Have a look at this square root algorithm. It's interesting that it is posted by a reform math advocate. Many reform math programs are accused of overemphasizing estimation and rounding to the exclusion of precision and accuracy, yet in this case the typical traditional solution method involves estimation while his method involves precision. Curious.
On a related note, I just got my hands on some teacher manuals for TERC Investigations. It's an outdated elementary level book, but it still should provide for an intriguing read. I will be posting my personal assessment shortly.