I’m not stupid. I know I am fairly intelligent, because as a young student, they give you tests in school, and I scored in the very highest percentiles on those tests. I was “gifted.” They put me in gifted classes, called TAG. I think I went for an hour a day, five days a week, from fourth grade through seventh grade. The rest of the time, I was in regular classes, with regular kids. We all learned the same stuff. Most of it came easily to me. Until we got to fifth grade math.
In fifth grade math, I spent a lot of time doing exercises, over and over, with no apparent reason for doing any of them. I wasn’t figuring anything out. I was just given a formula or an example of some sort, and then I was supposed to learn how to plug things in to make the “problem” and the answer look the way the teacher wanted it to look so that she could mark it correct. Except that there really was no problem; I wasn’t expected to figure out how to do anything. I was just expected to learn how to solve a problem that they were already telling me how to solve. So, i remember spending every spare moment I could find at school reading books.
I probably didn’t explain this very well. You are probably thinking, aren’t those math problems you were doing? What I’m saying probably doesn’t make much sense to you. It will if you read the article I read this morning, which explains it pretty damn well. I felt like i was reading an article written about me. I actually almost cried a couple of times while reading it.
The article was given to me by a friend. She and I both have kids in first grade. Kids who are, to be honest, kind of bored with the school curriculum in general. Take the following example. For homework, my son was supposed to use his weekly spelling words to create five sentences. Each sentence had to have a spelling word in it. (He has not received a spelling word yet that he couldn’t spell. He does not have to study his spelling words. He already knows all of them. They also get “robust vocabulary” words which are supposed to be difficult, and he has also been able to spell every one of those. He has not had a challenging spelling word yet, and he is receiving the “advanced” homework packet.)
Rollie can read the instructions for his homework on his own, meaning i don’t sit with him and do his homework with him, but rather tell him to do his homework, he does it, then I check it and discuss anything amiss. (Which is usually a problem of a) legibility or b) not reading the instructions closely and missing a step in them. I attribute both of these to rushing through the work, because he finds nothing particularly challenging to slow him down.)
So, on this particular day, he produces the following:
This was a crappy scan job, and I am too impatient to fix it, but it basically is as follows:
? ? ? ? Rollie
Who is she?
Is he nice?
Isn’t school supposed
to be fun?
Why do we have to do
homework?
Why is it not fun
at school?
Below that, it reads,
Look back here, mom. ————>
Outside on Scooter.
Do i think my kid doesn’t read instructions well? Well, i think he read it. I think he just thought it was fucking stupid, and so he did something different. I think he was trying to tell me that he thinks it’s stupid. I think he would rather be outside riding his scooter.
I also think he needs to work on his penmanship.
And then there’s the math. School started up in early August. It is almost October. They are still doing simple addition with single digits. One of his homework sheets is a page of five columns of addition exercises. Each column has 25 very simple addition problems. It is supposed to be completed as a drill. Meaning that the kid is supposed to do the column as fast as he can, see how many he gets correct and how quickly. (There is a total for x/25 at the bottom, and for the minutes and seconds it takes to complete.) They do it five times, once for each column. I time him, he rushes through, he misses none of them, he tries to beat his time.
What is he learning? As far as I can tell, not a damn thing.
He learns nothing new. No creative juices flow. He doesn’t have to struggle for anything. No light bulb goes off in his head when he figures something out.
Do you like Math? I never did. I hated Math. Turns out maybe no one ever taught me anything about Mathematics. Turns out I just learned some sad shell of math, and that all along, I detected the senselessness in it all, and I checked out. That “smart kid” (according to their tests) that I was should have been able to do this stuff easily. But I didn’t do it, because I had no motivation to do it.
I ended up in remedial Math in 9th grade. Remedial Math. And I truly believe that it was because I was bored, uninspired, and totally saw through the curriculum to the pointlessness of learning that way. There was no learning going on.
Do I seem stupid to you? I’m not stupid. But I was failed, in a way, by the very same state that I am entrusting to educate my kids.
I don’t want my kids to check out. I want them to get excited about learning. Is that too much to ask? I hope not. Because I am going to fucking ask it, and I am going to ask it a lot.
Here is a page with an introduction to the article, A Mathematician’s Lament, and a little information about the author of the article, a Mathematician and teacher, named Paul Lockhart. It is long (a 25 page PDF), and I think that if you have a kid and you don’t take the hour to read it, you are doing your kid a serious disservice, if only in refusing to take a fresh look at the way we teach math in our country. Please read it. Please.
I included a few quotations from the article below. . .
Sadly . . . if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education. Everyone knows that something is wrong. The politicians say, “we need higher standards.†The schools say, “we need more money and equipment.†Educators say one thing, and teachers say another. They are all wrong. The only people who understand what is going on are the ones most often blamed and least often heard: the students. They say, “math class is stupid and boring,†and they are right.
And when I read that, I thought of the boredom and frustration that ten-year-old Anne felt sitting at a desk in elementary school. And I got weepy.
And this, echoing the senselessness of what i was learning. I remember thinking, but why am i doing with this?
By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth†but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you deny them mathematics itself.
And these interesting dialogues are interspersed through the article. They are too lengthy to put them all here.
