Like Guin, I’m a literature and history person. Why? Stories. Literature is stories that people made up and history is stories that actually happened. I’m oversimplifying here, but really that’s what grabs me. Math has no stories. There’s nothing to sink your teeth into.
I can do math if it has to do with financial stuff. If you put it in terms I can understand, like dollars and cents, I’m right there with you. Probably if I worked hard at it, I would be able to understand higher math, but what’s my payoff? I’m no longer in school, but reading enhances my life everyday. It brings me joy, challenges me, teaches me amazing new things about the world and myself. Math? Math just means I have a balanced checkbook.
While I was never a young Newton, I did reasonably well given that, from first grade to Freshman at college, Math Teacher were astoundingly dull.Its like they actually tried to make it as boring as possible.
There was an exception, but his teaching ability and “humor” were so lame it was worse than the dull ones.
Keith Devlin recently wrote a book, The Math Gene in which he touches on this topic. Devlin writes a monthly column that can be found atthe Mathematical Assn. of America.. (I’m gonna guess that you math-types have heard of this guy) The thesis of the book is that mathematical skills evolved along the same lines as language skills, and that everybody possesses the basic ability to “do math”. As for why some people “don’t get it”, he says that there’s no one reason, but that almost anybody who recognizes a need to “do math” is able to conquer what they need to get by.
As for me, I’ll agree what what’s been said here (especially Anthracite) about teachers. I’ve had very good ones and ones that were worthless. The way I got thru with bad ones was realizing that somebody out there understands this stuff - why not me too? - and getting outside reference material (Schaum’s outlines saved my bacon more than once).
I can see how a bad teacher can turn someone off to the topic altogether.
But, in defense of the teachers, I think it’s almost impossible to find the right technique that will work with all (or just most) students, I don’t envy their task. (I’ve never taught math, but the thought scares me.)
FWIW, I’m an engineer, working (not very seriously) at a math degree, and you’ll find me at the end of the craps table drinking Jack on the rocks, and trying to hit that hardway parlay.
Okay, maybe “put the 5 boxes back down” was a bad way to phrase it.
Lemme try again:
Take 5 boxes of M&M’s. Each box has 10 M&M’s in it. You now have 50 (5 times 10) M&M’s. Now eat the M&M’s, so you’ll have a clean slate for the next step. Go on, eat them. Yeah, they’re a bit salty to eat all at once, well boo hoo. Wash them down with a glass of milk or something. I don’t care if they go straight to your hips, this is for science!
Okay. Now. Take 3 boxes of M&M’s. Each box still has 10 M&M’s in it. You now have 30 (3 times 10) M&M’s. Now eat them to clean your slate again.
Now take 7 boxes of M&M’s. Each box still has 10 M&M’s in it. You now have 70 (7 times 10) M&M’s. Now eat them.
Now take 14 boxes of M&M’s. Each box still has 10 M&M’s in it. How many M&M’s do you have? Right, you have 14 times 10, or 140. Now eat them.
Now, take 0 boxes of M&M’s. Each box still has 10 M&M’s in it.
Well, I’m a math teacher at a community college and try to be the kind of teacher that Anthracite mentioned in a previous post. (I’ve gotten some feedback from students over the years that indicates that I am doing a pretty good job)
The last few semesters, I’ve learned a few things that are worth mentioning, especially since I’ve been teaching a few classes that are online.
At a faculty inservice last year, I was told that the entrance testing showed that our incoming freshman read at about a sixth grade level, however, most of the math textbooks for freshman level courses seem to be written at a much higher reading level.
This presents a real problem, especially for online students.
Another thing I’ve noticed is that students often have a different set of study habits and problem solving skills for mathematics. Many students sit down and open the textbook up to the page where the homework problems are, write the problem down they are trying to solve and then backtrack through the text to find an example close to the problem. (as opposed to reading the text first, asking questions about the material in class or during office hours, working through the examples in the text, filling in the steps which textbooks often omit, and then trying the problems)
An interesting experience I had today…a student was working on a problem about the percentage of adult women who are not eligible for the army based on height requirements. The student was able to set up the problem correctly and computed that 98% of women were eligible. I complimented the student on the correct work, and asked him to then finish the problem by telling me the percentage of women who are not eligible. The student then asked what page the formula would be on. I had to say, “close your book, put down your notes and just think on this for a minute…if 98% are eligible, what percentage are not?”
And just a final note…when I tell people what I do for a living…they usually answer back with “oh…I was always very bad at math”. Do people in other professions get this too? (do people tell you accountants out there that they always are bouncing checks?)
Maybe, but I never managed to get above a C- in a math course since third grade.
It’s not that I didn’t try. I faithfully took the highest math offered to me every year. I’m not lazy, and I’m not dumb. I had some good teachers, and some bad teachers. I understood concepts fine. It’s hard to explain exactly why math is so hard for me. But once I get about three steps into the problem, I lose my hold on what the numbers are, what they mean, and what I should do with them. It’s like trying to read but having no concept of sentence structure. I couldn’t understand why I should manipulate them, why I should do this step or that step, or even why I was going through all this work to get a result that is just another set of symbols. I longed to create, but instead I had to sit around making mysterious chicken scratches, doing strange ritualistic things to them, and then coming up with another set of chicken scratches that had to be a certain set of chicken scratches or else I’d fail the class and not go on to college.
