You Can Lead a Horse to Textbooks

Or a mule, maybe. You can lead a mule to textbooks.

About a month ago, there appeared a Conversation article by Rachel Marks, a researcher in primary education at the University of Brighton, in England. Based upon research for which she was the Principal Investigator, Marks’s article was about a UK government program, launched in 2016, where primary schools were offered matching funds to purchase mathematics textbooks. Marks and her colleagues concluded that schools substantially rejected the program: few schools took up the offer of subsidised texts, and fewer stuck with it.

The goal of the UK program was to have primary schools adopt a “mastery approach” to teaching mathematics, including the use of “east Asian style” textbooks, and with accompanying training and online resources. The two textbook series approved for the program were Maths – No Problem!, which Tony Gardiner has praised here, and Power Maths. Marks and co make clear, however, that having most primary schools adopt any text would have been a dramatic change. A TIMSS table included in the Marks’ research paper makes clear how infrequently mathematics texts are used in English primary schools as a primary source:

We have only skimmed Marks and her colleagues’ report on the survey, but what we read was informative and interesting. The paper seems devoid of the usual ideological language and is clearly written, with care taken to describe the varied usage and semi-usage of textbooks and the (commercial and ad hoc) alternatives; such use generally lies upon a spectrum, making it difficult to summarise textbook use as a simple yes or no. Nonetheless, it is obvious that in England there is much more “no” than “yes”.

Of the schools which responded to Marks’s survey, just a third eligible for funding took up the UK government offer (p 10). Then, of those schools that gave it a go, 37% had “largely or completely abandoned” using the approved textbooks, with a further 24% continuing to use the textbooks “in a partial manner but putting no further funding into the provision of consumables associated with the schemes” (p 76). The percentages speak clearly enough, and is the basis of Marks’s Conversation article:

In all, only just over 10% of [presumably responding] primary schools that were eligible for the textbook scheme took it up and are still using it in full.

If the results seem clear, and we’re not really contesting them, there are nonetheless a couple points worth noting: on the validity of Marks’s survey; and, more importantly, about the message Marks feels that these results send, and that she herself sends.

Marks indicates that the survey was distributed to all 17,038 English state primary schools, of which the researchers received 664 “valid” responses. That doesn’t sound like a great response rate, although Marks throws around some “power calculation” jargon in an attempt to assure us that this 644 is “in excess of the minimum ideal sample size”, and makes for a “representative sample”. We are not so assured.

Marks might have had a suitably representative sample if the sample had been random in some reasonable sense, but of course it was not. Schools chose whether or not to respond to Marks’s survey, and there are very good reasons to suspect which schools would have been inclined to complete the survey, and which would have chosen to ignore it. It seems a fair bet that the textbook program was received significantly worse than Marks suggests.

As for the supposed implications of the survey, Marks and co end their paper with an Implications and Recommendations chapter (p 78), with Key Messages for all concerned. These key messages are highlighted in the Executive Summary (p 10), including:

Department for Education: “Consider fewer, full or majority-funded, strategically targeted, funding initiatives.”

National Centre for Excellence in the Teaching of Mathematics: Support schools to match or tailor existing resources to their pedagogic approach.”

Publishers: Further investigate why teachers adapt materials and provide support for this.”

School Leaders: Enable teachers to be involved in decisions about which scheme to adopt and how / when to use it.”

Researchers: “Deepen understanding of uptake and attrition patterns in the [Department for Education] textbook-funding, to enhance the implementation of future initiatives.”

So, plenty of recommending that anyone and everyone pay greater attention to teachers, to what they want and why. And this is the message with which Marks closes her Conversation article:

Our research underlines that we need a solid understanding of how maths teaching is done in England before adding in any new initiatives or policy – not only what’s happening in classrooms, but the complex reasons behind why it is happening. We hope governments learn from the inefficient administration reported here before implementing further new or borrowed policies.

