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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 think that it is right that the children learn the tools of mathematics first. It is like any skill, the pupil needs to know how to use the tools before going on to building the concepts. What good is a woodworker if he doesn't know how to use a saw or a chisel?

But then, where is the profit in training a child to be a mathematician if that child has no intention of pursuing mathematics as a career? Every science and technical field contains the mathematics applicable to that field. Other than this, the child will only need to learn the arithmetical skills necessary to get through life.

Forcing something onto a child is only going to have a negative result.

Open Mind

I think that our educational system fails us all by teaching us what to think but never preparing us to learn how to think. We need a more sophisticated citizenry if we wish to avoid self destruction.

coberst;1110695 wrote: Open Mind



I think that our educational system fails us all by teaching us what to think but never preparing us to learn how to think. We need a more sophisticated citizenry if we wish to avoid self destruction.


That is why there are elective courses.............



I got more out of my "Bachelors Survival" or "Film Study" classes than English or History.



Your assumption is ALL that is offered are classes that pertain to "maximizing production and consumption"



Poppy ****

coberst;1110695 wrote: Open Mind



I think that our educational system fails us all by teaching us what to think but never preparing us to learn how to think. We need a more sophisticated citizenry if we wish to avoid self destruction.


And what would that be?



A dumbed down student that feels everyone should make the same, no matter their effort?

No extra credit if you are better at what you do than the next citizen.



Ain't gonna happen.......

If I were stranded on a desert island and had to live on it for years, ala "Robinson Crusoe", I would prefer some fellow survivors with less sophistication, critical thinking skills and intellect and more savy in how to build a shelter, start a fire, trap animals and fish. That's not to say that the intellectual could not have these skills, it's just not likely. Now once my belly is full and I am warm and cozy, I would be receptive to listen to the critical thinker pontificate. Society will survive not because of sophisticated and critical thinking citizenry, but because of those with the skills of basic survival who can then hire the sophisticated ones to organize and run the infrastructure. Sort of a chicken egg thing isn't it?

Critical thinking is required and encouraged at the university level of education. Not everyone will have a propensity or desire to pursue critical thinking. I see critical thinking as a form of mental athletics and not everyone wants to be an athlete.

At school age, I would agree that pupils should be taught life skills and problem solving as these are essential.

Lon;1110972 wrote: If I were stranded on a desert island and had to live on it for years, ala "Robinson Crusoe", I would prefer some fellow survivors with less sophistication, critical thinking skills and intellect and more savy in how to build a shelter, start a fire, trap animals and fish. That's not to say that the intellectual could not have these skills, it's just not likely. Now once my belly is full and I am warm and cozy, I would be receptive to listen to the critical thinker pontificate. Society will survive not because of sophisticated and critical thinking citizenry, but because of those with the skills of basic survival who can then hire the sophisticated ones to organize and run the infrastructure. Sort of a chicken egg thing isn't it?


Our technology has placed into our hands great power. Such technology can be managed only by an equally sophisticated understanding. We are like children sitting in a pool of gasoline while playing with matches.

OpenMind;1111052 wrote: Critical thinking is required and encouraged at the university level of education. Not everyone will have a propensity or desire to pursue critical thinking. I see critical thinking as a form of mental athletics and not everyone wants to be an athlete.

At school age, I would agree that pupils should be taught life skills and problem solving as these are essential.


I see CT as being philosophy lite. It is well within the ability of a normal human to comprehend. It should be required of all high school graduates.

coberst;1111145 wrote: I see CT as being philosophy lite. It is well within the ability of a normal human to comprehend. It should be required of all high school graduates.


The term 'high school' means nothing to me. I was raised in England. We do not have 'high schools' here.



I do not know why you have such an issue with critical thinking. There is a lot of critical thinking on this forum alone. Critical thinking, after all, is a natural ability.

I never see you partake of this forum other than to post threads about philosophical issues. It would be interesting to see your argument in some of the subjects posted here.

OpenMind

CT is an acronym for Critical Thinking. Everybody considers themselves to be a critical thinker. That is why we need to differentiate among different levels of critical thinking.

Most people fall in the category that I call Reagan thinkers—trust but verify. Then there are those who have taken the basic college course taught by the philosophy dept that I call Logic 101. This is a credit course that teaches the basic principles of reasoning. Of course, a person need not take the college course and can learn the matter on their own effort, but I suspect few do that.

The third level I call CT (Critical Thinking). CT includes the knowledge of Logic 101 and also the knowledge that focuses upon the intellectual character and attitude of critical thinking. It includes knowledge regarding the ego and social centric forces that impede rational thinking.

Most decisions we have to make are judgment calls. A judgment call is made when we must make a decision when there is no “true or “false answers. When we make a judgment call our decision is bad, good, or better.

Many factors are involved: there are the available facts, assumptions, skills, knowledge, and especially personal experience and attitude. I think that the two most important elements in the mix are personal experience and attitude.

When we study math we learn how to use various algorithms to facilitate our skill in dealing with quantities. If we never studied math we could deal with quantity on a primary level but our quantifying ability would be minimal. Likewise with making judgments; if we study the art and science of good judgment we can make better decisions and if we never study the art and science of judgment our decision ability will remain minimal.

I am convinced that a fundamental problem we have in this country (USA) is that our citizens have never learned the art and science of good judgment. Before the recent introduction of CT into our schools and colleges our young people have been taught primarily what to think and not how to think. All of us graduated with insufficient comprehension of the knowledge, skills, and attitude necessary for the formulation of good judgment. The result of this inability to make good judgment is evident and is dangerous.

