Math Education: An Inconvenient Truth

What a b....

The cluster method was what I taught FM after school - it made so much more sense to him than any other way he had learned this stuff before, as I said in my mental math post. Obviously, as the woman says, the textbooks seem a little absurd, but really they are no more absurd than the insistence that all students use the standard algorithm (which she continues to call the most efficient, least error-prone, based on what evidence I wonder?) to the exclusion of all others. Certainly, it is often the best algorithm for multiplying five or six numbers by hand, but when will such a skill be neccessary or even useful? As far as division goes, until I started teaching I had used long division maybe once or twice in eight years. Clustering in division problems makes so much more sense.

Furthermore, the fact that this is being debated as the part of standard 4th and 5th grade math curriculum is almost as ridiculous as the fact that I am teaching in to high school freshmen. Whole number multiplication and division should be mastered by the end of third grade. Students should be able to compute fluently in decimals and fractions by the end of fifth grade, and in sixth grade should begin a two year course in algebra I. In 8th grade they should take geometry, algebra II in ninth grade, Precalc and Trig as sophomores, calc as juniors (basic single variable derivitive and integral calculus) and some elective their senior year, whether it be a serious statistics course, linear algebra, or multivariable calculus. Maybe I'm wrong - I don't know that much about how the brain develops at a young age and I am basing this mostly on my own experiences, which apparently are not the norm. Besides, to have anything like this actually work, we'd have to have middle school teachers who understand algebra and geometry and high school teachers who can explain eigenvalues and integrals in spherical coordinates. Not to mention students who want to learn.

Mental Math

Very often, I'm amazed at what my kids can't do. The fact that they can't do any sort of mental math has astonished me over and over again, as I wait on things like 30 divided by two or 46 divided by 10. Only today did I realize that even skills like these need to be taught.

I started thinking about a week ago about what I do when I divide something in my head. For example, if I wanted to divide 68 by 2, I first divide the sixty by 2, to get thirty, then divide the 8 by two, to get 4, and add to get 34. Pretty standard, I thought. But today after school, as I watched FM labor through the same problem using long division, I realized it might not be the standard thought process for my kids. So I stopped him and told him how I did it. Oh yeah, he said. That's so much easier. That does make sense. Hopefully, it is a little more intutive for him. FM has become my mental math experiment. A few days ago I caught him laboring over a multiplication problem where he had to multiply something by five. Just take half of it, I told him, and put a zero on the end. Works anytime you have to multiply by 5. That astounded him. And when I explained why, it was like a little light went off. It made sense.

Today, FM stayed after school along with DB. (DB was in my class for a few months in the fall before he got moved to pre-algebra. He is the sweetest kid in the world, and would kill to be back in my class. That's why he stays after school.) Anyway, DB was showing off his solving equations skills, while FM was solving some quadratics. FM was simplifying a square root, trying to make a factor tree for some number, and asked me what went into it. So I decided to tell them about how you can tell if three goes into a number. I told them any number they gave me, I could tell them if three went into it 5 seconds or less. They gave me some horrendous numbers, 5 and digits, and were amazed when I told them yes, three is a factor or no, three isn't a factor as soon as they had finished writing. Finally, after about five minutes of them giving me bigger and nastier numbers, I told them the trick, which had them holding their heads and laughing and generally being amazed at math. As they walked out the door, DB told me he was going to go right home and show that to his mom. FM said he was going to show it to his friends tomorrow. I need to think of some other "tricks" to have ready for them next time. I also need to decide what to do with the last month of the school year. Three weeks for seniors. Oh man.

Oreos

When I have a bad day, I have a few different coping mechanisms. One is to work in my garden. Another is to lay on the couch and read. Neither of these are very helpful. A third, more helpful mechanism, is to think about my favorite students and how wonderful they are.

HC is one of my favorite. Maybe my favorite, these days, I'm not sure. She's brilliant, but can get an attitude, and has told me more than once to shut up talking to her. Today, after a hectic day of testing, she came up to me in the hall.

"Mr. G., don't forget about those oreos."
"Right, the oreos. I'm heading back to my room now, come and I'll get them for you"

During a makeshift "game" that we were playing today, I awarded points for getting questions right as we were prepping for the test. HC, sure that she would come out tops, pressed me about what the winner would get, and finally, I cracked and said some oreos, after school.

