Getting Kids to Love Mathematics
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Hey, you droogs,
There was an interesting post on the 
Whallah! blog about an article in the Associated Press,
http://news.yahoo.com/s/ap/20080626/ap_on_go_ca_st_pe/teaching_math;_ylt=Apnza3sjYQ1Rx08Q5.nf0IOs0NUE
concerning the education of math teachers in public schools.
Apparently the National Council on Teacher Quality has done a comprehensive study to come to the conclusion that everyone who is not an “expert” has known for years: Teachers are not being taught math adequately, and generally fail to teach it well to their students. (Do tell…)
Isn’t it funny that the “establishment” will never admit that? It takes an expensive academic “study” to show what is already known, yet Universities (in general) will not do anything about the way they teach teacher how to teach math. They will try some new, expensive methods that some textbook company has lobbied for, of course. But they won’t try anything that might actually work.
That’s why homeschooling and afterschooling are becoming more and more important. Taking an interest in your own child’s education is more important than ever, as public schools tank in their ability to actually teach, thanks to the natural entropy of society, and the idiotically simple-minded ways some people like to deal with it, as with the subtly(?) sardonically named “No Child Left Behind” act.
According to the AP article:
Author Julie Greenberg said education students should be taking courses that give them a deeper understanding of arithmetic and multiplication. She said the courses should explain how math concepts build upon each other and why certain ideas need to be emphasized in the classroom.
Teacher candidates know their multiplication tables, but “they don’t come to us knowing why multiplication works the way it does,” said Denise Mewborn, who heads the University of Georgia department of math and science education.
This is the key to most of what every student needs to know - how multiplication works. Addition is almost intuitive. It is an extension of counting. Once you extend addition to multiplication, though, you need a good understanding of how the base ten system works, and the commutative, associative, and distributive laws. You don’t need to know the names of those laws, of course, but you need to understand how to use them in order to understand multiplication. You also need to know that multiplication is not just repeated addition - a misrepresentation that is prevalent in education. (I should know, I only recently “saw the light” about this.)
That’s the big issue. Just being able to recite multiplication tables is not actually being able to understand multiplication. And just going through the motions and repeating math steps that a teacher has “taught” you by show-and-tell methods, so you can prove that you can jump through the hoops for the big test at the end of the year usually does more damage to your understanding that anything.
So what is there to do about it? First, as a truly concerned parent or teacher, make sure you, yourself understand some of the nuances of multiplication. Like why when you multiply by a fraction, the product is smaller than the multiplicand. (Did I get you with that one? Leave a comment below requesting the Math Mojo take on that one, and I’ll cover it in a new post).
Second, make sure you have at least two ways of explaining to your students how multiplication works. Not just how to do it, but how it actually works. I’m working on a video series about this now. Send me a nudge (again, in a comment below) to make it a higher priority to get it done and available to you faster.
Third, make sure you have a way to assess if your child or students understand what you taught them. The assessment doesn’t have to be a test. Tests are more about beating kids over the head. Asking questions and asking to demonstrate, in a non-threatening way would be my first strategy. If you must beat someone over the head, start with someone in an administrative position.
Here’s one of the reasons why:
According to the AP article:
Since states oversee the preparation of the nation’s school teachers, the report recommends they set tougher coursework and testing standards.
Why is does the solution always involve browbeating the learners? Why are the words “tough” and “testing” so often involved? How on earth does that teach or inspire? The problem isn’t that, “those who can’t do, teach.” The people who run those studies and teach university level education courses usually can do the math they are supposed to teach quite well.
The problem is that “those that can’t teach, teach.” Then they “train” teachers, instead of teaching them. No wonder those teachers have problems teaching.
As I always say, look up when you look for where the problem lies. You can’t blame a third grader for not learning (unless there is neurological damage, of course). If it’s behavior problems, there might be an issue beyond the teacher’s scope, but most behavior problems are dealt with by good teachers.
But beyond those things, start looking up the chain for someone who needs the butt-kicking. If the teacher can’t teach, were they taught well? (Are they even allowed to teach well in that school?) If the teacher’s teacher can’t teach, were they taught well? Is their administrator constantly putting monkey-wrenches in their teaching techniques? Is something going on at the School Board mucking up the school? Is the State requiring more tests, but providing less resources for teachers and students?
Keep looking up. Here’s a hint: Besides the handicapped, who’s got the parking spot closest to the school entrance? Start with him/her.
Remember, when things are looking bad, begin to look up.
I hope to hear from some of you soon,
Brian (a.k.a. Professor Homunculus)
Tags: get kids to like math , get kids to love math , get students to like math , get students to love math , getting kids to like math , getting kids to love math , getting students to like math , getting students to love math
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Comment by Dave
I just stumbled upon this site trying to find an answer to a simple math question and have been pleasantly surprised. I found this article very interesting. I will definitely be checking this site out more.
