A book review this week, but first, thanks to Will Bickford Smith, founder and editor of conservativeteachers.com for a lively and probing round table with Nick Gibb at Portcullis House. There are more Conservative teachers, and more variety in our experience and opinions, than our opponents would have us believe, and it was good for people to be able to say what they thought without the filters of organisation and hierarchy. Nicky Morgan has agreed to host a future meeting, and in the meantime I hope more Conservatives will read the blog – here is an entertaining starter – and that more Conservative teachers will write for it.
The book is Jo Boaler’s Mathematical Mindsets, a companion to her website. Professor Boaler is an opponent of ours, and signs off emails with “Viva la revolution” (she is a professor of maths and not Spanish). She believes in mixed ability teaching and is opposed to textbooks, “procedures” (standard methods of calculation) and homework, which she considers inequitable as some children don’t have anywhere quiet to do it. She told the Telegraph that multiplication tables caused “crippling anxiety”, and was opposed to testing them, though she did not argue that they were “not worth knowing”, a paradox to which I’ll return.
To my surprise, I found many of her teaching tasks quite brilliant, and have started to use them. They are interesting and challenging, promoting mathematical reasoning and the flexible application of knowledge. Her criticism that textbooks interfere with this by presenting only the most simple examples – eg only hexagons that are regularly shaped – is often true, though it should not be. She is also correct in saying that school systems too often put sheer speed before understanding, and that this penalises some gifted mathematicians, including the Fields Medal winner Laurent Schwartz. No sensible person would argue against varied and interesting maths teaching.
Her book, though, is about politics as much as maths teaching, and here the glass is very nearly empty. The American temptation to simplify and then exaggerate begins with the introduction, where she describes the OBE as the “greatest honor bestowed in England, given by the queen”. No disrespect to holders of the Order, and particularly not to Mary Beard, but Professor Boaler must know that neither statement is true.
The same fast and loose attitude applies to the presentation of studies and data. A UK school dubbed Phoenix Park is compared with another, Amber Hill (amber – slow down and stop) on the basis of work that took place in the 1990s, though the dates don’t appear in the text. An interesting critique of this study is here.
Professor Boaler’s flagship “Railside School” in California, is equally controversial. Her account of the work has been attacked for selective use of data by a group of California academics, whom Professor Boaler has in turn castigated on her university website for alleged bullying and intimidation. I hate bullying, but in a 2008 paper cited in a US Supreme Court case, she concedes her critics’ main point – Railside pupils did very well in algebra, but not so well in other aspects of maths. Professor Boaler says that this may be because of the pupils’ lower attainment in “language arts” – English, to us – but the available evidence suggests that it might equally well be the result of paying more attention to algebra than to other aspects of maths, particularly calculation. On reflection, this is the basis of Professor Boaler’s “revolution”. She wants to replace arithmetic with algebra as the foundation of school mathematics.
Which brings me back to the humble 2x table. Some schools teach children to count in multiples instead of teaching the table, and some as a preparation for it. In either case, I have always found that this makes learning the table more difficult, and see it as an problem of co-ordination rather than maths, as nearly everyone can add two to a given number.
One of my current pupils, now aged 11, was indeed in a state of “crippling anxiety” over maths at the age of ten, chiefly because he did not know any number facts without working them out from scratch, including the 2x table beyond 2×2. Careful teaching of the 2x table provided a template for the others, in which he is now fluent, and a model for learning other key facts, including addition and subtraction of numbers to 20. In each case, I followed Professor Boaler’s principle of unpacking and explaining, so that he understood everything he learned, but also the principles of memory development set out by the Nobel winner Eric Kandel, whose work does not appear in her list of references. My pupil has gone from not liking maths to expressing a wish to become a maths teacher. Whether he will become one or not, I don’t know. I do, though, see learning tables as a key step in opening up the possibility, and in enabling him to enjoy maths.