A an example in crutch leaning.
Published on June 4, 2007 By greywar In Current Events

 

     When I was in school there were always kids (myself included) who would bitch and while that we should be allowed to use calculators for even simple math. Would my school have done me a favor by allowing it? Probably not and here is why.

 

     There are two questions listed below. One of the questions should be able to be answered by any Joe or Jane off the street without hesitation and the other isn’t really esoteric knowledge but it is not a question I would expect to have answered unless the answerer had a bit of training.  You tell me which is which:

 

 

  1. What is the subnet mask equivalent of the CIDR notation /30?

 

  1. What is 7+3?

 

     The ability to quickly answer 7 + 3 has been a given for so long that in our most recent hire we didn’t think to ask. Can he answer? No, he cannot and it may well cost him his job.

 

     I work as a network engineer and analyst so I am expected to know the answer to #1 without hesitation but only because I have received training on the subject matter. We frequently hire people with little or no experience (like hiring a pizza-guy) in networking on simply OJT them to the appropriate level. This is of course limited to people who can demonstrate that they have some native intelligence, the ability to learn, and the desire to do so.

 

    We don’t care if you don’t have a CCNA, Network+, or bachelor’s degree (although all of those things are good) but we do care if adding 7 + 3 has you reaching for a calculator.

 

     How can a high school education be viewed as a valid certification of any level for mathematic when the only thing taught is the ability to punch in numbers on the key interface of a calculator? How can a student judge whether they have made an input or formula error when estimating 256 x 2 results in nonsense answers starting at 400?

 

     Most of the time spent in OJT in most IT fields is spent learning the basic building blocks of technology and the lexicon thereof. Many IT concepts which appear impenetrable to an outsider are actually very simple math operations disguised by jargon or a different number base (IP addressing leaps to mind). One you have the jargon and had the system explained it all becomes clear unless you can’t do the simple math itself.

 

     Anyone who deals with networks or computers in general will recognize the following number set :

 

2

4

8

16

32

64

128

256

 

     These are the powers of two from 21 to 28. This subject takes about 3 seconds to understand if you actually had to memorize multiplication tables in elementary school. Explaining it to someone who did not even have to memorize which single digit number pairs add up to 10  is virtually impossible.

 

     The person in question is by no means stupid but they are uneducated despite having a high school diploma and currently being enrolled in college. The problem is that instead of forcing him to learn the concepts involved with basic math his school advocated and allowed the use of calculators from an early age.

 

     The result is a man who when asked, “Ok, so 16 – 8 leaves you…?” answers with, “14?” This answer doesn't seem odd to him because number in general don't mean much to someone without a solid education in basic math. Numbers are just buttons on a calculator to him. Devoid of meaning and therefore beyond his ability to intuit in the case of drastically wrong answers. 

 

     If I give him his calculator he gets the answers right much more often but still only at about a 90% success rate since he has no ability to check for errors. He thought he punched in 28 so he thinks that 512 is the answer (hint : it ain’t).

 

     Additionally this makes every operation very slow. Answering #2 takes an educated person less than .1 seconds but takes him the time to find the calculator, turn it on and punch it in.  Furthermore no one in his educational history ever even attempted to explain estimation to him. The concept is alien and unfathomable.

 

     Long division? Shorthand multiplication? Addition or subtraction of numbers beyond 5? It might as well be nanotech to him.

 

     Calculators are for college-level and higher problems (even then there is a pretty solid argument against using them except in extreme cases) not 7 + 3.

 

     Thanks Mom (for teaching me math and reading before kindergarten) and thanks Minnesota education system for not giving me a goddamned calculator.

 

P.S. I had no actual reason for this most recent hiatus so umm sorry.

 

 

 

 

 

 

 

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Comments
on Jun 04, 2007
I wrote a similar article about 6 months ago, so I could not agree more with you.  When I jumped into the TCP/IP math, subnetting came second nature to me (and still does).  Yet several of my co-workers have to write it down, or crank out a calculator.  The first Calculator I got was when I graduated from HS.  These guys have never known a life without one.
on Jun 04, 2007
Aackk! I hated math in school, but I was always able to do it. We weren't allowed to use calculators until we got to graphing operations, and even then it was only for graphing. It amazed me when I took my test to apply as a teacher's aide back in TX how many people couldn't pass the math portion of the exam, especially considering you were allowed to use a calculator. I never did. It's a crutch. It makes me feel lazy to use one, even when using larger numbers.

Glad to see you back, greywar.
on Jun 04, 2007
You are so welcome, son. I agree wholeheartedly with your conclusions. You may be sure that all the students that I ever had the privilege of teaching in the elementary schools always were required to learn the basic math skills.

