OK readers, we want your help.
Suppose, hypothetically, you were asked to write 2000 words on What Went Wrong with Maths Ed – or just plain Ed – in, say, the last 50 years. What would you write? What are the major causes of that decline? What are the essential arguments and examples to support the actuality of the decline, and the reasons?
Of course we’re not at all short of ideas. We’ve written 500 posts on What Went Wrong.* But, we’d like to know what readers regard as the absolute musts.
*) Literally. This is our 500th post.
“What are the major causes of that decline?” I am generally sceptical of arguments about cause and effect. I am not even sure what “A causes B” means. I am particularly sceptical about the notions of cause and effect in social sciences such as health and education.
Christ, Terry. What is the alternative? Just declaring “things happen” and leaving it at that?
OK Terry, lets say I accept your argument (I do in part but don’t tell Marty…)
Could we say that IF A does not happen, then the incidence of B declines, AND if A does occur then the incidence of B increases, then we have a correlation, but perhaps not a causation?
A scientist in Scotland in 2007 published a paper saying they could prove global warming based on the increased sales of ice cream and other frozen confectionary alone… Correlation? Yes. Causation? Maybe.
Education is not an experimental science and there are way too many variables, but this does not mean we can just ignore correlations. Sure, we can question them, but to do nothing would be a bit like… climate change debate.
Indeed. Just because it’s a correlation doesn’t mean it’s not also a causation. And I’d bet London to a brick that most of the correlations that many experienced teachers see are also causations.
What is Terry’s argument? The only sense I can make of what Terry wrote is that there are effects, and that there’s no point in trying to figure out the causes, or maybe to even suggest that there are causes.
“Education is not an experimental science” – yet many published papers in the field of education are based on experiments.
Yes, poorly designed, and poorly (often falsely) interpreted ‘experiments’ whose main purpose is to justify the existence of so-called education ‘experts’.
Education is a wannabe experimental science, full of quackery. And schools hoover it up by the ton. You could burn every last paper published in education research and probably end up with better teaching and learning outcomes.
And then we could debate whether ending up with better teaching and learning outcomes was a correlation rather than a causal effect of the number of papers burnt …
Serves you right.
I’m not going to write 2000 words. Personally, I think trying to write 20 words on what went *right* with Maths Ed in the last, say, 35 years is more illuminating …
Nevertheless, I’ll propose some dot points which I think are relevant to the last 35 years (I think things in Victoria were OK prior to the mid-80’s). As to *why*, my argument is simple: Compare maths Ed pre-mid 80’s and post-mid 80’s and look at the changes that were made. Many of my points overlap and some could be considered subpoints or consequences of other points.
1) The change from VUSEB to VCAB, then VBOS, then BOS and then …. VCAA. Particularly VCAA.
OK, I know that the change to VCAB from VUSEB was pre-mid 80’s, but I think there was a certain momentum maintained by VCAB from VUSEB that had well and truly spluttered out by the time VCAA came into existence. VCAA was certainly the killing blow.
This totally removed mathematicians from having any influence over the quality of curriculum and exams and directly led to 5) below.
2) The increasingly impoverished and disjointed syllabus. Culminating in the syllabus as outline 2023 – 2028 Study Design.
3) The increasingly poor and vague ‘Study Designs’. Compare the syllabus books under VCAB to the VCAA Study Design, in particular the 2023 – 2028 Study Design.
4) The introduction of CAS. This was the poison that really killed the mathematics curriculum.
5) The rise in influence and power of the so-called mathematics education ‘experts’ and, in particular, the cadre of teachers who jumped on the CAS band-wagon, sycophanted themselves to VCAA and misrepresented themselves as mathematics experts (when their only expertise was button pressing) to the gullible mathematics teachers of Victoria who were only too willing and stupid to swallow the swill that got presented. That little gravy train is still alive and kicking and keeps the CAS poison alive.
6) Arrogant leadership at VCAA that could never admit mistakes, never listened to feedback and was too busy trying to show off how smart it was (the reality was that this leadership was nowhere near as smart as it thought it was).
7) The SAC system of assessment (and before that, the CAT system).
8) A lack of willingness of teachers to demand something better. I have previously speculated on reasons for this: fear, apathy, lack of time, stupidity.
9) An increased focus on administration and red tape rather than teaching in the classroom. Together with a decline in experience and knowledge. And, what seems to me, an educational cultural cringe in having a strong mathematical knowledge.
10) A culture that enables a lack of resilience in students. And don’t get my started on the huge emphasis on ‘student voice’. (Yes, I know I sound like an old school fire-and-brimstone football coach and that we get told that the modern player doesn’t respond to this. Still …)
Thanks, John. Maths ed has gone pretty much nuts everywhere. So, pointing to Victorian changes seems to be missing underlying causes for those changes.
The only reason I make Victoria specific is that the points I’ve offered about Victoria don’t apply (or apply so strongly) to states like NSW. In fact, I think you could easily write 2000 words on what’s gone *right* in NSW.
Back in the late 80’s mathematics in NSW was a disaster compared to Victoria. How the worm turns …
You’re missing the point.
I get the point. But I’m restricting my comments to what I know from experience. Outside of Victoria and NSW I have no experience. But can only speculate that most of what I’ve said about Victoria is relevant elsewhere.
What is your thing against student voice John? What does the term mean to you? Of course a student voice fad thing being forced into a mathematics classroom would be questionable, but my experience as a student suggests that even Victoria is by no means sufficiently infested with any semblance of huge emphasis on student voice.