Yeah, well, maybe. Undoubtedly, the textbook program didn’t go according to plan, and there are lessons to be learned. But it is not at all clear to us that Marks has learned the most important lesson, and the most obvious lesson.

In the introduction to the survey results, Marks and co note the current low usage of textbooks, with the table above, and contemplate the reasons for this:

Possibly because of the previously poor quality of texts available, textbook use is somewhat controversial in England, particularly in primary schools. Across the UK, pupils tend to hold critical views of textbooks (Wang & Fan, 2021), citing textbook-based teaching as ‘boring’ and ‘tedious’ (Ni Shuilleabhain et al., 2021). Indeed, it is concerns that textbooks may come across to pupils as dull which leads many teachers to supplement the resource (Silver, 2022). Further, while textbook-schemes have been demonstrated to increase teacher subject knowledge and confidence, resulting in pupils holding a more “robust understanding of mathematics” (National Centre for Excellence in the Teaching of Mathematics [NCETM], 2015, p.1), many teachers worry that such textbook-schemes have the potential to exert curricular and pedagogic directions. There is a fear that textbook-schemes have the potential to reduce the role of the teacher to that of a ‘technician’ (Boyd & Ash, 2018, p.221), delivering pre-packaged lessons to a compliant class and eroding teacher autonomy (Gear, 2022; Turvil, 2021).

One could write an entire post, an entire book, about the nonsense beliefs outlined in this paragraph, and of the depressing implications. But we’ll make it short. We’ll simply note that with this background it is entirely predictable that the generous textbook offer would fall on barren ground.

In Marks and co’s summary, they note that the East Asian model of teaching was “not being replicated with any fidelity”, and that “This is not surprising” (p 77):

England has a very different educational history, and, importantly, a different relationship with design of and approach to using textbooks. Pedagogical practices in primary mathematics in England are – and have always been – far removed from a single jurisdiction-wide mandated textbook model.

Which is really the point. Less time and money could be spent on offering teachers things, less pandering to teachers’ nonsense beliefs, and more energy could be spent on instructing teachers on what to do, on mandating the use of good materials in practices that work.

31 Replies to “You Can Lead a Horse to Textbooks”

  1. Do any of the readers/commenters here have experience with pre-service teacher training in Primary Years?

    If so – is there “one way” primary teachers are trained to teach numeracy (I cannot bring myself to call it Mathematics) or arithmetic?

    My memories of primary school were some standard “activity” books where we had working space to show our long-division or subtraction with borrowing and then there were a few sets of photocopied (or spirit-duplicated in some cases) problem sheets that asked questions but didn’t specify a solution method. We worked through them, the teacher randomly came around and corrected our work and that was it. But there was a book of some kind.

    What is the Australian “norm” with regards to teaching number skills? I’m most interested in Years 4 to 6 if anyone here teaches those levels.

    1. Good question, RF. I don’t have the details of what is taught to will-be primary teachers (and would love to get them). But there is a mountain of circumstantial evidence, reaching the Beyond Reasonable Doubt standard, that the majority of Australian will-be primary teachers are indoctrinated with garbage education philosophy (and sociology and politics), and are presented with garbage methods to employ.

      1. Well Marty asked for it!
        And the rest of you can skip what follows – which has to start with some politics. (Oh for a [democratic] country in which everyone agrees that education has to be largely independent of party politics. Japan? Italy?)

        It is bound to be an oversimplification (we were not there, so inevitably overlook all sorts of things), but wiser souls than me have concluded that one can identify particular textbooks as central to almost every lasting change/improvement in school mathematics in the UK over the last 400 years.
        (Which is not to deny that there have also been many very bad textbooks.)

