> Math used to be taught with more drill style. This comment has engendered a lot of responses. Some arguing a position on personal experience and others argui

> Math used to be taught with more drill style. This comment has engendered a lot of responses. Some arguing a position on personal experience and others arguing the supposed science of learning. A different and perhaps useful way to look at this is to consider how outcomes differ between large groups of schools around the world following different strategies for teaching math. The Program for International Student Assessment does world wide testing of 15 year olds in mathematics (and other subjects as well). The evidence suggests that whatever the US is doing isn't working. The USA ranks 25th in 15 year olds' mathematical ability with overall scores far lower that many other countries. Unfortunately, I can't read Mandarine, Japanese, Korean or Estonian so most of the effective text books (based on the PISA student scores) are inscrutable to me. However, Singapore's students have always scored near the top in math (second place in the most recent tests) and their text books are in available in English. I used Singapore math books to help my daughter improve her math after her school switched to Everyday Mathematics, a typical US math program developed at the University of Chicago. It wasn't terrible, but it wasn't good. The Singapore Math books are quite small and printed in black in white. They introduce the concepts with diagrams, etc. and have a set of easy introductory exercises to make sure the students understand the concepts. The books then have harder problems using the concepts and include word problems. The focus is on learning and practicing the techniques of mathematics. In Singapore Math, there is rote learning going on; in Everyday Math there is a kind of impressionistic emphasis where alternative approaches are encouraged, unusual methods of computation are introduced, inefficient solutions are treated as just as valuable as better approaches, and calculators replace fluency with basic operations. I've read the research paper the Everyday Math web site uses to justify the principles underlying the program. It's garbage and not any sort of science of learning. It even cites Knuth's Art of Computer Programming: Searching and Sorting as justification for introducing multiple non-standard ways to perform subtraction, multiplication, and division to elementary school children. This is completely ridiculous.