So are you opposed to teachers offering partial credit for problems that are mechanically correct but have clerical or arithmetic errors?
For me, algebra is easy, but writing out steps is very difficult, and sometimes I prefer to use a process other than the one taught in class. Should the goal of math education be to solve problems or to learn processes?
In the real world, it’s solving problems that matters—I wouldn’t say “being right”, necessarily—but it’s also important to be able to weigh different potential solutions to find the best or most efficient. Programming is a decent example of this—don’t go for the O(n²) algorithm when the O(n log n) is just as easy to implement.
But even better, consider a startup. If you want to build an online store application in 1995, and doing it in Lisp means you expend less effort than your Lispless competitors to get to the same “right answer”, then you should take the advantage. The amount of effort does matter.
For me, algebra is easy, but writing out steps is very difficult, and sometimes I prefer to use a process other than the one taught in class. Should the goal of math education be to solve problems or to learn processes?
That is a false dichotomy. The goal of math education is to "learn processes" to "solve problems". You can't skip the processes and jump straight to solving. Before you can pick a proper algorithm, you have to already know a few -- that's the learning processes part in programming. This holds for any skill you choose to learn; before you can do something well, you have to be able to do it in the first place.
Since you bring up Programming; yes, it is a good example.
It is a good example of the need not to ignore any errors.
Double-guessing how some incorrect maths or code may have worked, given a lot of imagination and goodwill, is the start of the slippery slope. It is not something computers can do, as we all know.
The 'procedural' approach to maths is a good thing, though the right initial description is not to be underestimated. It boils down to good teaching.
There are many similarities between maths and computing and often the keen game-players are quite good at maths too, so perhaps the problem is how to motivate those who are not in this category?
I agree that reducing the effort does matter. Especially in maths, where it often leads to a better method. I was trying to argue against giving credit for increasing the effort leading to the wrong answer.
For me, algebra is easy, but writing out steps is very difficult, and sometimes I prefer to use a process other than the one taught in class. Should the goal of math education be to solve problems or to learn processes?
In the real world, it’s solving problems that matters—I wouldn’t say “being right”, necessarily—but it’s also important to be able to weigh different potential solutions to find the best or most efficient. Programming is a decent example of this—don’t go for the O(n²) algorithm when the O(n log n) is just as easy to implement.
But even better, consider a startup. If you want to build an online store application in 1995, and doing it in Lisp means you expend less effort than your Lispless competitors to get to the same “right answer”, then you should take the advantage. The amount of effort does matter.