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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.  Of course, they make me proud.  Yet, my goal 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. ... read more

Dazzling pocket PCs are aplenty for the children of today. Kids roll into the classroom with iPhones, Blackberries, and various Android devices capable of supporting myriad complex applications. We are living in a wonderful age where handheld computers help us tremendously and continuously. Alongside all of the fancy apps (that allow us to manage everything from our finances to our fantasy football teams) is a standard utility application that accompanies every smartphone: the basic calculator. Need to carry out some quick arithmetic to figure out how much money you owe your buddy? Pull out your phone and type away. It’s that simple. So why the heck do kids need to memorize the multiplication table? Because it is still crucial to a successful math career and a promising life thereafter. Don’t believe me? Here are four reasons why mental math is still tremendously important and absolutely foundational. 1. Confidence Is Key You have likely heard people utter... read more

In elementary school, mathematics is often taught as a set of rules for counting and computation. Students learn that there is only one right answer and that the teacher knows it. There is no room for judgment or making assumptions. Students are taught that Arithmetic is the way it is because it's the truth, plain and simple. Often students go on to become trapped in this view of the universe. As fairy tales fade from the imagination, so is mathematical creativity lost. There is evidence that Mathematics and Arithmetic existed over 3000 years ago, but only the very well educated leisure class had access to it. The rules for simple computation only were developed recently, so much of the computation of sums and products was much more complicated. Imagine adding and multiplying Roman Numerals for example. Because of this difficulty, computations were laid out only to solve very specific practical problems. Although mathematics was mainly limited to solving... read more

When working with fractions, I find it effective to require students to convert each fraction that we work with to its decimal equivalent, to convert that decimal equivalent back into the original fraction, to convert that decimal into its percentage equivalent, to work a simple percentage problem using that percentage and finally to work the same problem using the initial fraction.   This comprehensive method helps students to see the relationships between fractions, decimals and percentages in a holistic way and to promote the necessary skills in each element.  

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