This does not necessarily mean the quality of maths teaching as a whole is improving but that teaching of a given area is better. On HMIs’ demand for “high expectations”, nobody I have met has ever disagreed, but much is dictated by the ethos of schools and their catchment areas. We work hard to have high standards but sometimes feel powerless to influence them.

The statement that “simple algebra covered in S2 in Scotland is covered in the equivalent of P6 in some countries” has enormous implication for the training of primary staff if we are to move in that direction. “More emphasis on number at the early stages” is usually well received, but do primary colleagues now have to do algebra as well?

Promotion of “a very participative interactive form of teaching fully involving pupils for at least half of a lesson with pupils frequently demonstrating solutions and explaining their work” must send shudders down a few spines. I work hard at involving and motivating pupils but to attain this level suggests a move from usual school conditions and tremendous training implications for teachers and their training institutes. Oh, and throw in the necessary magnetic boards and visual aids.

Recent research suggests that commonly used textbooks lack sufficient examples. True, and many departments produce their own material, but to do this properly requires writing teams, review teams, and so on. As for “all pupils having a textbook”, we try hard to achieve this, but it is expensive and the nature of the school dictates that some do not want them.

Mixed feelings surround the aim in the Achievement for All paper of broad band setting in S1. The key as far as I am concerned is when to do it. In my school we consider national test scores, primary 5-14 records and pupils marked out as potential “high-fliers” and then we want a period of our own assessment during S1. Do we regroup at the September weekend (a bit early), October break or Christmas? If this is left too late then how successful is the move by the end of S1?

We are now doing our own testing at level C and level D but a number of pupils have forgotten work during the summer holidays and so probably underperform. Knowledge does come back but how much should we repeat work? I absolutely agree with the advice to “reject the fresh start approach and build on prior attainment”.

One controversial aspect of the report is the condemning of individual schemes. Part of the problem is that teachers and their trainers need more support in managing schemes so that they run efficiently. Many staff do outstanding work on individual schemes and this is not recognised. They must feel depressed by the recommendations.

Calculator use always gets a mention and colleagues largely agree that “access should be restricted”. Working with my S1 group just now, the vast majority are very good at multiplying two-digit numbers by other two-digit numbers. Do I need to keep repeating this or should I now let them use the calculator, thereby accessing further work more quickly with a view to S2 to S4?

Exam bodies are recommended to “introduce papers requiring candidates to demonstrate competence in numerical calculation”. Yet how often do I do mental calculations outside my job? Very seldom, and then I just pick up the calculator. So how much do some pupils need to be able to do without a calculator and what about the easy access to modern technology? That said, keener numerical skills help all other aspects, and with mental calculation add a degree of sharpness and focus for the mind.

As I read the report I happily agreed with some recommendations, but the overwhelming feeling was of inadequacy because for reasons of finance, training, ethos and time I cannot at present attain the goals. Yet every day I see staff doing a good, conscientious and hardworking job, and I observe children in large numbers achieving well.

Peter Caddick is principal teacher of mathematics at Ross High School, Tranent. The views expressed here are personal.