As we walked back to my room, harried by a pair of her friends who seemed certain that their bus would leave without them, HC told me all about he new diet. She's keeping a list of all the things she eats and drinks, which she showed me, along with a list of exercises that she is going right home to do. She had tried this earlier in the year and given up after about a week, so I was excited and I hope she lasts a little longer this time. By the time we got to my room, I had forgetten why we had come. But of course, HC hadn't.
"Where them cookies at Mr. G?"
"Cookies? But isn't that counter to everything you were just telling me about?"
"Aw, it'll be alright. I ain't hardly but eat nothing all day."
"Would you rather have some gatorade instead?"
"Naw, just gimme the cookies. Well, no, gimme the gatorade."
"Alright.."
"No, I wan them cookies."
"You sure?"
"Yeah. No, I'll take that gatorade. I gotta go. Thanks Mr. G."
"I'm gonna have to start bringing fruit."
"Ok"

Infant Deaths Climb in South

NYT on symtoms of poverty in the Delta.

The Good Things

So, I can't teach 131 students in the cafeteria. Big deal. Some things are going right though. A former student, who was shunted out to pre-algebra, came to my class after school today. He never does anything in that pre-algebra class, and so he came to me for help. He smiles "I'm gonn be up in your class next year."

This leads to the theme of all the things that kids say in and about my class. "We don't do nothin up in here." "Girl, we don't never do nothin up in this classroom, he just be talkin'" "We ain't learned nothin up in here." "That man don't even teach." Today, I heard it from other kids, about every other algebra teacher. Kids are kids, and kids can complain like few other creatures on earth. I can't bother to take them very seriously.

One student's mother told me that he writes poetry, and that these people sent him a letter saying that they wanted to publish his poems. My first thought, of course, was poetry.com, who want to publish everyone's poem in a special, hardbound, coffee-table edition. Today, he brought be the poems, and the letters from, you guessed it, poetry.com. I guess I do have something in common with my students - I too submitted my early works filled with forced rhymes and the fleeting charm of feelings that seem, momentarily, eternal. The first poem that I submitted, was in fact entitled "Always." Today, as we were all preparing for the state test in what we called Academy One (unofficially: chaos in the cafeteria), he asked me if he would take me for algebra II next year. Not likely, I told him, since he was signed up for geometry, but I assured him that he could and should take both, especially if he hopes to satisfy his interest in architecture. Well then, if he does take it, could I especially request that he be in my class? Sure, I could do that.

Furthermore, in the cafeteria, my students made me proud. "I already know how to do this junk." "We been knowing how to do that." "When we learn this, back in August?" Even one of my most difficult students, and I have a few of those, called to me, across the caf, in that voice that can so often be a torment - MR. G, COME HERE. Oh no, god no. AIN'T YOU SO PROUD OF ME I DID THIS ONE ALL BY MYSELF. Yes, in fact, I am proud of you, very proud. Now do the rest.

Another happiness - the same student to whom I referred in an earlier blog, who claimed to have spent the night in the baseball dugout, showed up at the middle school to play soccer today. I throw out a casual invitation probably once every other week to any and all of my kids; I figure it would be good for all of them, and certainly better than whatever else they are doing. We threw him in goal for a while, then he came out and got his toe stomped on, but he soldiered on until the end, showing me later how purple it was.

I often forget that these kids are, well, kids. The guys, at least, often have the bodies of adults. Well, at least the seniors. The freshmen still appear as if they would fit in quite well in a middle school, but the two guys who came out today, if I saw them for the first time outside of school, I would judge to be between 20 and 22, rather than 17. One of them has two inches and at least 60 pounds on me. But they are kids, they need attention, they need to feel respected and listened to, and they need so much love. I can't do enough.

Unconscionable

Assemblyman Richard Brodsky, a Democrat, who voted against New York’s new budget, called it “an unconscionable, discriminatory addition to the school aid formula.” (nyt)

Brodsky is from Westchester county, where the median home value is in the range of $350,000 and high school graduation rates are near 99%. What is unconscionable is that in the Bronx, graduation rates hover around 50%, and more money is spent, per student, in Westchester County than in the Bronx. When children begin their academic lives three steps behind, of course the logical thing to do is to make sure that those children, slighted by the system and by a capricious fate, have all the advantages that the state can confer. As long as the graduation rate in the Westchester is 50 percentage points higher than that in the Bronx, all state aid should go do the Bronx and none should go to Westchester. The rich kids can hack it.

(Graduation rates, per pupil expenditure, and other stats taken from publicschoolreview.com)