Yet another error in new Mathematics Primary Curriculum: 'irregular'

Call me pedantic if you wish, but I do think that mathematical terms used in the Mathematics National Curriculum should be used correctly. The misuse of the word 'irregular' is my latest find. This occurs in the measurement section of the Year 5 Mathematics Curriculum programme of study:

'Calculate and compare the area of rectangles (including squares) ... and estimate the area of irregular shapes.'

This statement seems to imply that a non-square rectangle is a 'regular' shape. The word 'irregular' is used here for two-dimensional shapes where you cannot calculate the area exactly using a formula, such as the outline of an island or that of a fried egg. These are irregular, but so are all rectangles that are not squares, all triangles that are not equilateral, and so on.

So, let's tidy this up. A regular two-dimensional shape is one where all the sides are equal in length and all the internal angles are equal. So, the only quadrilaterals that are regular are squares. All others are irregular, including non-square rectangles.

All these shapes, for example, are irregular polygons:

The National Curriculum needs another way of describing the other kinds of 2-D shapes that it has in mind for which Year 5 children should learn to estimate the area. I usually call them non-standard shapes or non-geometric shapes.

A further thought on composite numbers definition

Going back to the erroneous 'definition' of composite numbers in the Year 5 Programme of Study for the Mathematics National Curriculum for England ... where we read that pupils should learn about 'composite (non-prime) numbers'.

In my previous post I pointed out that you cannot use 'non-prime' as a synonym for 'composite' because the integer 1 is neither prime nor composite.

On reflection, I realised that the error here is much more substantial than this. The concept of 'prime' applies only to positive integers. So, a prime number can be defined as an integer with precisely two factors (which will be 1 and itself).

This means that 'non-prime numbers' would include all numbers that are not positive integers. So, the identification of composite numbers with non-prime numbers would imply that numbers such as –3, 2.4, ⅚ and √2, for example, are all composite!

Of course, they are not! 'Composite' is also a concept that applies only to positive integers – those integers with two or more factors greater than 1.

That was a sloppy bit of work by whoever wrote that programme of study.

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Any reader looking for professional help in the area of primary mathematics education might like to take a look at the recently-launched website of my colleague, Ralph Manning: www.manningeducation.co.uk

Mathematics national curriculum oddities

The statutory requirements for the new primary mathematics curriculum (to be taught from September 2014) have some odd aspects for which it is difficult to find a rational justification.

Here are two examples.

1) Under algebra, children (the curriculum prefers to refer to them as 'pupils') in Year 6 are required to learn how to

·    find pairs of numbers that satisfy an equation involving two unknowns

but nowhere are they required to find solutions to equations with one unknown!

2) In learning about geometric transformations, children will meet the concept of 'rotation' in Year 2, but then the word does not appear again in the primary curriculum. So, after Year 2 there's nothing at all about recognising and describing a transformation of a shape in terms of rotation and there's nothing anywhere in the curriculum about rotational symmetry.

Probability chapter rescued

I am delighted to day that at the last minute my publisher has agreed that we should reinstate the chapter on Probability in the 5th edition of Mathematics Explained for Primary Teachers (see my post on this site on 23 December). We were alerted to the fact that the enlightened Welsh and Scottish primary curriculums still include probability - and the book serves the other UK countries as well as England. And, of course, there are plenty of academies and free schools who do not have to follow the National Curriculum (ironic, isn't it!), so we want to make sure that teachers in these schools have the opportunity to understand this most important and interesting application of mathematics and to consider exploring it with the children they teach.

Now here's an intriguing use of numbers that turned up at home recently. I said to Mrs H, 'What's four plus one?' She replied, 'Thirteen'. She was right, of course. Can you explain?

And, finally, just to grab a little reflected glory: the amazing Jon Haylock doing astounding things around the Welsh coast with Griff Rhys-Jones on ITV this evening (8 pm) is my nephew.

Let's hear it for the Blob

Michael Gove has decided to pour scorn on the academic education community who oppose his imposed curriculum reforms by referring to them as 'The Blob'. It is incredibly arrogant of our Secretary of State for Education just to assume that his prejudices about education are necessarily right and thus to dismiss as worthless the views of those who have devoted their professional careers to researching and reflecting on the nature of learning and teaching, children in schools, curriculum theory, the aims of education, how to cater for the range of abilities and learnings styles, the nature of understanding, how to develop higher order learning, effective teaching methodologies, the promotion of positive attitudes and values, subject knowledge pedagogy, how to assess learning, creative and critical thinking, and so on. How come this branch of academic study is suddenly worthless and irrelevant and totally misguided?

Of course, I do not agree with all my colleagues in education about everything all the time. Sometimes, I do not even agree with myself. The study of children learning in classroom contexts is not a science and the practice of teaching is not a branch of technology. So there will always be different shades of emphasis. I recall, for example, being criticised by hard-line constructivists for calling one of my books 'Mathematics Explained for Primary Teachers' because, they argued, mathematics is not learnt by a teacher explaining but by children constructing their own meanings from their experiences. Yes, I agree with the constructivist viewpoint to some extent, some of the time, and in some respects, but it is not the whole truth. (Apart from anything else children like teachers who explain things clearly and help them to make sense of their experiences.) The debate and the sharing of different perspectives are helpful and important. Academic education conferences can be quite lively at times, with probing questions and challenges to various positions being adopted.

