There is a famous story about the great comic playwright George Kaufman, co-writer of the books for the Marx Brothers’ two Broadway shows and then the screenplays for three of their great films. Kaufman was supposedly chatting with someone backstage during a performance of The Cocoanuts, when he abruptly stopped the conversation. Kaufmann apologised:
“Excuse me, I thought I heard one of my original lines.”
Not everyone is inhibited by a script. Then again, not everyone is granted or simply demands as much license as a Groucho or a Chico, and not everyone is the master of improv to so justify that license.
Scripts vary, hugely, in form and in use. They can be better or worse, less or more detailed, and less or more prescriptive. They can be intended for, or at least eventually used by, either a genius improv artist or a nervous novice who will not seek to deviate one comma from the written text. It is almost meaningless to be for or against “scripts”.
Which brings us to my friendly-grumpy exchange with Greg Ashman. To recap for those who have failed to take notes: following on from a Grattan report, or two, Peter Sullivan took a whack at “scripted lessons”; Greg1 then took a whack at Sullivan; I then took a whack at Greg’s framing; and Greg then took a whack at my framing. You are now up to date; please remember to take notes in future.
Greg expressed some annoyance at my regarding his school’s lessons as “scripted”. He tempered this, however, by suggesting that my use of the term was figurative. I reject this olive branch. My use of “scripted” was not figurative. It was lazy.
Greg notes that there are truly ruly scripted lessons out there, which he contrasts with his school’s hemi-demi-scripts. Fine. Genuinely. It would have been more accurate for me to have queried the level of planning at Greg’s school, rather than the level of scripting. There are genuine issues here, and seemingly substantial differences of opinion between me and Greg, but word quibbles are boring and beside the point.
As I indicated, it is typically silly to attempt to form any firm opinion of scripts/plans/materials/whatevers without having seen these whatevers, and without having seen the use of these whatevers in practice. Sure, the whatevers might be so bad that no proper practice is conceivable, and this is anything but a fantastic hypothetical. But, assuming some basic sense in the whatevers, one still needs the details. I do not have and/or have not looked at those details. I am open to the merits of Greg’s lesson plans, or whatever it is I’m supposed to call them, while being concerned about the use of them even granted their intrinsic merits.
Beyond the word battle, Greg makes a few arguments for his standardised lessons. I think I have largely addressed these arguments in previous posts; the reader can look here, here, here, here and here. Greg and I have both laid out our positions pretty clearly.2 There are a few remarks of Greg’s, however, to which it may be worth responding.
Greg notes my emphasising the “what” rather than the “how”:
Marty is more interested in the what of mathematics teaching than the how. But there is a connection. By sweating the how we can make space for the what.
I’m amazed I never thought of that.
It is true that I emphasise the “what” over the “how”, but not remotely as much as Greg suggests. I’ve written plenty about the “how”. But what frustrates me is when I see Greg and Grattan and co, and subsequently the education reporters, who invariably go to Greg and Grattan and co for reportage colour, way underemphasising the “what”. This seems to me obvious, and obviously perverting of the entire debate.
In any case, why not avoid sweating the “how” by reaching for a textbook? Greg has an answer:
In principle, we could simply agree to use all the solution methods and explanations from a specific textbook. However, with the textbooks that are currently available, that would be insane.
It is insane that the textbooks we have are the textbooks we have, but that does not mean it is insane to use these textbooks unless one weighs up the alternatives. When it comes to school-produced materials – lesson plans and their close cousins – I have generally been less than impressed. They typically seem little or any better than textbook material, and often enough are significantly worse. I am sure Greg would suggest that his school’s materials are significantly better, and my guess is that he is correct. But then what seems to be going on here, consciously or not, is mission creep.
It is one thing for a school to look at the nutso textbooks and try to develop extra or replacement notes.3 It is a big leap beyond that to be standardising lessons. This may make sense; Greg argues the efficiency and ridicules the concerns. But it is mission creep.
