Ranting about Mathematics

Ok, I'm not usually one to rant about things for no apparent reason. My bit of a rant about mathematics isn't with out much reason either, though it may seem a bit random in the light of my usual commentary on life. Sometimes I sit on a rant for a while because I feel that I really shouldn't blurt about it. I find that I feel that it is a bit trivial and foolish to rant about some things, so I don't post them here for the whole world to view.

This matter, however, is not one of those things. I have held my tounge on this matter because I couldn't fully formulate my thoughts on it until recently. My ranting about mathematics is not on the subject at large. It is actually focused on one particular point.

The school district I work at is filled with several wonderful souls who bravely endevor to help young minds learn how to do the basic skills they will need to be successful in life. Among these skills is multiplication. As a person who has a mild learning disiblity with mathematics, I found learning multiplication to be hellish. It was easier to learn fractions and algerbra then to learn basic multiplication for me. Even now, I can barely perform simple multiplication in my head for any value greater then three times five. (Which is 15, by the way.)

When I learned that there was a "new" method for teaching multiplication that was being applied in the school district, I was excited. Perhaps this method would finally help me learn how to multiply from 1 times 1 to 12 times 12 with out having to resort to 'cheating' with a calculator. Then I found myself introduced to the most assinine concept I have ever encountered in teaching mathematics. I understood why children were having a nightmarish time learning these concepts, children who have no learning disabilities at all.

First, you have memorization. For most people, memorizing things isn't too much of a problem. It helps greatly to have some kind of a pattern when you are memorizing a vast amount of material. The old method of memorizing multiplication facts by the 1x1=1, 1x2=2, etc. method has proven success because it organizes the facts into a fairly intuitive and simple pattern. Unless you're some one like myself, who has problems with memorization as part of the learning disability, you can pick it up fairly quickly. Unfortunately, there is a requirement now by the state of NY to have this method put aside. What has replaced it is this bizzare color coding of a 12x12 multiplication chart at random with bingo markers. You memorize the color groups of multiplication facts that are unrelated except for the arbitrary color they have been given.

This doesn't help you memorize. It actually makes it harder. Still, if you're one smart cookie, or incredibly lucky, the memorization thing won't be a problem for you.

Instead, you have a different problem to worry about. That is the method of multiplication that is being taught. Now, when I was taught multiplication in elementary school, I was taught that a multiplication problem is the "fast" version of addition. One factor in the multiplication problem represented the number you were adding. The other factor represented how many times you were adding that initial number to itself. This fairly simple explination gave students a visual way to see how the numbers related to each other and a simple way to check our work.

Now, the lattice method is the preferred mode of teaching multiplication. If you look at the explination of the lattice method given here, you find that it is not simple at all. It's actually very confusing and difficult to follow if you don't have the basic understanding of how the factors in a multiplication problem relate to each other. Throw in even the slightest trace of a learning disiblity and you're functionally left with hardly any hope of ever understanding how to multiply. Even students who don't have the problems understanding numbers have a very tormented time learning this method.

The form of division being taught is a bizzare cousin to the lattice method. It makes the problesm hellish to work on. As I was working with students after school one day, I had some of them ask me to help them understand their work. Considering that I was helping a student a few grades higher learn how to do algerbra, I didn't think it would be too much of a problem. Then i got to see this lattice method for multiplication and it's bastard cousin for division.

I struggled to help these kids understand it. When I couldn't even make sense of it I took a different approach. I presented the multiplication as I had been taught. The kids lit up with joy as they realized that multiplication wasn't half as scary or complicated as it seemed with the lattice method. I presented division as I had been taught and these kids mastered it in minutes. Then I had a math teacher look over and see how I was presenting the material to the kids.

Then, I got in trouble.

Apparently, NY doesn't want math taught in a fashion that actually allows the student to master it. It made me so angry I could spit nails. As I looked into it and I learned more about how mathematics is taught in the schools right now, the angrier I became. Up until recently, geometry was removed from the curriculum. Algerbra was something that was taught in a cursory fashion before throwing the kids into trigonometry a few weeks later. There are math teachers who are celebrating the fact that algerbra and geometry are coming back into fashion. There are also science, shop and other teachers of subjects that have some relation to these topics who are happy with this restoration of common sense by the higher ups of the state education department.

These are not some skill that you will never apply in your daily life. You use algerbra to figure out how much of a product you need to buy at the store when you have a fixed amount of money. You use geometry to spatially relate how the items you are putting away from the grocery store is going to fit on your shelves. You use all of these things and basic mathematics skills everyday. But, apparently, NY feels that it's not necessary to focus on these skills for mastery.

You may know enough to spit it out on a test, but that's it.

Life is not about the damn test! As educators, we're responsible for giving the students who are under our direction the tools that will enable them to proceed successfully through life. We're responsible for teaching them how to think critically, make logical decisions, and to function with the basic skill set required for success - reading, writing, and arithmatic.

Teach to mastery. If a student can't do something well enough to pass a test with the state mandated grade, if a student can do something that well, it doesn't matter. Can the student use the concepts taught to them in a manner that will get the correct result? Can the student explain why the concepts work in some basic fashion? Can they present that knowledge to another in a fashion that they can understand it?

If the student can accomplish those three things, they have mastered the subject. They may not get the state mandated grade for success, but as a student (and you as a teacher) have succeeded.

That is what matters.