Tungsten, ignoring the (debatable) principle that students should have a greater voice, what specific benefit at this specific time can you imagine might be gained by such a voice?
Marty, much of student voice activity and effect should be based on school.
Statewide, and perhaps some readers of your blog may disagree that some of these are benefits.
Kill the new format GAT.
Demand good VCE exams with specific marking schemes published.
Teach phonics early and hard.
Guarantee student right to strike.
Thanks, Tungsten. You list four potential benefits.
1. GAT, I have no opinion.
2. Good VCE exams. Of course the exams are currently, um, not-good. I can see absolutely no reason to be believe that a student voice would improve matters.
3. Phonics. See 2.
4. Right to strike. But to strike for what? That’s just kicking the question down the road.
I assume it’s clear that I think current students are being absolutely screwed, and screwed up. They should be furious. Everyone should be furious. But I don’t see any reason to believe that students in the main will have any insight into the manner in which they are being screwed, or what it might take to fix it.
1. Kill the current maths exam format and I’m on board. The GAT is a farce (in the sense that how can it possibly provide valid data that enables a derived score for Specialist Maths, Chemistry etc. At best it might let you do this for some humanities subjects where reading, comprehension and writing is required). Voodoo mathematics strikes again. But how can students have an informed opinion on the GAT and who would listen and why?
A coordinated student voice on killing SACs. Now that’s what I’d love to see. Maybe students across Victoria would have the guts to call this out, when guts is in such short supply among teachers for calling out so many things.
2. A lawyer voice would do the trick. One day a student will lawyer up about errors on a maths exam and we can all sit back and enjoy the show. Better yet, a class (ha ha) action. I’m always happy to be called in as an expert witness for the prosecution. The earth turns slowly but the ox is patient.
3. This assumes that most students have been following the reading wars and are able to make an informed opinion. Most of my ‘disdain’ about student voice is that the voice is often not an informed one. Mind you, it’s probably far more informed than the education ‘expert’ voice.
4. Strike?? I’m with Marty. Strike for what? Strike for their rights? What rights? Their right to party? And this assumes that the student voice can get coordinated across the state.
The student voice should stay within its level of expertise. By all means have a student voice for things like school uniform, what’s sold at the canteen/tuck shop etc. But I don’t want to hear the student voice mewling about homework, tests, fun lessons etc.
Empowerment …? Often it’s nothing more than empanderment.
Strike for, say, climate. Some of the readers of the blog might recall the national student strikes of the 1970s to fight for decent treatment of students.
Both of Marty and John seem to think that we are talking about a singular body student voice. I would disagree. Student voice also means mass awareness to make sure that pretenders like VicSRC are not allowed to try to screw over students with stupid ideas like last year.
If there are issues with the education system, students are directly affected. That means that they should be not dismissed, because that is when you have those groups claiming to be representative freely proposing things that further harm students.
Do we need VCE examinations? Once I worked in a university in France, and I gathered that all students in France who graduated from high school could choose any university course that they liked – I admit that I did not know what graduating involved. The real hurdle was first year at university.
We certainly don’t need VCE exams – particularly mathematics exams – in their current form. And we need SACs like Custer needed more Indians.
So all France did was move the hurdle forward by one year …?
My thoughts exactly.
That’s one way of looking at it. The hurdles were not set nationally; they were set by individual departments/faculties in individual universities. No need for ATAR (FTAR?).
I recall asking why don’t all students enrol in Medicine 101? The answer was that medicine is a post-graduate course.
I imagine that the failure rates at universities may be high under such a system; but universities don’t have fees in France. They also tend to be more specialised – as specialised as our faculties in universities. I worked in Toulouse where we had three universities: one for science, one for humanities and one for social sciences.
Is that really the case? A long time collaborator and friend of mine loves to regale with stories of the admission interviews for certain French universities. They certainly did not allow everyone (hardly anyone in fact) to enrol. Maybe I should fact-check him.
We often end up remarking that having some kind of ATAR-like process would be much more fair.
Ah yes, post-graduate university courses …
So essentially the system adds a couple more years to school. So in Australia you would have primary school, secondary school, tertiary school and then – in reality – university. So you simply add another level of schooling before university. The big difference is that the universities control that extra level of schooling, meaning (hopefully) much better quality control …
It’s funny how everything old becomes new again. Because this system is EXACTLY what Victoria used to have when the VUSEB controlled the HSC and Form 6 (what we currently call Yr 12) was essentially a pre-university year. Before the social engineers – pre-cursors of the self-appointed educational ‘experts’ – decided they knew better: VCAB, VBOS, BOS. And then VCAA slithered out from under its rock.
So to ‘modernise’ the old system, all that’s needed is a Yr 13 and a VUSEB equivalent that controls it. Then VCAA can first become relatively irrelevant and then, hopefully, slither back under the rock it came from.
The only snag is that too many big egos would do their utmost to stop this. So here we are 45 years later dealing with a mess. And yet the clowns that created the mess are still consulted on how to fix the mess. Here’s a simple solution: STOP LISTENING TO THE CLOWNS.
“We have to get 2-3 times as many to study x. Even if it means the requirements are 5 times easier” “filosophy”.
@Glenn: My memory, like me, is old. So I can’t be sure.
However, it has been reported that “A large proportion (around 60 per cent) of domestic undergraduate university offers are reported as non-ATAR/non- Year 12.” See p. 7 of
Click to access crunching-the-number-exploring-use-and-usefulness-of-the-atar-mitchell-institute.pdf
I quote further from the Mitchell paper (see page v):
“60 per cent of undergraduate university offers were made on a basis other than ATAR.”
