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What are "Basic Skills" in Math?

 
 
parados
 
  2  
Reply Thu 11 Nov, 2010 05:47 pm
@maxdancona,
Quote:
But the real frustrating part was, as a teacher, seeing a kid mechanically start subtracting terms from both sides of an equation without even thinking about whether this made sense or not.

Math is about understanding and expressing ideas. It is not about mechanically following memorized instructions.


But that isn't how the real world works. When an electrician needs to know what size wire to use, he doesn't calculate it. He simply looks it up or has it memorized. It would be a waste of time to calculate it every time.

When doing electronic repair, knowing why something failed isn't necessary. It costs too much money to figure it out. It's cheaper to replace the $5 board than it is to figure out which $.05 part failed and replace only that.

What information is really necessary? A 14 year old can build a computer but he doesn't need to understand Ohm's law or C++. He only needs to know which parts to assemble because that is what works. Doing it different won't work.
parados
 
  2  
Reply Thu 11 Nov, 2010 05:50 pm
Let me ask you, as an educator, did you find different people learned differently?
maxdancona
 
  1  
Reply Thu 11 Nov, 2010 06:04 pm
@parados,
Sure Parados, nothing to argue with here.

Again my point is about "basic skills" in math, this doesn't mean that other shortcuts aren't helpful.

In my current job as software engineer, I have quite a bit that I memorized by accident. I didn't make any specific effort to memorize it, I just looked it up enough that it sticks. There are some things I need to look up quite often that I have printed out and thumbtacked to my cubical. Again I am making no effort to memorize them (since looking over at the chart on my wall is fast enough) but I find that as I use them more and more, I need the chart less and less.

Knowing these facts is a side effect of my job, not a "basic fact". I can be a damn good engineer without memorizing the charts because I understand on a deep level the concepts underlying them. However, someone with a few hours on their hands could memorize these charts. This would not make them a very good engineer.

I first learned to program computers when I was a pre-teen (I don't remember the exact year). I wanted to make a video game and needed to know how to make something move at an angle. This is how I learned basic trigonometry (sines and cosines), I didn't learn them by rote, I learned them because I had a specific problem that I wanted to solve.

A 14 year old learning to build a computer will learn quite a bit. She may not need to know Ohm's law, but if she finds she does have a problem that requires Ohm's law-- then she has a hell of a way to learn it, not by rote, but because she has a deep entry point into understanding what it is for on a real level.
0 Replies
 
Ceili
 
  2  
Reply Thu 11 Nov, 2010 06:46 pm
@maxdancona,
Quote:
Why do you think it BEDMAS instead of MESDAB?

Do you really need me to explain why?
Quote:
I would say "BEDMAS" didn't do anything to help you understand the "most basic concepts" of mathematics.

Ironic...
I used the term to illustrate that anyone who wants to be proficient in math must understand the fundamentals, such as addition, subtraction, division and multiplication and when and where to use brackets and equations, if and when you wish to understand algebra.
I didn't realize this was going to be taken as an insult. I think the basics or fundamentals are important. Clearly you don't. C'est la vie.
ehBeth
 
  1  
Reply Thu 11 Nov, 2010 06:49 pm
@parados,
parados wrote:

Let me ask you, as an educator, did you find different people learned differently?
cicerone imposter
 
  1  
Reply Thu 11 Nov, 2010 07:25 pm
@maxdancona,
Addition, subtraction, multiplication, and division. To me, those four are the basics.
0 Replies
 
Ceili
 
  2  
Reply Thu 11 Nov, 2010 07:43 pm
@maxdancona,
Ok, I don't think you have my point at all, either with Reading or Math. I thought it was obvious I was referring to writing not spoken language, as the learning of either skill differs quite substantially.
My kids went to a french immersion school and their spelling was awful for years. So believe me when I tell you I'm not a stickler for perfection, but eventually, kids do become able to write coherently, obviously some better than others.
So let me clarify. It's difficult to read if you don't know the abc's, but you can speak without reading.
We memorize letters, how words are put together but how we do this differs. I have no doubt your daughter hated learning by rote. Even three years olds, who may love watching the same movie over and over, would get bored soon with flash cards.
We learn language by repetition, by mimicking sounds, by pointing to our nose or belly button for the umpteenth time. We learn to pronounce letters or groups of letters, in varying ways, depending on the word or accent.
Most people love music, can listen to it, hum along with a song. It doesn't mean they could sing an opera. I'm a big proponent of learning to play music by ear. That doesn't mean, I don't believe musicians shouldn't learn to read music. The basic building blocks... the fundamentals of both music, speaking and math are similar. (Edited to say: But to become a proficient musician, practicing the same piece or scale is necessary, just like solving the same types of math problems ad nauseam.)
Creativity, whether it be in the sciences or the arts, is not diminished by learning the basics. How one person learns may not be consistent within a classroom, so I think its more important to cater to learning styles rather than one set method. Regardless, every student must understand the same material, however they learn it.
I think it is important to learn the basics, I didn't say problem solving wasn't one of them. Most people learn to read by reading, that is not unusual. If you don't understand a word, you flip through a dictionary. The same with a mathematical problem, if I wanted the area of a circle, I would use a formula.
Maybe your daughter will figure out another way to do it and that would be awesome, but for me π • r² works.
0 Replies
 