Although I would be satisfied with good solid textbooks, together with a deep and coherent curriculum that would make such textbooks feasible, I think Greg’s efficiency argument for standardised lessons is a strong one. I think a couple of his go-to examples – short-or-long division and the concept of functions – are confused, and I may write on this, but I still see the overall merits. But I also see drawbacks. It seems to me that Greg is willingly blind to the drawbacks.
Greg makes fun of “the cult of the individual” and “romantic” views of education, and he clearly sees me as part of that world:
Of course, mathematicians tend to be iconoclasts. They tend to be eccentric. There is a certain romantic rebel-without-a-haircut sensibility that will never be at peace with standardised lessons and will only be further enraged by talk of ‘efficiency’. I get that and I am never going to win those folks over. That’s fine. We can disagree and the world will keep turning.
Ying hasn’t permitted me to be a long-hair for a good decade but I’ll plead guilty to the eccentricity, and anyway the shoes thing is a smoking gun. But Greg may be surprised how much academic mathematicians also value efficiency; they are beleaguered, too. I always chose to base university lecturing upon a prescribed textbook whenever it was practicable. Other lecturers may use lecture notes and problem booklets, but commonly these materials will be used for many years.4 University mathematics teaching is not very hippy-ish, and it never was.
One can simultaneously value both solid structure and individuality. I assume Greg claims that he does, since he is quick to point out that Clarendon’s standardised lessons still permit individual style. But Greg can’t have it both ways and it seems clear that he regards individuality in school teaching as significantly less valuable than do I. Greg seems intent on classical music, whereas I’d prefer it if there were a little more jazz. Maybe not Coltrane, but some Count Basie wouldn’t go astray. And if it’s going to be classical, at least make it a little less Bach and a little more Beethoven.
A quick final point, on the well-known success of Greg’s school. One has to look at the intake and so forth, but I take Greg’s word for it that his school does not game the results, and these results are a strong argument for his school’s methods. Still, without trying to move the goalposts, it is fair to point out that the goalposts are very wonky. NAPLAN is a basket case, of course, and VCE is also a mess, and getting worse. University lecturers will tell you that a 35 in Methods, for example, does not mean what a 35 in Methods did ten years ago. The students simply have a weaker sense of mathematics than they once did. That is not to discount Greg’s school doing very well on the measures we have. But the proper evaluation of teaching is dependent upon the proper testing of mathematics from a properly solid curriculum. Which, to say the least, we do not have.
It is not nearly as simple as Greg and I disagreeing and the world still turning. The small but growing acceptance of standardised lessons may eventually make it much, much harder for romantic dissenters to teach any other way. Perhaps all in all that would be for the better, but don’t anyone pretend that this is simply a matter of each to their own.
1) Greg noted my referring to him by his first name and responded likewise. Of course it is proper academic form to use surnames but at this blog we care little for proper academic form (in case anyone hadn’t noticed). A first name, like “Mate”, can be used in either a friendly or nasty manner. In case there is any doubt, in my post I was definitely seeking to sound a more casual note.
2) If readers suspect that I’ve ducked some killer argument in Greg’s latest post, they are free to bring it up in the comments and I’ll do my best to respond.
3) Theoretically better, of course, is Ochre or whomever developing such notes, rather than a thousand schools each inventing their own wheel.
4) This reuse may be efficient but it also raises very active issues of autopilot and stagnation. Unless there is conscious attention to re-monitoring, the same issues arise with school-based materials.
