Reading Rudbeckia's post here reminded me of my own self-teaching experience in 8th grade.
My 8th grade math teacher took a few of us "math brains" aside and gave us a 9th grade textbook to work through on our own. We sat in the back of the class all year and worked on these books by ourselves, at a table. Like Rudbeckia's class, noone checked our homework and noone gave us tests. Every quarter, we got an automatic "A" on our report cards.
I, being the space-cadet wonder child that I was (I honestly believed, somewhere deep down, that all this work was for the other kids but not for me), didn't do a thing all year. I thought my thoughts and dreamed my dreams.
The kid who sat across from me at the table used to nag me to do something and tell me that I'd get in trouble if I didn't, but I didn't see that I was going to get into trouble at all. What trouble? I was getting As without lifting a finger, and noone was checking. Kim Osborn was her name, and she was a very earnest worker (Kim, wherever you are, you tried; it wasn't your fault).
And then, of course, I got into trouble. I took the Regents 9th grade math exam, and by the skin of my teeth and the dint of some generous grading, I got a 67. My Dad hit the roof when he found out what had been going on; he had assumed I was really earning those As, and he had never been to a parent-teacher conference and talked to the math teacher.
the moral of the story
Don't assume that your kid can work on his or her own, even if he or she is bright. Actually, the notion that a kid will do his homework, much less teach himself first-year algebra, without being nagged and ridden is probably wrong in a lot of cases.
a related thought about teaching
Much later, after I got interested in the subject, I became quite a good student. I got straight As in college math, without even realizing that not everyone in my class was in the same boat. I was quite shocked when I started teaching and found that students such as I had been were rare. My office hours were filled with students who just didn't get it. I was bewildered; it hadn't been hard for me; why was it so hard for them? Obviously some of them weren't trying, but many were. Most of them couldn't make it without a lot of extra help.
I was quite patient with them, but I lacked sympathy. And I wasn't the only one who lacked sympathy; everywhere I looked, the other student teachers and even professors were just as bewildered as I am by the difficulty their kids were having learning math, and by the resentment they felt toward the subject and us. In each case, you might say, we were haunted by the memory of the students that we had been. But each of us had been some teacher's dream student.
I think it's the hallmark of a mature teacher that she can learn to put aside her own experiences as a learner and give the kids what they really need, whether it's more or less challenging work, or a bit more support than they themselves needed -- just as it's the hallmark of a good parent that they don't let their own experiences as children get in the way of rearing their own kids.
And this works the other way too. I think a lot of what fuels the constructivist engine is the loathing that so many people in the ed business remember feeling for mathematics when they were kids. They might think that they hated it because it was plug-and-chug, drill-and-kill, sage-on-the-stage, and so forth; I suspect they really hated it because, at some point, they got left in the dust and every experience after that was one of failure. People who get through math successfully, but just don't like it well enough to pursue it further, don't have the same feelings of bitterness I so often see expressed by constructivists. Might I suggest that they, too, need to let their own childhoods go?
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-- CatherineJohnson - 02 Nov 2005
"Don't assume that your kid can work on his or her own, even if he or she is bright. Actually, the notion that a kid will do his homework, much less teach himself first-year algebra, without being nagged and ridden is probably wrong in a lot of cases."
This is so true.
I had an interesting conversation with a mom friend the other day. This mom is very involved with her kid's education and we've had many discussions about the math curriculum, as well as other concerns. One of her sons is very bright and is in my youngest's algebra 1 class. The other day I was lamenting about how much homework my son was getting between the math and all of the other teacher's assignments. I said that at the very least my son was getting 40 min. to an hour of math homework a night and that if he had a problem with it, it could go even longer with dad then having to help him figure out what he missed.
Well, she paused and said something about how "funny" that was since her son was getting hardly any homework. Big pause again. I told her that the algebra class had homework EVERY night and weekends with few exceptions. Another pause. Then she said something like, "Oh no."
Now these are two educated parents, but admittedly weak in math, according to her. They have not checked his homework even once because they feel they wouldn't know how to help him if there was a problem. He just says he did his homework at school or that they didn't have any and they've accepted what he says at face value. She was a little surprised that he didn't pass the last quiz, though. I told her that the teacher does check to see if they DID the homework and they do go over problems in class, but there is no way to know if your child is understanding what's going on or just getting further and further behind.
I did mention to her that the answers to the odd numbered problems were in the back and at least she could see if he was having a problem and maybe take it from there, but she figured that he probably already knew that they were there. These parents did hire a tutor to get him ready for the class, but that was very expensive.
I realize that there are not enough hours in the day for a teacher to check every homework problem of every child, especially when they are doing 30 problems a night, but parents need to realize that this is where the gaps occur. Again, this is an involved parent who supplements her child's education and knows her child very well, but his immaturity (or as we discussed before, basic cluelessness) might be getting him into some trouble.
And like we've said before, most kids really don't know what they're supposed to know and what will be critical for them to know in the future.
-- SusanS - 02 Nov 2005
I had the same thing happen to me. In junior year I was scheduled to take precalc first semester and trig second semester. Then I transferred schools in November (halfway through precalc). My new school took trig first then precalc.