dadpad
 
  3  
Reply Thu 11 Nov, 2010 07:49 pm
I never learned anything till i needed to know.
Pi only applies to a trees circumfrence diameter and/or radius as far as i am concerned. Combined with length I can tell pretty damned closely how much timer is there, how fast the tree is growing
I was close to 40 when i learned this.
why? because i WANTED to know.
cicerone imposter
 
  2  
Reply Thu 11 Nov, 2010 07:54 pm
@dadpad,
I believe Ceili said as much about different folks learn at different times of their life. The key being "I wanted to know." There has to be that innate motivation inside the person to learn no matter what the subject or area of interest.

I was a slow learner too, but managed pretty well in my career.
0 Replies
 
maxdancona
 
  0  
Reply Thu 11 Nov, 2010 08:29 pm
@Ceili,
Quote:
Quote:

Why do you think it BEDMAS instead of MESDAB?


Do you really need me to explain why?


Yes Ceili. This is a very important point.

Many people know the rule as a rule without understanding the mathematical idea behind it. Understanding the idea is far more important than the silly mnemonic-- in fact if you understand the idea, you don't need the mnemonic.

It bothers me that so many people focus on the silly rule without understanding the ideas behind them. This is missing the whole point of mathematics.

Fundamentals should mean core ideas. Fundamentals are not silly rules. Silly rules can get students to mechanically solve problems-- but only to solve the small set of problems that they have seen before.

If you focus on the core ideas, you can not only solve the rote problems as well as someone can with silly rules, you can also create solutions to new sorts of problems.

This is real math-- meaning the sort of math that mathematicians and engineers do.


maxdancona
 
  0  
Reply Thu 11 Nov, 2010 08:41 pm
@ehBeth,
parados wrote:
Let me ask you, as an educator, did you find different people learned differently?


OK, I missed this question. I think the question kind of misses the point.

The answer, of course, is yes. Different people learn differently. But the real issue here is the goal of learning.

As I said before, there is a big difference between mathematics and arithmetic. The purpose of math is to provide a framework for expressing ideas and solve problems. No matter how someone learns, critical thinking, logic and creativity are essential.

If all someone learns is a set of mechanical fill in the blank templates to solve a specific set of problems, then they haven't learned mathematics. Unfortunately, many people think that focusing mechanical turn the crank techniques are somehow important, and this is the reason we force kids to do the same problem over and over again. Not only is this useless to teaching kids real mathematics, it is damn tedious.

There are many ways that people gain the critical thinking and problem solving skills that are the heart of mathematics, but all of them involve critical thinking and solving problems.

Expecting rote drills to lead to mathematical ability is akin to expecting Mad-Libs to improve your ability to create literature.


cicerone imposter
 
  0  
Reply Thu 11 Nov, 2010 08:56 pm
@maxdancona,
max, Well stated.
0 Replies
 
fresco
 
  3  
Reply Fri 12 Nov, 2010 01:53 am
@maxdancona,
Speaking as a former teacher I commune with maxdonna's enthusiasm for "real math". However the fact is that over 95% of a class of children are NOT going to be mathematicians or engineers, and they need to be equipped with a "feel" for arithmetic such that everyday transactions make sense. Such a "feel" comes in part from their familiarity with mundane calculations in which knowledge of multiplication tables and basic addition and subtraction bonds is the "oil in the wheels" for such skills. People with a natural flare in the subject can put up with what they see as trivia. The "happy clappy/ instant access" philosophy of elementary teaching which has developed on the back of the information revolution seems to have had statistical effect of dumbing down the end product for the majority.
aidan
 
  1  
Reply Fri 12 Nov, 2010 02:36 am
@fresco,
Amen! What he said- Laughing Laughing

You know - WHY does it always have to be one or the other? Why can it never be both? Why do we always have to insist on throwing out the baby with the bath water?