But for all our different enthusiasms and insights, there is a remarkable consensus in the field of education that Gove's reforms are driven by prejudice and reactionary opinions and that his new curriculum is a disaster, that it fails to put the needs of the child at the centre of learning, and that it has the wrong balance between learning facts and the development of higher order learning. In the proposed mathematics curriculum for primary schools, for example, most of the negative feedback in the consultation process has been ignored. There remains, for example, an over-emphasis on the rote-learning of formal written calculation methods, at a level which, in a technological age is obsolete and anachronistic. There remains a glaring mismatch between some of the laudable aims stated in the introductory paragraphs and the details of the actual content of the statutory curriculum. Mathematics is conceived in this curriculum as being mostly about doing calculations, the harder the better. This is arithmetic, not mathematics. For mathematicians the subject is about the beauty of pattern and generalising, making connections, equivalence and transformation, application, problem solving and creativity. Where is all that in this curriculum?

For Mr Gove to dismiss this consensus within the field of academic study of education just by labelling his opponents 'The Blob' and not to be prepared to listen to those who do not agree with him is arrogant, prejudiced, pig-headed, ill-mannered and, sadly, – for the next generation of children who have to live with his arid, ill-conceived, dull, narrow, inappropriate, constricting, reactionary and antideluvian curriculum – disastrous.

Let's hear it for the Blob! Somebody has to go on challenging the Govian prejudices and presumptions that are driving the current education policy in this country.

Letter to Gove

I was pleased to be one of the signatories to the letter sent this week by 100 academics in the field of education to Michael Gove about his proposals for the National Curriculum in Key Stages 1 and 2.

Here is a link to read the considerable coverage given to this letter by the Independent newspaper.

http://www.independent.co.uk/news/education/education-news/100-academics-savage-education-secretary-michael-gove-for-conveyorbelt-curriculum-for-schools-8541262.html  

Petition to reformulate the proposed national curriculum

I just signed the petition "Re-formulate the proposed new National Curriculum (Primary)" and wanted to ask if you could add your name too. 

This campaign reflects a lot of my concerns about the current proposals. The more support we can get for this petition, the better chance there is of succeeding. You can read more and sign the petition here: 

http://you.38degrees.org.uk/petitions/re-formulate-the-proposed-new-national-curriculum-primary 

Can you also take a moment to share the petition with others? It's really easy – all you need to do is forward this email or click these links: 

Share on Facebook 

Share on Twitter 

Thank you! 

High-quality mathematics education

The latest draft of the proposed new National Curriculum framework is now published for consultation.

http://www.education.gov.uk/schools/teachingandlearning/curriculum/nationalcurriculum2014

Clearly, my interest lies mainly in the proposals for mathematics in Key Stages 1 and 2. Herein lies one of the greatest inconsistencies I have ever observed in a curriculum document!

The mathematics curriculum section begins with an excellent statement of the purpose of studying mathematics, including:

A high-quality mathematics education ... provides a foundation for understanding the world, the ability to reason mathematically, and a sense of enjoyment and curiosity about the subject.

And then three Aims are stated, that the curriculum aims to ensure that all pupils:

 become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems  

 reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language 

 can solve problems by applying their mathematics to a variety of routine and non- routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

This all sounds great! All the right words are there: understanding the world, reason mathematically, enjoyment, curiosity, conceptual understanding, enquiry, conjecturing, relationships, generalizations, justification and proof, problem solving, applying mathematics ... whoopee!

But then look at the actual programmes of study for Key Stages 1 and 2! There is hardly anything here that seems designed to promote these laudable aims. The programmes of study are dull, lacking in genuine application and problem solving, and out of touch with the real world; they ignore the development of mathematical reasoning, and focus principally on mastery of routines rather than conceptual understanding.  And the problem is that these statutory requirement are what teachers will use in practice to plan their teaching - and the requirements are so packed with demands for practice and mastery of abstract, formal arithmetic calculations that there is very little chance that teachers will give time to providing pupils with experiences that will contribute to the purpose of study and aims stated at the beginning. The only part of an 'aim' that looks likely to get a look-in is the the bit about 'varied and frequent practice', and this will be principally practice of formal, written methods of calculation. 

Schools will be judged on how well children do in national tests. The national tests for mathematics will presumably test only the 'statutory requirements'. So, teachers will, I fear, teach only the statutory requirements. This means that all the stuff that warms my heart in the opening statements in the mathematics curriculum will probably have no effect at all on the actual experience of children learning mathematics in primary schools. 

Unless we can get Mr Gove to change his mind ... there is a consultation going on. The link above will get you to it!

New Primary Curriculum for England Dropped

The new primary curriculum, following the Rose Review, had been accepted by Ed Balls and published in the government's website as being statutory from 2011. It has been distributed to many schools, teachers are already engaging positively with it and in some LAs teachers are being trained to implement it.

However, the proposal for this to become statutory was incorporated in the Children Schools and Families Bill, along with various other more controversial legislation. Progress through parliament was consequently slow – and on Thursday the new primary curriculum was dropped from the Bill in the so-called 'wash-up' that takes place when a general election is called. The opposition could have agreed to it going through, but they did not.

This leaves all of us involved in primary education in a bit of a mess. A huge amount of time, effort, expertise and funding has gone into the development of this curriculum, including the Rose Review itself and the extensive consultations about the proposals. The outcome was something that primary schools seem to support and which was research-based and contemporary. Schools may well determine to implement it anyway – but we are left now with the statutory curriculum for primary schools still being the one that was published in November 1999.