I suppose I fall somewhere between the two
When I’m taking a class, all I need is a whiteboard, a whiteboard marker, and the name of the concept to be taught. I come prepared with my own questions for a topic (the drill questions often kidnapped from textbooks/online), some multi-step problems (usually written by myself or stolen from actually good writers), and some abstraction questions for those kids who get it and want to actually learn some real, non-curriculum maths
It works for me because I’m really high energy and don’t stop moving and talking, but it obviously wouldn’t work for every teacher, nor would they have the time to source their own problems (or so they say)
The kids love it (generally). The two schools I worked at were very low socio-economic and extremely diverse behaviouraly and intellectually, but I haven’t met a kid that I didn’t get through to on some level. Other teachers and administration on the other hand…
This is all to say that prescribed lesson plans with a general script can be useful! … if we had a solid (and not insane) curriculum, with solid mathematicians writing and vetting the lesson plans, and solid teachers who could actually teach the content
Thanks, Fox. I don’t really understand your last paragraph, which seemed go degrees from what came before. Are you saying that you do not need lesson plans, but that you can imagine them useful for others?
I think we’re at the point where the difference is between more or less autonomy for the teacher. The Clarendon Way is a very strong cultural element at the school is my understanding and that suits those who are there, but wouldn’t suit everyone.My personal view is that I don’t like to be told exactly how I must teach something. happy to have a discussion about how I could improve my teaching (although meetings to actually do this are pretty rare in my experience). This may also reflect a cultural difference, where my understanding is that the UK has gone down a much more directed path for education, to the extent of even having line managers for teachers. They seem to have regular observations of teachers by senior leadership. And they still have School inspectors. This has advantages and disadvantages. I don’t think I’d like to work under this regime, but some clearly like it.
Thanks, JJ. I think “culture” is the key word.
The more you have culture, the less you need rules. If there were a strong mathematical culture in Australian education then there would be much less call for lesson plans, much less their more prescriptive kin.
If you’re against scripted lesson plans using power point, what do you suggest is the more optimal alternative? Both you and Greg seem to agree on the merits of providing curriculum to teachers, it appears to different levels of detail (or structure?).
I recently undertook a professional learning where the merits and drawbacks of scripted lessons (using power point) were on display. The presenters used power point and a very detailed workbook to present materials, and two very different presenters adapted this. Despite the 2nd paragraph in the workbook describing cognitive load theory, the 2nd presenter was clearly newer to the material and relied heavily on the power point, often reading from the slides. This was obviously sub-optimal, but what is the alternative for that teacher if they have no resources to work from? They would spend hours of time developing sub-optimal resources and still have sub-optimal delivery? At least with the power point and script, they can spend their time and energy perfecting the delivery. The 1st presenter, on the other hand, who was obviously more experienced, was able to adapt the power point, and go off on tangents through story telling, use of humour etc to deliver the content, which was much more engaging. Having said this, he often neglected some of the important content from the work book which the 2nd presenter didn’t (because presumably they had spent more time recently reviewing this support material), meaning some concepts were not covered well. This I think is another thing to be conscious of with scripted resources, the curse of knowledge for the more experienced educators who may also neglect some of the underpinning principles.
Having scripted lessons developed by experts is flawed, but it’s far better than the alternative, and gives teachers time, and a model, with which to understand theory’s underpinning their design. At the very least, it should free up less experienced teachers to focus more on the science of learning and their pedagogy.
Thanks, Cameron. I’m guessing you’ve come from Greg’s Curios post.
I’ll think carefully about what you’ve written, and will reply more later, but in brief:
*) I think your first paragraph is getting to the heart of Greg’s and my disagreement. We’re strongly agreeing about the necessity of good “resources”, and are despairing of the general resources out there. The question is how planned/prescriptive such resources should be.
*) In your third (and second) paragraph, you used the evil word, “scripted”, and you refer to the benefits to “less experienced teachers”. I think both are a far larger aspect of what is going on here than Greg will concede. I am also not convinced that teachers following a script is the optimal way to teach teachers to not follow a script. But, of course, Greg would not call it a script.
Let’s calls them standardised lesson plans and resources!
I agree individual brilliance from high-level practitioners, à la the Marx Brothers, is the ideal scenario. However, there are structural constraints we must acknowledge, and there’s huge variation between the best and worst teachers. Schools are hiring teachers who struggle with year 9-10 maths problems, and many are teaching maths out of method. Given these constraints, I suspect providing highly structured resources/lessons is our best solution to closing the gap, at least in the short term.