Because I'll tell you something. I've got two kids - one has a naturally inclined math brain and one doesn't. And the one who doesn't has made it almost all the way through school- and I'm talking about good schools in two different developed countries- and she can't add fractions.
Why? I guess because these days it would have been looked at as 'cruel and unusual punishment' to make her learn them- along with memorizing her times tables.

She was in one school in fourth grade in a school system that had been ranked #52 in the US and at her conference in November her father and I were called in to be alerted to her abysmal performance on math tests. Okay - three months of the school year gone, I worked in the same school system, and never a breath or hint of trouble...not a note or word from the teacher expressing concern.
We sat there and she told us that Olivia was consistently failing every math test. I'm like, 'Huh? Why are we just hearing this now?'
And she said, 'Well, I wasn't aware until I gave them an individual test that it was a problem,' and I said, 'An individual test? What are you talking about?'

This young teacher had been putting the kids in groups and giving them work to do and so of course, if you have a smart person in your group and you don't know what the hell you're doing and the smart person is giving you the answer and as a member of the group, you're allowed to take credit for that answer and legitimately write it down as your own - HELLO - what kid who hated math wouldn't take advantage of that situation to hand in all the math work perfectly done?
She'd even been giving the group TESTS - until someone clued her in that she needed to get a better handle on who in the group knew what.
It took this woman THREE months and someone else to help her figure out that maybe she needed to know which members of the group did and didn't grasp the concepts.

I had my daughter switched to another class the next day.

Hasn't seemed to help much though.
Fortunately - I've got the GED curriculum and I figure if I can get her at least up to GED or GCSE level in what I consider 'basic math skills' - she'll at least be functional in society.
Ionus
 
  1  
Reply Fri 12 Nov, 2010 02:46 am
@maxdancona,
Quote:
Can you explain why BEDMAS is not EBDMAS or SABMDE?
Because dyslexic hasnt posted yet ???
0 Replies
 
Ionus
 
  1  
Reply Fri 12 Nov, 2010 02:47 am
@aidan,
Quote:
I don't know anyone ever who has or was taught addition by memorization!
Seriously ? Whole generations were taught to chant their times tables....I didnt know they had stopped.
Ionus
 
  2  
Reply Fri 12 Nov, 2010 02:54 am
@maxdancona,
Quote:
It bothers me that so many people focus on the silly rule without understanding the ideas behind them.
That silly rule is adequate working knowledge. I dont need to know ionic theory down to string theory level to disolve salt in water and gargle. Teaching too much theory results in students dropping out. Not everyone is going to be a brain surgeon...people dont have that many brains.
0 Replies
 
aidan
 
  1  
Reply Fri 12 Nov, 2010 03:13 am
@Ionus,
I said 'addition' = not multiplication.

I don't know - I've always seen addition taught with manipulatives - you know there's one apple in a basket - if we add another apple how many apples do we have now?

I've never heard or been made to or made any one else chant - one and one is two- one and two is three - one and three is four....
Have you?
Maybe I just missed it.
Ionus
 
  1  
Reply Fri 12 Nov, 2010 05:54 am
@aidan,
Quote:
I said 'addition' = not multiplication.
My error, but same method.
Quote:
I've always seen addition taught with manipulatives
Thats certainly true of the concept, but the final process is chanting. At least, that is what my two primary school children have just confirmed to me...and it was that way when I was at school...my other two sons (young men) are not here tonight to confirm any changes that may have occured about 10-15 years ago when they came through primary.

I think the very basic aritmetic concepts are picked up before school now, watching Seasme street and like.
0 Replies
 
maxdancona
 
  1  
Reply Fri 12 Nov, 2010 06:29 am
@fresco,
Quote:
Speaking as a former teacher I commune with maxdonna's enthusiasm for "real math". However the fact is that over 95% of a class of children are NOT going to be mathematicians or engineers, and they need to be equipped with a "feel" for arithmetic such that everyday transactions make sense


This is an interesting theory. But I disagree with the idea that doing the same problem over and over again mad lib style does any good. This argument doesn't sound too crazy for addition and subtraction, but you all slaved away for weeks learning how to factor polynomials. I bet 95% of people not have never needed to factor a polynomial, most people couldn't name a situation where one might want to factor a polynomial. This is a completely useless exercise.

Mathematics is about creativity, expressing ideas and problem solving. This is what a math class should be about. Learning about how to approach a problem or express an idea is beneficial for students whether they are going to be mathematicians or not.

Quote:
seems to have had statistical effect of dumbing down the end product for the majority.


Since this is a thread about mathematics, wild claims like this should at least be backed up with data.
 

 
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