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Syntax Junkie
Syntax Junkie
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I was never a professional mathematician, and I am no longer a professional educator. I hope this answer isn't too far off the mark.

I think the problem is the expression "solve the equation." I simply would never use that expression in a basic algebra class. I didn't come across it myself until using differential equations in college. (Before that I would have physics professors as us to "solve the equation" in class, and that expression left the class scratching their heads. Solve it in what way?)

At least from my experience, such a request was always to "solve the equation for x."

Having said that, if your colleagues or you wish to use the expression "solve the equation," then the trick is to clearly and unambiguously define what that means. That will almost certainly require a compare and contrast to the more explicit "solve for x" request. As long as you define your terms, and don't expect the students to just intuit the distinction, then the rest is a matter of how pedantic you want to be about "standard form."

For students that are still learning basic algebra of linear equations, I have a feeling that the distinction between "a solution set with one member" and "an equivalent equation" may be stretching their ability to take on too much abstraction at once. A better time might be after they have mastered quadratic equations. Then the distinction between a solution set, and a particular solution, might make more sense to them.

I was never a professional mathematician, and I am no longer a professional educator. I hope this answer isn't too far off the mark.

I think the problem is the expression "solve the equation." I simply would never use that expression in a basic algebra class. I didn't come across it myself until using differential equations in college. (Before that I would have physics professors as us to "solve the equation" in class, and that expression left the class scratching their heads.)

At least from my experience, such a request was always to "solve the equation for x."

Having said that, if your colleagues or you wish to use the expression "solve the equation," then the trick is to clearly and unambiguously define what that means. That will almost certainly require a compare and contrast to the more explicit "solve for x" request. As long as you define your terms, and don't expect the students to just intuit the distinction, then the rest is a matter of how pedantic you want to be about "standard form."

For students that are still learning basic algebra of linear equations, I have a feeling that the distinction between "a solution set with one member" and "an equivalent equation" may be stretching their ability to take on too much abstraction at once. A better time might be after they have mastered quadratic equations. Then the distinction between a solution set, and a particular solution, might make more sense to them.

I was never a professional mathematician, and I am no longer a professional educator. I hope this answer isn't too far off the mark.

I think the problem is the expression "solve the equation." I simply would never use that expression in a basic algebra class. I didn't come across it myself until using differential equations in college. (Before that I would have physics professors as us to "solve the equation" in class, and that expression left the class scratching their heads. Solve it in what way?)

At least from my experience, such a request was always to "solve the equation for x."

Having said that, if your colleagues or you wish to use the expression "solve the equation," then the trick is to clearly and unambiguously define what that means. That will almost certainly require a compare and contrast to the more explicit "solve for x" request. As long as you define your terms, and don't expect the students to just intuit the distinction, then the rest is a matter of how pedantic you want to be about "standard form."

For students that are still learning basic algebra of linear equations, I have a feeling that the distinction between "a solution set with one member" and "an equivalent equation" may be stretching their ability to take on too much abstraction at once. A better time might be after they have mastered quadratic equations. Then the distinction between a solution set, and a particular solution, might make more sense to them.

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Syntax Junkie
Syntax Junkie
  • 1.4k
  • 9
  • 10

I was never a professional mathematician, and I am no longer a professional educator. I hope this answer isn't too far off the mark.

I think the problem is the expression "solve the equation." I simply would never use that expression in a basic algebra class. I didn't come across it myself until using differential equations in college. (Before that I would have physics professors as us to "solve the equation" in class, and that expression left the class scratching their heads.)

At least from my experience, such a request was always to "solve the equation for x."

Having said that, if your colleagues or you wish to use the expression "solve the equation," then the trick is to clearly and unambiguously define what that means. That will almost certainly require a compare and contrast to the more explicit "solve for x" request. As long as you define your terms, and don't expect the students to just intuit the distinction, then the rest is a matter of how pedantic you want to be about "standard form."

For students that are still learning basic algebra of linear equations, I have a feeling that the distinction between "a solution set with one member" and "an equivalent equation" may be stretching their ability to take on too much abstraction at once. A better time might be after they have mastered quadratic equations. Then the distinction between a solution set, and a particular solution, might make more sense to them.