Comment by Ryan
Well said! As a mathelete myself, I realize the “philosophical, artistic, and romantic” qualities that math has. Math can be made interesting; all that is needed is a different perspective.
Comment by socialscienceplus
Thank you for your insights and your Blog! I will visit often… Lisa
Comment by Dunmire
I like the idea of teaching mathematics as a lab. I have begun instructing that way the past couple of years. I also believe that students are capable of computing many math problems in their head, but I do require them to show their work for two very simple reasons. One, it helps me understand how they view a problem and what concepts they may be missing. Two, many students cheat. If they still cheat, at least they will have seen and copied the process along with the answer. I teach students who are boarderline failing. I am always looking for ways to involve my kids. Thank you for your ideas.
If you have a better idea for assessing student work, without requiring them to show work, please let me know.
Dunmire
Comment by Brian
Hi, Dunmire,
I appreciate the dilemma. It’s a personal call for everyone. If someone had a “one best way,” all these blogs would be moot, eh?
My favorite solution, when I was working in a Job Corps (great kids, rotten program) was basically to casually ask each kid, in some context other than a test, if he could tell me, say, what 84 * 9 was. Then I’d watch him or her do it. If the kid could do it, that was that. I never needed to see his/her work for that kind of problem again.
That’s not always feasible, I know. But it was a Job Corps, and the way that rotten program worked, was that it would farm kids who normally the program wasn’t mandated to take, like from prisons, crack-houses, etc. It was a joke.
So there was a high percentage of kids who might have been tempted to cheat, because Job Corps is a kind of twisted system that sets kids up for failure. These kids had every reason not to trust me or anything about the place.
After a short time in my class, I think all but the most incorrigible kids felt they could trust me. I felt I could trust them on tests, too. Not that they’d snitch on each other (”snitches get stitches” was the operating mantra in that place) but I think they were operating on this premise:
If they cheated on my quizzes, and that got them out of my class into the G.E.D. class, where they’d be learning “higher” things, they’d be stuck in a G.E.D. class where they were sure to fail. And that would devastate them, and they wouldn’t get too many more chances.
On the other hand, if they failed in my class, I knew one thing - the kid was honest. I’d give them more credit for being honest than I would for passing a stupid math quiz. And, of course, once they failed, we could talk, and pinpoint the problem, and work on it.
So maybe some kids would fail some quizzes. But they would be fast quizzes, without them having to show work, which many (most?) kids find distracting or besides the point. The upside was that they didn’t resent my quizzes. You can’t pay for that!
Another thing I tried, with mixed success, is to insist that every question that was answered be correct. I was teaching basic math, not rocked science. If there was any problem at all for a kid to do, say, 369/27, then there was a serious problem.
One more thing I used, when I subbed at things other than math, was, when I had to give multiple choice quizzes, I’d add three extra boxes -
How sure are you of your answer?
a) not too sure
b) pretty sure
c) very, very sure
You can learn a LOT about which kids fool themselves and want to fool you from that. It’s about my favorite testing scam.
As for grading standardized tests, usually you have to do what the testmaker tells you to do - give partial credit, check how they do it, etc. I hate those things.
All in all, I think the only way to assess basic math skills is to give quick, short quizzes, give no partial credit, or look at any work, and then discuss each wrong answer with each student individually.
With the back- and soul-breaking workload teachers have nowadays, I don’t know if any of these Ideas are feasible. That’s why I quit Job Corps and won’t teach in public schools.
If you can get away with the extra three questions, I’d give them a try, though.
I don’t know if any of this will be helpful. I’m aware that every situation is different. Those are just some things that either worked for me, or I amused myself with.
All the best!
Brian
P.S. - What kind of place do you teach in? Ages? (Just curious!)
Comment by Dunmire
I teach 8th grade and up . . . Algebra A, Algebra B, Investigative Geometry.
I teach the kids that really, really hate math. The ones I teach in Investigative Geometry, I’ve taught for 3-4 years. We build great relationships and have a pretty good time.
This year, my 1st hour class (Algebra A) has several students who hate school and hate authority. I asked one student what his goal was after high school and he said his goal is to draw disability. I have students in that class who would play with Algebra Tiles all day long, unless I ask them to do something specific with them. Then, they don’t want to touch them.
I try to relate to them, but then I have to be careful how much I relate. For example, I have revised some word problems in the past:
Johnny was sentenced to 18 months for possession. Due to good behavior, he only served 40% of his sentence. How long was Johnny in jail?
My geometry students learn trig ratios with:
Some Old Hippie, Came Around Here, Tripping . . . Over Apples . . .
with the strategically placed pause, student insert their own words, and they remember their ratios.
I never try to be the “cool” teacher. I try to be the dependable teacher that they can feel comfortable with. So far, it is okay, but I know there has to be a better way. . .
I’ll keep reading, see what comes up.