Kids and Math

[iflookscouldkill]

not all of us are blessed with math skills

 

[okstatecowboy]

Is it me or does today's youth have a total lack of math skills? I tutor chemistry at my former highschool as my way of giving back and today i was totally floored. ALL of the kids had the same problem, they couldnt do the simple math behind highschool chemistry. Totally over their heads.
Mind you, I graduated a mere 8 years ago but back then Calc was requiered, now you can stop after algebra 2 in 10th grade and be done with math.
How is that helping kids?

Has anyone else noticed this alarming trend?

It isn't helping kids. A lot has changed in the last 15-20 years in terms of education. I am a middle school math teacher and can relate to your experiences. My 7th graders can barely do simple addition without whining that they need a calculator. Teachers simply cannot compete with the amount of NCLB testing, outside activities, and the such. Expectations in a number of classroom have been lowered. Kansas 3rd graders are no longer required to know their multiplication facts!

The good thing is that the National Council of Teachers of Math has finally realized some of their mistakes and are revising some standards and expectations in attempts of reversing this poor trend. But God help us until the young'uns are brought back to speed...

mikey

 

[slobone]

The NCTM standards were quite good, the problem was there weren't enough teachers who knew how to teach to them.

The basic idea is to emphasize problem solving over algebraic methods. When I took algebra in high school, we spent virtually all our time manipulating equations. The 1% of us who were good at that did quite well and enjoyed ourselves. Everybody else struggled through and never looked at an equation the rest of their lives.

Virtually no attention was paid to what an equation was good for, apart from the occasional "word problem" that had no relation to real life.

It would have been much more valuable for students to take a real life problem, figure out what's needed to solve it and what kind of math to use. Only then do you start working with equations. This is what the NCTM was basically recommending. Students who learn math that way retain more AND do better on tests.

But the NCTM standards were widely misunderstood and misinterpreted. The election of Bush was the coup de grace, as his education department basically told schools not to experiment with math education. Conservative parents and school boards finished off the job.

So now we'll have another generation of Americans who hate math and think it has nothing to do with their lives.

 

[slobone]

^^^ To take another example, there are aspects of calculus (yes, calculus!) that can be introduced quite early if you stay away from the theorems. You can have students examine graphs, familiarize themselves with the concept of rate of change, and even learn about first and second derivatives (via velocity and accleration). Integral calculus can also be introduced as a way to compute areas.

Then later, when they need to have a more rigorous treatment, they already have a head start. Even if they never take a calculus class per se, they will have a better understanding of graphs that they encounter when they study economics, science, social science, etc.

The point is that introducing these basic concepts can begin in middle school or even elementary school. That's part of what the NCTM was trying to accomplish.

 

[slobone]

Here's another point. A lot of parents were freaked out that their kids weren't learning long division (or at any rate not spending very much time at it).

So what exactly is the value of long division? Before the advent of calculators, you needed to learn it in case you had to divide 2 numbers. Nobody does that today unless they're on a camping trip and didn't bring a calculator along.

But isn't it a good way to learn mathematical concepts? Not especially. The specific tricks you use in carrying out a long division don't really show up in any other part of mathematics (unless you're studying something really, really nerdy).

The most important thing about dividing 2 numbers is learning to estimate the answer. If I ask a student to divide123456 by 402, I would hope he could tell me that the answer would be somewhere around 300. If he can do that off the top of his head, I would feel that he'd learned all he needs to know (that, and how to press the calculator buttons correctly).

Heck, when I was in school I even learned Newton's method for taking square roots. And I wasn't in an especially advanced class -- we all learned it. I'd wager anything there isn't a single one of us today who remembers how to do it (including me).

 

[RenaissanceMan]

not all of us are blessed with math skills

That's exactly why many should ACQUIRE them instead: first through practice of basic arithmetic (there isn't really any other way to have it relatively at your fingertips), and then more problem solving as slobone discussed.

Having just made the highschool-university transition into a rigorous pure math program, I think that there needs to be more development of mathematical "intuition", which is either as simple as estimation of products or quotients or a bit more complicated as estimating areas under curves.

Of course I'm rather pissed off about how low the level was in my final year of highschool compared with my (albeit rather advanced) first year calculus/analysis course...but I'll half accept that fact, since not everyone is intending on majoring in math.

I also tutored lots and lots of students from gr.9 to 12 and most of them either had a hard time with algebraic manipulation (fractions being a total mess), arithmetic or simply understanding the concept of, say, a function.

I'm not sure what can be done...I just know my tutor when I was 10 did something that changed the way I thought about math and finally started understanding it.

 

[me12121]

When I took algebra in high school, we spent virtually all our time manipulating equations. The 1% of us who were good at that did quite well and enjoyed ourselves. Everybody else struggled through and never looked at an equation the rest of their lives.

I always hated that they taught math in high school like that. It made me think it was pointless, so in Grades 9 to 11, I didn't really learn much algebra. Because of this, when I first took Calculus in Grade 12, I failed it. Took it a 2nd time and learned the algebra while doing the calculus and got the highest mark in the class! My algebra still isn't perfect (I hate simplifying equations), but it's a lot better than it used to be.

 

[slobone]

my math sucked...i was too busy trying to look down all my class mates shorts. when i went home and tried to do my math homework...somehow after 10 mins i would end up on my bed with the book closed and my pants on the floor rubbing my penis thru my tightie whities thinking about fucking all the boys i had gym with.

If you had 37 classmates and it took you 9.5 minutes to fuck each of them, what time would the train get into Cleveland?

 

[slobone]

I also tutored lots and lots of students from gr.9 to 12 and most of them either had a hard time with algebraic manipulation (fractions being a total mess), arithmetic or simply understanding the concept of, say, a function.