The best actors move beyond needing the script and can improvise brilliantly; the very best might not need a script at all. But that’s not the reality in most schools. I also disagree that providing standardised lessons is a bad idea to support novice teachers (or actors!). The worked example effect tells us that having more explicit sequences helps novices develop expertise. ‘Algebra by example’ comes to mind.
At some point, we’d hope teachers develop sufficient content knowledge and pedagogical skill to adapt these resources, identify when to follow the script and when to deviate, and respond effectively to student misconceptions in real-time. But standardised lessons create a higher floor that ensures all students receive quality instruction while teachers build toward that expertise. The goal isn’t to constrain teaching indefinitely but to scaffold both teacher and student learning in a systematic way that leads to greater capability and autonomy over time.
I think it’s fairly obvious that Ballarat Clarendon is an outlier in VCE results (beyond just maths subjects). Standardised lessons are only one piece of the puzzle, but an important one none the less.
Hi, Cameron. Thanks again for your comments, sorry to be slow to reply, and sorry that I don’t have much of a reply even now.
There is not a whole lot of point talking about “standardised lessons” if a teacher is permitted to stray far from the standard. So, the first thing is, I think you or Greg or whomever must declare how standardised are the standardised lessons. Until there are stationary goalposts, I’m not going to bother much arguing this.
A key purpose of a curriculum or a lesson plan or a prescribed text is to constrain the teacher. Constraints are good and necessary, both because they constrain teachers to travel an accepted (maybe broad) main road, and because they free up a teacher to think and plan within those constraints. It is all a matter of degree. As I have said, repeatedly, I do not know what Greg’s/Ochre’s/Joe-Blog’s lesson plans look like and how they are used in practice, so I won’t comment on any of it with much strength.
However.
PowerPoint is a very rigid and a very static medium. What is on the slides is on the slides, in a pre-determined order. It is much less easy to adjust-on-the-run a PowerPoint-based lesson than a whiteboard based lesson. I am also nauseated by the idea of someone else telling me, for example, which example I should use to explain a concept or technique. Would I be permitted to choose my own example if I were teaching at Greg’s school? If not then I think Greg’s school is fucking up. it is one thing to offer a “lesson plan”; it is a very different thing to micro-mandate it.
You talk long about bad teachers, which is off Greg’s point, but which is definitely others’ point. I think it is very weak ground. *Of course* you want weaker teachers, and all teachers, to have good resources. That is a far, far thing from mandating the use of pre-cooked lesson plans.
For the thousandth time, I think this is a bad take on a secondary battleground. The primary battleground is for a decent curriculum to be covered by decent textbooks and to be taught by properly trained and unencumbered teachers.
These fucking lesson plans are seriously getting up my nose. They may offer some benefits to some teachers, and will certainly, if effectively mandated, create drawbacks for many other teachers. But they will do essentially nothing to fix things.
What is lacking is not a “science of learning”. What is lacking is a properly healthy mathematical culture. But no one gives a shit about that.
Ah Marty
You speak of a properly healthy mathematical culture.
Is this a Marty mathematical monoculture?
I give to you from the interweb:
Mathematics and culture are intricately linked, with cultural influences shaping how mathematics is developed, taught, and understood. This connection is explored through ethnomathematics, which examines the relationship between mathematics and various cultural groups, acknowledging that mathematics is a cultural product rather than a neutral, abstract system. By recognizing the cultural diversity of mathematics, educators can create more inclusive and engaging learning experiences.
That is what is rammed down the throat during “teacher training” and during professional development sessions after successfully attaining the “license” to teach.
Mathematics MUST be taught to the 20 different cultures in a classroom in such a way that all students see mathematics through their own cultural “lens”.
It is modern educational mathematics.