        In the period 1960-90, the UK witnessed dozens of curriculum projects. Each project had its own inspiration, and its own guru(s). And almost all had their own “resources”. At that time “resources” usually centred around a *textbook series*, which embodied the main thrust of the project .
        The biggest of these projects (SMP) lasted for ~50 years: it almost ended with a series that was used in ~60% of our secondary schools – a series that had some truly excellent material, but which also helped to get textbooks a bad name.
        This was largely because in the mid 1980s the school system was in disarray, and no textbooks series could expect to compensate for the widespread problems. The spirit of the 1960s and 70s had been very creative, and many good things were attempted. But it was chaotic, and the profession did nothing to acknowledge or to relieve, the chaos – leaving politicians to intervene in the 1980s.
        Until the late 1980s we had no central (or local) curriculum: each school could choose. Their choices had only been constrained by local industries – and by *examinations* (at 10/11, and at 16 and 18). And with the demise of selection tests at age 10 (in the 1970s), primary schools were left with no external constraints at all. So there was then no central or local control of primary school *endpoints*. The idea that *all* students should master certain key ideas and methods was unfahionable; so those from even a single school were “all over the place”. Since each secondary school had perhaps 5-10 *main* feeder schools, with a few students from up to 10 other primaries – this meant they had no possible “starting point” for first year secondary pupils! So the idea of a secondary textbook series-for-all hit the wall. You can imagine the rest.

        There followed a political reaction: a period of attempts to increase centralised control. But such control always has to work *with* prevailing forces, institutions, and professional leaders. The 1979-1997 governments (all of the right) dug in, faced down opposition, and introduced a national curriculum and testing; but it was a mess – and after 18 years in power they rather lost the will to continue.
        The replacement party won support by vowing to be more strict than those they were replacing (in the economy, in policing, in education, etc.); so they continued in 1997 with “more of the same” – only different. At first this looked promising. For example, they tried to fix the curriculum (which, after the initial disaster in 1989 had been subject to emergency revision every 2 years); the resulting 1999 curriculum for mathematics was rather decent. But the government undermined this potential progress – failing to enforce the *obligatory* curriculum (which was never going to deliver quick results or headlines) and instead pouring money into a *voluntary* “Numeracy Strategy”, which offered training and blow-by-blow schemes of work that told teachers how to teach. (This was a remarkable and unprecedented move, and had a considerable impact: almost all primary schools participated; and they all had to have a daily maths hour – often at the start of each day.) But the Strategy also had flaws (e.g. its methods were followed slavishly without being understood, or questioned, or refined; and it it never generated any lasting material, such as textbooks). And it lost focus.
        Moreover, the curriculum agency resented being sidelined. Ministers took their eye off the need for curriculum, and support (such as textbooks). And the curriculum agency “went native”: their 2007 revision of the curriculum (coordinated by KGB – an Australian, who had made his name running the NSW Dept of Education 1992-2002) essentially replaced the idea of a carefully structured content list by “key processes” (such as problem-solving).

        Recent history:
        This was the background for the next switch of power – to the right (in 2010). The new administration (rightly) set out to undo some of the whackier latter-day nonsense, and chose to focus strongly on maths. Their basic aims were crude, but fine (it is one of the strengths of politicians that they are obliged to simplify).
        But politicians have very different priorities form those on this list. To achieve those priorities (in short, to maintain “power”) they mostly choose to work with those already in post (who were appointed in the previous climate, so may well not share the new aims!); and where they recognise the need for new institutions, they tend to invent these too quickly, and behind the scenes – which leaves them at the mercy of Snake Oil salesmen.

        Already from 2007-8, those who expected to be Education Ministers (Gove, Gibb, Truss) recognised – among other things – the remarkable underuse of maths textbooks in England (<15%), and saw this (roughly correctly?) as a post-modern reluctance to accept a recognised mathematical canon. Instead of devising an institutional way of supporting the development of textbooks which was acceptable to publishers (as in the US in the 60s and 70s? – where *projects* were supported centrally, and the market was then allowed to take over), they (i) specified certain curriculum-based requirements (including emulation of certain features from the Far East); (ii) announced an "approval" mechanism for declaring that a series met these requirements; and simply (iii) put up money for schools to claim half of the cost of any approved series.

