My district has also been struggling with this issue. We have, after much discussion and deliberation, concluded that students can be introduced to the traditional computational algorithms once they have a solid conceputal understanding of the mathematical opperations involved. We don't "test" kids on their ability to use these algoithms, but we do offer them as one strategy to solve computational problems. After all, sometimes the algorithm is the quickest way to the "answer". Personally, I feel that when students are ready for a short cut of any kind having exposure to a new way to get the answer is all most kids need to try it out themselves. If the student is really "getting it" then the short cut procedure will make semse and be usable by the student. My understanding about the philosophy of Investigations is that we need to allow students to bulid their own mathematical understandings, at their own pace. they will move along a continuum, for example, of counting out blocks. to using tally marks, to noticing that tens and ones can be added separately then combined using number strings, etc., etc. until many of these problems can be solved mentally. If accuracy and efficiency are goals of the program, then children will continually try to find quicker and more accurate methods to compute. If we try to force a method on a child whom isn't finished doing the preliminary experiential part of the learning, the method may be applied improperly some or all of the time and will therefore be neither quicker or more accurate. Just my opinion.