This chapter is devoted exclusively to strategies for computational estimation. It seems to me that estimation strategies are quite specific teachable algorithms. Furthermore, after an adjustment in the problem, there is always a mental computation to be done. Here I do believe that estimation comes after mental computation and invented strategies. It is also true that the same flexibility with numbers that contributes to computational fluency will also contribute to computational estimation skills.
Relating Estimation to Mental Computation
Since most, if not all, mental computation strategies begin by computing the largest part of the answer first and then adding on the smaller parts, an estimation can often be had by simply beginning a mental computation but not finishing it - not figuring out the small parts. Sometimes this is the same as using front-end approaches. However, it does not require the general estimation approach of first substituting more easily handled numbers followed by a computation done with the substitutes. One section of this chapter explores this approach explicitly and builds on ideas from the previous chapter. Of particular note is the use of cluster problems, an idea borrowed from the Investigations program and described in Chapter 13.
There are identifiable strategies or algorithms for computational estimation. The research suggests that these strategies are teachable and that instruction aids in their use. There is an added difficulty with estimation, however, and that is developing an understanding of what an estimate is; what is meant by "about.
It may be worth your time to distinguish between computational estimation, measurement estimation, and quantity estimation. Often these are confused or mixed together, even within some excellent resource books. The issue of "estimate" as distinct from an outright guess does apply to all cases.