Manual Subtraction

An interesting question was posed to me today.

How do I subtract two number manually when the answer is negative??

For instance, 3896 - 4321 (to which the answer is -425).

I originally set up the problem in vertical columns

3896
4321
------

and tried to subtract..

3896
4321
------
?575

which obviously does not work.

So I thought about it.. the only obvious solution was to say, when subtracting always put the larger number on top.

4321
3896
------
*425

As this answer is positive, it is still incorrect. It requires an additional rule, that when the order is changed, the sign of the answer is negative. Thus the answer is -425.

I'm sure everyone knows this (and it's just one of those odd cases I haven't come across before), but it could be an interesting short investigation for upper primary or lower secondary doing directed number exercises.

.. and I have a stupid cold, my nose is dripping like a tap and I can't hug my daughter. It's made my day!

Rubrics

I sat through another round of someone extolling the benefits of rubrics/analytic marking keys/explicit marking keys. There was no doubt a lot of effort went into constructing them, but the usual issues were there amongst the generic template.

Assessment is supposed to be Fair, Explicit, Comprehensive, Educative, Valid

Rubrics vary between too vague to be of benefit (fails the explicit test - makes marking easy but cannot be easily connected to assignment without 'dejargoning') or so explicit that most students can get an A if they put some effort in (fails the comprehensive/valid test - can a student do it without the rubric??).

The position put forward was that marking should be quick. I'm afraid I can't see how this is true. The only comments students read, are ones in red pen. If you circle where students lie in a marking key, they normally just skip to where the final grade is. Students will read every line written in red pen and ask for clarification of it.

This is where investigations today fall down a little. Typically we guide students through the investigation (so that it becomes more like self teaching than investigating) - but the other side of the coin is that students can't be expected to rediscover what mathematicians took millenia on their own. We need to find a middleground.

We have collected a wide range of investigations, categorised and standardised them. I must admit I have struggled with selecting, generating, marking and guiding students with regard to investigations and marking keys. It needs more work and thought.