        This system was seriously flawed. For example:
        (a) The panel set up to "approve" the texts had no experience of making such judgments, and was controlled by inflexible civil servants who seemed unable to bend (one excellent series was repeatedly turned down for trivial reasons).
        (b) The market failed to deliver: the only series that got written and approved emerged from a tiny company owned by a Canadian couple with no experience of school maths. (Fortunately, they collaborated with an excellent Singapore educator and Editor.)
        This failure to generate options became embarrassing, and eventually a second series was "approved" (even though in my view it was awful, and I am told that the approval panel never saw most of the materials before being obliged to "Approve" it).
        (c) The funding system encouraged schools to *buy books*, but offered no support for the associated training to help teachers use the materials: Singapore's effectiveness is rooted in an understanding of how maths is learned, how material needs to be structured, and how to teach: in particular, it is rooted in *whole-class teaching*, which had been largely abandoned and forgotten in England (if everyone in the class is encouraged/allowed to be "at their own level", then the idea of a common textbook makes little sense). So most of those who bought into the only system that was available for the first few years, never had the chance to attend a training session in order to re-discover the simple, but unfamiliar, principles which underpinned its effective use.

        And having spent public money, government insisted that its training agencies should *never* recommend the textbooks that had resulted, or to tell teachers which ones were provenly effective. (The excuse given was to avoid law suits from rival publishers.) So courses run in the 40 Maths Hubs across the country (which provide the only official maths in-service provision) remained "generic" – leaving schools to do all the research for themselves, or to trust the grapevine.

        For whatever reason (market forces? the inability of a small company to use its maths texts as a loss-leader?) the original approved series was not cheap – though its training was excellent. And they found the lack of realistic support from the Ministry (see previous paragraph) consistently uncomfortable. Those schools that bought in to this original programme were often totally won over. But when financial support came to an end, I suspect there may have been a decline in the number who could afford the annual maintenance charge. And as new teachers, who have not may have come in to the school

        When the second series was approved (very late), there was probably an uptick in schools applying for the available money, because the books were much cheaper – and much glossier (and published by a very large publisher, with a much greater reach). I cannot avoid the suspicion that these schools may since have discovered that they are rather hard to use. (I can find no independent evidence of efficacy – but will keep looking. I may be missing something, but they seem to me to be a very English version of Far East maths teaching, with the page designer dominating over the author/editor, and with no awareness of the thought that goes into a typical Singapore, or Japanese, or Chinese page/chapter. It looks as though the material was initially written in England, but with named editorial advisors from China. However, I wonder what these advisers thought of the process? I cannot imagine *any* Chinese student trying to learn primary maths from these books – but I will spare you my reasons.)

        I spent 10 years trying to argue that carefully crafted maths textbooks were much more needed at *secondary* level. (To see why, consider England performance in TIMSS. At Grade 4, England average scores have climbed dramatically ever since 2000 – in 2003, 2007, 2011, 2015, 2019: this is astonishing. At Grade 8, they have essentially flat-lined – with a small step: so the marked Grade 4 "improvements" are not ones that have had any subsequent observable benefit!!)

        1. Fascinating – thanks! History, ideology and politics are always crucial.

          I am curious about ‘differentiation’ which seems to have become popular in the 90s (while I was out of teaching). This appears to be a worthy goal, but I have considerable difficulty is seeing practically how to apply it under any sensible workload. Is that a factor in the whole mix of trying to use textbooks or not?

          1. I used Maths, No Problem. The textbooks aren’t bad but it was a dreadfully dreary experience to teach and pitched at a level that did not remotely stretch most chn in the class. It was an experience of wanting to teach maths but having to bend to parrot an approach that would fulfil accurate completion of questions. Motivation was low

        2. Thanks, Tony. It’s fascinating to read. A few questions and thoughts, if you’re not yet sick of reliving the whole thing.

          (1) Who was KGB?

