While I have recently discussed the continuing domination of trendy teaching ideas over OFSTED there’s one subject where one would assume traditional methods still hold sway if one has listened to Sir Michael Wilshaw. When signalling his departure from enforcing progressive teaching he hasn’t hesitated to identify secondary mathematics for his examples of the acceptability of chalk and talk.
In his RSA speech he described an outstanding maths teacher he knew in this way:
[The teacher] was somebody in his late fifties. He was the head of maths. He was a very traditional teacher. He taught in a pretty didactic way, but the kids loved him across the ability range. He knew how to teach maths. You know what a great maths teacher does? Builds block by block to ensure that youngsters don’t move on until they understand the ground rules. He would spend many, many hours in the evening every night preparing powerpoints for himself and for the staff in his department and he would disseminate good practice, in terms of how to use powerpoints, to other people in his department and beyond his department to other schools in Hackney and beyond. And he produced absolutely fantastic results although some people would say he was a very didactic teacher.
He also mentioned that “the structured reinforcement of mathematical formula” was an acceptable use of time and in his London Festival of Education speech he even said:
If a teacher on a wet Friday afternoon is doing a fairly boring lesson on quadratic equations but the children are learning, that’s fine as well.
So nobody can doubt that OFSTED have nothing against fairly traditional maths lessons where things are explained rather than discovered and no gimmicks are used to make it entertaining. Well nobody could doubt it except those who work for OFSTED. Here’s what they actually like. This is the only maths good practice video added since Sir Michael made those speeches. Update 30/3/2013: The OFSTED good practice videos were all removed immediately after I blogged about them. If you’d like me to send you a transcript, email me.
Update 5/5/2013: Current version of video below:
Highlights include the teacher, Katharine, saying:
I’m not going to tell them how to do anything. So the challenge for me is the questions that I’m going to be using to make sure that they get out everything that they want to from the lesson. And that they discover things for themselves rather than me just telling them, oh this is how you do it – in algebra we write 3N instead of 3 times N. So I want them to find things out for themselves which sometimes you need to really think about the questions that are the probing questions that I’m going to be going round and asking them.
We then see the students try to work out how algebra works from discussing the 12 Days of Christmas.
The HMI who, as I understand it, is one of the top “specialists” in maths explains:
Katharine teaches for understanding throughout her lessons. She does that in various ways… she doesn’t just leap in with the right answer at any stage…If we contrast that with what we often see in other lessons we tend to see a compartmentalised approach to algebra. Where students are just taught a basic skill about you replace a letter by a number… And no really understanding about the role of the letters involved. So this school, this early work on algebra contrasts very sharply with what we see. And I would encourage all schools to think very carefully about laying the foundations for later learning of algebra in ways, similar ways to this.
Clearly this HMI was unaware that far from condemning a “compartmentalised approach” her chief inspector actually favours building “block by block” and “structured reinforcement”. Or perhaps she doesn’t care because it is her, and not Sir Michael, who will actually be judging maths teachers in lessons. Still, I’m sure the three recent studies of best practice in secondary mathematics have more traditional contents.
How about the one for Loreto High School in Chorlton? What maths teaching methods does that describe? Well there’s no reason to think they don’t use plenty of traditional methods, but this is what is singled out for praise:
Students enjoy a range of sorting and matching activities, often in pairs or groups that promote discussion and help to develop their understanding. Students of all abilities, but particularly those who are less able, respond well to opportunities to explore mathematics through, for example, recording their ideas informally on mini-whiteboards.
What about Archbishop Temple School?
The outstanding teaching in the department makes use of published resources, such as text-books and worksheets, but only selectively. There is no set text-book. Teachers aim for active learning, using a range of sorting and matching activities that engage students and encourage discussion.
So more discussion and card sorts. How about Allenbourn Middle School? Not strictly a secondary school but there should be some overlap.
Working from that secure starting point four years ago, and with pupil behaviour that was reliably good, the first step was to begin to encourage teachers to try new approaches. The only constraint placed upon staff was that outstanding quality of learning in mathematics in the school was to involve pupils using and applying their learning for the majority of theirlessons and, as a part of this, always wanting to ‘get right into the corners’ of their understanding. They made it clear that this approach wasn’t to be reserved for the occasional lesson – it had to become the way that mathematics is learned and taught throughout the school.
