The blog site is now up and running. Mathsolutionz.org has been set up with the non-specialist mathematics teacher in mind. In my travels up and down the country I have noticed in recent years that many mathematics departments in secondary schools are staffed by a significant number of non-specialists who have been drafted in to help with the high demand of teachers of mathematics that is suffering a shortfall in supply. Mathematics can be one of the most daunting of topics for any non specialist to teach and this is true for primary colleagues too. The direction I have chosen to take with the blogs on this site is that of opening up the reasoning behind the mathematics in order that the teaching of it can be better understood by our pupils.

The blogs will be on all aspects of mathematics education but particularly in subject knowledge enhancement but including pedagogical support also. The topics I intend to write about will range from key stage 1 mathematics through to A level with the aim of explaining the mathematics through concrete imagery to the fully abstract.

You have an invitation, and that is to send via the message box on the site, subject matter that you would like blogs written about to (hopefully) make life easier and more rewarding in the classroom. I admit I am slightly nervous about this as I do not know the level of response I will get to this offer. Whatever the response the offer is genuine and I look forward to creating information that you will be able to make use of in your schools. This offer is of course free of charge so contact me with your requests as soon as you are ready.

One of my year 5 pupils questioned the following ‘fact’ that we so often say as teachers:A rectangle only has 2 lines of symmetry. This was after a previous lesson where I stated: “All squares are rectangles, but not all rectangles are squares”. Therefore, would the following logic apply: Rectangles can have either 2 or 4 lines of symmetry. I thought it was really smart for the pupil to pick up on this discrepancy.

Hello Paul, I have left a reply at the bottom of your other question. This area of mathematical logic in primary schools is quite exciting. I will get a blog started on it as there are other areas where logic can set things straight for us.

After a few years of teaching back in the 90s I decided to write my seven with a line through it (similarly for the letter z) to avoid confusion with the number 1. So for the last 15 or so years I’ve told my students to do likewise. Then, all of sudden, a colleague adamantly told me that I should write it without a stoke and that pupils’ SATs papers would be marked wrong if they used a stroke! Wow!! That’s the first I’ve heard about such a thing. I know numbers are now required to be written with commas (e.g. 100,000 instead of 100 000) but this ‘7’ business is news to me. Any thoughts on the matter?

No pupils will not be marked down. There are lots of annoying differences that some people get really uptight about. In mainland Europe for instance 5.6 actually means 5 multiplied by 6 and 5,600 is not five thousand six hundred but five point six zero zero. I believe British youngsters are at a real disadvantage because of all of this. We teach mm, cm, m, and km but road signs are all in miles! Quite mad. I think you should continue to cross your sevens and zeds as I do. I can assure you this practice has not stunted my mathematical knowledge or love for the subject.

The wonderful subject of mathematical logic helps us here. If I have four pound coins in my pocket then I also have two pound coins. No one would argue I suspect. Applying the same logic to a square, if it has four lines of reflective symmetry then it also has two. Voila!

As a post script Paul, if you look at most British mathematical publications, the comma is rarely used in numbers over 999, I have a theory that this happened around the time of our joining the EU in the early 70s. You will notice that the number two million is written 2 000 000 with a gap separating each group of three digits from the right.

Is zero a square number? Most people identify 1 as the first square number. I told my pupils that if you multiply any whole number by itself you will get a square number. They then challenged me when I said zero is not a square number! Well it doesn’t make a square, after all! Any thoughts?

An interesting question. Unfortunately the jury is still out on this one. Some published mathematics authors state with confidence that it is, but equally others state quite the opposite. I am of the opinion that it is not a square number, but as I say it is merely a humble opinion. My reason for this is as follows.

If a perfect square is defined as n^2 = n x n, this implies (n^2)/n = n. In order for a number to be a perfect square then the left hand side must be true. 0^2 = 0 x 0 is a true statement but the implication from this that (0^2)/0 = 0 is a false statement as division by 0 is an illegal operation.

As a post script Paul think of a square (n^2) of having 4 equal sides of length n. Now think of a square (0^2) it will have 4 equal sides of length 0. Hmmm! Finally ‘zero’ has been with us for a relatively short time and was introduced to western mathematics in the late middle ages to amongst other things aid computation. Its position on a number line is the

borderbetween the positive and negative numbers and as such is neither one nor the other. I am a massive fan of the number zero after all I would struggle to do any computation with the Roman number system that went before it, but zero is a special character that makes it different in lots of ways to the other whole numbers and we must often treat it with at the least an element of respectful caution.