          I hunted a little, but couldn’t figure it out. It’s also interesting your suggesting that the UK authority “went native” in 2007. In Australia, it feels as if the entire education system has gone native, and there has only been a recent fight at all because of one “traditional values” Education minister, and a Ballarat physics teacher.

          (2) You suggest, if I haven’t misrepresented you, that SMP largely floundered because the system was in too much disarray for such a formal structure to work. To what extent do you think that still affects the (non)acceptance of textbooks in England? Yes, the curriculum may be in better, or at least clearer, shape, but is the needed sense of unity and formality there? Is the simple understanding of the requirement to sit still and pay attention there? You emphasise later the importance of whole class teaching, and that this has been abandoned and forgotten in England (and Australia). Hence, I guess, your emphasis on the need for training. Still, even with training, the cultural forces against an entire classroom paying attention for any length of time are presumably strong.

          Note the temptations/demands of differentiation, as alluded to by JJ, and John Berry’s suggestion that MNP was “dreary” to use, and under-challenging “for most [children] in the class”.

          I think these issues are even greater in Australia, where, for all intents and purposes , there is no coherent curriculum. That for me, is not an argument against textbooks: I can think of no sane alternative. But the anti-text forces are so strong, and the proper implementation is premised on so much other change, it is difficult in Australia to even know where to begin.

          (3) Can you indicate the name of the “Canadian couple” textbook series from around 2007?

  2. Odd Rachel and co didn’t attempt to follow up the jumpmath lambeth study 2009 to see if the success there was sustained. Given they exactly succeeded in the area England has a problem.


    1. Thanks, Stan. It rings a bell, but I don’t know about jumpmath (but note Tony Gardiner’s comment, below). To be fair to Rachel and co, their focus wasn’t on the success of the program in terms of results or whatnot (if only because, I think, it’s too early.) They were very much focussed on the reception of the program.

  3. That is an excellent topic, Marty. The lack of school textbooks in the UK for every subject, not only math, was and is a massive surprise for me. The textbook does not make the teacher redundant; such a belief is preposterous. The situation with school books in the UK reminds me of medieval times when only priests could read the Bible and be the source of knowledge.
    However, a textbook helps a student come back and revise; it helps the teacher understand the baseline of knowledge and see where their class stands against it. It also might help a talented student to run faster. Obviously, a textbook is just a ‘device in the hands of a teacher’ and can be utilised well or made useless.
    From personal anecdotal experience, books by Art Of Problem Solving are excellent. They have Beast Academy books for primary school written in comics style and Art Of Problem Solving books for secondary and high school. These books are certainly some of the best in the world, in my view. Also, in the UK, there is an excellent book by Tony Gardiner and Alex Borovik, ‘The Essence of Mathematics Through Elementary Problems’. The latter isn’t necessarily a school book per se, but it could be an excellent aid device in the classroom.
    The problem of the UK schools, and I quote a math teacher from a very good math-oriented school, is: “I suspect that the biggest issues in UK maths education are to do with pedagogy rather than content. I was trained to let pupils discover mathematics for themselves (which works best for those who are curious to do so), but nowadays, I think there is much more teaching by example and then expecting the children to practise the same things (which is very boring for the ones who got it the first time). This is surely connected to the scarcity of maths teachers with degrees in mathematics (or confidence in their grasp of the subject).”.

    1. Thanks, Dr. M. Yes there are some excellent texts or resources or whatevers around: I wrote about Gardiner and Borovik’s book here. But I think this misses the point.

      What you want, what you need, is a coherent curriculum and with good textbooks written for that specific curriculum. It is a nightmare, and inefficient madness, for individual teachers and parents to scouring, trying to find the appropriate materials.

      There is something great about AoPS, and AMT (in Australia) and so on, and the more I read about it and learn about it, the more it really pisses me off.

