It’s definitely the sign of a good classroom when students hold the teacher accountable for their work. My students are quick to point out if I’ve made mistakes or been imprecise in how I’ve constructed or described a situation.

While mathematics is more than just the details, as you suggest, attending to the details helps create the right problem-solving environment.

I still love maths but most of my maths is stuck at A level standard (calculus, basic stats, vectors etc). So the content of your blog is at the right level for me.

As for your comments you are dead right. Things that were drilled into me at secondary school (high school in US speak) were:

- label your graphs
- scale graphs properly
- always give units on the answer to any calculation
- always show your working
- if doing a calculation only quote the requisite number of significant figures (no spurious accuracy or necessary decimal places)

It was drilled into me and I am pleased it was. It lays the foundations of being able to do maths and provides a discipline and rigour that can be used in solving problems that are not mathematical.

If I had been given this question I would have made sure my answer said:
1. I think it is lazy and imprecise not to label the axes of the graph
2. To answer the question I will assume each square is one unit long and high.

But to be frank I cannot imagine any of my secondary school maths teachers ever setting a question with un-labled axes cos we were so well schooled in the basics, the whole class would have had a go at them for being so sloppy.