Archives For October 2014

DoodleMaths 111

The world of education is constantly changing, and over my 20 years in teaching there has been a general shift towards praising a child as a means to motivating them. This has been a hugely positive move in my view: at my Grammar School in the early 1980’s, most teachers ruled over the boys by fear and occasional casual violence; by the time I moved to a more forward-thinking comprehensive in the late 1980’s, I personally responded far better to the praise, encouragement and positive feedback offered on a routine basis.

So it’s interesting today to read of the study by The Sutton Trust suggesting that praise can in fact be counterproductive. Unlike Christine Blower, leader of the National Union of Teachers who dismisses this as faddy thinking, I think this is in fact an important piece of research and one that concurs with discussions I have had with some of my colleagues over the years.

Here’s the issue: children know for themselves whether or not they have done a good piece of work. Therefore they know when to expect praise, and when to expect criticism. They are anticipating it. Here’s where it can go wrong:

If a child is expecting praise and it is not received. Your child spends two evenings on their history project, but then it’s not marked for a month, or worse, ever. This is not common but does occur in teaching from time to time – and we all remember when it does.

If a child has done a poor piece of work but gets praised all the same. This is VERY COMMON, especially amongst low-achievers where a teacher might be grateful just to get any work at all from them. The issue is, the child is receiving praise on what they know is a poor piece of work. It has two results:

1) It lowers expectations
2) It makes all future praise meaningless. When the child does produce a great piece of work, where do you go?
3) It erases confidence. Children like to know where they stand.
4) It sets them up badly for the future – the “real world” it’s so often called.

So how should we deliver praise and criticism? The answer is to target our praise. In the same way that we should criticise specifics, it’s no use saying to a child, “that’s really good!” without explaining what is making it good. “It’s fantastic that you have set out your working exactly as expected” or “You’ve clearly learned how to accurately estimate angles” is specific and can also be balanced with areas to work on.

And if a piece of work is not good enough, it is fine to ask them to do it again. Not all of it, but the areas that need improving. My own son, who is 6 and in year 2, has made fabulous improvements in his drawing this term. He is fortunate to have a highly-skilled teacher who, in studying Matisse with the class, has encouraged them to draft, and then re-draft their drawings five times, often using peer feedback, to the point where they produce work that they are truly proud of.

So, far from dismissing this study as “faddy and fashionable” and suggesting that “teachers know their students best” I’d like to see leaders such as Christine Blower actually engaging in the debate – the vast majority of teachers are more than happy to accept they’re not the finished article. There’s a lot to be learned from this!

For the original article, click here.

We’ve written similar articles to this in the past:
Maths: when giving help isn’t necessarily helpful
5 ways to raise your child’s self-esteem in maths
Why league tables have failed to raise standards
Choice vs Autonomy

For more about DoodleMaths, click here.

Prime Numbers

October 17, 2014 — Leave a comment

Prime numbers are the building blocks of maths. Prime numbers cannot be broken down (they have no factors), and so every number can be written as a product of prime numbers (for example, 210 = 2 x 3 x 5 x 7). The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19… They have fascinated mathematicians over the centuries because they do not follow any particular pattern, and thus it is impossible to predict the next one from the previous. They have many practical uses, most notably in cyber-security, but also in nature (for example, locusts only reappear to mate every 11, 13, or 17 years – always a prime number). Try these quick prime number questions, which recently appeared in our newsletter:
1) What is the only even prime number?

2) What is the first prime number with consecutive digits?

3) Apart from 2, prime numbers always end in the same four digits – what are they?

4) A prime quadruplet is four prime numbers as close together as they can be within a decade. The first such example is 11, 13, 17, 19. What is the next example?

5) A palindromic prime reads the same forwards as backwards. The first three digit palindromic prime is 101. What is the next?

Scroll down for the answers!

1) The only even prime number is 2. As you may well have worked out, all other even numbers have 2 as a factor.

2) The first prime number with consecutive digits is 23. This is one reason amongst many that some people believe that 23 is special (in fact, there’s even a group called the 23rdians who believe it has mystical powers). In maths, and particularly prime numbers, it has some unusual properties, for example,

11,111,111,111,111,111,111,111 (there are 23 number 1’s here) is a prime number

10^23 – 23 = 99,999,999,999,999,999,999,977 which is the largest 23 digit prime

And in science, to create human life, each parent has to contribute 23 chromosomes, and the Earth is currently tilted at 23 degrees…

3) Since primes have to be odd (apart from 2) and cannot be a multiple of 5, they must always end in 1, 3, 7 or 9.

4) 101, 103, 107, 109 is the next one. Incidentally, if you cross decades, prime quintuplets and sextuplets also exist. Incredibly, 43777, 43781, 43783, 43787, 43789, 43793 are all prime.

5) The next is 131. Their search can rapidly be narrowed by a process of elimination. For example, we can immediately discount palindromic numbers in the 200’s since they will also end in 2 and thus be even. And we can discount 4-digit, 6-digit, 8-digit palindromes (etc.) because these can all be shown to be multiples of 11. So the next few are: 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, for example.