Moebius Stripper thinks she’s making progress with her precalculus class, but worries about some students.

In particular, although I hate (not really) to make predictions at this point, I think that it’s a pretty sure bet that when a student asks “what do I need to get in the rest of the course to get the 65% I need?,” and you say “well, here are your test marks and quiz marks, and your tests so far are worth 40% and the quizzes so far are worth 8%, so you can figure it out from that” and they say “how do I do that?” – they’re not likely to get that 65%. Just sayin’.

I tutored three boys for their algebra midterm yesterday. One needed no help. In fact, I kept asking him if I had it right, since it’s been nearly 40 years since I took algebra. The other two . . . Well, I wondered what it’s like to live life without an attention span. I guess every moment is fresh and new, and you can’t remember what the x-intercept is, even though I JUST TOLD YOU TWO SECONDS AGO!

Yup, that’s my biggest challenge in precalc: they don’t LEARN the material I teach them, they just remember it, and so their knowledge of the subject matter is only as good as their short-term memory, which is to say, not very. I don’t know what to do about this; they seem locked into the memorization study pattern. Requiring anything more complex of them just resigns them to failure.

For instance, half of them still expand (x+y)^2 as x^2+y^2. I don’t know why they still do this. It’s not because I didn’t correct that mistake, in front of the whole class, after the first quiz. Nor is it because I didn’t explain it AGAIN after they made that mistake on the second quiz. And when I announced “ok, next time I see this mistake I give a zero on the question”, that had only minimal effect. Ugh.

Some people are just wired that way. I have an easy time with math, but a hard time with foreign languages. Not everyone can learn algebra, and I don’t understand why the education system thinks that everyone can.

Moebius Stripper: I agree that if they can’t figure out what “they need” given the information you provide, they’re probably not going to pass. I, however, take a different approach. When students ask me what “they need”, I tell them, “It doesn’t matter what you need. It only matters what you get. So study the material and do your best, and let the numbers fall where they do.” *Then* I provide the same type of information you do–but they never go calculate.

And Rex: your comment reminded me (geek alert! geek alert!) of a scene in Star Wars: The Empire Strikes Back. Luke Skywalker couldn’t use the force to lift his X-Wing fighter out of the swamp. Yoda exerts little effort in doing so. Luke says, “I don’t believe it!” Yoda replies, “*That* is why you fail.”

I was like that math student that you mentioned. I struggled and struggled to understand the most basic mathematical concepts. The only thing I was able to master was the spelling of arithmetic (a rat in the house may eat the ice cream.) Teachers used to get furious with me and accuse me of not even trying. My guidance counselor talked me out of going to college because I would fail at math. When you are 18 y/o you tend to believe the “grown-ups,” especially how I was raised.

It wasn’t until several years later that I finally went to a two-year college. After working very hard at my “Intro to Math” course with a very understanding professor I discovered some information that would have changed my life. I was not “stupid!” I have a mathematical learning disability called DYSCALCULIA. This is a little bit like dylexsia only it deals with numbers, directions and the way my brain learns.

Funny thing is, all of the things that my guidance counselor used to throw in my face (you write so well, you excel in language arts, you are very creative) are just some of the signs of dyscalculia.

Could it be that a student that is making you crazy and can’t seem to get it right actually has dyscalculia. I’m not pushing a learning disability, but when I spoke with my son’s counselor he had never even heard of this problem. I thought I was math stupid and beyond help and it really did change the course of my life. Turns out, once I learned HOW to learn math and what I had to do to make it happen, I got an A – on my final exam!!

Never discount the idea that the way a child learns could be what you are seeing and not just a child trying to slide by with memorization. Much of what is learned in school is required memorization – we memorize the rules of reading, we memorize historical dates/places and people, we memorize the laws of physics and geometry. If these children are tactile learns, it makes the math applications very difficult.

Hang in there. I know how hard it was for that college professor to hang in with me!! However, you really do have the opportunity to change the direction of a child’s life.

“You can’t remember what the x-intercept is, even though I JUST TOLD YOU TWO SECONDS AGO!”

Let’s get away from the snide comment and consider what is going on with that student. Too often kids like that get dismissed as lazy or unmotivated. But obviously this kid is not so lazy– s/he is going to tutoring, after all.

And then, think of how hard it is for you or me to remember what was said two seconds ago. It’s no effort whatsoever, right? We don’t have to TRY to remember. We don’t have to WORK to remember. It happens automatically. Well, it doesn’t happen automatically with this kid, and I don’t see how the kid can be blamed for that. S/he doesn’t deserve your scorn or your snideness.

My son has learning disabilities, and we homeschool. Sometimes it’s so frustrating when he has trouble with something that I can understand in an instant. But I just have to persevere and try some other way of presenting the material. And sometimes, whatever I do, he’s just going to have to work very hard to do something I can do effortlessly.

So, Joanne, good for you for tutoring. Patience. Press on. Just one little piece of advice on how to think about this kid and other kids like him– it’s probably not attention span. It’s something else preventing what you say from getting into his brain.

I love it when, during the last couple of weeks of the semester, some loser comes up to me and asks, “What am I missing?” What does it matter what you’re missing? If you didn’t do it when it was due, what makes you thing you’re going to do it now? Or, “Can I do any make-up?” Of course. Just put it in the “I’ll-Get-To-It-If-And-When-I-Feel-Like-It” file. Or, “What’s my grade?” The biggest freakin’ F in the history of education with Christmas lights and a warning beacon for passing aircraft.” And, “Can I do any extra-credit?” No problem. Mail it to me over the summer. I’ll be in Tahiti.

