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## Thursday, June 27, 2013

### Long Division as a Symptom

Laurie H. Rodgers, in an article entitled "In defense of long division: Pro-reform professor capably shows why reform math doesn't work" has given a strong defense of long division, and has done so while helping to show that the math reforms (coalescing nationwide the in Common Core State Standards) are not necessarily for the better. (Her article can be found here.)

Speaking of long division, I will add to Ms. Rodgers' argument by using a quote from her article: "Many don’t even know their basic multiplication facts.."

Long division, when it is taught, is generally the last of the four basic operations. As an algorithm, its use and fluidity depends greatly on the user's knowledge of basic multiplication facts. It also relies heavily on subtraction. We all know that multiplication and subtraction are largely taught in their relation to addition. Thus virtually all one's basic number knowledge comes into play in constructing long division. Weaknesses in addition, subtraction, and multiplication will all help in crashing the edifice known as long division.

When confronting long division, anyone with weak mental arithmetic skills in the other operations will generally "mess up."

As a high school teacher I made a point when analyzing a student's work of trying to detect the specific error(s) that caused students' solutions to be in error. I wish I had kept good solid data, because the fact was that the vast majority of errors (my sense is 80% or more) were caused by faulty addition, subtraction, and or multiplication. (Leaving out the errors based solely on conceptual weakness). And this was in the calculator age in the New York Regents program.

Speaking of calculators, I found students "dial wrong numbers", get erroneous calculation results, and have no clue that they were off. Even adding 23 and 2, for example, a student might hit the multiplication button, and then write down 23 + 2= 46, and let it stand.

Needless to say, I hold the position that our educational systems are having students race through arithmetic so we can get them to "higher thinking skills" where all the alleged importance is. I believe this if more time, energy, effort, and resources were spent teaching children all about numbers, the higher order items along with a love of math would follow in due course.

I suspect the English Language standards are missing the mark as well, since I have searched through them and I have not yet found a reference to "spelling".  The first grade has a standard that says "Write opinion pieces in which they introduce the topic or name the book they are writing about, state an opinion, supply a reason for the opinion, and provide some sense of closure."  In essence, first graders will be writing book reviews. Without being able to spell?