Wednesday 5 September 2012

A running start in algebra

I have developed a brief introductory algebra book.  The book is intended for use by students who will be taking high school algebra, and for general readers.

Students who invest 15 hours in reading and studying my book, prior to beginning the high school algebra course, have their investment repaid many times over in terms of achieving better results in the course.

My book demonstrates the basic, practical algebra topics and techniques used most often by scientists and engineers out in the real world.  Science and engineering are the largest areas of use of algebra.

My book is entitled "Algebra Real-World".  To view the entire book, please hover the cursor over "Algebra Real-World" immediately below:

Algebra Real-World

+  Click on "Algebra Real-World" once it lights up.
+  You should immediately see the first page of the book.
+  Scroll down to see the entire book.
+  To return to this page, close the tab at the top of the screen.

Please contact me at in case of question concerning algebra generally, or concerning my book.

Summer Camp

I offer a free on-line program to take students through the book.  The program is offered to individual students or to groups of students.  When there is a group, there is additional opportunity to learn, because of the greater variety of student perspectives and questions about the book.

The program is offered in summer because most students have more time in summer.  However on request the program is offered at any time in the year.

A running start in algebra

The book is intended to provide "A running start in algebra".  Ideally, students read and study this book BEFORE beginning high school algebra, i.e., before beginning 9th grade algebra.  However, at any stage of algebra study, students benefit from reading my book.

The book does two important things for students, and for general readers:

The book shows where equations come from and what they mean.  The concept of the "equation" is introduced in a real and practical way, not as an abstract concept.  

The book demonstrates that there really is a use for algebra, and explains the importance of algebra in our technological society.

The book is covered by copyright.  Viewing the book on-line, or downloading the book, is free of charge to students for their own personal use, and to teachers and education administrators who want to evaluate the book.

It is important to read pages i, ii, and iii.  People who have already studied algebra can then skip to page 6 and continue at that point.  Some of the chapters are stand-alone.  Readers can skip to later chapters such as Chapter 12, and at another time come back to earlier chapters.

How algebra is actually used

Among people of all ages, I think most people are not aware that there is any practical use for algebra.   Many people who graduated from high school years ago think that algebra is an annoying, useless, abstract topic that they had to suffer through.  Many students currently taking algebra in high school feel the same way.

On the other hand, some people have a general idea that there are uses for algebra, but have no idea what these uses are.

As already noted, algebra is used in science and engineering.  Algebra is also used in business organization, in the work of actuaries, and in many other work and research areas. 

I am a chemical engineer and I use algebra in my daily work.  In my employment with Canadian Gas Research Institute, I developed new technology to control refuelling of motor vehicles powered by natural gas.  Specifically the technology acts to stop the refuelling process automatically when the maximum allowable vehicle fuel tank pressure has been reached.

My technology was licensed to a manufacturer.  A new company, Fillminder, was set up by the manufacturer to further develop and commercialize the technology.  The technology is currently used in an estimated one million refuelling processes daily! 

How did I develop my method?  How does it work?  I used the simplest aspects of high school algebra, combined with equations expressing relevant principles of science and engineering.  I used a critically important feature of algebra.  I call this feature "the derivation capability of algebra".  When we use the derivation capability of algebra, we can develop new equations that we did not have before.  These new equations can provide new understanding of a physical situation, and/or new technology as in my work.

I believe the derivation capability of algebra is not presented in depth in the standard high school algebra curriculum.  Therefore high school algebra students do not become aware of the real importance and use of algebra in our technological society.

What is the idea behind my book?

I believe separation of algebra from its main use out in the real world is the reason why many students do not have a constructive experience in high school algebra. 

In my book, I use high school physics as an example of the general field "science and engineering".  Then, algebra and selected principles of physics are presented together, completely integrated, in the same way that scientists and engineers use algebra in their daily work.   

The derivation capability of algebra is presented and explained throughout the book.  By presenting algebra and physics together, there are two great advantages:

+  demonstrate how algebra and science/engineering work together

+  provide a familiar real-life basis for each step in algebra.

Prior knowledge of algebra and/or physics is not required to read and benefit from my book.  My book is not in conflict with and does not duplicate material in the standard curriculum.

Going beyond my summer camp program, high schools should utilize my book in the first one to two weeks of the year, before beginning the existing standard algebra curriculum.  The time will be more than made up because students who have been through my book are able to learn more quickly and more pleasantly in the standard curriculum.

One further issue

My book devotes much more space to words, in comparison with a typical algebra book.  Anyone referring to or using my book has to do a lot of reading!  But this extensive verbal presentation and discussion is exactly what is needed to fully explain algebra and how it is used.