As a way of advertising my new book which will be available soon at Amazon. com called "Convent Life and Beyond," I am including a story from that book apropros to your article.:
"A great youngster, Bobby, is often in my memories. This boy loved school, but he had a hard time with math. Try as he might, he just couldn’t seem to learn the multiplication tables. His classmates took turns helping him but he often became very discouraged. One weekend, this innocent boy was riding in the family car with his older brother. They rode along on a gravel road and the car overturned. Death came upon this child in an instant. On that terribly blue Monday morning, I met my class with deep mourning in my heart. Bobby was the first student that I had ever lost through death. It was so hard to counsel the children, though most of them had parents who knew how to approach tragedy from a faith outlook. While we discussed how much we would miss Bobby, one child raised his hand and sagely offered, 'Now, Bobby knows all of his multiplication tables without any trouble. He knows a whole lot of things that we will have to learn the hard way.' This response brought a smile to everyone’s face and hope to these young maturing hearts as well as to their grieving teacher. As time passed, we could not forget Bobby and we remembered the joy he had brought to our lives.

Keep writing!
on Jun 04, 2007

We weren't allowed to use calculators until we got to graphing operations

That was the way I remember it as well and even for those you only used the graphing calculator if you could afford to buy one.

Yet several of my co-workers have to write it down, or crank out a calculator.

Generally we wont employ folks who have to think about it too hard. If they can't do subnetting on the fly while on the phone with a customer they don't usually last. I hope this guy can make up the lost ground but it doesn't seem likely.

 

'Now, Bobby knows all of his multiplication tables without any trouble

 

Your capacity to remember these stories never ceases to amaze me. I can't remember things that happened 5 years ago with any clarity.

on Jun 04, 2007
If they can't do subnetting on the fly while on the phone with a customer they don't usually last.


You're right. if you're working with IPv4, You better know 2 up to the 8th power. Of course, you're gonna be a dinosaur real quick if you ain't learning base 16...lol!
on Jun 04, 2007

You better know 2 up to the 8th power

True and you can use 2 to the 8th as an easy stepping stone to figure out higher powers if you don't feel like memorizing the tables... unfortunatly when I ask him what 1024 x 2 is it usually starts out as "five thousand and..."

 

I try not to sigh out loud.

 

Of course, you're gonna be a dinosaur real quick if you ain't learning base 16...lol!

IPv6 makes my head hurt.

on Jun 04, 2007
Of course, you're gonna be a dinosaur real quick if you ain't learning base 16...lol!

IPv6 makes my head hurt.


I like spelling words with it.
on Jun 04, 2007
My wife did a research paper on this topic. We both couldn't believe how many college professors have written in defense of students using calculators even in elementary school.

The number of students taking sub 101 level math in college shows how important it is to teach concepts in math, not just numbers, or worse yet.. buttons.
on Jun 04, 2007
As a way of advertising my new book which will be available soon at Amazon. com called "Convent Life and Beyond


Completely OT...WOOOHOOO!!!! I remember reading your stuff before and I will definetely buy it......

And as for the issue at hand, I am one of the kids who was crippled as a child. I never was forced to learn my multipication tables and MOST of my math errors (I made it to calculus in HS) were simple math errors. Even now, I resent not being able to double check my math with a calculator. I only wish that I had not been given a calculator so young.
on Jun 04, 2007
I love calculators, but I know about what the answer should be before I put in the numbers. When you're adding up a lot of numbers, it's best to use a calculator or adding machine. Or excel formulas. But, everything we do gets checked on the calculator before it goes out, regardless of how my mental math is.
on Jun 04, 2007

Or excel formulas

And double check the formulas!

on Jun 06, 2007
Admitting from the start that I am handicapped by CSL (computer as second language) and am not able to understand two thirds of this thread...I would like to contribute a little about something I do know about...deteriorating math skills in this here USA.

Hate to start off sounding like grandpa, but, I AM Grandpa...and when I went to grade school, hand held calculators did not exist. Our calculators were long and skinny with a lead point on one end and a much used eraser on the other. We had to memorize the "facts" and pass timed tests on them or not pass to the next grade...yes, actually be held back. As we learned to build on those facts and apply them to problems, we were required to "show your work"...and that is where the concepts of mathematics were learned. It wasn't enough to find the right answer...some could actually do that intuitively...but to show HOW that became the right answer was required.

I find in my day to day life that I use those facts and problem solving skills quite often. I am also amazed at how many young people do not have those skills. The young lady at Souper Salad who for three weeks running has not been able to make change correctly. The fast food workers at almost every burger/taco/pizza/chicken joint in town who have to find the color coded buttons on the cash register in order to figure out what you owe and then how much you get back.

Numbers are just buttons on a calculator to him. Devoid of meaning and therefore beyond his ability to intuit in the case of drastically wrong answers.


SOOOO true.

Not everyone is mathematically minded. Some people never see the point of "higher math". Many who can easily grasp the "facts" never "get it" when it comes to calculus or trigonometry or any of a number of disciplines that I will never get. Thank heavens for you all who do. But the rest of us have a contribution to make, also, in this big ole world...so long as we don't have to show our work.

on Jun 06, 2007

yes, actually be held back

It is hard to overstate the importance of standards and consequences for failure.

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