I have not blogged for years, partly due to fact I have had little worthwhile that has not or could not have been expressed better by others with greater clarity, and partly due to time pressures.
However, I have spent much of my holiday so far catching up on blogs, articles, videos and generally tweets which I had ‘liked’ as a signpost to revisit them at some point.
I have therefore done much reading about the traditional v progressive debate and have been introduced to Greg Ashman’s excellent Filling the Pail blog (https://gregashman.wordpress.com) – should Craig Barton ever get so desperate for guests on his podcast that I find myself on there, this will be number 1 in my ‘Top 3’ section – and through his blog, and others, I have come to the same realisation as many teachers who clearly trained and began their careers at roughly the same time as me – that much of what we were taught and experienced early in our careers was complete nonsense. Brain Gym, learning styles, student led activities – you name it, I did it. I knew it didn’t work – I just assumed it didn’t work for me.
As I stated above, however, I don’t see the point in repeating what others have already said more eloquently than me, so I wanted to take things in a slightly different direction.
As part of my training, either for my initial PGCE OR the maths conversion course I did a few years later, I distinctly remember reading Jo Boaler’s book “Experiencing School Mathematics: Teaching Styles, Sex and Setting”. For those of you who have not done so, let me describe briefly: this is a write up of a research project comparing two schools, one of which exposed its maths students to traditional teaching, and the other of which taught students using projects and themes, where students directed the learning.
I say I remember reading it; rather, I remember trying to read it. It wasn’t mandatory reading, and I struggled to understand much of the technical jargon around the actual scientific research. But I remember the book and, as a UK teacher who had moved to the US, I was interested in Jo Boaler’s work and her career.
As time has gone by, I have discarded Boaler’s methods, and from my own experience have arrived at the conclusion, borne out by my results, that traditional methods are better, certainly for me. This certainly seems to be backed up by many of the articles I have read, and much of the anecdotal evidence I have seen in the blogs of others. I suppose one caveat is that I am susceptible to living in a bit of an echo chamber – so if you have experienced success with a progressive, reform curriculum, let me know – I have changed my mind once, and will gladly do so again if the evidence persuades me to do so.
One of the bees in Jo Boaler’s bonnet at the moment appears to be the idea of ‘maths anxiety’ and that this is caused, at least in part, by timed tests. As ‘evidence’ for this, she offers this paper – which notes that where students are already anxious about maths, their brains show more activity in areas associated with anxiety, and their accuracy is lower. It shows that students identified as having ‘high maths anxiety’ had a lower difference in their response time for simple and more complex problems than those who had ‘lower maths anxiety’ (i.e. ‘anxious’ students took a similar time to answer both types of question, the implication being that students with ‘lower maths anxiety’ answered the simple questions quickly, and took longer for the more complex problems – which is what I would expect as a maths teacher). What this paper DOES NOT show, at least to my eyes, is any link between the timed nature of the tests and increased maths anxiety (if I have missed this due to inexperience, please let me know and I will retract this). So Boaler is being obfuscatory, you might say.
Skip forward a few days to this: https://twitter.com/joboaler/status/895695882431062016
Here is where I begin to have a REAL problem. From the article linked to in this blog, it becomes crystal clear that Boaler is pushing her progressive, reform agenda by refusing to accept of the benefits of factual memorisation AT ALL. You can find an excellent rebuttal of this article, bit by bit, here (written by @iQuirky_Teacher).
I actually find this post incredibly arrogant in its language and patronising in its tone, but that might just be my perception. Bits of it are laugh out loud funny – or at least they would be, if we weren’t dealing with the education of children (note – we don’t say ‘right honorable [sic] minister’, and nor was Michael Gove the ‘education minister’, but I’ll let that go). The fact that she starts by asserting that not knowing the answer to 7 x 8 is a ‘harmless error’ is worrying. 7 x 8 is a short, indisputable fact. Not only that, but it is a simple mathematical fact. Not as simple as 3 x 5, granted, but simple nonetheless. I don’t see why a man in his 40s should get this wrong at any point, whether being interviewed on radio or not. I would be quite annoyed if any of my year 7s got it wrong. It is a fact to be learned and practiced to the point of automaticity.
The rest of the article makes a number of preposterous arguments that Boaler advances as a way of pushing her own resources, articles and website. Now I don’t have a major problem with her doing this APART from where the points she makes are damaging towards children and teachers. It would be quite easy to dismiss her as someone working in the US, where the system is different and we can ignore her and so on, but this would be a mistake. In an internet age, where I can instantaneously read the blogs and tweets of British academics working in Australia and America, ideas spread quickly. Which means bad and damaging ideas spread quickly.
So without trying to replicate the work of @iQuirky_Teacher, let me discuss a couple of points from Boaler’s article:
- “the memorization of math facts through times table repetition, practice and timed testing is unnecessary and damaging” –
No, no, a hundred times no. The memorisation of maths facts is VITAL. Maths facts are like strong, sturdy foundations. Without foundations, a building cannot be constructed. Without maths facts having been memorised, we cannot begin to construct solutions to complex problems.