I find this extraordinary and very difficult to believe. Could it simply be a misrepresentation of the fact that many offers are made not just on the basis of the ATAR but also on the basis of interviews, tests (such as the UCAT), portfolios etc (which possibly carry more weighting than the ATAR).
But IF true, it is certainly a very, very well kept secret. And I would wonder who is making sure it’s a well kept secret. (Answer: Usually those who have the most to benefit from the ‘usefulness’ of the ATAR …)
@JF: I would guess that many domestic u/g students are mature age students; i.e. aged 21 or more. I wrote a report for one university some time ago that showed that more than 50% of its first year domestic u/g students were mature age – and this seems to be not considered in marketing what the university has to offer. But I don’t know much about the bigger more recent state of affairs. Anyway, many of these students would not enter by ATAR.
“I wrote a report for one university some time ago that showed that more than 50% of its first year domestic u/g students were mature age”
That’s an astounding datum.
Then again, maybe not. Maybe the key word is “domestic”.
@JF: In 2020, nearly 40% of domestic students starting Bachelor degrees in Australian universities are at least 21 years of age.
https://www.dese.gov.au/higher-education-statistics/resources/2020-section-1-commencing-students
I can’t provide specific dates of things and it will likely differ from state to state, but my feeling is that the following factors have all contributed in some way:
1. Universities lowering pre-requisites to get more students in courses (OK, a lot more are failing or withdrawing than used to happen and cheating is off the scales, but at least money is being made)
2. Graphing and later CAS calculators have meant a lot of “good” type exam questions just can’t be asked any more and the dominance of the CAS-active exam means exam papers have become insanely confusing – a test of reading comprehension more than Mathematics.
3. “Out of field” teachers; the figure that gets thrown around a bit is something like 25% of Year 10 students in Victoria have never been taught by a “qualified” Mathematics teacher.
4. The rise of other subjects that look good in advertising brochures, so more focus is put on them by private schools at the expense of teaching time for Mathematics and English.
5. Multiple generations of students listening to celebrities and their parents casually say “I was never good at Math” so it has become not just accepted but NORMAL to not be good at the subject.
I could go on, but that is my opening offer.
Thanks, RF.
Thanks RF, 1) is a very good point (that I forgot to mention). Look at what happened to Physics once it was dropped as a prerequisite for Medicine. The lack of advanced mathematics prerequisites for things like Engineering has had a devastating effect on student enrolment in those subjects. The fact that students can enter Engineering with only Further Maths is a disgrace.
The universities bleat and mewl about the declining standards of students when they enter university and how they have had to introduce ‘bridging’ mathematics subjects to compensate. Yet I have never heard them acknowledge that *they* are the ones responsible for this, by lowering pre-requisites to get more students in courses and make more money. (But you can hardly blame them when Govt funding is abysmal).
I should have also added that VCAA’s decision to allow Further Maths and Maths Methods to be studies together was, in my opinion, another killing blow for Specialist Maths.
@JF: Not to mention the disastrous decision to drop Latin as a pre-requisite for medicine. Working in a hospital, I often saw clangers such as “ad-hoc” – once I saw “add hoc”; people don’t know the difference between e.g. and i.e. I recall writing to the authors of a document who replied that “ad-hoc” is a common expression.
The evolution of English language, Terry. Enough people screw up words or phrases for long enough and it becomes acceptable. For example (correct then incorrect versions):
Strait-laced; straight-laced.
Fount of knowledge; font of knowledge.
Just deserts; just desserts.
Buck naked; butt naked.
Chaise longue; chaise lounge.
Free rein; free reign.
Bated breath; baited breath.
A shoo-in; a shoe-in.
To home in on; to hone in on.
Fazed by; phased by.
Sleight of hand; slight of hand
I found the sign here amusing:
https://www.bbc.com/culture/article/20150605-your-language-is-sinful
@JF: Many students write
. Does this make it acceptable?
Maybe on Mars, not on Earth.
Not even on Mars.
, for example).
(And I’ve seen worse from Methods 3/4 students:
Yes, mathematics is a language. No, it will NOT evolve to something like you suggest. Because the language has gatekeepers – mathematicians. The general public does not get to use and abuse the language of mathematics so that the abuse becomes the acceptable norm over time, unlike the English language.
(btw Terry, don’t even get me started on how many students set out their work for finding the inverse of a given function).
And if you’d like another reason for “What Went Wrong”, you might like to reflect on why I haven’t included mathematics teachers as a gatekeeper …
I will also not write 2000 words. I don’t have much to offer except my perception that a lot of people are very happy with how things are.
Therefore I would offer that the reason for a decline is that there is a lack of consensus on what the goals for mathematical education are and should be. If it was everyone’s goal for each student to be able to do basic arithmetic and understand what an equation is, at a minimum, then we could do that. We could work on that and figure it out.
But that is not everyone’s goal. Instead such skills are seen by some as mere barriers in the way of accessing the mathematics curriculum. Their goal is something else. And in order to access the curriculum, everyone can have a calculator and students no longer need to be able to do arithmetic. In order to access the curriculum, they can type ‘solve’ on a calculator so they don’t need to worry about annoying algebra. In order to access the curriculum, we can take out all the confusing fractions so they don’t have to deal with them.
I have my own goals, but I don’t exactly know what we as a group are supposed to be aiming for anymore. And when things take effort and time, it’s hard to convince people to allow for that if they don’t agree that such things are the point.
