Australian mathematics curriculum

My apologies to anyone out there who might read this blog from time to time. I have sadly neglected you for the last three months or so, such is the busy nature of my life as a 'retired' academic! I am now back from a wonderful holiday in Provence and able to give some time to writing the occasional post.

At my publisher's request I have spent quite a bit of time mapping the Australian primary mathematics curriculum to the content of the 5th edition of Mathematics Explained for Primary Teachers, to help them with marketing the book in that country. I must say I found the curriculum considerably more intelligent in its construction and content than the shoddy and embarrassing curriculum that we now have in place in England. It has quite clearly been written by people who actually know something about mathematics and mathematical pedagogy.

I drew on this Australian material when talking about algebra at a conference for primary school teachers in Cambridgeshire a few weeks ago. We noted that the English curriculum does not recognise algebra until Year 6! By contrast the Australian curriculum has an algebra strand all the way through from the start of primary education.

For example, all these are given as examples of algebraic reasoning developing in earlier primary years:

·      Sort and classify familiar objects and explain the basis for these classifications

·      Copy, continue and create patterns with objects and drawings

·      Describe patterns with numbers and identify missing elements

·      Solve problems by using number sentences for addition or subtraction

·      Describe, continue, and create number patterns resulting from performing addition or subtraction

·      Explore and describe number patterns resulting from performing multiplication

·      Solve word problems by using number sentences involving multiplication or division

·      Use equivalent number sentences involving addition and subtraction to find unknown quantities

·      Use equivalent number sentences involving multiplication and division to find unknown quantities

·      Continue and create sequences involving whole numbers, fractions and decimals

·      Describe the rule used to create the sequence

My contention has always been that the most fundamental component of mathematics education is not doing harder and harder calculations (the message in the English curriculum) but algebraic thinking and reasoning. This is where real mathematics emerges, powerful, widely applicable and creative. So, a proper mathematics curriculum must recognise and seek to develop algebraic reasoning right through the primary years; and not see it just as an add-on in Year 6. So, well done, Australia!

But I still hope you lose the Ashes.

Outrageous Performance Descriptor Maths KS1

The Department for Education in England is engaged at present in a consultation about their proposed performance descriptors for children in Key Stages 1 and 2 in relation to the new primary curriculum.

I have just been looking at the mathematics descriptors for Key Stage 1.

The proposal includes the requirement that children who are to be judged as working 'at the national standard' at the end of Year 2 will be able to ...

     add and subtract numbers using ... the written columnar methods ...

They can't be allowed to get away with that! Columnar methods for addition and subtraction are NOT in the curriculum for Key Stage 1 mathematics. They are mentioned in the non-statutory guidance for Year 2, but they are quite clearly not required in the actual curriculum.

Non-statutory guidance is non-statutory!

But these proposed performance indicators will be statutory. Key Stage 1 teachers will be requried to assess pupils against these criteria. So, de facto, they will become the key focus of the curriculum.

This is an outrage. We must protest strongly at what looks like a deliberate attempt to give non-statutory advice about formal traditional written calculation methods the same status as what is in the actual curriculum.

Key messages for Mr Gove

Tuesday 16 April is the closing date for responses to the DfE consultation on the proposed reform of the National Curriculum.

If you are planning to respond, go to:
https://www.education.gov.uk/consultations/index.cfm
Registration is easy and the response form provides plenty of opportunity for free comment.

Here are some of the key messages I hope the government will receive from the consultation.

• The previous proposals for reform of the primary curriculum, abandoned by the present government in 2010, were better than these, because they involved genuine consultation with the profession so teachers generally felt they could be delivered and that they reflected the learning needs of children in this age range.
• The current proposals are unlikely to help children in primary schools to learn how to learn mathematics in a meaningful way. They will not see mathematics as something they can make sense of, but mainly as a collection of rules and procedures to be learnt and memorised in isolation.
• Children will not learn that mathematics is an enjoyable and relevant subject that can be learnt in a purposeful way. Using and applying mathematics is lost in the detail of the content, rather than given the prominence it warrants.
• There is a huge mismatch between the stated aims and purposes of study of mathematics, which are good, and the statutory content, which seems obsessed with arithmetic processes. Genuine mathematical reasoning is largely ignored. 
• Similar criticisms have been made of the proposals for other subject areas. The aims and purposes of study seem to have been written by a different group of people from those who wrote the statutory content.
• The expectations for operations with fractions and other formal written calculations year by year are unrealistic and seem destined to promote failure by a greater number of children. This will increase the number of people who think they cannot do mathematics and dislike the subject.
• Some calculation requirements (particularly those for long division) are quite irrelevant in today's technological world, in which knowing what calculation to do and how to interpret the result are more important than being able to do a complex calculation.
• The emphasis on arithmetic processes is based on a false premise that these are somehow what mathematics is really all about. Mathematics is not mainly about learning how to do calculations, but this is the underlying message of this curriculum proposal.
• The phrase 'efficient method' for doing a calculation is not defined and its use to refer to traditional formats for subtraction by decomposition, long multiplication and long division is open to challenge.

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!