This often meant turning traditional lessons on their head. For example, in a Year 8 lesson on percentage increase and decrease, pupils don’t spend any time listening to reminders of the basic ideas about how calculations are done; they move straight into a buying and selling simulation with laminated ‘money’ and cards representing merchandise in the six ‘shops’ around the room. Traders are told the cost price of items and set prices; and buyers are encouraged to haggle by requiring percentage reductions. Reductions in prices in multiples of 10% are used initially and it is evident that some pupils can handle the idea quicker than others; it is also clear that those that can’t appreciate that understanding how someone can rapidly calculate a 30% reduction on a price of £5 is an important skill! Pupils learn quickly from each other and the lesson gets pacier and more demanding as some begin to demand 35% reductions and more complex discounts. For more complex calculations calculators are allowed, but they have to be used intelligently and this brings in the need to turn percentages into decimals quickly and fluently in order to keep up with the pace of haggling. Throughout, the teacher is closely monitoring pupils’ rates of understanding and skill acquisition. The plenaries are short and sharp, focused on specific skills, and are continually ratcheting up expectations. By the end of the lesson, all pupils have developed a ‘feel’ for the topic and have the capacity to deal with the mathematical concepts confidently and with a fluent recall of knowledge. Just as significantly, they show a rare level of confidence in problem solving.
Similarly, in a Year 5 lesson reinforcing techniques for addition and multiplication, pupils do not spend time responding to a long list of questions from a text book. Instead, it’s a game of Cluedo. The various clues around the room require a range of calculations to be made (and checked using an alternative method) and the answers provide pieces of evidence for these young sleuths to identify the killer. (It was Professor Plum!)
Oh. Well that’s all I can find about good practice in secondary maths that’s been published recently. Can anybody else find anything OFSTED have published about secondary mathematics which in any way suggests anybody other than Sir Michael will celebrate, or even tolerate, traditional teaching in the subject?
If you are wondering why I have singled out maths here it’s because the other good practice videos don’t need this much explanation. I’ll come back to them later in the week. The English one is just great.
Update (2/3/2013): There has been some discussion (not so much in the comments but elsewhere) as to the effectiveness of the lessons shown here, so I thought I’d add a few comments.
The point of this blogpost was to show how much OFSTED’s example of good teaching in secondary maths differed from that of its chief inspector rather than to say that these were particularly bad lessons. There is much that is praiseworthy within the lesson, one could almost believe it is the work of a highly effective teacher who was just putting on a show. However, if the case was to be made as to why the lesson shouldn’t be an example to all, I would suggest that some of the methods fly in the face of the evidence. Firstly, children “discovering” the ideas for themselves is not as effective a teaching method as telling them. The key paper to read about this is here. Secondly, the use of a sorting exercise is not necessarily particularly effective. I haven’t looked into the primary evidence but according to this blog the effect size for manipulatives in general is 0.37 and for manipulatives in algebra is 0.21. If you are familiar with the use of effect sizes, you are probably aware that John Hattie suggested that anything below 0.4 was of below average effectiveness. Finally, with regard to the content, if the whole “12 days of Christmas idea” is meant to make substitution and formulas more accessible, one has to wonder what the use of negative numbers in the second class was meant to mean (“On Christmas minus five days, I debited my true love’s account with 10 presents”?)
Now these considerations do not mean that children will never learn well from these methods; even I am not that prescriptive about methods. Whether the teacher shown is effective or not would have to be judged by looking at the success (or otherwise) of her students. However, there is no good case for OFSTED repeatedly presenting this sort of lesson as good practice, and criticising the alternative when even their own chief inspector is aware that traditional teaching in secondary maths can be highly effective. There is definitely no excuse for OFSTED’s chief inspector going around telling teachers that traditional teaching is fine while his organisation is using their unaccountable power to enfore the progressive consensus quite brutally at the school level.