The Story and the Hope of this book
It was in my 10th grade Geometry class in 1973 where I gained a life long love and passion of mathematics. One day the teacher told us that he would prove to us, that the angles of all triangles add up to 180 deg. I immediately wondered how he could possibly prove this for all triangles since there was an infinite variety of them. He did prove it and I was satisfied the proof was true. I was impressed that such a thing could be done. After this I saw many other interesting proofs. As a class we were given 3 to 4 proofs every night as home work. We all (those in my Geometry class) became very capable mathematical problem solvers, and I for one was inspired with a love of mathematics and the power and problem solving ability that studying mathematics imparts to people.
Four years ago, my oldest son was taking Geometry. I wanted the same experience for him that I had had. Unfortunately I learned that in the years since I taken mathematics in Junior High and High School, math education had become dumbed down. My son was 3 months into his Geometry class and still hadn't done any proofs. In looking at his book I couldn't find any. All I could find were questions on about Geometry facts and very easy problems. Gone for the most part were proofs and any medium or hard problems. I contacted the teacher and it was explained to me that Geometry education had changed since the days I had gone to school. Proofs had been de-emphasized, but not to worry, there would be a two week section where they would do proofs.
I was very disappointed. The next school year, I told my son not to take math from the school, that I would teach him his geometry, from the book I used when I took Geometry, "Geometry by Moise and Downs". I complained to the School District Math supervisor, who told me she had heard this complaint before from others, she then asked me if I would be willing to serve on the Geometry text book selection committee. I told her I would be more than happy to. I immediately began to search the internet for a good geometry book (that was still in print). For quite some time I couldn't find one. Geometry education, nation wide had become severely dumbed down.
I contacted the publisher of my old Geometry book to see if Davis County Utah could secure the rights for its use. In the process of trying to do this, the publisher told the Davis county math supervisor, what I was trying to do and she had withdrew my invitation to serve on the committee. I wasvery disappointed and pleaded to be able to serve, but she was firm.
I had given up hope, thinking all I would be able to do would be to ensure that this dumbing down of Geometry education would not affect my own kids.This to me was not enough, If others had only been concerned about their own kids when I was young, I would not have had the opportunity to get thequality education I was fortunate to get.
I found that all areas of math education not just Geometry had been watered down, however Geometry was the most severely impacted. Many elementary schools had given up teaching students to add, subtract, multiply or divide - fractions or decimals, preferring to use a calculator instead.In Algebra, at least in the school my kids were attending, word problems weren't being taught anymore, and something called the foil method, was being taught to teach kids to multiply monomials i.e. (x+5)(x-1), this is a dumb little method that had taken the place of the distributive law. The problemswith the FOIL method is it is simply a memorized procedure that imparts nonumber sense and it only works for this case, it will not work for somethinglike (a+b+c)(d+e).
I also found in that in many modern trigonometry books, many proofs are being put in the an appendix where the chance of them being looked at is nil. When I took math, seldom did we ever make use of any mathematical procedure or theorem without first proving it. This gave us the ability to see for ourselvesthat it was true, why it is true and helped to teach us how to do proofs on our own. To teach math, without teaching the proofs provides a shallow math education. I am an Electrical engineer, in my vanpool there is an other engineer who sometimes substitute teaches math. He told me that when he went to substitute teach Calculus at one of our local high schools, he was told by the lead math teacher to teach the students to use the chain rule, but not tobother teaching the proof. He got the impression, they wanted to teach to the test to make the school look good, and proofs were not going to be on the AP calculus test. He very much disagreed with this approach and taught gave the students the proof anyway, then went on to teach them how to use the chain rule. He said that he was never invited back to teach there.
When my oldest son was taking physics, I noticed he was using a 3x5 card with the formulas on it, when doing his home work. When I asked him why he was using this, he said the teacher let them. I asked him if the physics teacher had ever proven any of these formulas to the students or had the students prove any of these formulas for themselves. He told me no. When back to school night came. I asked the physics teacher why he was just handing the students formulas without proving them or giving the students the opportunity to prove them. He looked at me and said he agreed that he should be doing this and told me he used to do this, however students and parents complained that he was making the class to hard so he backed off. He explained to me that students today are not as mathematically well prepared as we were when we were going to high school.
Let me say, it wasn't necessary for me or others when I took physics in high school to have a 3x5 card to put the formulas onto, this because the teacher either showed us the proofs or had us prove these formulas for ourselves, and once you prove a formula it becomes yours. If you do forget it you can quickly re-derive it, and then you have it again. Proving a formula helps provide an in-depth understanding of physics, merely handing the kids the formulas means they don't learn why the formulas are true, and they don't learn how to come up with formulas for themselves. The way physicsis taught now, provides only a shallow superficial understanding.Unfortunately this is necessary because the math education community isn’tdoing their job properly.
I could give more examples, but won't here. In short the math education community in the Unites States has dropped the ball, they have lost theirway.
Why did I write this book and others? Writing these books are a result of me tutoring my own kids. I found while tutoring them that I was coming up with some high quality and very interesting math problems on my own, as well asfinding great problems from old out of print math books on Google books, I also found some very good problems on various websites on the internet. At first, as I was teaching my oldest, I would dispose of my lesson materials after each lesson. I have 6 kids. It occurred to me that I might not be able to again come up with these great lessons next time when I teach my youngerkids, so I decided to keep a written record of each lesson. That’s how thesebooks got started. After a short time, keeping records of my lessons took on a life of their own. In teaching my oldest trigonometry (my first book), I had practically written a trigonometry book, when I saw what I had almost done, I then decided to actually do it. After that, I taught my oldest analytic geometry and wrote a book on this also. After that I began this book on coordinate geometry. I have also begun a book on classical geometry. (necessary because the Great Geometry book by Moise and Downs is no longer in print and even though it is a very good book, I can see many areas of possible improvement).
Of all the books, this book on coordinate geometry is the best compared towhat is out there already. It wouldn't surprise me if this is the worlds best coordinate geometry book.
To help combat this decline in mathematics education, I decided to make all these books available to everyone, and that has been a major motivation in my putting even more effort into all these books than I would have done otherwise. I hope I can make a difference and help to turn back this tide of mathematics education mediocrity.
If the United States is going to continue to be a world leader in science and technology, we have to give our young people a quality math education where they can be inspired by the beauty and the power of mathematics, they need tobe given many opportunities to solve challenging problems if they are to ever become able and adept mathematical problem solvers. If we don't turn this around, our decline is inevitable and will manifest itself in the form of fewer scientific innovations, more failed and lackluster engineering projects. More than this, mathematics if taught properly opens up the mind to possibilities and understandings that are too valuable to just be set aside. We can turn this around, but for this to happen many math education professionals will need to stop denying that a problem even exists.