"Math Facts"

Rant on.

In another thread, a comment was made that other skills were more important to learn than simply "memorizing math facts".  While I don't disagree that there are other very important skills to learn in school, the term "math facts" makes me sad because it represents so much of what is wrong with math education these days.

Why are people teaching kids that 7x8 and 8x8 are completely unrelated concepts?  Just facts to be memorized?  If kids don't learn that eight 8s is one more 8 than seven 8s, they're never going to be able to move on beyond whatever set of "math facts" they're told to memorize.  I've seen this in university students who can't multiply by ten without the help of a calculator.  (And this is science majors I'm talking about, so they've got as much math 'education' as most are ever likely to get.) 

How on earth are students supposed to develop any sense of numeracy if they don't understand what they're doing when adding/subtracting/multiplying/dividing?  ; How will they learn to work out whether or not they have enough money to pay the bill when they go shopping?  How will they learn to cut through the crap when someone's trying to sell them something with "just ___ small payments of $___" and realize what the total cost is going to be?  Math is not some obscure unimportant skill that we make people do in school but will never be useful in real life.  (Okay, not a lot of people use calculus in real life, but I'm talking about the basics here.)

Rant over.

I've maintained for a long time that the sciences make you useful, and the arts make you interesting.

People seem much more enamoured with the idea of being interesting than useful these days.

Of course, useful people tend to be engineers, and engineers are nearly always social retards... so I can see why people shy away from that.

 One could always opt for trying to cultivate the ability to present useful things in interesting ways.

 I think a lot of engineers go through larval stages in their early careers where their brains don't have enough room for both Engineering and Socialization HowTo's. Most grow out of it.

'course, one can take the opposite tack:

 Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe and not make messes in the house.
--Lazarus Long, "Time Enough for Love", (Robert A. Heinlein)

(Seeing as I've forgotten most of the calculus specifics to the point where I need to look'em up if I need to use them I rather hope that I don't need to pass a written test on that to qualify...)

A lot of the process of learning math in school is designed to build cognitive skills.  Beyond basic math, most kids will not use a lot of what they learn again.  Therefore, the goal behind a lot of math that you aren't going into a career involving is just the cognitive building process.  The idea of memorizing instead of understand is defeating the purpose.  :P

Its like using a motor scooter to go jogging.  Math is jogging for your brain, doesn't matter if you'll ever apply it!  :P

I'm a math minor (economics major) and the skills i learn in calculus are the most applicable to real life.

For example, weight loss = change over time, if I lose 5 pounds in 5 weeks than my rate of change (derivative) is 1/1. If I were to integrate those 5 weeks to find out the area below the curve it would equal 5 pounds.

No, I clearly don't have to do that but I look at my weight loss "equation" and immediately see it as that - an equation just like everything else. Math skills apply directly to business and a million other professions. I'd be hard pressed to find a professional career path (white collar) that doesn't apply math in some way shape or form. 

Math is a skill - it's not something you can memorize and apply successfully. It's a logical process, not a series of facts like history. (don't get me wrong, I enjoy history - but it is a series of facts)

Original Post by susiecue:

Why are people teaching kids that 7x8 and 8x8 are completely unrelated concepts?  Just facts to be memorized?  

I'm thinking it varies from school to school and/or teacher to teacher.  My 8 year old is not only learning memorization skills, but on every single piece of math homework involving addition, subtraction, decimals, and fractions, there is always a section on recognizing patterns in how the problems are figured out (ie: recognizing place values, common denominators, equivalents like 50% = 1/2 = 4/8).

However, even if my son's teachers weren't doing this, I WOULD BE.  Should the schools be teaching practical skills?  Of course.  But a child's first and most important educators are their parents.

For extra geek points:

Target weight is a simple function of caloric intake. Given a fixed amount of calories every day and no external factors (exercise, illness, et al), the body will naturally lose or gain weight limited by this function:

Kd = 20kcal/kg * m

Where:

Kd is BMR in kcal
m is the mass of the person in kg
and 20kcal/kg food energy by weight, determined empiracly (this is a rough approximation).

Thus, if you're eating 2000kcal a day with no exercise, your ultimate weight would be

2000kcal = 20kcal/kg * m => m = 2000 kcal / 20 kcal/kg=> m = 100kg, or around 220lbs.

Caloric deficit results in weight loss at a rate of around 3500kcal/lbs, or 7716kcal/day. So:

Wd = (20m - Kd) / 7716

Where Wd is the amount of weight change per day

The curve that weight loss follows is a standard exponential decay. For geek points, determine the lambda of that curve.

For bonus geek points, assume a person is, say, 125kg. How long will it take that person to reach 100kg?

For bonus BONUS geek points, how long would it take the same person to reach 100kg if intake was dropped to 1500kcal/day?

---------------

Why?

In this case, the exponential curve will give a much more accurate predictor of weight loss over time than a simple linear extrapolation, because weight loss is a function of caloric deficit and caloric deficit drops as your weight drops relative to the amount of intake.

Math gots it uses.

I love giving cashiers things like $21.56 for a $6.31 bill so I can get a ten, five and a quarter back and they look at you like you're from another planet.  Just punch it into your cash register and you'll see...