Thanks, wst. Who do you think is happy with how things are? Precisely, which people and/or bodies?
Roughly half of the mathematics teachers that I’ve met. Many seem overall pretty happy with what and how students are learning. Also, my mathematics education professor at uni was very happy with, for example, how Geogebra had ‘transformed geometry’ (their words).
ETA: not that I have any problem with Geogebra. I just don’t think it has transformed geometry.
Thanks, wst. Why do you think those maths teachers are happy? (And do you think they’re really happy, or is it possible they just profess to be happy?) Do you care to name the Geogebraphile?
My sense is that they are happy. They have a different understanding to me of what mathematics is. Students are learning that thing. I can’t even say they are wrong necessarily. They say all these things are very important in our modern world. I don’t like them. They’re not the mathematics I like. But they say the mathematics I like isn’t appealing to most people. It puts students off and isn’t necessary. Not every student obviously. I guess it comes down to deciding whose taste is more important. I won’t name people. I’m not even naming myself!
You can name offline …
What do you think is the happy teachers’ understanding of what mathematics is? Are they *really* happy that the majority of students can’t perform any actual computation without the students pissing themselves? Do they *really* think this doesn’t matter?
I think happy teachers would include:
* a sort of vague enthusiasm for patterns and ‘mathematical’ beauty.
* interpreting solutions to equations in context.
* using specific mathematical jargon in a sentence.
* bullshitting with statistics and sounding smart
* setting out your book neatly
* performing well at whatever is on mathematics exams
Another one: my mathematics education professor told us in all seriousness that understanding aspect ratio when interpreting graphs on a CAS calculator was an important skill, totally worth devoting an hour of class time to.
As for whether they are happy that “the majority of students can’t perform any actual computation”: I think they think they can, because they can do problems like 16 divided by 4 or 22 + 76. I suspect certain things that used to be run-of-the-mill are now considered ridiculous to expect of the average student.
Thanks, wst. I wasn’t really doubting that many maths teachers think this way; I was just confirming. I am well aware of teachers’ utter cluelessness.
I agree with John that things in NSW are moving in the right direction and quite the opposite in Victoria which isn’t really addressing your question but is certainly of interest.
But to speculate on the answer to your actual question, what has gone wrong in education… I’m guessing you don’t even just mean primary or secondary but rather ALL education.
The problem isn’t screen time or short attention spans in kids. It’s a lack of guts in the “adults” in charge to actually hold standards high and work from the premise that young people of all ages (well, people but especially young people) have an enormous capacity to learn hard things. Instead we wimp out and we lower the expectations, remove “hard things” from the curriculum year by year, make tests easier, get rid of tests altogether, whinge about standardised testing, reduce the weighting of exams, the list goes on. Who’s at fault? We are, obviously.
Thanks, Beans. Why do you think adults have lost their guts? Why has the demand for high standards disappeared? Why have we removed hard things from the curriculum, and who is “we”? Also, why do you think the problem is *not* kids’ screen time or short attention spans?
I mean if you trace it back, iPhones as an example came in in the 2000s and the problem started before then. Not that I am saying screen time and short attention spans are not A problem, I just don’t think they are the reason. Kids always have short attention spans for anything which isn’t super interesting to them. And they are right, most of the curriculum has become less interesting, filled with faddish approaches which appeal to adults whose only objective is to make everyone feel good instead of think deeply, be challenged and have the guts to challenge others.
Thanks, Beans.
Words are cheap.
Beans, I totally agree with all you say. In particular, I agree that there is a lack of guts to “actually hold standards high” and “we wimp out and we lower the expectations, remove “hard things” from the curriculum year by year, make tests easier, get rid of tests altogether, whinge about standardised testing, reduce the weighting of exams, the list goes on.”
I was trying to think of a way of articulating this in my first post and then wimped out.
I think the main reason for this is that it’s all about not wanting to get complaints from parents:
Don’t shatter the fragile confidence of the poor little things by holding them to a high standard, don’t upset their poor child with a bad result, don’t discourage the poor child from doing advanced maths and destroy their dream of studying medicine etc.
Because every child is a genius and evidence to the contrary causes trouble.
All these things cause ‘trouble’ and most teachers prefer to avoid it. So it becomes a feedback loop in which standards continually creep downwards. I see it with Progress Reports, where 45% (not that we’re allowed to give numerical scores) becomes ‘Performing at a satisfactory standard’ or the lily-livered ‘Working towards the expected standard’ rather than ‘Not performing to a satisfactory standard’.
Teacher’s aren’t allowed to be honest – the glass has to be 3/4 full rather than 1/4 empty.
Nailed it John
John, I am of course aware of the ‘Working towards the expected standard’ lunacy, that it is the culture to never say anything that could be construed as negative. But is this non-negativity also mandated? Either by schools or by Education authorities?
(Most) Schools mandate it.
I once wrote a report on a kid who couldn’t work in an iron lung that said
“X is capable of writing his name on the front of an assessment. He is also capable of writing on paper. X has the ability to achieve more than this. In order to improve he is encouraged to do all the work that is set, pay greater attention in class, take notes, ask for help when he needs it, and to prepare more thoroughly for assessments.”
I knew the report would be proof-read and returned, but it was my small way of pushing back. What was funny is that it didn’t get proof-read. It slipped all the way through to the last stage of vetting, when the Head of House saw it. So I ended up pushing back in other unexpected ways.
btw I would have changed it if it had passed that final proof-reading hurdle.
A lot of people were pretty unhappy but I simply said it served them right for mandating that the truth be wall-papered over with bullshit.
