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Comment by SagelyGuru | Hacker News Reader

'My own son can get quite frustrated after performing a lengthy series of computations to solve an algebra problem, only to be told that the answer was wrong due to an arithmetic error; I am sure this experience is common to many other schoolchildren'

This frustration is largely due to the fact that such a useful lesson for life is generally neglected, skimmed-over or outright deliberately denied in order to satisfy the ideologues of 'modern education'.

Thus many people are way too much surprised that being right is what matters, not the amount of effort it took to get there.

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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.

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.

I agree that difficulty is a good lesson; but it doesn't seem to be working for a lot of people in the US. Many students give up on math early. That might not be economically sustainable. I don't think math education is optimized to make the most of intuition and motivation, and I really don't think experimenting with improvements is harmful.

I concur. Hard life lessons should not be taught in the context of learning a new skill. Those can wait until after a degree of proficiency has been attained lest we undermine their efforts completely.

I believe this is at best an unfair comparison between school and a "real world" environment. Out in the working world it is assumed that you are going into the work with the necessary knowledge to complete a task, this is not the case in education. We specifically develop a sandbox environment for kids to develop skills at school. At the end of the day students do not have the fear of losing a job to motivate them. We must instead encourage kids to keep going, even after they make mistakes. I stand firmly against people who believe tests are unfair, because at the end of the day children show they can stand on their own before moving on, but in the time that they are learning new material the focus must be on building them up and encouraging perseverance.

I don't think the lesson is "being right is what matters" (working hard is praiseworthy, even if the results aren't always great), but this encourages students to work carefully and list out their steps instead of trying to do everyhing in their heads.

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