Yesterday I was shown a video of a Y6 classroom working on some maths, reasoning about fractions to be precise. The extracts from the classroom were interspersed with comment from their teacher.
It was a joy to watch. The relationship between the teacher and the pupils was tangible; the pupils were (dare I use the word) engaged, there was plenty of useful and informative discussion amongst one another, the teacher listened in but didn't overpower and gave children time to work on their ideas. Surprise surprise; children answered in whole sentences (!) and paid attention to the teacher (without 'tracking'), they took responsibility for their task and their learning. There was plenty of teaching. And, shock horror, there was laughter.
It was all a Y6 maths lesson should be; content rich, enjoyable, puzzling, memorable and collaborative: building a community of mathematicians. And Mr Malyn of St Margaret's C of E Primary School taught as if no-one was watching (thank you @EnserMark for this phrase).
Now some of you might know where I am going with this.
(Deep breath) So there are plenty of videos lessons out there, in particular on the NCETM website, purporting to demonstrate 'good' maths lessons. Some of these are of teachers brought over from Singapore as part of the government's push to adopt Chinese teaching methods in mathematics to raise our position in the. PISA and TIMMS league tables. My problem with these videos that I have seen is this. This is a visiting teacher, often encountering this class once and only once. Thus the culture of the classroom and the relationships between the learners and the adult are all missing. This is not unimportant. The reliance on 'from the front' instruction and the underplay (even elimination) of talk, discussion and the role of problems to situate and add context to the learning displays a particular type of lesson. And one I have worked hard to break down over 30 years because research has shown us how ineffective this is for many learners. Importantly, it is the teacher who is doing the maths, rather than the learners. I used to ask myself at the end of a lesson "who did most of the work there?" if the answer was me - well that's not really what should be happening, is it?
My question is this. If it was fairly straightforward for this publisher to find this English Y6 class to film (and in a school that has been in and out of challenging circumstances), how difficult would it be for NCETM to video the expertise and skill around in our UK classrooms? In a situation where a visiting teacher teaches an unknown group of children it is easy to slip into 'instruction' mode (let's leave aside here considerations of cultural differences). I know this as I have taught a fair few lessons in other's classrooms over a number of years.
So let's watch these videos with a critical eye. What has it got to say to us, with what we know about our students' learning? What am I persuaded about? What am I left wondering about?
In short - let's look nearer home and remember what it is we already know about learning maths. And let's all teach like no one's watching.
This video is in the public domain and is part of the package: "No Nonsense Number Facts: Teaching for mastery: Fluency through reasoning with number facts Y1-Y6" Published by Raintree and Babcock https://www.raintree.co.uk/products/9781474749541
Thanks for this Helen.
ReplyDeleteI haven't seen the NCETM videos specifically, but have seen others, and think I know what you are talking about.
For what it's worth, it is my believe that learning (mathematics) can and does happen in a number of ways.
However, I believe that one of the fundamental aims of education is to mentor children towards becoming responsible - to become able to meet the demands that will be made of them, according to their own conscience, and become able to justify their own actions. And this not only for human reasons, but also for mathematical reasons.
If we agree that this is an important aim of education, then it seems to me that a teaching approach that is too heavily biased towards instruction, and classrooms of largely subservient children, is problematic to say the least.
I can see why teachers adopt 'instrumental' methods, as they may seem the simplest, and even the most successful, approach for training children how to pass what are still largely instrumental examinations.
As you point out, it may take a wider view to appreciate what we might be missing if education continues to go down this route.
So much to think about here. I particularly want to focus on this extract from your blog though: "The reliance on 'from the front' instruction and the underplay (even elimination) of talk, discussion and the role of problems to situate and add context to the learning displays a particular type of lesson... research has shown us how ineffective this is for many learners." I would find it really useful if you can cite the research you refer to here. I ask this not as a cynic of what you have written but because if we are going to be able to argue against the kind of teaching currently being supported by NCETM videos, then having access to research which counters this approach would be useful. Thanks Mike
ReplyDeleteOk here goes Mike. I'm not sure if it's what you're asking (but I'm sure you'll tell me if it's not!) and It's kind of backwards, but two main points I would make in relation to this, I think.