That’s very funny! But *how* do schools mandate it? Is a guide ever written, or is it simply understood (and checked).
Many schools have guides but only publish them on their intranet and then only enforce them when they (where “they” can refer to anyone in the school who has an opinion that they wish others to know about) feel it is appropriate.
A common trigger is parents complaining and managers telling the teacher to do better without much of a thought about whether the teacher is right or wrong. It is easier (for managers) this way.
Maybe someone can send me such a guide offline …
Coming soon to an inbox near you…
Every school has a format that must be followed, and a ‘style guide’.
The typical format these days seems to be:
1) First few lines: What the student did well. Then:
2) How the student can improve.
3) No ‘negativity’ is allowed. It must all be expressed in a positive way. So “X couldn’t work in an iron lung” has to be written as “X is encouraged to work a bit harder.”
What happens is that parents don’t think things are nearly as bad as they really are (because 35% on the exam often becomes a D or a “Working towards the expected standard.” Very rarely will “Below the expected standard.” appear on a report).
If you don’t adhere to this format, the report is returned with the command to change it so that it does. I also know of reports that have been changed further up the food chain to make them more flattering. In the past I have suggested to parts of the food chain that they would be wise to check the legal consequences of doing this.
Thanks, John, but I don’t care about a “typical format”. I care about precise, written instructions.
@JF: My school does not have a format that *must* be followed. To be sure, reporting is proof read, and we are warned of common errors, and we get some guidance. When you have a large number of teachers writing reports, then one can expect that some will make errors in spelling, grammar, and punctuation; this does not look good on a report from a school.
Some negative comments may not give students or parents much guidance on how a student could improve. To take your example – which I realise was written with tongue in cheek – “X couldn’t work in an iron lung” is not helpful. (BTW, there was a famous ballet teacher, Elizabeth Higgins, who taught from an iron lung.)
Terry, you’re smarter than that.
If my dates are correct (they may well not be) Auckland University introduced CAS calculators in first year Mathematics in 2004 (at the time they were not used in schools – I do not know if this has changed) and the decline in “intuitive logic” such as calculating limits when done without a calculator declined measurably. One of the University academics wrote a paper on it, do not remember the year.
Actually… I would like to add to where I think it all went wrong: the day Education (read Teacher) conferences started being sponsored by TI, Casio and HP.
Yes, the big tobacco of the education world.
There’s a story about how TI got their big ugly CAS foot into the VCE curriculum that will get told one day.
I’m not sure education can be said to be declining or improving over decades in that there is no objective measure. If maths education is for society, then surely we could say that we’re doing ok. I feel like if one agrees that maths supports science and technology, then maths education overall is keeping up as each decade science and technology continues develop in incredible ways. Just consider the whole surviving this global pandemic. That sure seems thanks to many technologies.
Personally during my life I’ve enjoyed the constant increases in standards of living driven by more powerful personal computers, music and media streaming to my phone from all over the world, GPS tracking on a map at all times… I still remember when the internet was some magical thing you had to disconnect your home phone temporarily for, how one had to go to a fancy video store to find a movie from overseas, and how going driving to a new place meant having to splay out a map and hope you could find the right roads once you set off…
Thus while I’m not sure everyone or the “average” person is better off or worse off due to mathematics education, it sure seems like society as a whole is advancing and I’m quite sure maths is being used by the people leading these advancements.
As far as Australia, as long as we can somehow transition to a sustainable economy beyond digging up our finite rocks, then we’ll be ok importing technologies even if we can’t develop them ourselves.
In other words, you regard education as nothing other than training.
Juan, I can see how you have come to this conclusion. In essence, you suggest that because we have more stuff and can do some more stuff that we must be educating ourselves appropriately. On the surface we look so clever.
But we haven’t solved the big problems for our human race. We aren’t even really trying. We have made it significantly harder for ourselves to sort between truth and fiction with a deluge of “information” which we are poorly equipped to critically evaluate. Why? Because our education system no longer asks us to tackle hard concepts and hard problems and have hard debates which lead to everyone walking away cleverer and better off for it. The purpose of education, like all the other clever things we have surrounded ourselves with, has become “instant gratification”.
Hi Marty. I’m not qualified to answer your very important question. I think what any of us can do is point to things that are clearly bad, and argue why they are bad. However there is in my view undeniably a larger picture here, because without fail almost every country, every state, every school even seems to be experiencing the same trend.
I think it must be related to how mathematics education as an academic pursuit has changed globally, although I’m not sure. I’m a details guy. Sorry.
Not too much to add to what’s been said so far, but a couple of brief thoughts.
1) WST’s point about differing opinions on the aims of mathematics education generalises to education more broadly. And I think this may be a significant cause of the phenomenon Beans described. If we can’t agree on what education is for, then the result is a push towards a lowest common denominator, easy, contentless curriculum because it’s all about “generic 21st century skills” anyway.
2) If one hasn’t already, then I’d suggest reading Frank Furedi’s book “Wasted: Why education isn’t educating”
Thanks very much, SRK. I hadn’t heard of Furedi (except it rings some very vague bell). His Spiked articles seem pretty and predictably shit, but he seems to have mostly chosen the right targets. I’ll look.
Hmm. Furedi is clearly an asshole, and has the ability to be a complete idiot. It doesn’t preclude the possibility of some worth in his writing.
Thanks to everyone who has commented so far. It’s been genuinely helpful.
