If the human mind is like a computer, then language is like the programming language. That's partly why it's so important to use language effectively. Thoughts become beliefs and beliefs become who we are. Let's take a look at an example from math education.
"Problems"
The word, "problem", has come to be used very inappropriately in math education. It's used synonymously with "exercise", and almost synonymously with "question". The problem is, these words also have meanings outside math education, and they inherit a lot of unintended meaning from their non-mathematical uses.
Outside of mathematics, a problem is some dilemma, some troubling circumstance which gets in the way of things. It can even be used to refer to an acute personality flaw, as in, "that girl has problems!"
An "exercise", on the other hand, is something which we do to become stronger. Exercise is a good thing. It makes us feel good. Exercise motivates us. It makes us healthy and strong and sexy. A mathematical "exercise" suggests something we can use to enhance our mental powers, the same way that lifting weights enhances our physical powers and beauty.
Likewise, a "question" suggests some kind of curiosity, maybe even some deep philosophical pondering.
A "problem" suggests an annoying nuisance, a meaningless task that has to be completed to meet a class which you're only even taking because it's required by your major, or whatever. And that's what it becomes.
Language becomes thought, thought becomes belief, belief becomes reality.
I'm always trying to be a better teacher, and part of that is, removing the word "problem" from my classes unless it's actually appropriate. For mathematical "problems", you can always use "exercise" instead, which is both more appropriate and better sounding.
Real Mathematical Problems
Mathematics does have real problems. These are unsolved mysteries which prevent us from fully understanding the nature of the universe. Every few years, a mathematical problem gets solved, and it usually makes big headlines. Sometimes it may even affect our everyday lives, by pushing technology forward.
What is assigned in basic calculus classes, is not a set of problems. It's a set of exercises, simple "weights" for the student to "lift" to build their mental "muscles". It's inaccurate and deceptive to call these exercises "problems", and it devalues the word. Humanity's understanding of the profundities of nature doesn't hinge upon whether an undergrad business major can successfully solve a linear equation. That's not to belittle the undergraduate taking the algebra class; to him or her, that linear equation is a valuable exercise that'll increase his or her intelligence.
A basic mathematical exercise is not a "problem", any more than a dumbbell lying on the floor is a "problem" to a weight lifter.
(If this article seems shorter than the articles I usually write, it's because right now I'm writing shorter articles, despite great resistance from within, in an effort to fight and explore perfectionism in myself)
Here are some other articles I wrote, they'll build your mental muscles as you read them.
The Higher Infinite
How Fashion Works
Running On The Treadmill
Ergative Verbs
"Problems"
The word, "problem", has come to be used very inappropriately in math education. It's used synonymously with "exercise", and almost synonymously with "question". The problem is, these words also have meanings outside math education, and they inherit a lot of unintended meaning from their non-mathematical uses.
Outside of mathematics, a problem is some dilemma, some troubling circumstance which gets in the way of things. It can even be used to refer to an acute personality flaw, as in, "that girl has problems!"
An "exercise", on the other hand, is something which we do to become stronger. Exercise is a good thing. It makes us feel good. Exercise motivates us. It makes us healthy and strong and sexy. A mathematical "exercise" suggests something we can use to enhance our mental powers, the same way that lifting weights enhances our physical powers and beauty.
Likewise, a "question" suggests some kind of curiosity, maybe even some deep philosophical pondering.
A "problem" suggests an annoying nuisance, a meaningless task that has to be completed to meet a class which you're only even taking because it's required by your major, or whatever. And that's what it becomes.
Language becomes thought, thought becomes belief, belief becomes reality.
I'm always trying to be a better teacher, and part of that is, removing the word "problem" from my classes unless it's actually appropriate. For mathematical "problems", you can always use "exercise" instead, which is both more appropriate and better sounding.
Real Mathematical Problems
Mathematics does have real problems. These are unsolved mysteries which prevent us from fully understanding the nature of the universe. Every few years, a mathematical problem gets solved, and it usually makes big headlines. Sometimes it may even affect our everyday lives, by pushing technology forward.
What is assigned in basic calculus classes, is not a set of problems. It's a set of exercises, simple "weights" for the student to "lift" to build their mental "muscles". It's inaccurate and deceptive to call these exercises "problems", and it devalues the word. Humanity's understanding of the profundities of nature doesn't hinge upon whether an undergrad business major can successfully solve a linear equation. That's not to belittle the undergraduate taking the algebra class; to him or her, that linear equation is a valuable exercise that'll increase his or her intelligence.
A basic mathematical exercise is not a "problem", any more than a dumbbell lying on the floor is a "problem" to a weight lifter.
(If this article seems shorter than the articles I usually write, it's because right now I'm writing shorter articles, despite great resistance from within, in an effort to fight and explore perfectionism in myself)
Here are some other articles I wrote, they'll build your mental muscles as you read them.
The Higher Infinite
How Fashion Works
Running On The Treadmill
Ergative Verbs
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