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What are "Basic Skills" in Math?

 
 
maxdancona
 
  1  
Reply Fri 12 Nov, 2010 03:13 pm
@sozobe,
Quote:

That again seems to be presenting a false choice, though -- that because this is a good thing, memorization is a bad thing. I think that this is a good thing AND memorization has its uses.

I think that what you describe is great way to learn multiplication, and that's how my kid learned it too (at least part of the way, and how she was introduced to it at the earliest stages).


Sure. I have no problem with this. If my daughter decides she wants to make flash cards for herself, I will go along as long as it doesn't interfere with her understanding.

What makes me bristle is the idea that so-called "basic skills" (meaning rote memorization and mechanical ways to solve problems of a very specific format) are necessary.

From personal experience I know that memorizing the multiplication table is not that important even for someone like me in an engineering career. When I see 6 x 8 my mind takes a little trip through 12 and 24. This means that your kid might be able to solve this problem twice as fast as I, maybe in .15 second where it takes me .3 seconds. This has really never been much of an impediment (or I would take the time to learn them now).

But my thesis is this,

At the core of mathematics are expressions and objects and ideas. The goal is to develop and express new ideas using creative thinking and logic and problem solving.

You clearly don't need FOIL or BEDMAS or silly tricks or rote memorization to get to the point you can do real mathematics. I didn't need them. My daughter is doing real math without any such tricks.

I will accept the idea that these tricks are helpful to some people. My objection is when these tricks become the focus of mathematics. In my opinion it is essential to make the ideas focus of mathematics. And, thus, I feel it is best to start with the ideas.

That being said, you are correct about different people learning differently.




cicerone imposter
 
  1  
Reply Fri 12 Nov, 2010 03:42 pm
@maxdancona,
I think creative thinking and problem solving is a whole other issue.
0 Replies
 
Ionus
 
  2  
Reply Fri 12 Nov, 2010 08:47 pm
@maxdancona,
Quote:
What makes me bristle is the idea that so-called "basic skills" (meaning rote memorization and mechanical ways to solve problems of a very specific format) are necessary.
An animal barely escapes from a predator...it stops on a rise and looks back. It is memorising. It wont need to stop and analyse when it sees that predator again. Grazing on grass, it accumultes experience as to what is best to eat and looks for it. It doesnt have a learning mechanism that is not based on either rote or shock. Which one do you prefer ?
maxdancona
 
  1  
Reply Fri 12 Nov, 2010 09:44 pm
@Ionus,
Quote:
An animal barely escapes from a predator...it stops on a rise and looks back. It is memorising. It wont need to stop and analyse when it sees that predator again. Grazing on grass, it accumultes experience as to what is best to eat and looks for it. It doesnt have a learning mechanism that is not based on either rote or shock. Which one do you prefer ?


I prefer evolving an uncharacteristically large brain that is capable of abstract thought and problem solving skills allowing this animal to control predators using tools and eventually technology.

And opposable thumbs.
Ionus
 
  1  
Reply Fri 12 Nov, 2010 10:24 pm
@maxdancona,
Quote:
abstract thought
Abstract thought is left over mathematical computing power from when we used to calculate distance in trees and branches. It was redudndant on the ground but was eventually put to good use. It has nothing to do with how we learn. Your love of the abstract is no reason to force everyone to do it. What does the average person need in an education and when is the best time to get it. And there are only two learning methods.....rote/copy and shock/horror.
talk72000
 
  1  
Reply Fri 12 Nov, 2010 10:27 pm
@Ionus,
I agree. Many have given up on math when New Math came in. Personally I have no problem but the population in general was harmed as they skipped basic sciences and math in high school.
0 Replies
 
maxdancona
 
  1  
Reply Fri 12 Nov, 2010 10:40 pm
@Ionus,
Quote:
abstract thought is left over mathematical computing power from when we used to calculate distance in trees and branches. It was redudndant on the ground but was eventually put to good use. It has nothing to do with how we learn.


I can't tell if you are joking or not. If you mean this to be a joke, it is really funny. If not, I suppose I can attempt a response. Have you heard of Piaget?



Ionus
 
  1  
Reply Sat 13 Nov, 2010 01:54 am
@maxdancona,
Quote:
Have you heard of Piaget?
Yes, but if you want answers I wouldnt ask me too much detail.
0 Replies
 
 

 
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