To push the replies in another direction, I’m curious about what people regard as the very specific examples that most illustrate/argue the points made. That’s very ambiguous, since there are layers of awfulness. So, the implementation of CAS could be considered an example, since it is the supplanting of reality with image, and of proof with It’s The Vibe. Nonetheless, examples within this CAS example are required to make the case. Ditto to the generalised example of VCE Exams.
So, what are the strongest, flashing red light examples? (For the hypothetical and non-mathematical readers of my article, examples relating to primary and lower secondary would work better.) Of course this blog contains tons of examples, and it’d be helpful if people just indicated which such blog posts are the most telling. But the World is full of crap. Other examples would be great.
One only has to look at the Algebra area of study for Mathematical Methods in 2002 to 2005 compared to the same area of study for Mathematical Methods (CAS) for the same year range to see what CAS did to the curriculum.
I’m sure comparing the exam papers from when the CAS and non-CAS subjects existed in parallel would give similar evidence.
Some things in school education have improved. Corporal punishment is not longer used. There is a greater emphasis on considering the background of our students in our teaching. There is a greater emphasis on the well-being of students and staff. IT has changed the face of education – and everything else in society; how we would have coped during lock-downs without the internet? There is more emphasis on educating all students about the cultures of Indigenous peoples in Australia. School camps are in all schools – my school never had camps. There is more emphasis on the performing arts in schools than there used to be. Of course, change also brings challenges and we wrestle with them every day.
Terry, without arguing the merits, what do you regard as the causes of these improvements?
I think that they just happened but I would see them as improvements.
You mean like acts of God? So we just wait for further acts of God, and hope that these acts also improve things?
I have no expectation that the future will be like the past. I just wait and see what turns up.
“Corporal punishment is not [sic] longer used.”
OK, I can’t dispute that. (Although back in my day, the only claim to fame some students had was how many ‘cuts’ they got in a week …)
“There is a greater emphasis on considering the background of our students in our teaching.”
Yes, this is good.
“There is a greater emphasis on the well-being of students and staff.”
I agree with the former. I disagree with the latter (Talk is cheap. Actions are what count. What I consistently see are actions that create more and more stress for teachers, not less. Despite what the cheap talk says and claims).
“IT has changed the face of education – and everything else in society; how we would have coped during lock-downs without the internet?”
IT includes CAS in the classroom and it has poisoned mathematics in schools.
Coping during lockdowns … I suspect there would have been no lockdowns if remote teaching hadn’t been available and the Govt hadn’t been able to squeeze teachers dry. Generally speaking, politicians act out of pragmatic self-interest, rather than in the interest of the public. Look at how different things are now because of an election in November, than they were 9 months ago.
“There is more emphasis on educating all students about the cultures of Indigenous peoples in Australia.”
Yes there is. A good thing up to a point. The point being where it became totally politicised.
“School camps are in all schools – my school never had camps.”
“There is more emphasis on the performing arts in schools than there used to be.”
Debatable.
“There is a greater emphasis on the well-being of students and staff.”
Bullshit.
Let me try to justify some of my claims about improvements in education over the last 50 years.
At the schools in which I have worked recently, there is a well-being team. We did not have any such people when I was at school. These people look out for the well-being of staff and students. I have been to a number of in-service events that help us to understand the issues surrounding the well-being of students and staff. This year I have been to two such all-day events for all the staff.
I was not suggesting that all IT influences are positive; only that IT brings some benefits to teaching. For example, communicating with parents is facilitated by parents having access to the learning management system, and email messages. The internet is a major resource in learning and teaching.
All the schools in which I have worked have a vibrant performing arts department; the annual school musical is a big event; the prowess of students is on display at the annual speech night (or whatever it is called).
My point is that there have been some improvements in education over the last 50 years. Change is a slow process in large systems.
But again, and again without arguing the merits, you simply don’t reflect upon the causes of those improvements? You think there is no purpose in asking why?
“I have been to a number of in-service events that help us to understand the issues surrounding the well-being of … staff.”
Words, Terry. Meaningless rhetoric. ACTIONS are what count, not words. What ACTIONS have you seen that have made a MEANINGFUL contribution to the long-term reduction of teacher stress.
Talk is cheap. Saying it’s so doesn’t make it so. Never has, never will.
In my school, the principal has repeatedly emphasised the importance of putting some of the ideas from the in-service workshops into action, and it is clear that teachers have started to adopt many of the ideas. I see it every day.
The news today is that the education minsters are going to tackle to some of the big problems in education. They will develop a national action plan by the end of the year. Now we can all relax until Christmas.
Name one good idea that isn’t blindingly obvious.
The ideas presented in these workshops might be well described as obvious. However, there are many such ideas and it was good for me to be reminded of them. Many teachers already incorporate many of the ideas in their own teaching.
Sometimes a speaker might present an idea which was not new to me but it sparks off another idea. Let me offer a personal example. I am very enthusiastic about chess – but not a particularly good player. I am sometimes torn between spending time at home on chess and spending time on teaching matters (reading, preparing, writing, thinking). But in one of the presentations dealing with staff well-being, it occurred to me that devoting time to chess might be part of caring for myself. I had not thought of this connection before. ‘Twas not obvious to me before.
I take back my sarcasm.
Yes, the circus has come to town – the big meeting in Canberra about the “teacher shortage”. So a big talk fest (aka public relations exercise) is needed to try and figure out workload, pay structures and attracting and retaining teachers (but does not address increased school funding). NEW ideas are needed, apparently. Because, apparently, OLD ideas such as reducing paperwork, increasing pay, decreasing class sizes and, in general, valuing what teachers do and just letting them get on with teaching won’t work.
