4 ms·

That gave me mixed feelings. On the one hand, the teacher did an admirable job (for a teacher) of seeing the correct thinking behind the "wrong" notation. On th

by gohrt 11y ago

That gave me mixed feelings. On the one hand, the teacher did an admirable job (for a teacher) of seeing the correct thinking behind the "wrong" notation. On the other hand, the teacher still accused the student of making a mistake.

Natsu 11y ago
If nobody else understands your right answer, it may not be worth much. At this level, it doesn't matter at all--anyone can see based on the constraints what they're doing and understand them. But this may not always be the case. For example, when they get to intervals and suddenly need to properly discriminate between intervals like (1,2], (1,2), [1,2) and [1,2]. I might ding that by just one point--if you use non-standard notation, you must properly define it. You won't always be dealing with cases where your idiosyncrasies have obvious answers and it's better to form good habits that allow you to communicate clearly with others. There may be many good ways to depart from convention and I'd hesitate to stop anyone from doing that, but I think that if defining your departure from convention is too burdensome to be worthwhile, then you do not have a compelling case to depart from it in the first place.
Gibbon1 11y ago
If I were a teacher and I saw a student come up with a peculiar but correct notation, I'd be ecstatic.
- jacobolus 11y ago
  Indeed, developing new notation should be not only allowed, not only encouraged, but even required as an assignment at various points during mathematical training, at every age level. Also to be encouraged is conscientious analysis and critique of existing notations, algorithms, and explanations. Society advances in two ways: in small incremental steps, and in large leaps. When we stick to existing notations and concepts we can make incremental improvements. But the large leaps often come from creating better notations and better conceptual understandings, which can turn substantial amounts of knowledge and logical thinking into obvious consequences of an organized and intuitive system.
  - daniel-levin 11y ago
    Agreed. Feynman diagrams are a great example of this phenomenon. They might be 'pictures', but they are still mathematical notation.

by gohrt 11y ago

Natsu 11y ago

If nobody else understands your right answer, it may not be worth much. At this level, it doesn't matter at all--anyone can see based on the constraints what they're doing and understand them. But this may not always be the case. For example, when they get to intervals and suddenly need to properly discriminate between intervals like (1,2], (1,2), [1,2) and [1,2]. I might ding that by just one point--if you use non-standard notation, you must properly define it. You won't always be dealing with cases where your idiosyncrasies have obvious answers and it's better to form good habits that allow you to communicate clearly with others. There may be many good ways to depart from convention and I'd hesitate to stop anyone from doing that, but I think that if defining your departure from convention is too burdensome to be worthwhile, then you do not have a compelling case to depart from it in the first place.

Gibbon1 11y ago

If I were a teacher and I saw a student come up with a peculiar but correct notation, I'd be ecstatic.

jacobolus 11y ago
Indeed, developing new notation should be not only allowed, not only encouraged, but even required as an assignment at various points during mathematical training, at every age level. Also to be encouraged is conscientious analysis and critique of existing notations, algorithms, and explanations. Society advances in two ways: in small incremental steps, and in large leaps. When we stick to existing notations and concepts we can make incremental improvements. But the large leaps often come from creating better notations and better conceptual understandings, which can turn substantial amounts of knowledge and logical thinking into obvious consequences of an organized and intuitive system.
- daniel-levin 11y ago
  Agreed. Feynman diagrams are a great example of this phenomenon. They might be 'pictures', but they are still mathematical notation.