Isabel’s math blog is one of those rare things – a mathematics blog; let’s hope it will inspire others. Isabel is a fourth-year undergraduate mathematics student at MIT who has been marking first-year students’ homework. She makes some excellent points that are relevant at all levels including A-level.
I hope she won’t mind me quoting some of what she says at on grading homework:
- If the problem calls for some numerical answer, or for some symbolic expression as an answer, and the student produces a wrong answer, they can’t get full credit. (Very near full credit, say nine out of ten, is possible.)
- Not surprisingly, if you know what the answer to a problem is supposed to be, it’s easy to make errors that “cancel each other out”; if you know where the target is you’ll make some pretty strange logical leaps to get there. (I’ve been guilty of this too. Potential approaches to a problem that seemed incredibly stupid at noon the day before the homework is due seem quite reasonable at three in the morning.)
- The question is, how does one teach students “clarity” in mathematics? One of the things I notice is that the students don’t realize the power of the English language. They write down endless strings of equations, and make no effort to connect these with words that explain what they’re doing. Fortunately for them, as the grader I know what they’re trying to do. But at the same time, sometimes I don’t know what they’re trying to do; they manage to confuse me quite thoroughly.
There seems to be a flaw in mathematics education – that we don’t teach students how to write mathematics.
My thoughts exactly 🙂