Tuesday, March 26, 2013

How do you add?

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A number of papers today have an Associated Press story about the recognition that the development of math skills starts early in life, before first grade. The version from the web page of station WKRG out of Mobile, Alabama,  (click here) says "Scientists say that what children know about numbers as they begin first grade seems to play a big role in how well they do everyday calculations later on."

They just figured that out? How many billions of dollars have spent deducing that fact?

Counting my own days as a student I have spent 50 years in classrooms, and it hit me in the head early on that those who started strong tended to finish strong, and those who started weak tended to finish weak. There were crossovers, strong starters who weakened and weak starters who got stronger, but they were exceptions. The weak starters becoming strong finishers were the rarest. I am not speaking only about mathematics, either.

As long as they are addressing reasons for poor student performance in mathematics, perhaps they should look at some other oddities in the learning and teaching of the subject.

The biggest oddity is the standard method for adding multi-digit numbers using paper and pencil. We read left-to-right, we write left-to-right, yet most people learn to add (and subtract and multiply) right-to-left. Operating the natural way, left-to-right, is even considered by some of those "in the know" as a TRICK!  For an example, check out this site: http://mathtricks.org/addition-tricks/addition-tricks-addition-from-left-to-right/.

The web site FoxyMath even says "Right to Left is so important when solving column addition equations that FoxyMath gives it its own page." (original page here). Right-to-left is so embedded in our culture, and so awkward for many, that it becomes one of the big stumbling blocks in math education, as well as an cause of the early demand for calculators. (Note: on most calculators, we enter numbers left-to-right). Right-to-left arithmetic is one of our major cultural flaws, not as big as the Roman Empire and its number system, but big enough.

Now there is a socio-political reason for operating left-to-right. That has to do with the tendency, when performing a calculation with many steps, to start out correctly before any errors creep in. With left-to-right arithmetic, the portion of an answer most likely correct is to the left, the part of a number that is more meaningful in general. If you question that, go to http://www.brillig.com/debt_clock/ and tell me what is more significant: the digits after the dollar sign or the digits after the decimal point.

Worth noting is that the skill (art?) of estimating is geared around the leftmost digits in any number. To be a good estimator you must have some basic knowledge that the left hand portion of a number is the more important portion.

Our country has become so addicted to right-to-left arithmetic that other methods are largely ignored, if not treated with suspicion. To get a taste of some options, check out this page, from Rockwood School District, in Eureka, Mo. It only shows one example of each method, but it might be eye opening.

This country spends hours and weeks and months and years teaching youngsters how to do arithmetic operating from right to left. Just about the time we have them totally befuddled and a far ways down the path of math phobia, we introduce division, operating from, drum roll here, LEFT TO RIGHT! Paper-and-pencil long division then becomes the least-learned, and perhaps least-taught, of all the basic operations.

Back to the beginning, today's news story. What are the chances that a parent with a weak base in basic arithmetic will be a positive role model for his/her child in this regard?  Won't the behavior the child picks up on have more to do with picking up a calculator, or, worse yet, ignoring arithmetic completely?

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