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.