Estimation and Using Mental Math

This area of mathematics is one that many teachers dread, and maybe even skip in their textbook.  Why? I think it is because textbooks attempt to proceduralize estimation by teaching rounding, or some other procedural method.  In order to really be able to do mental math or estimate one must have number sense and a strong working knowledge of the concept.  For example:  One may use mental math to solve the problem 3,459 + 998 by adding one thousand to 3,459 and then subtracting two.  This requires the person to know the relationship between 998 and 1,000.  If students don’t have a great enough number sense, which requires a lot of opportunity to work with this size of numbers, they only know a computational procedure.  If I were to ask you to estimate what 7 1/8 divided by 6/8, if you don’t have a strong conceptual understanding of division and fractions, you would not be able to give me a close estimate.  Most teachers can not give a close estimate themselves.  Students need to learn conceptually before they move into a procedure.  If we don’t allow this time, estimation and mental math is an unattainable.