuing to watch the presentation.

After watching the slide show presentation view the slide show entitled “Key Stone”. It presents one or more exercises designed to help you internalize the lesson's content. Again we suggest that you try to do the exercise on your own before viewing our solution and other comments. Even if you do get the correct answer(s), we suggest that you view our solution and comments because they often shed additional light on the discussion of the content.

When you think you have internalized the content that was presented in the lesson, go the slide show entitled “Problems”. You will be given a number of problems (usually, five) to solve. The problems go a step beyond what was specifically discussed in the lesson's content and are designed to test whether you can apply what you have studied to problems that you have not seen previously. Our feeling is that this is the only reliable way to ensure that you have internalized the content of the lesson.

• When you have finished doing the problems, even if you did all of the problems correctly, you should view the solutions (as well as additional commentary) in the “Solutions” slide show. Note: In a way, the “Solutions” slide show may be viewed as a self-contained “mini-course” for anyone who has studied the content previously and simply wants to check whether their material has been retained.

As additional reinforcement for internalizing the content, you may also choose to view the videotaped version of the content. However, it is our hope that the slide show format is sufficiently self-contained; at least to the extent that no supplementary material is needed.

Integrating the Two Parts of Our Presentation

Until now we have presented each of our two approaches to learning algebra as being self-contained. However, it you wish, you can easily integrate them. For
example:

If you are using our ”Algebra by Example” program, you can obtain additional practice doing problems by doing the exercises in the “Problems” slide show and checking your answers. You can obtain possible other valuable pieces of information by viewing the “Solutions” slide show.

You may find that the animated slide shows are a more user-friendly vehicle for internalizing content than the static presentation in the textbook and solution manual.

If you are using our Game of Algebra” slide show presentations, you may view the “Algebra by Example” textbook and Solutions Manual as being supplementary reading and reference material. You are now ready to begin your study of algebra -- Good luck!!

Click here for Classic Algebra Course

Click here for Algebra Slide Shows

Click here for all videos to supplement Gateway to Algebra