So effectively I missed two months of trig and took the first half of precalc twice. The result was that I had to teach myself trig in one of my free periods. Let's just say I designed an easy course for myself in which solving problems wasn't required.
(Actually, the free period was carved out of the Math Review and Problem Solving elective class I was put into. It was a college prep review class for the track right below the honors track. Let's just say that I was the only student able to consistently solve any of the math problems (basic algebra). The teacher realized I was wasting my time, so he let me work on trig by myself most days.)
-- KDeRosa - 02 Nov 2005
space cadet wonder child
That's really what I was. I would have had myself on ADD medication so fast it would have made everyone's head spin. I really, really needed it. Along with some attitude adjustment.
-- CarolynJohnston - 02 Nov 2005
I still have ADD, by the way. But now, I compensate by being obsessive about organization and task-completion.
-- CarolynJohnston - 02 Nov 2005
OCD + ADD = someone who passes for normal
-- CarolynJohnston - 02 Nov 2005
I think it's an interesting Armchair Science question.
If I'd been given Math Packets as a child, and told to work my way through them, what would I have done?
I'm guessing I would have worked my way through them, while also Talking To My Neighbor a whole lot.
I was a teacher's pet kind of kid, the voluble kind, the kind who got in trouble for Talking To My Neighbor.
-- CatherineJohnson - 02 Nov 2005
Well, she paused and said something about how "funny" that was since her son was getting hardly any homework. Big pause again. I told her that the algebra class had homework EVERY night and weekends with few exceptions. Another pause. Then she said something like, "Oh no."
Someone needs to write a Very Brief Book for parents of middle schoolers explaining the homework situation.
It was shocking, to me, how completely and totally I missed what was going on in 4th grade.
I was under a horrific deadline for ANIMALS IN TRANSLATION, working nights & weekends, and I had no clue.
I didn't even find out Christopher had flunked the 5th unit test, in addition to the 6th unit test, until months later.
-- CatherineJohnson - 02 Nov 2005
Never, EVER, trust a kid to do his homework.
And if it's math homework, CHECK THE ANSWERS.
-- CatherineJohnson - 02 Nov 2005
I, of course, am managing to miss everything that's going on in every subject BUT math.
So far Christopher has had Fs on tests in....English, Spanish, &, I think, Music.
-- CatherineJohnson - 02 Nov 2005
I'm calling a Team Meeting.
heh
-- CatherineJohnson - 02 Nov 2005
Let's just say I designed an easy course for myself in which solving problems wasn't required.
LOL
I just bet you did.
-- CatherineJohnson - 02 Nov 2005
OCD + ADD are an extremely good combination.
That's pretty much me, I'd say, except I don't have the spacey kind of ADD, which I think you do. (I have the Talk To My Neighbor kind of ADD, which we call ADHD.)
-- CatherineJohnson - 02 Nov 2005
When I interviewed Walid Shekim years ago, when the idea of adults with ADHD was just surfacing, he said that people with ADHD and OCD are often very successful.
The ADHD gives them huge amounts of energy & pizzazz, and the OCD forces them to stay on-task long enough to get things done.
-- CatherineJohnson - 02 Nov 2005
Speaking of which, I'm supposed to be writing a Book Proposal.
-- CatherineJohnson - 02 Nov 2005
Why don't I go do that?
-- CatherineJohnson - 02 Nov 2005
My original tale was editted for length, leaving out some of the secondary facts. The main reason that I did the math packets? On a bulletin board in the math classroom was a pre-printed list of all the students on the team*, and next to each student's name was a series of boxes (1 box for each possible packet), and each time you complete a packet (and passed a "test" on it) the teacher would color in another box next to your name. There was a competetion between the best students to see who could complete the most packets the fastest. Also, we saw that there were only a finite number of packets and once we finished them all NO MORE MATH.
*"team" = middle school jargon roughly meaning "about 100 - 120 students"
-- KtmGuest - 02 Nov 2005
[Grr... I have not yet found the right cookie or setting to zap on my office computer. (Probably this is a sign that I should stop using Safari and switch to Firefox.)]
-- KtmGuest - 02 Nov 2005
Were you able to check your own problems???
Answers in the book??
-- CatherineJohnson - 03 Nov 2005
I do not remember if we could check our own problems or not. All I remember was that if you didn't pass the test on the packet that you had to go back and work on it some more and try again until you did pass.
And I will reiterate that from 8th grade through 12th grade not one person EVER checked my math homework. The upside of it was that I DID do it when I thought I had to; the downside was that it took a few shaky episodes for me to learn when I did and didn't have to do it. (Example: I am right now very bad at graphing polar equations in my head because I did no homework on polar equations when I was in 10th grade; I am as calculator-dependent as my students when it comes to graphing in polar.) I was super-insulted when I was a freshman in college and we had to TURN IN our homework EVERY CLASS. I ranted, "This is so childish. No one has checked my math homework since I was in SEVENTH GRADE."
-- RudbeckiaHirta - 03 Nov 2005