Another from the interweb:
Incorporating cultural perspectives in mathematics education can help students connect with the subject matter in a meaningful way and appreciate the diversity of mathematical thought. This approach can also help to address inequities in mathematics education by leveraging students’ cultural knowledge and experiences as assets.
Ah, edubabble to achieve edutainment.
No matter how much I agree with your statement:
The primary battleground is for a decent curriculum to be covered by decent textbooks and to be taught by properly trained and unencumbered teachers.
there is no way in modern educational hell that will ever happen.
And to finish, you mentioned having more Beethoven and less Bach:
Bach’s music, particularly his counterpoint, is often described as intellectually dense and precise, requiring a dedicated listen for full appreciation. Beethoven, while also complex, often uses more immediate and emotionally charged melodies, making his music potentially more accessible to a wider audience.
As your responses to comments are often emotionally charged I see why you want more Beethoven and less Bach.
Regards
Ian
Thanks, Ian. Three swing and three misses.
1) The culture of mathematics teaching, or lack thereof, has nothing whatsoever to do with the highly dubious and perverting claim that “mathematics and culture are intrinsically linked”.
2) Given that we cannot win the primary battleground of decent curriculum/texts/sanity, I should waste my time on secondary battlegrounds? What the hell is the point?
3) The practice of learning mathematic is not remotely the same as the art and technique of teaching it. The former can be more Bach, even if less so than robotic pedants may imagine, while the latter can be, and arguably should be, more Beethoven.
Ah Marty.
In this day and age 3 strikes is not enough to strike me out and I come to bat again.
The only 2 teacher led movements, that I know of, that changed education in a substantial way are:
1) PLATOWA
https://en.wikipedia.org/wiki/PLATO_WA
from the interweb
PLATO WA, or People Lobbying Against Teaching Outcomes, was a Western Australian community lobby group that campaigned against the implementation of Outcomes Based Education (OBE). Led by Marko Vojkovic, the group played a significant role in the public debate and was instrumental in ultimately influencing the government’s decision to revise OBE policies
Involved in that movement was Professor Igor Bray.
2) PLATOQLD
http://www.platoqld.com/
This effort was based on the PLATOWA model and Professor Peter Ridd was involved from the start.
Igor and Peter were able to involve other like minded university professors to get involved.
In both movements there was enough university “people” support and more than enough support from high school physics/maths teachers to make sure the movements were seen and heard.
Not being a Victorian and not having heard of similar organizations / movements in Victoria I now swing for a fourth time:
Has a similar mass math teacher movement happened in Victoria in support of improving maths education in Victoria??
If yes why did it fail?
If no why not?
Swing five: Since Australian education is beholden to international educational covenants/laws the chance of:
1) an excellent curriculum is very low
2) an excellent textbook is very very low as there are only about 5 or 6 mega publishers remaining globally.
3) Sanity – I quit teaching for mine after 32 years of science/maths teaching
Adieu
Farewell
I’ll take my 6 swings and misses and wish you all the very best.
Thanks again, Ian. I should have made clear that I am very happy for you (or anyone) to keep swinging.
I believe I have heard about PLATO WA but don’t know much about it. There was an OBE fight in the 90s, and a successful counter-offensive against it. That counter-offensive was led by Victorian mathematicians more than anybody, and Tony Guttmann in particular. Perhaps the Western Front of that war had different heroes.
I have zero knowledge of Victorian mathematics teachers, as a body, standing for anything other than mediocrity, for at least the last thirty years. The MAV, at minimum, created a forum for the 90s counter-offensive. But that was a long, long time ago, and it was an era when the MAV had a strong input from strong mathematicians. To expect the MAV to stand for anything these days is beyond optimism, and is simply madness.
This all brings up something I had been pondering posting on. Your comments have encouraged me to bump it up the list. Tomorrow, hopefully.
I would certainly agree that the odds of there being good textbooks/curriculum in the next N years is very low, even for a high value of N. But I’m not sure I understand your reference to “international educational covenants/laws”. If Singapore can do it, why can’t we?