Wednesday, September 22, 2010

How to complicate maths education

Having had success in encouraging illiteracy over past decades by removing phonetic teaching from classrooms—refusing to teach children the very abstract tools by which they can decode text, replacing them instead with guesswork and a multiplicity of random concretes—educators the world over have also been doing the same with mathematics, quietly removing (for example) the means by which children can make sense of simple multiplication tasks.

In this video, Washington State educator MJ McDermott just how thoroughly today’s educators have made a complicated mare’s nest out of simple mathematical tasks, replacing reliable and easily understood algorithms with complicated procedures and guesswork.

If you understand the phenomenon Ayn Rand called the crow epistemology, you might understand just how successfully the “new” systems being taught for multiplication won’t teach students mathematics so much as “blow their crow.” 

[Thanks to reader Falafulu Fisi for the link]

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6 Comments:

Anonymous RW said...

One could be forgiven for thinking that there is a socialist...sorry "progressives'" conspiricy to undermine parents inclusion in education. The examples she was showing are just bizzare.

9/22/2010 09:47:00 pm  
Anonymous Anonymous said...

They seem bizarre because the weather girl makes a meal of them, almost certainly on purpose.

The methods she explains in such a, no doubt intentionally, turgid manner are in fact really good ways of solving simple maths problems accurately, quickly and without paper. Much faster than using algorithms, which are not necessary for such straightforward problems. To use such methods you have to understand what multiplication and division are in the first place, but no one's suggesting otherwise.

I know everything's a communist plot to you guys, but really.


Judge Holden

9/22/2010 11:18:00 pm  
Anonymous Lance said...

"They seem bizarre because the weather girl makes a meal of them, almost certainly on purpose.

The methods she explains in such a, no doubt intentionally, turgid manner are in fact really good ways of solving simple maths problems accurately, quickly and without paper. Much faster than using algorithms, which are not necessary for such straightforward problems."

Yup, this is how I solve relatively simple problems in my head. The algorithms were how I was taught, and they were all fine and dandy but for 133/6? Unnecessary. It was concepts similar to the other method shown I used in my head for short and simple problems. In a split second I would look at a problem like 133/6 and (in a split second mind you) reduce 133 to a more manageable 12. 6 would then go into that twice, then make it 120 again so 6 goes in actually 20 times then add 2 more sixes for the 13 we left behind and look there's a remainder of one. 22 r 1.

A slightly more complex example lets say at random: 1467/26 In my head, using techniques and concepts similar to those disparaged in the vid I can still do it faster than algorithms by hand.

I would instinctively make the 26 a more manageable 25 and toss aside the 1 for a moment. Then to quicken things up I make the 25 into a 50, there are 2 50s in every hundred and here we are dealing with 14 "hundreds" so 28 50s or 56 25s add two more for the 67 part gives us 58 and 17 remainder then bring back the 1 I tossed aside earlier and divide 58/26 = 2 with 6 remainder take 2 from 58 and 6 from 17 = 56 remainder 11

Of course this looks absurd and convoluted on paper. It's not intended to be expressed that way. No one ever taught me maths is this manner, it's just how my approaches to maths problems developed. I excelled in the subject at school, taking advanced math classes in intermediate by studiously ignoring those silly and painfully slow "carry the one"/working ass backwards paradigms.

9/23/2010 01:09:00 am  
Anonymous Lance said...

Just to add: I have never seen or even heard of this approach before, it's just something that I have always done. Had it been taught at school along with the by hand algorithms it would have saved me a lot of trouble.

I found basic multiplication (i.e. 5x7) to be taught in a counter intuitive manner too. They basically taught it as a kind of repetitive and consistent addition. Which seemed daft because we were made to think of a wonderfully simple, compact and efficient formula 5x7 as 7+7+7+7+7 or 7 14 21 28 35

"What's 5 x 7?"
"35"
"Yes but how did you work it out?"
"I know what 5 x 7 looks like."
"What do you mean? What does it look like?"
"35"

9/23/2010 01:24:00 am  
Anonymous Kimble said...

"Much faster than using algorithms, which are not necessary for such straightforward problems."

Ummm, they are all algorithms.

If you teach a process you want to make it the simplest process possible to teach. That way, even if the kids cant understand the reasons each step in the process, they can replicate it successfully. Fewer moving parts is better, as there will be fewer things to go wrong.

Now, I THINK in the cluster-calculation way. But that has its foundations in the simple algorithms I learned early on.

In any case, no primary school mathematics textbook should contain the directive to "just use a calculator".

Why not just use a spell-checker? Or a grammar-checker? Or just use a report generation engine? Or just use someone else.

9/24/2010 04:43:00 pm  
Anonymous Anonymous said...

The folks that are leaving negative comments are missing the point. These so-called "straight-forward" methods do not teach what's neccessary to move on to higher-level mathematics. For those that have no interest in ever moving on to study of trigonometry and calculus, I suppose that this is fine. Problem is, 4th and 5th graders have no idea what they are interested in. They should not be precluded from the study of higher-level mathematics at the 4th and 5th grade. Should they decide to become a computer scientist, engineer, architect, pharmacist, etc., or apply to Business School, they will be at a tremendous disadvantage.

8/23/2011 08:41:00 pm  

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