DeleteFirstly, the accumulating evidence is so overwhelming of talk playing a key role in cognitive development and perceptual learning, across a wide range of curriculum areas, that talk is now recognised as central to learning by both constructivist and cognitive theorists: Wegerif and Mercer 1997, Mercer 2000, Barnes D 2008, Monaghan 2010, to name a few. However, research has also found that productive talk (such as 'exploratory talk') occurs only rarely, if at all, in most classrooms (Howe and Mercer 2007:8).
Secondly, over at least the past 20+ years much research has been undertaken on pupils’ attitudes to mathematics and there is ongoing documentation of all ages of learners’ disengagement from the subject, despite their level of educational achievement (Buxton 1981, Hughes 1986, Askew and Wiliam 1995, Hannula 2002, Nardi and Steward 2003, Klein 2007, Boaler 2009, Askew et al 2010, Borthwick 2011). For e.g., evidence from 1999 TIMSS shows that in both England and New Zealand students’ attitudes to mathematics declined over their school years (TIMSS 1999, Askew 2008, Walls 2009).
I think this supports my statement that a lack of peer-to-peer and adult-to learner discussion in particular, hinders mathematics learning.
I don't feel there is anything 'wrong' with 'from the front' instruction, or any other mode of interacting with children, but it all depends on what/how/when it is done, and what *also* happens.
DeleteIn my experience, things that are problematic are (1) talking, and then staying, 'at the front' (2) an over-reliance on talking from the front, and (3) thinking that because the instruction was 'logically' sound, the children must have therefore learned what was intended (connected to (1)).
At the same time, I have seen teachers have difficulties due to being reticent to talk at the front, or initiate more generally.
There is research justifying more or less any type of pedagogical approach, which I suspect is because a range of approaches are useful, of which talking from the front is one.
Mike is right that listing research might be seen to be useful for some, but an advocate of the 'NCETM' approach will then reply with a set of conflicting research, and then where are you?
It seems to me that we must research our own practice, with others doing the same thing. What does our experience tell us? To what extent is what we do, and what we notice, dependent on our beliefs? What basis do we have for these beliefs? And so on.
Research about this or that pedagogical approach has been of limited value to me as a teacher, they are only starting points from which to research my own practice with others who are able to challenge me to think and act differently, to go beyond my habitual pedagogical actions and beliefs.
The issue for me with the videos is only partially with what they portray.
Yes, I *believe* that the view of mathematics teaching portrayed by NCETM etc. may be detrimental to the wider mathematical/educational development of children, but this belief is (only) based on my values and experience.
What is also of concern is the (government-sanctioned?) pedalling of a particular approach, the suggestion that this is the best way to teach, dissuading teachers from researching their own practice. It is up to teachers to place what is shown in the videos against their own experience, to watch carefully what the students are doing in their classrooms.
"... if we are going to be able to argue against the kind of teaching currently being supported by NCETM videos, then having access to research which counters this approach would be useful."
DeleteWhat I am trying to say above is that it might seem necessary to present research to counter the research presented by others. But this suggests that citing research and counter-research is of any value in presenting a case for one pedagogical approach against another, if even this was a thing that was of any value in itself, which it may not be.
The flaw of the current over-emphasis on 'research-based pedagogy', the hope that someone else will have found the answer to our dilemmas, that because he or she says this is true, it is true.
What use is there in trying to argue against (with research, or otherwise)? I suspect that (online) arguments against will be of little point, as people will choose whatever research fits with their beliefs and practices, unless they commit to researching their own experience, with others who can challenge these beliefs and practices.
The research of others, then, may only be a starting point: the only thing that might change beliefs and practices is the experience of some disturbance, resulting from noticing something not previously noticed.
How can we encourage teachers to interrogate their own beliefs and practices, to take heed of that which they previously may not have?
It's a good point about one-off lessons, Helen. I rely a lot on yesterday. And on a kind of tuning in to each other. I'm finding it a bit harder this term as there are more children who are more comfortable in French and Spanish, most of them, and a boisterous bunch of boys. Luckily a third thing I rely on is stuff to play with, and there's no shortage of engagement there.
ReplyDeleteI really like the 'tuning in' metaphor Simon - and used it for my MPhil, so thank you for reminding me of it.
DeleteIt strikes me (another good metaphor - have you come across "Metaphors we live by" Lakoff & Johnson?) that even in a one-off lesson you are able to tune in to the learners; you have maybe to work harder at it. However, many of the one-off videoed lessons I have seen don't make the effort to tune in - it's as if the children might not be there at all - or at least - it wouldn't matter which children were there, the teacher's delivery would be the same.
I'm glad you mention metaphor, Helen, even if it's off at a tangent. I like L & J's widening of the idea of metaphor a lot. It's often exclusively taught as a literary device, but of course it's everywhere (language as dead metaphor for instance). Toys are metaphors, stories often are, mathematical manipulatives and symbols. Wherever one thing 'stands for' another.
DeleteYour 4th paragraph hits the nail right on the proverbial, Danny. Thanks for that.
ReplyDeleteDanny's last paragraph: "What is also of concern is the (government-sanctioned?) pedalling of a particular approach, the suggestion that this is the best way to teach, dissuading teachers from researching their own practice. It is up to teachers to place what is shown in the videos against their own experience, to watch carefully what the students are doing in their classrooms.'' This is so important. Researching one's practice is, I believe, essential to developing one's practice. Practitioner research, which includes reflective practice, was encouraged through the excellent MAST courses and continues to be the case with those teachers recently and currently on the MEI Teaching A-level Mathematics (TAM) courses.
ReplyDeleteMy concern is how the government through the mouthpiece of the NCETM is encouraging a specific, political agenda to raise England's standing in the PISA league table, by seeking to copy approaches used in Shanghai and Singapore. This feels like another version of the failed National Strategies brought in by a Labour government; prescription, prescription, prescription.
This comment has been removed by the author.
DeleteI completely agree that the current emphasis on research-based pedagogy is not only stifling debate and experimentation, but reducing education to a "one answer" solution. Maybe this whole response should be prefaced with - in England. That is why I prefer to use the phrase 'research-informed'. And this I think ties in with that you are saying, Danny, that research is only a starting point for my own developing beliefs and practices based on what I read and what chimes with what I am observing in my classroom(s). The problem, at the moment more than ever, is that the government, via the NCETM, rather than encouraging debate about, for example, videos taken in classrooms, are using videoed lessons to promote a particular approach to teaching mathematics (yes, I agree with you absolutely on this, Mike). And this approach runs counter in many ways to much of what we have learned about teaching mathematics over the past 30+ years, which is what I am pointing out above. This is not to say we don't always have something more to learn, but we don't learn anything by having discussion suppressed; and neither do learners.
ReplyDeleteTo encourage teachers to interrogate their own practices I believe they need to stop being 'told' things and start being given 'stuff' (or metaphors!) to stimulate discussion and thought. @gfletchy 's stuff does this. Caroline Ainsworth's Cuisenaire videos do this. Simon, your stuff does that. This is the stuff we need to point teachers towards; in order that the question pops up; "Wow, I wonder if my kids would do that?"
I don't think there is anything 'wrong' with telling people things, but perhaps in telling them to do something and not something else. There seem to be two senses of the word telling here.
DeletePerhaps the different senses are in telling as presenting a possibility (could), or telling as an imperative (should). Perhaps the issue with the NCETM (videos) is the sense of imperative, that teachers *should* teach like this, that this is the best way?
... btw here's some more video of a (my) classroom, which is certainly not presented as a best way, but just because it exists: https://undergroundmathematics.org/calculus-trig-log/inverse-integrals-teacher-support... I liked the 'students presenting their ideas' video - as they do all the maths!
This comment has been removed by the author.
ReplyDeleteThis article by David Pimm is relevant to this: http://flm-journal.org/Articles/21DF013F06A07E4BCE711019C10CF.pdf
ReplyDeleteI don't see prescription and direct teaching being in the same boat. The difference is when Government's prescribe SsoS for education (Estelle Morris being the exception) the do not understand the nature and the complexities of T&L, apart from the fact they all went to school! Direct teaching is an aspect of my practice and so is student enquiry and exploration. It is all about finding a balance, and that balance will be different for different teachers.
ReplyDelete