Ah, but is memorisation of maths facts damaging, though?
No, of course not. Don’t be ridiculous.
2. “[the ideas] that math facts are the essence of mathematics, and, even worse that the fast recall of math facts is what it means to be a strong mathematics student….are wrong and it is critical that we remove them from classrooms, as they play a large role in the production of math anxious and disaffected students.”
If maths facts are NOT the essence of mathematics, what is? Granted, maths facts are not exciting, or sexy, but without them students won’t be able to do the fun, exciting and sexy stuff later on – or they will, but it will take them far longer, and they will experience much greater struggle. Maybe this is what Boaler wants – maybe she thinks students SHOULD spend years and years of their lives working on maths, protected in a bubble where they are never tested and they work everything out for themselves. Surely THAT is damaging for them?
And as for playing a large role in the production of maths anxious students – what could possibly make you more anxious than an inability to tackle something because you don’t have the basic skills?
3. “When students focus on memorizing times tables they often memorize facts without number sense, which means they are very limited in what they can do and are prone to making errors –such as the one that led to nationwide ridicule for the British politician.”
I don’t know if Boaler is suggesting here that the only possible opposing view to her own is that EVERYTHING is memorised, but I do hope not. 7 x 8 always equals 56. This is what makes it a fact which is so easy to learn, remember, and apply automatically. Once this has been committed to memory to the point of automaticity, then of course any teacher worthy of the name would ensure students are using this fact in a range of contexts. I can assure Jo Boaler than in the time she has been away from the UK, schools have not become rote memorisation factories filled with ‘teachers’ whose sole job it is to ensure students memorise everything mathematical.
4. a) “Some students are not as good at memorizing math facts as others. That is something to be celebrated”
No, it’s not. It’s something to be practiced. Saying ‘I’m not good at memorising things’ is rather similar than saying ‘I’m not good at maths’. It’s damaging and it’s unacceptable. Luckily, you can do something about it.
b) “many of us would probably assume that those who memorized better were higher achieving or “more intelligent” students.”
Maybe you would. I would assume that those who memorised better were better at memorising, and would use them if I could to help the others.
c) “Some students will be slower when memorizing but they still have exceptional mathematics potential. Math facts are a very small part of mathematics but unfortunately students who don’t memorize math facts well often come to believe that they can never be successful with math and turn away from the subject.”
So what, we test them once, and let them live with those scores forever? Or we encourage them, help them, support them – you know, like good teachers do ANYWAY – and help them see improvements?
This is where I believe we are getting to the most revealing and damaging part of this whole article, and, by implication, Boaler’s whole philosophy. She seems to have the following thought process:
- Timed tests are bad, we shouldn’t do them
- This causes maths anxiety for some students
- Students who can’t do them are made to feel bad and will want to give up
- This will damage those students for the rest of those lives
This makes no sense, but if Jo Boaler wants to bang this drum in her own home, let her. But these ideas are fundamentally dangerous and must be challenged. Here is my take:
- We should be doing timed tests, as these promote automaticity. However, we must make them low stakes/no stakes. I personally would recommend low stakes, where scores are recorded, and students are rewarded on the basis of improvement, not simply for getting 100%. We should not expect a class of students to get 100% every time. But we should definitely expect students to improve their scores over time, and we should support them, whether in class or without, to ensure as much as is in our power than this happens.
- Despite Boaler’s claims, I am yet to be persuaded that maths anxiety is a thing; furthermore, I do not believe that any such condition, if it does exist, would solely be caused by timed tests. In any case, I refer you to point (1) immediately above.
- Who is making these students feel bad? Not any teacher I am aware, nor, I imagine, any teacher worthy of the name. If this is happening, it is happening because of the importance attached to these tests, be that by the teacher, the school, the ‘system’, or the parents.
- This is a ridiculous argument, and much as I hate to bring the subject up, seems very ‘fixed mindset’ to me. As teachers, we have a responsibility to convince students that they will improve with hard work. There are any number of examples to draw upon from all walks of life. Andy Murray didn’t quit tennis after years of failing to win a Grand Slam; Thomas Edison didn’t quit after thousands of failed prototypes; JK Rowling didn’t give up after 12 publishing houses turned down Harry Potter. None of this is to say that ALL children can be 100% successful 100% of the time, but it IS to say that it is possible for 100% of children to improve 100% of the time.
And with all of this, let us not forget – we are not talking about timed tests all lesson, every lesson, for every skill. We are talking about short periods of quick recall of basic facts. I am, anyway. Maybe in America they do spend hours on timed tests. But I doubt it. What I do not doubt is that if Boaler is allowed to continue to propogate her ideas about maths anxiety, then maths anxiety will become an issue. It may even become a ‘cool’ badge, the new ‘well I’ve never been good at maths’ or ‘I have a rubbish memory’. This will be incredibly damaging for our current and future students. We have a duty to kill this weed before it takes root in our educational conversations.