  4. Not sure what Stan was hoping for.

    I have been a quiet admirer of John Mighton for many years (his program breaks the mould, and seems to be fairly effective).
    There clearly was an attempt (probably supported by JUMP) to get disadvantaged communities in England to consider using JUMP materials. This seems to have been a very blinkered, short-term attempt (a short program in 2006, with a view to having an immediate impact – based on students scores on national tests *in the same year*). It is unclear whether the program was then extended, or simply allowed to “muddle on” for a year or so, and then die: there is a 2009 inside report; and then …… nothing. What is clear is that it was not adopted. (There is no outside evaluation.)
    Certainly no-one thought of looking at how the same kids then performed in Junior High School.

    The position with regard to standard textbooks in the UK (including Maths No Problem) is more complicated, and I will try to comment later if anyone wants to hear.
    Here I will only say that
    * a good textbook series provides a considered architecture which frees teachers to teach (rather than spending their preparation time collecting disconnected materials taken from here and there);
    * this leaves them free to think about the teaching (rather than cobbling together sheets that have no connecting structure, and so leave no trace in the students’ minds).
    The text can be carefully paced; can use a fixed collection of “characters” on the page to which kids begin to relate; can focus on a small number of key standard models – which are used over and over again, allowing slower kids to revise previous versions of the ideas each time they are revisited for extension; etc. In short, the texts can be (a) mathematically correct; (b) pedagogically sound; (c) consistent; (d) cumulative (reinforcing earlier material as they go along); and (e) liberating. A good textbook is like a detailed map-and-guide; a friend and support (rather like Wainwright’s books for those who spend time in the Lake District).

    Maths teachers emerge from their preparatory training with very little idea how the mathematics they are to teach needs to be structured: at secondary and tertiary level many sort this out to some extent over the first 3-5 years *with the help of a good textbook*.
    Primary teachers are generalists, so are in even greater need of a good guide; and – given the limitations of their own education and teacher training – it is not enough just to give them the book and leave it at that. So a school needs not only to buy the books, but to invest in training their staff in (i) what the books are trying to do, and (ii) how to use them effectively. This is especially necessary in a system which has decried the use of textbooks for 40 years (as indicated by the the table Marty displays: the figure of 15% regular usage is probably a massive overestimate: the teacher respondents here to the TIMSS/PISA questionnaires do not know what it means to “use a textbook”).

    After years of despair, I found working through the twelve Maths No Problem books utterly breathtaking – regularly cheering out loud. And when I then made an effort to go round the country and see how they were being used in those schools that had bought in to the scheme and the training, I found it genuinely moving: teaching and teachers had been transformed, and students of all abilities were thriving.

    So why did they not take over the world? I can try to explain if anyone is interested.

    1. Thanks very much, Tony. I gave my “Why would you expect other?” reasons for why I thought MNP didn’t conquer England, but I would very much like to read your thoughts on it all.

      As for the purpose and value of textbooks, of course I agree with you entirely. The suggestion that using textbooks somehow reduces a teacher to being a “technician” is so maddeningly clueless, at that point I threw Marks’s article out the window. And I was on an airplane.

      You’ve indicated previously that you regard the textbooks as the architecture, and that the training is also necessary. I can believe it, but at the moment I’d be happy with the architecture, which simply does not exist in Australia. Perhaps it’s naive of me to be thinking, “If you build it, they will come”. But if you don’t build it, they will certainly wander aimlessly.

  5. My school (years 7-10) does not use textbooks except in Year 10 Mathematics. So I write my own – Year 9 only – and give it to the students. With about 2 years of experience, they are in fairly good shape, IMO.

    Well-written text books are useful. Prices are an impediment especially for our students.

    I saw the booklist of another school: AUD15 for a ruler; the justification was that it had formulae on the back.

    1. Yeah, yeah, Terry. All teachers can do what you did. First get a PhD in mathematics, then …

      You are simply ignoring the fundamental madness. Teachers shoudlk, cannot, be in the business of compiling theeir own resources from scratch. Textbooks are essential and, one way or the other, they are damn cheap. The amount of money flung randomly in education dwarfs whatever would be required to supply schools and/or teachers and/or students with textbooks.

