New curricula are coming into vogue that in large part replace the systematic teaching of algorithms with discovery learning, in which students are asked to find their own methods of solving problems (and reinvent the wheel :-)). The new methods also deemphasize memorization of multiplication tables in favor of reliance on calculators.
These new curricula are bad for several reasons: First, the instructional methods used are very time consuming, and much less material can be covered. (How quickly could you reinvent the wheel, let alone reinvent mathematical methods that took centuries to develop in real time?) Also, if you develop your own algorithms, they may well not be as powerful and efficient as the standard ones. Indeed, the history of mathematics is full of small (and large) improvements in methods over time. One's first solution to a problem is rarely the best. As a result, students come away with less mastery of the material they study, and it takes them longer to solve new problems whose solution would be immediate if they had learned comprehensive, efficient algorithms.
Proponents of the new teaching methods (a.k.a. ``fuzzy" math) claim their students are learning higher order thinking and that they are learning on a deeper level and retain the material better, but these claims are unsubstantiated, and a lot of the new instruction appears to be a huge waste of time and effort (e.g., ``hands on" exercises in learning to count or multiply).
Mathematicians around the country decry fuzzy math, and most college math professors believe it doesn't properly prepare students for college math. There will be serious problems when these students get to college.
A number of parents, mathematicians, and educators are disturbed by these trends, to say the least. Indeed, at a time when American students have been falling behind even third-world countries (e.g., Singapore, which tends to place first) in international math and science tests, it seems sheer folly to adopt such methods. A number of groups are forming to try to strengthen our math curricula in traditional ways. One of them is NYC HOLD, which has formed around a curriculum battle in New York City. See also the Mathematically Correct web site.
Some good articles: