Michaela’s Knowledge Deficit

mih

I wish to make it clear that this article is not a personal attack upon anyone named or otherwise referenced. Michaela Community School say they welcome debate on their methods so I invite them to consider this a contribution to that debate and not to repeat their spectacle from December. To debate Michaela’s methods in lieu of any hard performance data we must be able to present the bones & sinews of those methods for examination, their pedagogy & their practice.

All information & excerpts used in this article are publicly available and comment represents legitimate analysis & review. If any information here is factually incorrect then please comment and I shall attend to any errors. Thank you.

 

The Myth

The myth upon which Michaela is founded runs like this: “British schools do not teach knowledge but we are here to change all that with our knowledge curriculum“. It’s a myth rehearsed by Michaela staff frequently, as exemplified by these four excerpts from The Guardian and from the blogs of Michaela Head of English Jo Facer & Deputy Head Joe Kirby:

mcs-kb-guardian-1

mcs-jf-ratb-ctamc

mcs-jk-pr-akls

mcs-jk-pr-akls-b

Michaela staff have delivered this myth so frequently now, to each other and to us via their blogs and their ticketed salons, that they likely believe it themselves. Deep down they know as well as we do that knowledge has always been at the heart of British education and that their pretence otherwise is cynical marketing. Allege systemic failure; announce you are the revolution who will fix things; sell flags:

 

 

Much Twitter flag-waving followed this speech from teachers eager to signal their ideological alignment with Comrade Katharine:

tt-fw-mb

I’m sure the publication of this book and its sale to hopeful readers was intended as a landmark in British education at which Michaela handed teachers the keys to the Kingdom of Knowledge. If we count book-selfies as reviews then it succeeded. Of course, we don’t and we must look elsewhere for these. I’m grateful for the thoughtful work of reviewers such as Dr. Debra Kidd whose generous & successful two-part analysis saw Michaela cancel her personal invitation to a tour of their school and, in what is becoming a customary response by Michaela and its allies to fair enquiry, her subsequent unwarranted vilification.

 

Exposing the myth

Kidd’s review pays close attention to Michaela Deputy Head Joe Kirby’s chapter on knowledge. She points out that while he is correct to agree with Prof. Daniel Willingham on the possession of knowledge as a necessary condition for useful thought, neither he nor any of his staff devote any ink to what useful thought involves or how it may be taught & developed. Is “relentless drilling” of facts a successful programme upon which to build a school? No, training of this kind serves only inexperienced, unqualified & uneducated teachers, nor is the evidence for its potential to communicate knowledge positive even in the book intended as Michaela’s showcase and as the manifesto for their knowledge revolution:

 

Look at these two instructions from the page pictured above:

Identify the name given to the amount of space that matter takes up in a three-dimensional object.

Define mass.

The first, requiring a single word response, is correctly answered by the entire class but individual pupils stumble over the second. Mischa attempts to paraphrase the first question and Said doubles down on their error by attempting to give that definition more fully. It’s no reflection on either pupil that they have been trained to automatically respond to closed questions with fixed definitions nor that they find longer questions more cue-rich than shorter questions. It’s no reflection on them that they find shorter answers easier to recall than longer answers but it is disappointing that, despite their misappropriation of psychological tropes, Michaela’s teachers practise and promote this wrongheaded strategy for cognitive inflexibility as a school-wide policy and mistakenly regard it as radical to the construction of informed, agile thinkers the equal of any in the country.

Legitimately sceptical observers and readers of this book might ask themselves whether “relentless drilling“is all that Michaela staff can manage, given their lack of experience, subject knowledge and their proud scorn for traditional initial teacher education routes and, thereby, those teachers so qualified. It may be so, I cannot say, nor are we likely to know given Michaela’s prescribed teaching methods. I am certain that given enough time drilling and asked in the conditioned way that many Michaela pupils could reproduce their “Knowledge Organisers” almost perfectly. Attempted seriously, rote learning is not difficult. No special institutional culture or structure is required, just time and effort. The question then becomes one of whether what Michaela requires to be learnt by rote and requires to be “relentlessly drilled” is knowledge, that is to say verifiable fact. Here there is significant cause for concern in the core subject of mathematics.

 

Michaela’s Mathematics Department

I do not have overview of all Michaela materials but what I have seen of their mathematical content and discussion is very worrying. For context it’s useful to know that only half of Michaela’s six maths teachers studied the subject to degree, the other half studied Philosophy, Politics, & Economics. The first three do not include its departmental Head.