Moebius Stripper wrote:

For instance, half of them still expand (x+y)^2 as x^2+y^2.I’m not a schoolteacher, but I’ve tutored individual kids occasionally over the years. I’ve always found that relating a new concept to something one already knows helps one remember it.

So, to expand (x+y)^2, I told my students to think “(x+y) squared is (x+y) times (x+y)”, then to put the multiplicands down on paper exactly as they would multiply, say 19*23. 19 is 10+9, and 23 is 20+3, so

x + y

x + y

_____

Then multiply it out just as

19

23

___

Learning by doing that seems to help memory.

This might be the funniest comments thread I’ve read in a month. Unintentionally, of course. Made me choke on my pizza as I read it. Tsk tsk.

***”I love it when, during the last couple of weeks of the semester, some loser comes up to me and asks, “What am I missing?”***

***The biggest freakin’ F in the history of education with Christmas lights and a warning beacon for passing aircraft***

While I agree that a student who comes to you in the last couple of weeks needs to be taught to use a little more discipline do you really feel that they are a loser? The CHILD failed to do what was necessary. If they receive an F…which is what they earned and what they deserve, perhaps it will help that child to realize that they have to pay more attention. I have to wonder if you are just blowing off steam or if you really feel this away about your students?

If this is really how you feel, these are the things that make this parent shudder.

How do you know that BadaBing teaches children? Sounds to me like he teaches college students- young ADULTS. And very likely those young adults unfortunately had parents who, with the best of intentions, always made excuses for their nonfeasance, with lasting damage to their characters as the result. I’m sure BadaBing will correct me if I’m guessing wrong here, but as to the the scenario I just outlined, been there, done that.

I have been teaching math for 15 years now and understand the frustrations that many teachers feel and that many students feel.

Addressing the (x+y)^2 issue, the reason they do it is because they know that 2(x+y)=2x+2y and that (xy)^2=(x^2)(y^2) but don’t understand why the same rule doesn’t work with (x+y)^2. They are just trying to distribute the exponent! I have always found that proving something invalid with numbers tends to convince them. Make x=3 and y=2 and show that it doesn’t give the same answer. Then on the next test, have a question like this, “Prove numerically why (x+y)^2 doesn’t equal x^2+y^2.” I think they will probably not forget again.

As to the learning differences, I married a man who is a math phobic. He has not finished his degree because he is scared to go back to school and take a math class! Many of the kids like this either learn differently or had one horrid experience in the past that basically scarred them against math for life. We as educators need to teach things from many different perspectives, understanding that not all kids learn the same way. My daughter is currently in my Algebra II class and definitely doesn’t learn in the way I usually teach. She is making high B’s and is being successful not because of any favoritism I show, but because I present the concepts from 2 or 3 angles and let the students choose which method works best for them.

Don’t give up on your precal kids, Moebius. Some of their memories are 2 seconds long, but we keep on trying to cram the knowledge in…

Sigh…I know a dozen ways of showing that (x+y)^2 is not equal to x^2+y^2, and I’ve shown the students all of them. Distributive property! Try it out with numbers! Here’s an example of why it doesn’t work!

But what they really need is a good grade eight-level math class, which they should have had five years ago or more. I try my hardest to teach them the basics, but I also have the actual curriculum to deliver.

Moebius Stripper wrote:

Sigh…I know a dozen ways of showing that (x+y)^2 is not equal to x^2+y^2, and I’ve shown the students all of them. Distributive property! Try it out with numbers! Here’s an example of why it doesn’t work!But what they really need is a good grade eight-level math class,That’s why I suggested hooking into a rote procedure that (a) always works, and that (b) they likely already knew by eight grade: namely how to do long multiplication of two integers.

Implicit in the approach is also the notion that an integer is expressed as coefficients of a polynomial in powers of the base. If they make that leap intuitively by doing the procedure, then they’ve gotten a learning bonus.

If they don’t make that leap, they still learn a sure-fire method to do the task which isn’t different from what they already know how to do, ie: long multiplication of integers.

They might have known how to do long multiplication of integers by grade eight, but many don’t know how to do it now. These students were all using calculators by grade four. Many NEVER learned the basics.

I’ve tried explaining this using long multiplication. Also used long division of integers to lead into long division of polynomials. It was Greek to many of them.

Moebius Stripper wrote:

I’ve tried explaining this using long multiplication. Also used long division of integers to lead into long division of polynomials. It was Greek to many of them.You hit the nail on the head: they never learned the basics. That’s truly an indictment of elementary education methods in arithmetic.

One must wonder, as you undoubtedly have, why these kids are taking “pre-calculus” when they haven’t even learned basic arithmetic skills.

You have my sympathy. You might as well try to teach formal poetics to students who can’t read.

Don’t these kids take some sort of placement test before they can get into Precalculus? Or is this the lowest level of math your school offers? If they kids’ skills are as bad as you say, they shouldn’t be in PreCal.

Jill, the prerequisite for precalculus is C+ in grade 11 math, or pass in grade 12 math. Which would be perfectly reasonable if students in this province learned anything in high school, which they don’t. I was actually planning to talk to my department head this week to suggest a placement test; as you say, students doing math at grade-school level have no business being in my class. It’s not doing them, or me, any good to have them around.

The problem is, where are they going to learn the basics? They didn’t learn them in high school the first time around, so they likely won’t learn them in high school if we sent them back there. And I teach at a college, and it shouldn’t be our responsibility to teach high school material.

Moebius, do you teach at a four-year school? If so, wouldn’t a community college be the best place for these students to catch up on what they didn’t learn in high school? (Of course if that becomes a widespread practice it will create what actuaries call a “moral hazard”- there will be even less pressure on high schools to do their job.)