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Calculation without Understanding


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#1    coberst

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Posted 16 January 2009 - 05:08 PM

Calculation without Understanding

Early in our institutional education system we learn arithmetic.  We learn to add, subtract, multiply, and divide. We learn to calculate without understanding.  

This mode of education follows us throughout our formal education system.  We learn to develop answers devoid of understanding.  We do this because, in a society focused upon maximizing production and consumption, most citizens need only sufficient education to perform mechanical type operations; that is perhaps why our electronic gadgets fit so well within our culture.

If we think about this situation we might well say that this form of education best serves our needs.  It is efficient and quick.  However, beyond the process of maximizing production and consumption we are ill prepared to deal with many of life’s problems because we have learned only how to develop answers that are “algorithmically friendly”.

In grade school we are taught to manipulate numerals (symbols) not numbers (concepts).  We are taught in grade school not ideas about numbers but automatic algorithmic processes that give consistent and stable results when dealing with symbols.  With such capability we do not learn meaningful content about the nature of numbers but we do get results useful for a culture of production and consumption.

We have a common metaphor Numbers are Things in the World, which  has deep consequences.  “The first is the wide spread view of mathematical Platonism…[it] leads to the metaphorical conclusion that numbers have an objective existence as real entities out there as a part of the universe…Given this metaphorical inference, other equally metaphorical inferences follow, shaping the intuitive core of the philosophy of mathematical Platonism.”

Quotes from Where Mathematics Comes From by Lakoff and Nunez



#2    Orion von Koch

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Posted 16 January 2009 - 05:15 PM

coberst on Jan 16 2009, 11:08 AM, said:

Calculation without Understanding

Early in our institutional education system we learn arithmetic.  We learn to add, subtract, multiply, and divide. We learn to calculate without understanding.  

This mode of education follows us throughout our formal education system.  We learn to develop answers devoid of understanding.  We do this because, in a society focused upon maximizing production and consumption, most citizens need only sufficient education to perform mechanical type operations; that is perhaps why our electronic gadgets fit so well within our culture.

If we think about this situation we might well say that this form of education best serves our needs.  It is efficient and quick.  However, beyond the process of maximizing production and consumption we are ill prepared to deal with many of life’s problems because we have learned only how to develop answers that are “algorithmically friendly”.

In grade school we are taught to manipulate numerals (symbols) not numbers (concepts).  We are taught in grade school not ideas about numbers but automatic algorithmic processes that give consistent and stable results when dealing with symbols.  With such capability we do not learn meaningful content about the nature of numbers but we do get results useful for a culture of production and consumption.

We have a common metaphor Numbers are Things in the World, which  has deep consequences.  “The first is the wide spread view of mathematical Platonism…[it] leads to the metaphorical conclusion that numbers have an objective existence as real entities out there as a part of the universe…Given this metaphorical inference, other equally metaphorical inferences follow, shaping the intuitive core of the philosophy of mathematical Platonism.”

Quotes from Where Mathematics Comes From by Lakoff and Nunez


I highly suggest you read how the ancients learned life...Read: R. A. Schwaller de Lubicz, THE TEMPLE OF MAN.



#3    coberst

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Posted 17 January 2009 - 02:28 PM

Orion

I quote this from Amazon

"One needs to learn to read this book and then immerse oneself in it. Were one to do this, and assuming diligence, sincerity, determination and some ingenuity by the reader, the outcome toward which all human life is aimed, the evolution of consciousness is assured. "-- Atlantis Rising

Could you give a short statement as to the meaning of this statement.

It is a very expensive book to buy.





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