One criticism to be made of Secondary Mathematics PGCE courses is that they permit their graduates an inordinate amount of license to consider their immediate subject knowledge, supplemented by in-house SKE, equal to its teaching. It’s not. A person does not require a degree in maths to be at least proficient in it but to teach it, day in, day out, with the necessary fluency of skill & knowledge, let alone act as departmental head, this requires an undergraduate maths degree or equivalent, related study as a minimum . Let me exemplify this via the blog of Michaela’s Head of Maths:

mcs-dq-uikb-lts

Bear in mind that the above was written by a PGCE-qualified teacher in their second post as Head of Maths. Given this I’d like to recommend that that Michaela buy some legitimate maths textbooks as soon as is practical. Perhaps there are a few thousand pounds idling around in the balance sheets they could use.

Maths cannot be effectively taught to a particular level by someone who is still learning it to that level. It typically takes years of dedicated study & practise to build necessary, connected schemata. We’ve all heard of or know non-graduate mathematics teachers but I think you will find that responsible maths departmental heads, as those of any subject, ceteris paribus will unanimously prefer candidates with a degree in their subject to those without, and for very good reasons.

As we shall see, these things have important consequences for the wheel-inventing involved in Michaela’s construction of a maths curriculum but at least that department is not following the unusual strategy of Michaela’s Science department in openly buying their curriculum piecemeal:

 

 

There are numerous ways for a department to deal with a knowledge deficit, I suppose, and this represents one extreme but the rallying cry of “just tell ’em” would best be amended to “just tell ’em someone else’s knowledge wot you bought“.

 

Pedagogy Geeking

It’s often the case that people less capable of or productive in a particular activity will dress themselves in the aesthetics or theory surrounding that activity, hoping to impress as commentators if not as athletes, film critics rather than actors. We have seen a rise in the narrative of teaching of the substitution of passion and its comic sans cousin geekiness for craft & experience. Some pedagogues are practitioners and some amateurs are experts, of course, but we all know the difference.

During her time as Head of Maths at Dixons Trinity Academy, Bradford, we were told that Michaela’s Head of Maths describes herself as a pedagogy geek:

mcs-dq-guardian

If you see a parallel with the way Boalerian growth mindset teachers feel it necessary to authorise their practices by  prefacing their lessons with “the science bit” then you would not be alone. The appeal to cognitive psychology is at the heart of Michaela Community School’s practices & promotion but it’s something of a cargo cult with Prof. Dan Willingham cast in the role of John Frum. Sue Gerrard has some good blog posts on these issues.

Overall, Quinn’s blog is thoughtful but it is unusual for a maths department head to conclude that pupils, nationally given her use of “they” to refer to pupils & “we” to teachers, are not capable of learning maths as it is traditionally taught:

 

mcs-dq-uikb-tmmtmm

Falling away from traditional maths teaching and towards pedagogy in the hope of finding a way of teaching pupils the craft of generalisation in a way which does require pupils to generalise we are led to Skemp:

mcs-dq-uikb-mom-skemp-b1

In this suggestion that Skemp’s ideas “ignores what is happening in pupils’ brains as they work” we have the first intimation of a problem. Richard R. Skemp, known for his work on instrumental & relational understanding (IU & RU) and referred to in the first footnote above, was not ignorant of psychology. He was a doctor of psychology and helped found the International Group for the Psychology of Mathematics Education some twenty years before John Sweller’s work on working memory and some thirty years before Michaela reduced that to the pap currently funnelled through its blogs and served up at its salons. We might expect a “pedagogy geek” referencing Skemp to at least know these facts about him.

 

Skewing Skemp

Concluding correctly that RU is necessary but insufficient to mathematical teaching & learning but incorrectly that pupils “can’t generalisethe Michaela maths pedagogy attempts to reduce all RU to IU by heavy use in class and at home of something called “knowledge grids”:

mcs-dq-uikb-mom-codify

Yes, what does a knowledge grid have to do with teaching & learning maths? How this strategy is imagined to reduce cognitive load isn’t made clear, there certainly isn’t any research on the use of these sheets. If anything, immediately & cumulatively it will increase cognitive load as students must locate, load and interpret these “nuggets” from a range of grids (four of them are posted here) rather than relying upon the fluency of schemata gained through genuine traditional practise with exercises, examples & explanations.

mcs-dq-uikb-mom-kg-1

Note that there is nothing traditional about Michaela’s school-wide “knowledge organiser” innovation, nor are all innovations good things. These grids, organisers or whatever they wish to call them certainly aren’t, anymore than would be the innovation of KS3 pupils learning their English grammar & pronunciation from a dictionary, but if as a teacher you believe in them then it will mean less cognitive load for you. The perfect proxy for teaching and learning, adopt them and you will have none of those pesky repeat explanations to worry about, just refer pupils to a particular knowledge grid you sent them home with the night before and hope they can make sense of it. If they can’t then obviously it’s not the strategy at fault, it’s the student. More self-quizzing required. Detentions all round.

