Primary curriculum, what's happening?

Wales had a refreshing new one in 2009.

Scotland had an imaginative new one in 2010.

England nearly had a creative new one to start in 2011!

But it got lost in the turmoil of the General Election and has subsequently been scrapped. So, all we have here in England, officially, is the tired, old 1999 National Curriculum for Key Stages 1 and 2. And, as far as I am aware, nothing is happening about it.

Clearly, not as important as academies and free schools.

Or does anyone know different?

Fear of mathematics 1

On Wednesday this week, I spoke to an enthusiastic group of primary school mathematics leaders on an Every Child Counts conference at Edge Hill University in Ormskirk. I had been invited to speak about 'Fear of mathematics'.

One of the main points I made was about the relationship between mathematics anxiety and a rote-learning mind set. There is research evidence (see a study by Karen Newstead, 1995, 1998) that children aged 9 to 11 years are more likely to develop mathematics anxiety if they are taught by traditional methods that rely on memorizing and drill of calculation processes without a focus on understanding.

It seems that teaching that promotes reliance on rote-learning in mathematics generates more anxiety about the subject. The learner gets the idea that there is only one right way of doing any mathematics question, worries about which process to use for which problem, gets different processes confused and cannot cope with anything that is not immediately recognisable as requiring a standard, routine response.

But this is a viscious circle, because mathematics anxiety seems to reinforce reliance on rote-learning. The anxious learner is more likely to have given up expecting to make sense of mathematics and seeks only to try to remember what you have to do for certain kinds of questions. Anxiety inhibits learning with understanding.

The key seems to be to teach mathematics well! In other words, to teach in a way that promotes a meaningful learning mind set, that encourages children to make sense of mathematics, by making connections between language, symbols, practical and real-life situations and pictures. I have written about this extensively in Chapter 3 of Mathematics Explained for Primary Teachers, 4th edition: Learning How to Learn Mathematics.

Anniversaries solution

Last week I posed this question:

Is it unusual that a 45th anniversary should fall on the same day of the week as the original event?

Here are my thoughts on this.

First, we note that in a year of 365 days an anniversary moves on by one day of the week. This is because 365 is a multiple of 7 (364) plus 1. So a Saturday moves on to a Sunday, and then to a Monday and so on.

However, when the year following the anniversary includes a 29th February then the anniversary moves on by two days of the week (for example, an anniversary on a Monday will be on a Wednesday the following year.)

Since leap years (normally) happen every four years, then in a period of four years there will be one 29th of February. So anniversaries move on by 5 days in every 4 years. This is the general rule you can now apply to most questions like this.

For example, because 45 = 1 + (11 x 4), then in 45 years, the anniversary would move on by 1 + (11 x 5) days = 56 days. Since 56 is an exact multiple of 7, then the 45th anniversary will fall on the same day of the week as the original event.

But, wait! If the first year after the original event contains a 29th February, then the anniversary will move on by 2 days in the first year, followed by 11 lots of 5 days, making 57 days in total. This means that the 45th anniversary will fall one day later in the week than the original event.

So, here's a summary:

(A) If the first year after the anniversary does not contain a 29th February, then the 45th anniversary will normally fall on the same day of the week as the original event.

(B) If the first year after the anniversary does contain a 29th February, then the 45th anniversary will normally fall one day later in the week than the original event.

Clearly, because leap years occur normally every 4 years, then (A) will happen in about three-quarters of the cases.

Why do I keep saying 'normally'? Well, the above will have to be modified if the period in question contained the year 1900, which was not a leap year, or will contain the year 2100, which also will not be a leap year. Because a year in terms of the earth's orbit of the sun is an awkward length of 365 days, 5 hours, 48 minutes and 47 seconds, adjustments have to be made to the regular pattern of leap years. So, a leap year is every 4 years, but not every 100 years, except when the year is a multiple of 400 (as in 2000). That pattern just about balances things up.

One final thought: if the original event was on the 29th February, then the concept of an anniversary becomes rather weird. My advice would be not to do anything significant (like being born) on 29th February, unless you enjoy being a special case.

Anniversaries

Christina and I celebrated on Saturday our 45th wedding anniversary. Yes, 45! We married very young, of course.

Is it unusual that a 45th anniversary should fall on the same day of the week as the original event?

I'll leave that as a little problem for readers to ponder as in ten minutes time I head for Stansted to fly to Bergerac for a short walking holiday with some of my family. You'll need to find a way of coping with those annoying leap years.

Au revoir.

Mathematics Explained companion website

The new companion website for Mathematics Explained for Primary Teachers, 4th edition, is now up and running. There's an interview with the author, which you may find mildly interesting, information about the book, a table of contents, a compendium of all the key Teaching and Learning Points chapter by chapter, and some useful weblinks. A really useful inclusion is a complete glossary of all the key terms that appear in the book at the ends of the chapters, combined into one alphabetical list. There are also masses of freebies to support teachers and trainee teachers who use the book. Sage Publications have been very generous in offering so much free additional material for readers.

You'll find links for each chapter of the book with the mathematics National Curriculum programmes of study and level descriptions. When the National Curriculum does finally get revised I will update this. I've done the same with the new Scottish Curriculum for Excellence (more on this interesting approach to the curriculum in a later blog) – and I intend to do the same for the Welsh curriculum fairly soon.

You'll also find five free chapters from Haylock and Thangata (Key Concepts in Teaching Primary Mathematics) that you can download, plus masses of additional further practice material, taken from Numeracy for Teaching to help trainees with the Numeracy Test.

There's even a video of a lecture on Creativity in Mathematics that I gave recently to primary PGCE students at UEA. I think this just about works in this format, although occasionally the integration of my powerpoint slides into the video is just a little bewildering. My favourite moment in the lecture is when I manage to get nearly every student in the room to give the answer 'three' to the question, 'how many lines do you need to draw to cut a rectangle into four equal pieces?'