I am primarily interested in the judgment that adults exercise in regard to public issues. Of course, any improvement in judgment generally will affect both personal and community matters.

To put the matter into a nut shell:

1. Normal men and women can significantly improve their ability to make judgments.

2. CT is the domain of knowledge that delineates the knowledge, skills, and intellectual character demanded for good judgment.

3. CT has been introduced into our schools and colleges slowly in the last two or three decades.

4. Few of today’s adults were ever taught CT.

5. I suspect that at least another two generations will pass before our society reaps significant rewards resulting from teaching CT to our children.

6. Can our democracy survive that long?

7. I think that every effort must be made to convince today’s adults that they need to study and learn CT on their own. I am not suggesting that adults find a teacher but I am suggesting that adults become self-actualizing learners.

8. I am convinced that learning the art and science of Critical Thinking is an important step toward becoming a better citizen in today’s democratic society.



Perhaps you are not familiar with CT. I first encountered the concept about five years ago. The following are a few Internet sites that will familiarize you with the matter.

Critical Thinking and Its Relation to Science and Humanism

Critical Thinking Competency Standards

Critical Thinking: Expanding the Paradigm

http://www.criticalthinking.org/resourc ... sary.shtml

http://www.doit.gmu.edu/inventio/past/d ... sID=eslava

coberst;1111541 wrote: OpenMind



CT is an acronym for Critical Thinking. Everybody considers themselves to be a critical thinker. That is why we need to differentiate among different levels of critical thinking.



Most people fall in the category that I call Reagan thinkers—trust but verify. Then there are those who have taken the basic college course taught by the philosophy dept that I call Logic 101. This is a credit course that teaches the basic principles of reasoning. Of course, a person need not take the college course and can learn the matter on their own effort, but I suspect few do that.



The third level I call CT (Critical Thinking). CT includes the knowledge of Logic 101 and also the knowledge that focuses upon the intellectual character and attitude of critical thinking. It includes knowledge regarding the ego and social centric forces that impede rational thinking.



Most decisions we have to make are judgment calls. A judgment call is made when we must make a decision when there is no “true” or “false” answers. When we make a judgment call our decision is bad, good, or better.



Many factors are involved: there are the available facts, assumptions, skills, knowledge, and especially personal experience and attitude. I think that the two most important elements in the mix are personal experience and attitude.



When we study math we learn how to use various algorithms to facilitate our skill in dealing with quantities. If we never studied math we could deal with quantity on a primary level but our quantifying ability would be minimal. Likewise with making judgments; if we study the art and science of good judgment we can make better decisions and if we never study the art and science of judgment our decision ability will remain minimal.



I am convinced that a fundamental problem we have in this country (USA) is that our citizens have never learned the art and science of good judgment. Before the recent introduction of CT into our schools and colleges our young people have been taught primarily what to think and not how to think. All of us graduated with insufficient comprehension of the knowledge, skills, and attitude necessary for the formulation of good judgment. The result of this inability to make good judgment is evident and is dangerous.



I am primarily interested in the judgment that adults exercise in regard to public issues. Of course, any improvement in judgment generally will affect both personal and community matters.



To put the matter into a nut shell:

1. Normal men and women can significantly improve their ability to make judgments.

2. CT is the domain of knowledge that delineates the knowledge, skills, and intellectual character demanded for good judgment.

3. CT has been introduced into our schools and colleges slowly in the last two or three decades.

4. Few of today’s adults were ever taught CT.

5. I suspect that at least another two generations will pass before our society reaps significant rewards resulting from teaching CT to our children.

6. Can our democracy survive that long?

7. I think that every effort must be made to convince today’s adults that they need to study and learn CT on their own. I am not suggesting that adults find a teacher but I am suggesting that adults become self-actualizing learners.

8. I am convinced that learning the art and science of Critical Thinking is an important step toward becoming a better citizen in today’s democratic society.





Perhaps you are not familiar with CT. I first encountered the concept about five years ago. The following are a few Internet sites that will familiarize you with the matter.



Critical Thinking and Its Relation to Science and Humanism



Critical Thinking Competency Standards



Critical Thinking: Expanding the Paradigm



http://www.criticalthinking.org/resourc ... sary.shtml



http://www.doit.gmu.edu/inventio/past/d ... sID=eslava


Two of your links are unavailable. But, never mind. What I saw described as critical thinking is nothing less than what is required at university level.

By the way, CT is not an acronym.

Neither did you answer my question.

But I also restate that not everyone needs this skill. You cannot force anyone to learn anything against their will. It takes all sorts to make a society and quite honestly, it's just as well since critical thinkers are not going to want to spend their lives pressing a button to make the things we need. For these tasks, we need critical numptiness.

JAB;1111712 wrote: With the state of the world economy, it's not the critical thinkers that we need more of but the practical ones. When it comes to finding a new way, any way to put food on the table, practical means will do you more good then critical.


Oh now. Is this really the best bullet to kill that bear with? Are you sure that's the right calibre? Can you aim AND shoot?Are you sure your posture is right for handling that rifle? Come now, JAB. Think about it. Just make sure you get that bear before it gets you!:wah:

JAB;1111734 wrote: Short of a water pistol on a hot summer day, I've never shot a gun in my life. :wah:



I was, however, raised to be practical. I highly value my college degree. But while being degreeded (is that a word? ) in HR management, it's the practicality of doing more with less that was taught to me by my parents that will ultimately determine my success at survival.


There lies the true value of critical thinking. It's called making do.:wah:

MD is not an acronym!