If we adopt this Fordist pedagogy of attempting to beat into instruments all mathematical knowledge & skill then we ensure the generalisation deficit Quinn incorrectly assumes by removing from pupils the opportunity & obligation to learn how to generalise with learning reduced to the memorisation by pupils of as many instrumental & representational variations as possible:

mcs-dq-uikb-tmmtmm-question

Unnatural, ineffective, this is Frankenstein teaching by which Michaela believes it can paste together on a table axioms, formulae and algorithms and, after a jolt of discipline, see arise fully formed mathematicians. It won’t work and it will be failing right now. Yes, pupils will look busy, they will be able to recite the definitions to which they’ve been conditioned but, like Mischa & Said, they won’t be able to apply to the contents of their short term memory what they have managed to press into their long term memory. Relational understanding, to quote Skemp, is knowing both what to do and why, fluency in this arising from the “mental maps” of schemata, not from “fixed plans” of the kind found on these grids. These maps cannot be, as Michaela Deputy Head Joe Kirby might put it, “frontloaded” anymore than can gymnastic skill and the continued attempt to do so will waste pupils’ mathematical potential, turn them off mathematics as a subject and as an interest and deprive them of associated opportunities for success.

 

Vicious Circles.

Anyone reading this article to this point might decide that it’s refutation of Michaela’s claim to a knowledge curriculum can be dismissed as opinion so I will now post particular examples to show the lack of knowledge at Michaela Community School.

In mathematics visual representations do not need to be precisely drawn to be useful representations but they must at least be coherently drawn and correctly annotated that they can be seen to notionally represent what they are intended to represent. For example, by inspection, arithmetic & algebra angle sums must be correct: unlike in these Michaela teaching materials intended as examples to teach circle theorems:

mcs-ri-cotg-ct-asum-1mcs-ri-cotg-ct-asum-2mcs-ri-cotg-ct-asum-3

 

 

Labelled angles must accord with inspection, unlike these:

mcs-ri-cotg-ct-inspect-1mcs-ri-cotg-ct-inspect-2mcs-ri-cotg-ct-inspect-3

mcs-ri-cotg-ct-inspect-4mcs-ri-cotg-ct-inspect-5mcs-ri-cotg-ct-inspect-6

mcs-ri-cotg-ct-inspect-7mcs-ri-cotg-ct-inspect-9

mcs-ri-cotg-ct-inspect-8

mcs-ri-cotg-ct-inspect-10mcs-ri-cotg-ct-inspect-11

mcs-ri-cotg-ct-inspect-12mcs-ri-cotg-ct-asum-3mcs-ri-cotg-ct-asum-2mcs-ri-cotg-ct-inspect-13

 

By inspection, arithmetic or algebra in any triangle larger angles will always be opposite longer sides, unlike these:

mcs-ri-cotg-ct2-angle-1

mcs-ri-cotg-ct2-angle-3

mcs-ri-cotg-ct2-angle-4

mcs-ri-cotg-ct2-angle-2mcs-ri-cotg-ct2-angle-5

mcs-ri-cotg-ct2-angle-6bmcs-ri-cotg-ct2-angle-6c

mcs-ri-cotg-ct2-angle-7

Some of these errors will be obvious to you, some may require you to reach for a pencil and paper yet no mathematics teacher is going to present these to pupils under any circumstances. Many of them directly contradict the theorems they are are supposed to be introducing by exemplification. Incorrect examples are worse than no examples because they confuse the nascent geometer, algebraist & arithmetician in every pupil but some of these “examples” are so obviously wrong it’s difficult to believe that they were produced by a Secondary maths department and not by a lower KS2 pupil. Nor does the apology of “not drawn to scale” apply when you are presenting examples of theorems. If this is it the standard of material permitted in some maths departments then is it any wonder some pupils cannot learn to generalise?

