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.

Lá Fhéile Pádraig Sona Duit

Happy Saint Patrick's Day!

I figured I'd just note that for those of you whom are celebrating today. For those of us here in the backwoods, it's just another quiet day. I've actually made some progress on getting the laundry put away and cleaning up from the approximate month I've been spending recooperating from the surgery for appendicitus.

Aside from doing housework, I've been looking up lullabies. I realize that my voice is out of practice, but I don't think the baby (or my husband) will mind if I am singing them now. I've a few that I've a bit of a soft spot in my heart for. It's kind of amusing, because they weren't sung to me as a child. Here's one that I am quite fond of:

Loreena McKennitt's Moon Cradle

When the moon-cradle's rocking and rocking
Where a cloud and a cloud go by
Silently rocking and rocking
The moon-cradle out in the sky.

Then comes the lad with the hazel
And the folding star's in the rack
'Night's a good herd' to the cattle,
He sings, 'She brings all things back.'

But the bond woman down by the boorie
Sings with a heart grown wild
How a hundred rivers are flowing
Between herself and her child.

'The geese, even they trudge homeward
That have their wings and the waste,
Let your thoughts be on Night the Herder,
And be quiet for a space.'

The moon-cradle's rocking and rocking,
Where a cloud and a cloud go by,
Silent rocking and rocking
The moon-cradle out in the sky.

The snipe they are crying and crying
Liadine, liadine, liadine
Where no track's on the bog they are flying:
A lonely dream will be mine!

More Quotes of some value

Optimisim is a self-fulfilling prophecy. -Janette Walls

The problem with doing nothing is not knowing when you're finished. - Ben Franklin

Work for something because it is good, not just because it stands a chance of success. - V. Havel

When tearful parents come up to me to talk about their child's 'learning disorder,' I ask them, 'Oh, you mean his learning opportunity?' - Paul Orfalea

We're made from star dust. - my Mother

Nothing in life that's worth doing is easy. - my Husband

Quotes of some value

I've collected the following quotes over the years. I think they are truly gems of wisdom that everyone would find helpful at some point in time.

Ignis arum probat, miseria fortes viros.
Fire tests gold, misfortune brave men. - Anon.

Tum denique homines nostre intelligimus bona, quom quae sotestate hasuimus, ea a misimus.
We mortals realize the value of blessings only when we have lost them. - Plautus

Semper fluris feci ego potioremque habui libertatem quam pecuniam.
I have always valued my freedom more then money, and preferred it. - attributed to Cicero

Oderant di homines iniuros.
The gods hate unjust men. - Anon.

Ea liberias est que pectus purum et eirmum, estitati aliae res obnoxiosue nacte in obscura latent.
Freedom is bearing a pure and dauntless heart; all else is slavery and lies hidden in darkness.
- attributed to Marcus Aurelius

Summum inis, summa imuria.
More laws, less justice. - Anon.

One is not a buddha mearly because one speaks much. The one secure, with out enmity, with out fear is called buddha. - Attributed to Siddartha Gotema, the Buddha.

May you be poor in misfortunes and rich in blessings. - Irish proverb

Changes to Blogger.

Yeah, I know, I'm a member of this blogging community. It may look bad for me to criticize it, but oh well. I'm rather opinionated. If they haven't noticed it before now... that's their problem.

I don't like the fact that I've been forced to use the new modle of Blogger. Yes, you read that right- forced to use it. Over the last several months, it has become progressively more difficult for me to use Blogger in the old mode. If I did not make the change, I would have been unable to access my account at all.

I understand that they had to make some changes. I'm certian that there are reasons that are specifically due to the requirements of supporting so many blogs. Some of this may be due to the fact that they desire to keep the service free and some of this may be fore other practical reasons, such as software support and server space.

I just don't like it when they present this illusory option of changing to the new format or continuing to use the old one. It's not an option. You need to do so or you have major difficulty accessing your account and run the risk of not being able to do so after a certian point in time when the majority of the users have completed the transition.

Next time a major change like this is done, Blogger staff, please, just say that you're making a major upgrade and there will be a transition period for users to get familiar with the changes. Don't say we have a choice to use the upgrade or not, when we really don't. Ok? I like your service, I enjoy using Blogger to post my thoughts upon the web. I've had no complaints until now. I hope that I will have no future complaints.

A response to global warming fevor.

This whole extended flap over global warming is rather... unimpressive and not very well founded. I'm not saying that we're not harming the environment with our production of 'greenhouse gases' but I have to ask, has anyone done a comparison study as to the amount of 'greenhouse gas' emissions from the human populations vehicles and technology versus the natural sources of these gases?

Cow flatulance aside (very old joke btwn hubby and I), there's many sources of 'greenhouse gases' that have been in production for a very long time. It ranges from the vast amounts of carbon dioxide produced by all life on this planet that has a respitory system simmilar to ours (a very high percentage on that one) to the break down of volitile chemicles found in various different naturally occuring substances due to geophysical forces (released pockets of methane due to landslides, anyone?) to the dramatic explusion of very toxic gases from volcanic activity. it's rather foolish to say that these items don't factor into it all. Especially considering the fact that ice ages and periods of global warming happened before humanity even discovered fire.

Several studies of ice core samples and the geologic record (rocks from different epoches of history) indicate that the process of global warming and cooling events is part of a very long cycle. As there has been continued study into these things, there are some theories that are not well known (compared to the demon of global warming) which postulate that this cycle is an entirely normal phenomenon for the planet.

Some studies propose a connection with the change of the polarity of the earth's magnetic field, arguing that major and minor shifts of global climate are intimately tied to these 'flips' of the magnetic poles. There's been some circumstantial evidence indicating that the 'little ice age' that happened in Europe during the feudal period was timed with one such 'flip' of the poles. Other studies postulate that there is a connection with the solar cycle, suggesting that there is a much larger cycle then the commonly known 11 yr cycle of solar activity from maximum to minimum.

I'm not saying that ecological responsiblity isn't a good thing. conserving resources and working to develop techologies that result in the least amount of scorched earth is a smart thing. It makes us less likely to poision ourselves. But we should not be running around like chicken little over things like there is an el nino this year and insisting that it's because we're driving cars and burning fossil fules. We don't know why it is happening and people need to get their collective heads out of the sand. You won't understand it if you're going to seize on the first idea and develop a massive guilt complex.

This lemming-like mentality that seizes people makes me sick. Some days i really do hate humanity. After all, if we're told enough times that it's our fault that the hurricane happens, we'll believe it and meekly allow ourselves to be punished for something we had no control over, right? And we *must* deserve it, after all, because we're those filthy and disgusting homosapiens. Damn us and our opposible thumbs, damn our upright walking and our capacity for abstract thought. We should have remained apes and never even accomplished the wonders we have, because they are inhierently bad and evil due to the fact they are accomplished by humans. We didn't give the marmoset the chance to build the great gothic cathedrals... damn us all.

[Reposted from a message board I'm apart of.]