Being in an engineer in an R&D department, I actually still use calculus and differential equations at times.

As one who grew up with a calculator though, I can remember being impressed with some of my professors of the slide rule generation "approximating" answers to examples on the board as the class was checking the number with the calculator.  They had a lot of practice, from using a slide rule, carrying the decimals in their heads while most of us had always had a calculator available.  It just takes some practice and desire...

To add another disturbing dimension to the lack of numeracy in our population...I do research on cancer treatment decision making, and MANY, MANY people simply do not have the numeracy skills to understand treatment risks and benefits, which are of course, mostly presented in a numerical format by highly educated doctors (badly) translating that info their patients.

I agree with #5.  I don't think teachers are solely responsible for educating children ...   My view is that they have a limited amount of time each week to provide the bare bones of a topic and set homework but I, as parent, have a responsibility to expand on that with practical examples.   Same applies to other subjects.

One week, for example, he was covering 'negative numbers' (he's 8).  We got in the car one morning and the thermometer was on -2C.... Next day we both tried to guess was it warmer or colder that morning & by how much..... that one got quite competitive!  We play other 'maths games' like calculating what time we'll arrive at a destination if we're going at x mph for y hours.  Yesterday in a shop he was looking at a £60 item with 10% off and I got him to work out what the total was before paying.  We also talk about budgets, saving up for something, getting value for money ... never too young to be financially literate.

We're not talking differential calculus and quadratic equations... this is basic stuff.  If more people took the time to explain things to their children and not delegate it entirely to teachers we'd be better off all round

Original Post by gi-jane:

 If more people took the time to explain things to their children and not delegate it entirely to teachers we'd be better off all round

 

 I agree with this to a point.  It is important to play a role in educating your children, however a lot of word of mouth "facts" get implanted into childrens minds this way.  :P

Of course nobody said teachers are always right either.

Educated parents make for educated children!  Problem is a lot of parents are lacking in the brain department.  (Not trying to generalize, just personal experience from what I've seen through my life.)

Probably doesn't help much that kids tend to learn different things than their parents. I remember when I was in grade 11, starting on sums and limits leading up to pre-calc in grade 12 and asking my mother (who's an accountant, has gone to university to take statistics and probability courses and whatnot. She insisted that she didn't even TOUCH pre-calc let alone derivatives or integrations in high school.

My oldest kid only started in limits this year, and only because he specifically wanted a pre-calc math course. Different ages, different provinces...

... and as some have pointed out, unless you use it, it goes away. I couldn't tell you the dates of the Riel Rebellion or the battle of the Plains of Abraham. I'd probably get the dates wrong for when individual provinces joined confederation, or who all the PMs were.

But because I use it reasonably often, I can probably tell you how to find the area under the curve, and teach my kids how to do the same.

(BTW - If you're looking for an amazing reference from which to teach calculus fundimentals in a way that isn't as dull as watching a dead donkey rot, get a book called "How to Ace Calculus - A Streetwise Guide". 100% of the basics, only maybe 15% of the normal calculus boredom! Find it here: http://www.amazon.ca/How-Ace-Calculus-Streetw ise-Guide/dp/0716731606 )

why take so much extra energy in learning math when you have calculators and computers

Original Post by ching12:

why take so much extra energy in learning math when you have calculators and computers

I really hope you're either joking, or you're my 8 year old and learned how to create an account and post here (he just made that very same argument a couple of weeks ago to protest homework).

Original Post by ching12:

why take so much extra energy in learning math when you have calculators and computers

Because, unless you plan on taking a calculator in with you when you go to buy a car, you're going to get scammed using various sales techniques devised to make people who can't do math (i.e. most people) pay more.  Same argument at the furniture or electronics store.

Because you don't want to get yourself heavily in debt because you weren't able to work out how long it was going to take you to pay off your credit cards with their crazy high interest rates.

Because once you get past the basics, learning math is learning how to solve problems and manipulate data.

Because you want it to be easier to lose weight.  (It become lots easier when I turned it into a math problem.)

(I took grammar too.  Sentence fragments are not wrong when used for emphasis.  )

In regards to the original post and memorizing times tables... When I was in elem. school we had to memorize multiplication tables and we all understood how they were correlated (7x8, 8x8, etc). We understood that each one increased by the same number. I guess I don't see how this is an issue. 

Original Post by susiecue:

Why are people teaching kids that 7x8 and 8x8 are completely unrelated concepts?  Just facts to be memorized?  If kids don't learn that eight 8s is one more 8 than seven 8s, they're never going to be able to move on beyond whatever set of "math facts" they're told to memorize. 

um, when's the last time you were in a third-grade classroom, susie?  because trust me, kids are taught that those concepts are related. but they're also encouraged to memorize, so that when they get to more advanced math, they can spend their time and brainwork on the more complex calculations without being tripped up by stupid mistakes or wasting time doing arithmetic they should already know.  think BEDMAS: if you don't know the DMAS, the BE isn't going to matter.

there are plenty of things to get your knickers in a twist about when it comes to education, but this isn't one of them.