In a nutshell, I realize that Saxon math works for some children. However, it is not the way I would teach math.

Saxon math presents a concept in a lesson, then has a few exercises about it, and the rest of the lesson is review of previous concepts.

The NEXT lesson usually is not on the same topic as the previous lesson. It jumps around in topics tremendously. One lesson on geometry, next on fractions, next on addition, next on large numbers. It's unbelievably disjointed. It's not the concept presentation nor the exercises in Saxon math -- it is the way the lessons jump around that I dislike.

How can kids get a coherent view of mathematics studying that way?

Read how professor Hung-Hsi Wu has worded it (emphases and the additional note are mine):

"But I think that what perhaps disturbs me the most about Saxon is to read through it, I myself do not get the feeling that I am reading something that when that the children use it they would even have a remotely correct impression of what mathematics is about. It is extremely{Maria's note: this means teaching procedures such as the correct motions of the long division algorithm, or what to do to find the lowest common denominator, etc.}.good at promoting procedural accuracyAnd what David says about building everything up in small increments, that's correct, but the great pedagogy is devoted, is used, to serve only one purpose, which is to make sure that the procedures get memorized, get used correctly. And you would get the feeling that-I think of it as a logical analogy-you can see the skeleton presented with quite a bit of clarity, but you never see any methods, your never see any flesh, nothing-no connective tissue, you only see the bare stuff.

A little bit of this is okay, but when you read through a whole volume of it really I am very, very, uneasy. There are lots of things in it that I admire, but something that is so one-sided-you think once more about yourself and you think about what happens if this thing gets adopted. There might be lots and lots of children using it. And suppose that hundreds of thousands of students are using this book and they go through four years of it. Would you be willing to face the end result? That here arehundreds of thousands of students thinking that mathematics is basically a collection of techniques.

That impression by the way is very easy and is almost obtained-you get it by looking at the topics.There is no rhyme or reason about the sequencing of the topics.For example, thethings are really broken up. The report gives the examples. One of the grade levels, grade four or grade five, has exactlytwo sections on probability(that's right two sections). They belong together and without a doubt there is no increase in sophistication or techniques, and yet I think they areseparated by 200 pages. When I do this I want to emphasize that I do not single out one or two examples. I am trying to describe through one or two examples the overall the overriding impression that I have. And when that happens, you get the feel that if my students use this, how could they not get the idea that mathematics is just a collection of techniques? If that is the case, what happens to them when they go on to middle school, and then to high school, and after that, God forbid, you might be facing them in your freshman calculus classes. And that is a frightening thought!

References: http://www.arthurhu.com/2003/11/antisax.txt

http://www.pdkintl.org/kappan/k0111jac.htm

See also reviews of Saxon math left at HomeschoolMath.net. Some people DO like Saxon exactly because of the constant review, but several people also explain their frustration with it. Some math teachers have commented on that page about the total lack of organization of topics.