Clare is quoted as saying “You don’t just fix this with salaries, it’s more than that. Of course we want to pay teachers more, [but] it’s also about workload, conditions and wellbeing too.”
No shit, Sherlock. And in breaking news, water is wet.
A big talk fest is needed for Clare to come to that conclusion?? Someone should have told this to the Andrew’s Govt and the Victorian Teachers Union. They didn’t want to pay teachers more. And what was negotiated to reduce workload was pathetic. The Andrews Govt and the VEU have screwed over teachers AND schools for at least the next 4 years. This will accelerate the decline of education standards in Victoria.
Apparently “The NSW government pre-empted the meeting with its own set of reforms, to effectively offer performance pay for teachers with a new category of master teachers. Mitchell said the change was “intended to reward excellence” by “making sure that our best teachers don’t feel that they have to leave the classroom in order to get a higher salary or to get a career progression”. Clare said these were good ideas because a teacher’s salary “starts pretty competitive, goes up in grades, then tops out”.
So how do you define “our best teachers”?? A new category of “master teachers” …? Yeah, right. Just like we currently have a – relatively – new category called “Learning Specialist” in Victoria that is bestowed on applicants who present as bright and shiny. And in the meantime, the dinosaurs that just get on with teaching, ignoring all the beguiling bright shiny toys and refusing to play political games, get ignored. And don’t get me started on the Master Teacher bullshit and the Victorian Academy of Teaching and Leadership. Or the Bastow leadership program. Image, image, image. Teachers’ salaries must be dealt with across the board.
So Marty, if you want to know what went wrong (in Australia, at least), start by looking at what’s happened to workload and conditions in the last 30 years. And look at all the bullshit that has sprung to solve what’s gone wrong. Gravy train bullshit. (And the CAS poison, world-wide, of course).
On this supposed greater emphasis on wellbeing of students / staff.
1. It’s definitely true that schools are much better resourced to support students with acute wellbeing needs, and this is definitely an improvement. As far as staff goes, I know that the state government department has expanded employee support services, which in itself is a good thing. Although I agree with JF, that the government’s treatment of its workers has been poor, and the union has not fought hard enough on behalf of its members.
2. On the other hand, for many other students, my sense is that this “greater emphasis on wellbeing” is often just a pathologising of normal reactions to the challenges of education and growing up. Framing these reactions as adverse to wellbeing just adds to the expectation that education can not be challenging, that social relationships with friends, parents, school-mates, and teachers are always frictionless. Instead of supporting students to rise up and meet those challenges, the response tends to be to eliminate those challenges. In the long run, it’s the students (and the rest of society who will “absorb” these students) who suffer, because they don’t receive the benefits of a better academic education and the benefits of learning how to negotiate their social relationships in pragmatic and mature ways.
Great comment.
Hear, hear.
This 👆
Being new to teaching I can only point to contrasts between my education and the students I am now teaching.
Literacy is a major barrier where I teach, particularly reading. It’s not necessarily that students can’t read – it’s that they don’t or won’t. Only in specialist mathematics do I have (small) cohort of students who aren’t intimidated by reading questions, examples, answers, or solutions.
Part of this results from social media. The way people (not just children) engage online is very much feeling and interpretation instead of comprehension. One look at any mildly controversial post or comment reveals arguments where nobody responds to anything that was actually written. More broadly, engaging with the world more via audio and visual rather than text has perhaps made reading comprehension seem outdated. Stepping into a classroom where there are specific definitions, contexts, and initial conditions to be understood is quite a challenge.
Many of my students look at problems seemingly hoping to divine a method or solution. Upon being made to actually read the question most find they do understand how to solve it and how it relates to what we’ve being learning for however many days or weeks.
Whether it’s due to when or where I was educated, there just was not such a wide spread aversion to reading during my schooling.
Despite the “general capabilities” of the national curriculum I do not see literacy and numeracy being effectively connected prior to students entering my classrooms. I’m not sure this was a problem even in the early 2000’s
Thanks, Wilba.
I had some more thoughts about teaching and how complicated it is now, and it reminded me of this question. I think that if I as a teacher have a goal for what I want students to learn, then I can make a plan for how the students can reach that goal, and make sure they learn some mathematics. Things feel simple and achievable.
However, with modern teaching, everything is much more complicated. For example, when we teach a class, we are meant to make sure every student is constantly engaged in a learning activity at their level (while still having the same overall ‘learning goal’). We need to make “low floor, high ceiling” tasks that everyone can get something out of. Often we have to make sure our teaching aligns to some model for how you structure a lesson as well.
Suppose you want students to learn something, and there’s a prerequisite skill that 10% of the students already know. It’s not considered acceptable to say to that 10%, “just wait 20 minutes while I teach this to the other 90% and get them all up to date. Then we’ll move on together.” You need to have something for everyone and even a few minutes is considered important. No one should ever be bored. No one should ever be confused and not have a task they can do. This makes everything much more complicated, almost impossible. (Admittedly, it’s often a lie, but both students and teachers seem obliged to pretend this is the expectation.)
Now that I’ve written this out, perhaps it is just a grumpier reiteration of my previous point. If we mix in too many other goals and conditions and constraints besides our main goal, it becomes very difficult. I’m not sure if there was ever a wonderland where things were simple though! Is this new? Has teaching always been so complicated?
No, of course teaching has not always been insane.