SIMPLICIO: Are you really trying to claim that mathematics offers no useful or
practical applications to society?
SALVIATI: Of course not. I’m merely suggesting that just because something
happens to have practical consequences, doesn’t mean that’s what it is
about. Music can lead armies into battle, but that’s not why people
write symphonies. Michelangelo decorated a ceiling, but I’m sure he
had loftier things on his mind.
SIMPLICIO: But don’t we need people to learn those useful consequences of math?
Don’t we need accountants and carpenters and such?
SALVIATI: How many people actually use any of this “practical math†they
supposedly learn in school? Do you think carpenters are out there
using trigonometry? How many adults remember how to divide
fractions, or solve a quadratic equation? Obviously the current
practical training program isn’t working, and for good reason: it is
excruciatingly boring, and nobody ever uses it anyway. So why do
people think it’s so important? I don’t see how it’s doing society any
good to have its members walking around with vague memories of
algebraic formulas and geometric diagrams, and clear memories of
hating them. It might do some good, though, to show them
something beautiful and give them an opportunity to enjoy being
creative, flexible, open-minded thinkers— the kind of thing a real
mathematical education might provide.
SIMPLICIO: But people need to be able to balance their checkbooks, don’t they?
SALVIATI: I’m sure most people use a calculator for everyday arithmetic. And
why not? It’s certainly easier and more reliable. But my point is not
just that the current system is so terribly bad, it’s that what it’s missing
is so wonderfully good! Mathematics should be taught as art for art’s
sake. These mundane “useful†aspects would follow naturally as a
trivial by-product. Beethoven could easily write an advertising jingle,
but his motivation for learning music was to create something
beautiful.
SIMPLICIO: But not everyone is cut out to be an artist. What about the kids who
aren’t “math people?†How would they fit into your scheme?
SALVIATI: If everyone were exposed to mathematics in its natural state, with all
the challenging fun and surprises that that entails, I think we would
see a dramatic change both in the attitude of students toward
mathematics, and in our conception of what it means to be “good at
math.†We are losing so many potentially gifted mathematicians—
creative, intelligent people who rightly reject what appears to be a
meaningless and sterile subject. They are simply too smart to waste
their time on such piffle.
SIMPLICIO: But don’t you think that if math class were made more like art class
that a lot of kids just wouldn’t learn anything?
SALVIATI: They’re not learning anything now! Better to not have math classes at
all than to do what is currently being done. At least some people
might have a chance to discover something beautiful on their own.
SIMPLICIO: So you would remove mathematics from the school curriculum?
SALVIATI: The mathematics has already been removed! The only question is
what to do with the vapid, hollow shell that remains. Of course I
would prefer to replace it with an active and joyful engagement with
mathematical ideas.
SIMPLICIO: But how many math teachers know enough about their subject to
teach it that way?
SALVIATI: Very few. And that’s just the tip of the iceberg…
And I am struck by the memory of a discussion with my child’s teacher, wherein she admitted feeling “overwhelmed” by the curriculum. Where, in the past, she could rely on her teacher’s workbook to tell her how to challenge the more advanced students, now, she was completely overwhelmed by the technology, and the websites, and she couldn’t find time to learn how to use them to differentiate instruction for the more advanced kids. And I thought, what if the person who was teaching my child had a love of math, and just started, i don’t know, getting my kid excited with thoughts that challenged him, rather than looking for the next level in the math ladder that the website tells her my son should be doing?
It is far easier to be a passive conduit of some publisher’s “materials†and to follow the shampoo-bottle instruction “lecture, test, repeat†than to think deeply and thoughtfully about the meaning of one’s subject and how best to convey that meaning directly and honestly to one’s students. We are encouraged to forego the difficult task of making decisions based on our individual wisdom and conscience, and to “get with the program.†It is simply the path of least resistance:
TEXTBOOK PUBLISHERS : TEACHERS ::
A) pharmaceutical companies : doctors
B) record companies : disk jockeys
C) corporations : congressmen
D) all of the above
I don’t want to pick D. But i pick D. I cannot deny that it is all of the above.
If teaching is reduced to mere data transmission, if there is no sharing of excitement and wonder, if teachers themselves are passive recipients of information and not creators of new ideas, what hope is there for their students? If adding fractions is to the teacher an arbitrary set of rules, and not the outcome of a creative process and the result of aesthetic choices and desires, then of course it will feel that way to the poor students.
I also must admit that there is more than one issue here: Commingled with this fear of faulty math curriculum is also the fact that I fear my special needs child (and very intelligent children do have special needs, too) is being or will be failed by the system, simply because he is too far on one end of the spectrum.
One last thing. I am not criticizing teachers here. I know they work hard. I know they are overworked and that they have limitations in what they can do based on the curriculum, testing, standards-based crap, student/teacher ratios, and class sizes. I know this.
But it does not change that I fear for my child’s education, and ultimately for his imagination and love of learning.
Did you love Math in school? Hate it? Feel failed by the math curriculum in your school system? Were you in a gifted program? What was your experience? Are you a teacher, with a different take on this? Are you a parent struggling with these issues? And if you read the article, I would love to know your thoughts on it. I am really curious.