It is especially ominous that these errors are published on Michaela’s official website. That should be their first showcase, their first opportunity to make a good impression but did nobody review this material? We would expect that a school claiming that subject knowledge is the origin of their teaching would take pains to ensure that the contents of their website supported those claims rather than driving an HGV through them. We must conclude one or two things; that either nobody at Michaela was capable of seeing these errors in this material whether they reviewed it or not, or that nobody could be bothered to review it. This speaks loudly of Michaela’s true regard for knowledge.

Given the evidence we can be justifiably concerned for the mathematics education being received by Michaela’s pupils and by extension all lessons there.

 

The Evidence Is In

Groups such as the incipient Chartered College of Teaching and researchED pressure teachers to base our practice on research and on evidence so I invite you to consider the evidence Michaela Community School have published, actual teaching materials for a core subject which directly contradicts their claims for a knowledge curriculum. Consider also the ideas they put forward as pedagogy in that core subject, their school-wide conviction that all knowledge & skills can be reduced to lists. Now ask yourself whether the best teaching you’ve received, observed or achieved involved the use of lists? Can your own subject knowledge and skills be reduced to a grid?

Parents, teachers & teachers in training, don’t join the Michaela “revolution“, keep on the straight path; trust yourself and those around you. You’re likely doing great as it is.

Peace.

 

 

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8 comments

  1. MrsPigeons (@MrsPigeons)

    My only questions is this (and no, I don’t work at MCS) – every single school out there has it’s own quirks, foibles and errors. We are now tearing apart a school who want to promote a different way of teaching that they think will result in greater student learning and better teacher work life balance.

    Surely we should be seeing what we can take from them or ignoring them rather than tearing them to pieces and highlighting mistakes? There is no revolution. Are Michaela contagious? Are MCS staff able to influence the day to day practice of other teachers? No, I think not. MCS is one, very small secondary school who work in a different way to most schools. To be honest, I’m not sure that the way they work is even understood yet – I can’t say that I properly understand it.

    I know I could find as many errors in the day to day explanations, resources and home-grown worksheets at any school – but it is not useful to me to point them out. My job, when dealing with other schools, is to say what I can learn.

    • vinceulam

      Thank you for your comment. I appreciate that for different reasons many people identify with the staff at Michaela Community School so it can be difficult for people to acknowledge that there are problems there. It seems that you are more concerned with the fact of my criticism than the content but I will reply to what I feel are your core points:

      1. The operational systems at Michaela Community School differ only from those of other schools in degree (topical), not in kind, but the aesthetics determining their emphases have not resulted in a functional harmony.

      2. Other than Liz Speller’s teaching of coordinate grids for figurative work & reproduction (see below), there is nothing I have seen at this school which warrants emulation. Their innovations have yet to prove successful, their performance data pulled out of their heads. I recommend that anyone considering emulating the operational systems promoted by Michaela Community School think very hard about whether there is any evidence for what they are being told other than the reports of Michaela-selected visitors who have met selected pupils.

      null

  2. Jo Morgan

    Jo, I decided that the most efficient way to respond to your comment was in intersperse my responses per point. For others, Jo is in italics.

    I’d like to address readers of this post if I may.

    You have my permission. I hope you don’t mind that I eavesdrop this being, you know, my blog.

    I am worried that Mr Ulam has managed to insult a very large number of maths teachers here. I want to reassure them that his view (that one must have an undergraduate degree in mathematics to be a good Head of Maths) is utterly untrue, and based on no evidence whatsoever.

    Given the evidence for crap maths at Michaela Community School I think most people will agree it’s an exceptionally effective proxy, at the least.

    He has also shown a misunderstanding of the idea of subject knowledge development in mathematics education.

    Believing in the necessity of obtaining significant subject knowledge prior to commencing work as a maths teacher is not a view on subject knowledge development after commencing work as a maths teacher. If a person can’t do maths, if they have never studied maths to a significant level then they should not consider maths teaching a viable career option.

    I’m not clear what his reasons for attacking individuals are – it is both unnecessary and unkind – but in the process of doing so he has attacked the maths teaching community as a whole, and that is not something I am willing to ignore.

    So your belief is that my belief in the necessity of obtaining significant subject knowledge prior to commencing work as a maths teacher is not only “unnecessary and unkind” but is also an attack upon people who have commenced work as a maths teacher prior to obtaining necessarily significant subject knowledge. How can that be? Is it now a universal human right to teach maths in a Secondary school without first obtaining necessarily significant maths qualifications? If for you sharing a belief is an attack then it’s interesting to see that you are willing to attack me.

