**Andrew Day comments on the review**

Thanks for the review. Yes, I do like it, and am very interested by your comments. I think you have understood the main ideas of the book really accurately, and your reservations about some of it are well-founded. My comments in response to some of your points are:

In the chapter on place value, I meant to express as much doubt as certainty about how to teach it. I agree that teaching children to 'add zeroes' when multiplying by factors of 10 wouldn't help them to understand place value, and could even have a negative effect if not balanced by a genuine concept of place value. The point I was trying to make there was that 'banning' children from using certain tricks or rules of thumb can backfire - better to allow them at some stage but explain to the class that they are just tricks? Also, I was taught that 'the digits move to the left' when you multiply by 10 and the decimal point 'never moved'. I still can't see why saying the digits move is truer than saying that the decimal point moves? Happy to be enlightened on that one, though.

One thing I now wish I'd put in is that children are often introduced to the concept of place value when learning subtraction (when the subtracted digit in the units column is higher than the digit above it). It would help them a lot to explore place value a bit BEFORE then, so that they already know that a number in the tens column can be 'cashed out' into units. That is why I put forward the idea that the teaching of bases - at least introducing the idea that the way we represent numbers is one possibility among others - might... MIGHT be appropriate at a younger age. I just don't know.

I'm glad you think that the Things To Say and Key Words are up for discussion. I hesitated before adopting that approach as I don't like to be prescriptive. But in INSETS and CPD generally I find a lot of teachers - especially at primary level, where I usually work - get limited benefit from abstract explanations, even when they understand them fully. In order to get the teachers to put the ideas into practice I have to say 'do this' more than I would like to. Having said that, I have also found that certain instructions and questions, such as 'Try again' 'Why is that?' 'Show us' and comments such as 'Isn't that weird?' and 'Good thinking' are very effective ways of steering the class and can be used a lot. The idea behind the Key Words is that many teachers already know them, or will encounter them soon enough, and it might help to say how my ideas relate to them. There are a number of over-simplifications in the book (partly deliberate, for ease of digestion, partly the result of the limits in my own mathematical knowledge).

Anyway, I'm very grateful for your support and interested in the work you do, Andrew. So thanks again.