      1. When I was at school, my Year 10 mathematics teacher wrote our text book. I recall that it was typed, photocopied, and had spiral binding.

        Clement Vavasor Durell made his career as a mathematics teacher and author of numerous textbooks in the UK.

            1. JJ mentions “differentiation” and asks how it fits.
              I have three comments and a remark.

              (i) Extreme differentiation (believing each student has to follow their own path) makes a kind of sense in the context of home-schooling; but not with institutions. The idea seems to me to be incompatible with the idea of “schools” and “teaching” – period. So once one accepts educational institutions, one has to find some way of keeping groups together – while modifying individual diets slightly. Hence we need a curriculum, and a mode of teaching that reflects this.

              (ii) In primary school, there are good reasons to keep kids together in age cohorts, and to teach them together. And this seems to be perfectly manageable (provided one does not allow extreme exceptions to distract one from the main task). In many effective systems, this communal approach is sustained throughout primary school, so that almost everyone gets a reasonable foundation. It gets harder from Year 4 onwards; up to that point, primary teachers are often rather good at addressing differences, while keeping everyone together.

              (iii) At secondary level, the problem gets more challenging. If almost all students have a reasonable foundation (up to Year 4 or so), then I can imagine a “common course” – with associated textbook – for the first couple of years of secondary, which starts by re-visiting ideas from the last couple of primary years *with a view to what lies ahead* (fractions, negative numbers, algebra, etc.).
              But, if one recognises that “teaching” means “whole-class teaching”, then at some stage one has to create “whole classes” that can be taught together, and that are working towards a common goal (= exam?); and a textbook series makes sense only if enough schools group students in approximately the same way.

              In England, after 30 years of rampant unthinking “differentiation” (with students being actively encouraged to gallop ahead: at one stage ~70% of students were taking the age 16 exam “early” – and either failing or achieving lousy grades, which they then tried to improve – with massively negative consequences) we had lost the art – and lost faith in the whole idea – of “whole-class teaching”. This is one reason why those who just bought the textbooks without re-training never understood what they were about. Many parents never understood that encouraging ordinary students to rush ahead often has subsequent negative consequences, and that ‘making haste slowly’ can provide much stronger foundations. So the Singapore primary series met with resistance.
              However, the reality I observed seemed to be that
              (a) the slower students benefited hugely from the cumulative development, and
              (b) almost all the more able students also benefited from the opportunity to establish basic ideas and methods robustly.
              However, many teachers clearly had difficulty imagining (and accessing) suitable enrichment material for able students in the upper years. This problem remains.

              1. Thanks again – very interesting. Your answers explain things in a rich and sensible way – much appreciated!

                My gut keeps saying some things appear to be crazy in the modern education system (of course it’s not just the education system) and this blog provides answers that chime with my gut.

                Another of your observations chimed with my gut. I have tutored a couple of bright students* at a Select Entry Accelerated Learning (SEAL) high school. While I’ve never told the students or their parents, I keep wondering the point of this acceleration as it just gets them a year ahead by Year 11 and dumps them into the last two years of school. Looks good as a marketing exercise in the modern world I suspect.

                *Their issue was a weird General Maths Advanced course (which I understand is being phased out thank goodness as to me it was a contradiction in terms).

  6. I wonder, frequently, if the biggest barrier to having quality textbooks for primary schools is TIME.

    It takes time to create a quality product and if the amount of time required is less than (or even remotely close to) the time it takes for some “authority” to bring out a new curriculum or set of “standards” that teachers/schools have to report against then there is not much incentive for anyone to create a textbook for schools.

    The textbooks I remember using at school had one author, sometimes two or three. The books I see now have up to ten authors.

    1. I was curious and asked whether primary schools used textbooks in a teachers’ Facebook group a couple of weeks ago. While totally anecdotal, most didn’t and the number one objection was about textbooks not supporting differentiation, followed by textbooks not being fun and maths needed to be more hands on.

