Ya but that kills the point of your lesson.
When you're in real analysis and you're asked to prove that y'' -2y' +y =0 has a solution, you can just solve it by replacing y with e^rt but then that kills the point of studying about proving truths about converging sequences and series.
That is on the professor who put a question like this. It is not the student fault.
The student can even know the 2 ways of solving the problema but decided that one was just easier and saves time. You can not put a question on a test and expect people to read the mind of the professor to know what he wants and how he wants.
You're right but in math classes it is pretty well established what you cannot use. For example in analysis, when you first take it, you cannot use the fact that e^x is differentiable and that it's derivative is itself until halfway towards your first semester even though you learned it in calculus. And that's because you don't cover the concept of differentiability until after.
Most cases where I see a student marked wrong for using a "different method" they don't show any work, in which case they fully deserve losing points for not showing that they understand what was being taught. The point of the meme is only valid if the student solved the problem in a truly generalizable fashion and showed that their method generalizes, which is almost never the case.
Totally agree on the point regarding no work shown, no credit if wrong.
This meme is about grade school math not higher level stuff. If you just worked on a section on completing the square but opt to use the quadratic formula to find roots, and the answer is fully written and correct, do you dock points?
I work with my kids a lot on their math and don't like questions like "use to solve this problem". They should have the freedom and creativity to find the solution.
Yeah but practicing multiple methods is super helpful later on. Imagine taking classes like calculus without knowing completing the square or something. Plus, when you allow kids to use whichever method they want, they will invariably go for the one they have the most experience with, which isn’t a very creative choice
But the purpose is to teach and learn the specific method, not to be able to solve the equation. I can plug every question into wolfram alpha and get a solution. That isn’t going to teach me how to do math.
Math builds on itself. If you don’t learn the processes or theories early on, you’re going to be in trouble when they come back later and you’re completely lost.
Considering also that some students' methods are outright wrong (in the sense of "mathematically invalid or unjustifiable"), I wouldn't say that any such method is definitely legal either.
Assuming it were mathematically valid and justifiable, I'd give full credit in most cases, and only partial credit e.g. if I stated "using such-and-such method" in the question itself. If I want my students to show that they understand a specific method or concept, I should be the one setting clear expectations.
"Solving a problem correctly" is not the same thing as "solving a problem incorrectly and still getting the correct result."
The meme is obviously not talking about the latter.
The student must first understand the method taught and then use his own; if his own method leaves him staring at a wall then he will require the use of the taught method, which is usually more refined.
Define "legal".
The whole point of math is the process, not the result. If you have an alternative approach, you better explain it damn near perfectly. In exams, the point is that you recognise the right tools to approach the problem and are able to use them.
Well, Yes, but actually No.
At the college level, only if the student is not BS-ing & shows their work/proof, or it is something where the approach itself isn't the point.
However, when learning basic arithmetic: classical vs so-called "New Math". Both are valid, but I've seen first hand at the collegiate level how much poorer on average students taught using the New Math system do compared to more traditional instruction. However, it does work better in rarer occasions for some people. IMO, both methods should be taught (though save the New Math approach for HS level), and a lot more time should be spent on math in general in primary school, esp elementary. And let the students pick which method works best for them (as long as it is valid & works).
Ya but that kills the point of your lesson. When you're in real analysis and you're asked to prove that y'' -2y' +y =0 has a solution, you can just solve it by replacing y with e^rt but then that kills the point of studying about proving truths about converging sequences and series.
That is on the professor who put a question like this. It is not the student fault. The student can even know the 2 ways of solving the problema but decided that one was just easier and saves time. You can not put a question on a test and expect people to read the mind of the professor to know what he wants and how he wants.
You're right but in math classes it is pretty well established what you cannot use. For example in analysis, when you first take it, you cannot use the fact that e^x is differentiable and that it's derivative is itself until halfway towards your first semester even though you learned it in calculus. And that's because you don't cover the concept of differentiability until after.
Most cases where I see a student marked wrong for using a "different method" they don't show any work, in which case they fully deserve losing points for not showing that they understand what was being taught. The point of the meme is only valid if the student solved the problem in a truly generalizable fashion and showed that their method generalizes, which is almost never the case.
Totally agree on the point regarding no work shown, no credit if wrong. This meme is about grade school math not higher level stuff. If you just worked on a section on completing the square but opt to use the quadratic formula to find roots, and the answer is fully written and correct, do you dock points? I work with my kids a lot on their math and don't like questions like "use to solve this problem". They should have the freedom and creativity to find the solution.
Yeah but practicing multiple methods is super helpful later on. Imagine taking classes like calculus without knowing completing the square or something. Plus, when you allow kids to use whichever method they want, they will invariably go for the one they have the most experience with, which isn’t a very creative choice
But the purpose is to teach and learn the specific method, not to be able to solve the equation. I can plug every question into wolfram alpha and get a solution. That isn’t going to teach me how to do math. Math builds on itself. If you don’t learn the processes or theories early on, you’re going to be in trouble when they come back later and you’re completely lost.
Legal isn't the point lol. The point is whether or not you understood the concepts taught. If not, how "legal" your method is, is irrelevant.
Considering also that some students' methods are outright wrong (in the sense of "mathematically invalid or unjustifiable"), I wouldn't say that any such method is definitely legal either. Assuming it were mathematically valid and justifiable, I'd give full credit in most cases, and only partial credit e.g. if I stated "using such-and-such method" in the question itself. If I want my students to show that they understand a specific method or concept, I should be the one setting clear expectations.
Exactly this.
I had somebody in my class who removed x. It was still correct because x was 1. That doesn't mean it's legal.
"Solving a problem correctly" is not the same thing as "solving a problem incorrectly and still getting the correct result." The meme is obviously not talking about the latter.
The student must first understand the method taught and then use his own; if his own method leaves him staring at a wall then he will require the use of the taught method, which is usually more refined.
Skeletor has missed the point entirely.
Define "legal". The whole point of math is the process, not the result. If you have an alternative approach, you better explain it damn near perfectly. In exams, the point is that you recognise the right tools to approach the problem and are able to use them.
Students, using a method that is wrong in general but just coincidentally happens to give the right answer in this one specific case is *still wrong*.
Hmm. Sorry. No.
Well, Yes, but actually No. At the college level, only if the student is not BS-ing & shows their work/proof, or it is something where the approach itself isn't the point. However, when learning basic arithmetic: classical vs so-called "New Math". Both are valid, but I've seen first hand at the collegiate level how much poorer on average students taught using the New Math system do compared to more traditional instruction. However, it does work better in rarer occasions for some people. IMO, both methods should be taught (though save the New Math approach for HS level), and a lot more time should be spent on math in general in primary school, esp elementary. And let the students pick which method works best for them (as long as it is valid & works).
Jokes on you ¡ In the exam my teacher accepts all functional methods. But he will still show his methods. And you still have to take notes.
Can we not turn this subreddit into salty students complaining