It’s pretty hard to explain why you don’t comprehend something you don’t comprehend. But it was a big problem for me. I got "A"s in every other class, but math could have easily kept me out of college. The pressure was intense to say the least. How would you feel your entire future depended on something as unlikely and irrelevent to you as running a three minute mile? I got through, but I certainly don’t want to have to spend the rest of my life being ridiculed for not being able to do something I tried do for twelve years of school and consistantly failed, and which doesn’t otherwise hamper my life.
Nah, actually they all say “Well, I HOPE you teach students not to end a sentence with a preposition,” as if it were one of the seven signs of the apocalypse.
Some more scattered thoughts…
Teachers gravitate toward subjects they learned easily, and they tend to teach the way they learn best. Traditionally, the predominant teaching style in mathematics is individualistic (students work alone), passive (lots of listening and note-taking, few activities), and abstract (many concepts, few stories or concrete examples). This is not an inherently bad way to teach – it dovetails perfectly with some students’ learning styles, and these students often go on to become math teachers who teach in much the same way themselves. Many students, however, do better in active, group-oriented situations, and these students get turned off early because math classes seldom incorporate activities that would help them learn.
In other subjects, there seems to be a broader range of teaching styles in practice: one freshman Shakespeare class at a large university might consist primarily of lecture, another of discussion, yet another one might incorporate presentations and performances by small groups of students. Not all of these classes will be right for all students, but most students will find some English classes to their taste. Mathematics, on the other hand, has become a refuge for students and teachers with one particular (somewhat rare) learning style.
To complicate matters, a lot of people who are mathematically inclined – or perhaps I should say math-teachingly inclined – regard group projects and games as fluff, entertainment for slow students who can’t be reached any other way. In fact, students who learn well by watching the teacher work examples on the board are no smarter or more serious than students who don’t learn well by watching the teacher work examples on the board; math classes weed out students on the basis of learning style, not ability.
I also remember that the professor I mentioned would give us quizes with like, fifty five problems, and want them down in a half an hour.
Due to my learning disabilities, I had special extended testing time. The only problem was, his solution was to allow me to keep going at the quiz, while he taught the rest of the class. I had to get someone to take notes for me, copy those down, and I’d be doing double the work.
Even though not all jobs demand calculus, the higher-paying jobs, even non-science managerial jobs, do. For example, say that you’re a book publisher, and you want to know how your horror and romance sales will change in volume over the next year. You are most certainly going to need to know functions and how to calculate a changing rate over time or distance. That’s where calculus comes in.
Of course, even in retail, you still need to be able to use at least simple arithmetic. For example, last night I ate at Desert Moon Cafe in the Pentagon City Mall food court. When I looked at my receipt, I noticed that the .57 tax seemed too large for a $6.68 bill. Doing the math in my head, I came up with an 8.532% percent sale tax, which is wrong, because the sales tax in VA is 4.5%. I should have paid only .30(rounding up) sales tax. Of course trying to explain that to the Salvadoran counter person was fruitless (my Spanish is pretty good, but not up to explaining math problems<sigh>), but at least I knew I had been ripped off, so the principle is still sound.
I think all you guys who have been trying to explain the concept of multiplication have been making it too complicated.
When you think of a multiplication problem, just substitute the words “groups of” in place of the word “times”.
5 times 5 = 5 groups of 5, or 25.
2 times 5 = 2 groups of 5, or 10.
0 times 5 = 0 groups of 5, or 0.
Whenever you multiply by zero, you have zero groups of something, which is why the answer is always zero. “How many apples do you have if you have zero groups of five apples?” Well, I have zero groups, so that means zero apples. “OK, how many apples do you have if you have five groups of zero apples?” Well, it doesn’t matter if there’s five groups if there’s zero apples in every group, so the answer is still zero apples.
Just for trivia’s sake, the rule that “zero times anything is zero” is not an arbitrary convention. It follows from the basic properties of addition and multiplication. To whit:
Let a be an integer (i.e., a whole number, possibly zero or negative). Let’s consider the quantity 0a. Well, for any integer x, 0 + x is just x, it follows that 0a is equal to 0a + 0. Also, since 0 is an integer, 0 + 0 is 0. So 0a is equal to (0 + 0)a. By the distributive property, (0 + 0)a is 0a + 0a. So now we have that 0a + 0a is equal to 0a + 0. Remember the cancellation law? If a + b = c + b, then a =c. So it follows that 0a = 0.
I hope this clears up some confusion instead of creating more.
I think the problem with teaching math is that there is sooo much material. If one, or just a few students get stumped on a concept, the teacher would feel that she just has to move on. Who knows how long a stumped student will remain stumped: 1 minute, 1 hour, 1 day, or possibly a lifetime. But if the whole class is stumped, then the teacher is doing something wrong.
Anyway, there is simply too much material to absorb. I think teaching math at a much slower rate would do the trick. Then teacher’s won’t be so pressured to move on.
My point is, math isn’t really hard, it’s just taught too fast. That’s why only “geniuses” get through math. If it was taught slower, perhaps more “geniuses” would emerge.
For example, elementary algebra, 5 year study. That would do it. And the quicker, not necessarily smarter, students can take an accelerated course, or do independent study and just pass the final.