      I was out of teaching from the late 80s to recently. The rhetoric about individualised learning has changed, the teacher-student ratios have not. Some people believe the rhetoric. The gap would seem to be one cause of how difficult being a teacher has become.

  7. My comments on a common curriculum to age 13 or so (while acknowledging the need to provide increasing extension provision for some) were tentative, but sincere.
    The problem is to decide
    (a) whether distinctions in core provision are appropriate at some stage (in some admirable systems, such distinctions are illegal up to age 16, but I suspect the last few years are awkward);
    (b) at what age such distinctions make sense (testing and selection at age 10 seems a bit too early; but forcing everyone to do the same beyond early adolescence at age 13-14 looks like asking for trouble).

    The traditional English state system made selection at the end of primary school (age 10-11, often referred to as “the 11+”): this continues today for the surviving 162 grammar schools; but in practice this system has all sorts of flaws. Most of the country has rejected it, yet we seem incapable of thinking afresh. In particular, we cannot discuss and come up with a more rational way of providing different pathways that suit students, and that suit the needs of our institutions (e.g. in allowing them to devise such resources as textbooks, or to teach more coherent groups the sorts of things that they recognise as suitable).

    So I was astonished to discover a key historical document of which I was previously unaware: “The Green Book”, which was written by officials from our Ministry of Education to facilitate discussion with local school boards and others in the lead up to the 1944 Education Act.
    There we read [with my clarifying remarks in square brackets]:

    “In order to relieve Junior Schools of the incubus of the Special Place Examination [=11+ selection] it is proposed that children should be selected for transfer at this age to the different types of Secondary School on the basis of their school record, supplemented by suitable intelligence tests. It would, however, run counter to educational opinion to regard 11 as the appropriate age at which a final and irrevocable choice should be made of the particular type of secondary education which any given child should pursue. Indeed, there is a substantial volume of opinion that the right course to adopt would be to transfer all children at 11 to Modern Schools [= Junior High Schools for all], the age for transfer to Grammar and Technical Schools being fixed at 13. Such an organisation will, if thought desirable, become possible as new school accommodation comes into being. In the meantime arrangements will need to be made for a genuine review at 13 and transfer as between all three types of Secondary School [= Grammar, Modern, and Technical] in whichever direction may be found appropriate.

    In order to facilitate this interchange at 13, it is contemplated that the content of the education given in the first two years 11-13, though differentiated in detail, should in general be the same in all types of Secondary School.”

    1. Thanks, Tony. It’s fascinating history, mirroring, as you suggest, a depressing present.

      In Victoria until the early 90s secondary education was split into “high schools” and “technical schools”. I don’t think there was any testing, but my sense in my time (early 70s) was that the decisions were pretty automatic and definitely not, by and large, the kids’: it was all very class based.

      Now, with all kids expected (for no good reason) to complete Year 12, Victorian schools offer a weird mix of (vaguely) academic subjects and time-fillers and properly vocational offerings. But even well before that, and still without any testing, kids are effectively streamed, and many are screwed.

      Officially in Australia, for mathematics (and other subjects) there is one curriculum for everyone up to Year 10, modulo the “optional 10 material”. But this is a blatant lie, and everyone with half a brain, which seemingly includes not a single person at ACARA, knows that it’s a lie. The official dumbing down is turning Australia, once again, into a predominantly class-based system.

  8. IMO, it is a mistake to classify students’ learning by their age. “Stage, not age” is the mantra. For example, students should learn how to solve linear equations when they are ready for it. However, I don’t see how to fix this.

    Q: What size shoe should a 12 year old boy wear?
    A: One that fits.

    1. Nonsense, Terry. “Stage, not age” is not a mantra, it is an argument for teaching without goals or measures of success.

  9. Just bought a copy of Todhunter’s “Plane trigonometry for the use in colleges and schools” (1878). Fascinating.

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