Here's an interesting article from last month about an elementary school in L.A. that's shown stunning levels of improvement in its math test scores from using a set of textbooks from Singapore. Here is a website where you can buy them. I think it would be fantastic if this sort of thing caught on and proved successful on a large scale.
I've long thought that students were capable of better achievement if they were taught in more intelligent ways. Some number of years ago I had a co-worker who was struggling in the Algebra classes she was taking to fulfill her general education requirements at a community college. I tutored her for a few sessions and was pleasantly surprised to see that she was able to grasp the concepts quickly when we got past the memorization of techniques and instead moved into actually understanding them. She was able to perform well on her finals and is, I believe, some kind of teacher today.
Actually, I've had offhand thoughts about doing extra work as a math tutor... would any of you have any advice on how to approach this?
ALSO: Science, too. A while ago it struck me that until high school, science was taught to me in a very scattershot kind of way. Instead of one concept methodically building on another, you'd learn about concepts in isolation from each other. One week you'd be learning about the solar system and the next you'd be learning about how plants grow. Maybe some of that is necessary in the younger grades--- you need to expose children to a lot of different things in the world because it's all new to them and perhaps it's best for them to get a faint grasp of things first before moving on to more thorough explanations.* You get more breadth that way, but less depth. I think it would be good to develop a science curriculum that was at least somewhat more coherent than what we see now, but I think it probably gets short shrift these days because they don't do much (any?) standardized testing on science and, like math, a lot of teachers are probably not particularly confident in their abilities to go deep into the subject.
*Come to think of it, though, that's kind of how I do a lot of my learning these days as an adult. I'll come across a mention of filtration trenches in a document at work and spend some time on the internet learning what they are and how they work. I'll learn history by visiting a historic site and getting a snapshot of history there. I'll find out somebody owns a screen-printing shop and learn how that business works by chatting with them. Other things I'll learn in more depth by reading books on the subjects, but very rarely books specifically written as textbooks. One advantage with textbooks, I think, is that by making the reader do exercises or answer questions, the information sticks better. They do seem well-suited to learning the basic concepts one learns in K-12 school, as well as highly-structured subjects like math.