    We are currently facing a recruitment crisis in maths teaching. In a great many schools there are people teaching mathematics who simply don’t want to teach it and have no interest in developing their subject knowledge any further than the next day’s lesson. This is a real problem. In those same schools there are dedicated, intelligent and hard working maths teachers. Some of these teachers have undergraduate degrees in mathematics, some don’t.

    Allowing people to commence work as maths teachers prior to obtaining necessarily significant subject knowledge is not a solution to any drought in the supply of maths teachers. It’s a solution to the absence of warm bodies in class rooms.

    My own experience is that there is absolutely no correlation between the level of qualification held and the effectiveness of one’s maths teaching. In my own school, some of the best teachers do not have mathematics degrees, while some of those with mathematics degrees struggle with the content of the new GCSE. The link is simply non-existent.

    My experience is that there is a positive correlation between a maths teacher’s subject knowledge and their ability to teach maths. The link exists, as shown the crap diagrams in the post above and on Michaela’s website.

    I have a first class honours degree in statistics from UCL, but by Mr Ulam’s standards that does not qualify me to be Head of Maths – presumably he’d rather have a Head of Maths with a maths degree from the local polytechnic.

    In a heartbeat. A gnat’s heartbeat, if that comment is typical of your character. I can’t abide snobbery. Your attitude doesn’t speak well of your regard for those of your pupils who will attend their equivalent of “the local polytechnic”.

    It is not uncommon for mathematicians to have this arrogant and elitist view of mathematics, and unfortunately this is very damaging to our field.

    I imagine that if your most persistent experience of mathematicians is to have your maths corrected by them irrespective of how pretty are your resources then you might be inclined to regard them as arrogant, but genuinely damaging to our field and to the prospects of our pupils is the admission to our corner of the profession of people without any significant maths qualifications whatsoever. Further, that you would call me “Elitist” is satire of the highest order given your dissing of “local polytechnics”.

    Every maths teacher – no matter how qualified in mathematics – has a duty to continuously develop their subject knowledge. This means exploring alternative mathematical methods, developing an understanding of misconceptions, and discovering wonderful mathematical facts and oddities to share with our students.

    Such a duty exists only for people who, inexplicably & absurdly, enter maths teaching without any necessarily significant qualifications. A preference for teaching pupils “alternative mathematical methods” & holding forth on pop pedagogy is almost inevitably a symptom of significant subject knowledge deficit.

    Our thriving maths Twitter community is a place where maths subject knowledge grows everyday – this is not a community that Mr Ulam participates in, but a number of the Michaela teachers are there, learning and sharing alongside the rest of us. We find the resources and posts written by Michaela’s maths teachers to be high quality and thought provoking.

    No, I do tweet but, yes, I’m happy to say that I am not part of a community which excuses crap maths. Chums before sums seems to be the rule in that community.

    I do not know Dani Quinn well – my interactions with her have only been on Twitter and at maths conferences – but I am aware that she is an experienced and well respected Head of Maths.

    Yes, she is thoughtful. I said so myself.

    Michaela is privileged to have such a reflective, thoughtful and intelligent practitioner, and Mr Ulam is most ungracious to attack her in a weak and misguided attempt to undermine a school.

    Heroic attempt at hyperbolic contrast but when you can tell me where you materially disagree with my criticism of Michaela, rather than rant in hysterical, supercilious indignation at the fact that anyone dares to point out problems there, then that would be good.

    If Mr Ulam disagrees with my views on the necessary qualifications of Heads of Maths, I am most happy to discuss this with him. He can find me on Twitter (@mathsjem), developing my subject knowledge.

    You blocked me for not approving your post immediately so that’s unlikely to happen anytime soon, but snappy advertising for your link curation there, well done. Unblock me for a chat anytime you wish, no hard feelings but please arrive with a better attitude.

    Thanks for reading.

    You are welcome. Good luck with your subject knowledge.

    PS – Mr Ulam, I believe you spelt Jo Facer’s name wrong.

    That would have done.

  3. Brian

    Are you sure you have interpreted the information correctly Vince?

    I understand a currently unemployed traditional maths teaching guru who shall remain nameless visited MCS recently and I don’t recall any of this being mentioned in his comprehensive and balanced review. This nameless individual is also a staunch advocate of subject specialists and the notion that an undergraduate maths degree is the minimum for maths teaching.

    Maybe these reflections were going to appear in part 2 of his review of MCS and now you have gone and stolen his thunder.

    More power to your elbow.

  4. Pingback: going round in circles | logicalincrementalism
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