Don't start with functions, start with graphs -- everybody's familiar with them. Make time the independent variable -- another familiar concept.

"This is a graph of my trip to Abilene. Can you tell where I speeded up, where I slowed down, where I stopped, and where I turned around to cruise a hot guy?"

Hold of on the trig and exp functions until they're comfortable with the basics.

 

[teadrinker]

I teach university level mathematics, and certainly the mathematics skills our new students are entering our courses with are pretty woeful - and these are students who have passed upper high school maths! Some of our students are functionally innumerate, unable to guesstimate the result of a numeric expression.

I don't know quite where the problem lies, but I do know that any maths topic can be introduced quite early, if taught and presented in an engaging manner - slobone's comment that

the occasional "word problem" that had no relation to real life.

is right on the money - most problems which attempt to engage are dull, stupid and pointless.

A few years ago I ran a coding and cryptography inservice for the fifth grade of a primary school, and all the kids loved it. Now's there's some real maths!

Oh, and on another comment of slobone:

The specific tricks you use in carrying out a long division don't really show up in any other part of mathematics (unless you're studying something really, really nerdy).

Quite - long division of polynomials is essential for the workings of finite fields, which are themselves vital for modern crytpography.

-T.

 

[slobone]

Quite - long division of polynomials is essential for the workings of finite fields, which are themselves vital for modern crytpography.

Hmm, true, and without it you couldn't have that magical moment when you show the class how to factor x^7 - y^7. I guess I was a bit hasty on that one. And I'm not really advocating throwing long division overboard, at least not completely.

But I think it is true (over here, and probably over there) that parents get outraged when their kids aren't forced to spend as many hours doing meaningless computations as they were.

Cryptography of course is great for permutations, which lead to probability and group theory. Also modular arithmetic, Fermat's Little Theorem, etc.

Incidentally, I first really got into math through recreational problems -- in particular Martin Gardner's columns in Scientific American. As a result I felt quite at home when I finally got to algebraic topology many years later. And I still love nearly anything to do with John Horton Conway.

 

[teadrinker]

Martin Gardner, algebraic topology, AND John Horton Conway! Woo hoo!

-T.

 

[The_Reaper]

Yes, I suck at math...Get over it!

I have to agree with what my philosophy professor had to say on this issue:

That high school math has become a competition. To cram as much into a few weeks as you can, and do it as fast as you can. They don't teach kids that there's no shame in taking a little long to do math, and they don't take the time to actually help those kids who are having problems.

It's weird to hear another teacher condemning how other teachers teach...

 

[trawler69]

The best math teacher I had related everything to real life problems and derrived the formulas from observations. Now I use it all the time for solving all sorts of problems to do with electronics, water flow, construction, trigonometry. People look at me as if I'm some sort of freak as I scribble numbers on bits of paper without reaching for a calculator. The other day I was in a shop and knew how much my shopping would be. I had all the right change and gave it to the cashier. She just stared at it for a moment, not knowing what to do, then said "I'm sorry but how much have you given me?" I had to take it back and count it into her hand! how sad is that?

 

[slobone]

Martin Gardner, algebraic topology, AND John Horton Conway! Woo hoo!

-T.

Hi, my name is Slobone, and I'm a nerd... there, I said it.

Once saw a marvelous caricature of JHC in which the top of his head gradually metamorphosed into some sort of intricate three-dimensional structure like something out of Dr. Seuss. Wish I could get my hands on a copy.

 

[slobone]

What are you guys talking about? I was in high school a year ago and I do not think kids math skills have lowered?

No, neither do I. I once asked a high school teacher who was retiring after thirty years whether kids were smarter or dumber today than when she started. She said, "They're exactly the same, year after year."

I heard that many years ago, adults didn't even know how to do geometry untill they went to college.

Hmm, well that may be a bit of an exaggeration. But there was a time when most students didn't start on calculus till college, whereas today it's pretty common in high schools.

But I think the level of math teaching fluctuates. I once saw a test from around the year 1900 that required pretty good knowledge of intermediate algebra to pass. It was an entrance exam for high school! Of course in those days most people didn't even go to high school.

Look, there's no question that math can be very challenging and is much harder for some people than for others. But I see no reason why it has to be the Abu Ghraib/Guantanamo torture experience that it is for so many students.

 

[teadrinker]

Once saw a marvelous caricature of JHC in which the top of his head gradually metamorphosed into some sort of intricate three-dimensional structure like something out of Dr. Seuss. Wish I could get my hands on a copy.

Here ya go:

The structure is an Alexander Horned Sphere: an object which you can read about on Mathworld:

http://mathworld.wolfram.com/AlexandersHornedSphere.html

Enjoy!

-T

 

[gsdx]

Kids (and a lot of adults) rely too much on technology to give them the answers they need. They can't even make simple change without the cash register telling them how much they should give back.

I bought something for my computer many years ago and the young man who served me totalled it up to $10.50

I gave him $20.50

He needed a calculator to figure out the change.

Maybe I shouldn't have given him that 50¢.

 

[slobone]

Here ya go:

Enjoy!

-T

That's the one! V. impressive, td, especially considering Google Images came up dry.

 

[blackbeltninja]

I do recall when I was tutoring HS physics and chemistry that the bulk of not understanding a lot of the stuff was bad grounding in maths.

Most of the relationships between things, especially in physics, could be explained with a graph of eg velocity vs time or distance, but if they couldn't actually deduce things from the shape of the graph, all the grounding in that part of the physics falls to pieces. And when the foundation is bad, the advanced stuff might as well be written in Sanskrit for all the good it does them.

-d-