Textbooks

[fantasmaloco]

Hi,

 

I'm new and I'm wondering if anybody here is familiar with the Saxon mathematics curriculum, which I am currently using on a self-education endeavor that I have embarked on five years too late.

 

If you are familiar with the Saxon math series, do you agree with its pedagogy? And if so, why? And if not, why?

 

I am mastering John Saxon's first three books with great success, and will soon begin his Calculus text, but I fear that I am not truly absorbing the beauty of mathematics -- you know, the one mathematicians and physicists wax lyrical about.

 

The excessive repetition and tedious multiplication and division problems he throws at the student give the impression that mathematics is a dry subject that can only be mastered through mindless rote.

 

So I guess my question is, should I stick with Saxon, or should I seek a different Calculus text, one that not only gaurantees high marks on test scores (such as college placement exams [something I must confess Saxon delivers on), but also makes mathematics an awe-inspiring endeavor? ...Are there any such books out there?

 

Edgar

[Bignose]

Edgar,

 

While I am completely unfamiliar with anything by Saxon, I would like to just say a few words about repetition. In a lot of things, knowing how to do something and owning how to do something are very different. Case in point from my own life, I know how Albert Pujols hits a baseball, but I cannot copy it, time after time. Once in a while I can hit a baseball hard and far, but nowhere like Pujols can. I know how Tiger Woods hits a golf ball long and hard -- I know what actions he makes in what order he makes, and while I have hit a golf ball a far way once in a while, again, nowhere nearly as consistently as Woods can.

 

Now, I cannot deny that each of them have a significant amount of natural born talent -- but, a primary reason I am nowhere near either of them is also lack of practice. Through practice, you don't just know how to do something -- you own how to do it.

 

Maybe a few more examples are in place. I have taken apart and put back together a carburetor -- but I still take my car to a mechanic when it breaks down. I know I could do a lot of the things needed to fix it, given the correct tools and parts, but the mechanic can do it in probably a tenth of the time, because he is an expert. I know I can cut down a tree, but I still called a tree service to cut down four silver maples in my yard -- because they can do it probably one hundredth the time I can, and they are insured -- if they drop it on my roof, they'll have to pay to get it fixed. If I did it, it's on me. Again, they are experts.

 

It is very similar in mathematics. To become really good at it, to really own mathematics, you need to practice. Sure, you knew how to multiply the very first time you were taught how to do it. But the practice resulted in you owning it. You'd be surprised how many people who are in pretty advanced programs do not own mathematics. As an example, in a senior level engineering class I was TA'ing, several people who were working together on a homework assignment at one point has to multiply a three digit number and a two digit number -- and gave me answers with six digits in it. This was 10 or 15 people who all took the answer of the person who punched it into thier calculator at face value. Not a single one said/thought "hey! a number in the 100s times a number in 10s cannot multiply together to get a number in the hundred thousands -- we better check that again" They didn't own their mathematical knowledge. Being seniors in an engineering program, I don't have any doubt that they know how to multiply, but they didn't have an internal check to think about what their answer was and think to re-check the computed answer. Quite literally an example of garbage in, garbage out.

 

Another example from a junior level fluid mechanics class I TA'ed a different semester. The students where asked to calculate how large of a pump would be needed to pump water from a reservoir to the top of a water tower. Several of them came up with answers that were negative -- in other words, they told me in their homework that they would get energy OUT of a system by pumping water to the top of a tower (whose elevation was well above the reservoir's). Again, they just "plugged 'n' chugged" in that they just threw what they thought we the right numbers into the calculator and got an answer and said "done!" They didn't stop to think about what their answer actually said and meant.

 

This is NOT the goal of any education program. Not to put too fine of a point on it, but anyone can read about how to do something and have at least some knowledge of that topic. But, not many people own a topic, and have a strong intuition about it. The repetition ensures that you own it and have a very strong intuition about the subject. In general, I don't think that enough students do anywhere near enough repetition of mathematics problems. There is way too much reliance on computers and calculators. Again, like above, garbage in equals garbage out.

 

And, when you get to calculus, it's going to be the same way. Perhaps in calculus, the repetition may be even more crucial. You will have to develop a good intuition on how derivative and integrals are done, and that can only be accomplished by repetition unless you are some kind of savant. When I TA'ed those classes, again, the students were supposed to have had 3 semesters of calculus and one semester of differential equations, yet I had to review some of the most basic concepts. Edgar, you won't know it yet, but anyone else who read this through will understand how dumbfounded I was was I had to review what the derivative of [math]e^{2x}[/math] was. Or that I had to review separable differential equations. Again, these were seniors and juniors in an engineering program. They had not had anywhere near enough repetitions because otherwise they would have owned these fairly simple problems.

 

So, I hope that you won't turn away from the program simply because of the repetition. It is really the only way you will own the concepts in the program. You said it yourself that it delivers in terms of the tests. That's in no small way because you own the concepts by the time test time comes and a test is no big deal anymore. Once you own a concept, being tested on it is no longer the stressful event most people take tests as. If you don't understand what is being taught, then seek out other sources. There are many, many calculus texts out there. But, again, I sincerely hope that you won't give up on it just because of the repetition. If it way easy, everyone would do it.

[fantasmaloco]

I suppose you're right... Saxon Calculus it is...