Here is a good video criticizing some modern methods: Math Education: An Inconvenient Truth. And here is a good follow-up: Re: Math Education: An Inconvenient Truth. A fifth grader, Madeline, weighs in: Math with Madeline. I agree. Students need to learn the traditional basic algorithms. Other methods might be used to stress or build a concept, but should not supplant the basic algorithms, which teach students an efficient way to solve many math problems.