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Summary:  Mental math teaches students to see short, efficient solutions—rather than to blindly follow the brute-force, cookie-cutter, one-size-fit-all, show-all-your-work procedures taught at school.   To my youngest students, I lie—by omission—that vertical arithmetic does not exist.  I can usually get away with it for about a year. Until the school shows them the light.  Say, how to add 25 and 8 vertically, with the carry-over 1 carefully written on top of the 2.  By that time, my students are proficient in mental addition and subtraction of 3-digit numbers: carrying, borrowing, and all.  My goal though is by no means to turn them into human calculators.  So then, why bother? Vertical arithmetic is a convenient method for computing numerical answers.  Especially when the numbers to manipulate are multidigit.  But it is a procedure, requiring—once learned—little thought.  The entire process is delegated to the... read more