Hi wst. The goal and the plan for achieving it that you describe is not helped by the fact that students are automatically promoted to the next year level year after year regardless of whether they have passed the subject in the previous year. So you get students in Maths Methods 1/2 who cannot solve a linear equation. You get students in Maths Methods 3/4 who cannot solve a quadratic equation (and can barely solve a linear equation).
Students can get an S in a Unit 1/2 subject even when they get 10% for every assessment. As long as they sat all assessments, they get the S. And then they can do the Unit 3/4 equivalent the following year. In the public system, you cannot refuse a student to enrol in a subject. In fact, I’ve had students in Methods 3/4 who received N in Methods 1/2 but nevertheless were allowed, despite my strongest protests, to remain in the class.
“Let’s see how they go in the first test” I get told.
They get 10%.
“Ah, well it’s too late now for them to be moved into another subject”.
End-of-year result: Unscaled Study Score of 17 ( I guess these scores have to come from somewhere …)
It’s not helped when the school policy is that everyone must do Maths Methods 1/2 regardless of their Year 10 mathematics results.
I would suggest that it’s this system of automatic promotion to the next year level (and I can speculate on the reasons why this happens) that is a big reason for why teachers have so much extra work, both in and out of the classroom, not to mention all the extra administrative work that flows from this. This never happened “in the old days” …
I guess that could be part of it. I’m not sure I mind that so much. There’s always going to be some variation. I think what I’m feeling is more frustration with the prioritisation of minute-by-minute action in the classroom over long-term goals, and the need for the constant appearance of appropriate activity. Without that, maybe there’d be more time to help students catch up on what they’re missing. That’s one of my favourite things to do.
Also, I was one of those students who had to ask to be allowed to do 4 Unit maths because nothing about my track record suggested it was appropriate. The difference was I had no expectation that it was my teacher’s problem to catch me up or keep me constantly engaged. If I was behind, I studied and caught up. When I was ahead, I found a way to pass the time. Is it even a problem that they got 17 at the end of the year? Maybe that is what’s new?
Sorry, I just noticed this: “It’s not helped when the school policy is that everyone must do Maths Methods 1/2 regardless of their Year 10 mathematics results.” That does sound silly. If only for the sake of reluctant students having to buy $300 calculators!
Also, I should perhaps add: my viewpoint is biased by the fact that I’m currently in the situation where I am being mentored with one class and pressured to create perfect learning tasks that follow a format and anticipate everything that students could possibly do or need. With the others, I am not. They’re less stressful and I think actually my teaching is more effective. I was reflecting on why that is.
I believe the focus on tasks is part of the reason why the importance of teachers’ mathematical knowledge is overlooked as well. Even if they teach kids stuff that isn’t mathematically correct (I’ve seen it happen), it will still look like they’re doing a good job based on the appearance of activity in the classroom. But long-term, there is a downside.
Shorter version: it is all lunacy.
Hi wst.
“pressured to create perfect learning tasks that follow a format and anticipate everything that students could possibly do or need. ”
I won’t ask the school name (but I’d love to know, maybe an email to Marty …? Then I could tell you where the bodies are buried).
What is the year level for these tasks?
Are your Mentor’s tasks perfect? (I’ll bet they’re nowhere near perfect).
Are you working as part of a team? What sort of ‘perfect’ tasks have the other team members produced?
Finally, the $64 question – How come these perfect task don’t already exist? Or does your school re-invent the wheel every year? All you should be doing – at worst – is ‘tweaking’ existing tasks.
Personally, if I was told to write such ‘perfect’ tasks for every lesson in every subject that I taught and it had to be re-done every year, I’d be sending a perfect rocket up someone’s arse.
So here is a major cause of teacher work overload – a bunch of muppets demanding that you do impossible things that are 80% bullshit. I’ll guarantee your school is not making experienced staff do this – because those teachers would be sending the rocket. And these morons have to have their big Canberra meetings to come up with a plan for teacher workload and teacher retention.
btw I’ve found that people who want others to write ‘perfect’ tasks never do it themselves. They are hypocrites. The VCAA SAC audit system is a fine example. I could show you ‘final draft’ SACs written by some people who sold them to various organisation and the tasks are not fit for use as toilet paper. I know where the bodies are …
Oh, thanks for that. I shouldn’t really complain. It’s not so bad. Not every lesson, just once a week or so. And it’s a new initiative, so that’s why they aren’t all done, and they do give me something to start with. I don’t think they are holding me to a higher standard than themselves, just a different standard than the one I hold myself to. I find trying to mesh my own ways of thinking about things with theirs hard. I think that’s why I stress. (It’s Year 7 – Year 7 is the hardest year for me anyway.)
The
new initiative, I assume.
I guess that the justification for this policy about moving from Year 10 to Year 11 is that it is easier to move from MM to FM than the other way around. Both require the same CAS calculator.
Yep, let’s force the kid who got 30% for Year 10 tests and exams to do Maths Methods Units 1/2. It’s bad enough when parents have delusions of adequacy on behalf of their child, let alone when a school is simply trying to fabricate and perpetuate a particular image by forcing square pegs into round holes.
“Both require the same CAS calculator.” Yep, both require the same piece of shit.
But I suppose if only capable and competent students did Maths Methods Units 3/4 then:
1) Student numbers would immediately drop by at least – my estimate – 30%.
2) You’d have capable and competent students getting unscaled scores of less than 25, which is a huge embarrassment and would lead to a further decline in numbers. This is inevitable for a system based on rank rather than merit. (And is a damning indictment on the current system).
The current system needs plenty of weak and poor students who have absolutely no chance of success doing Maths Methods – these students are crucial to the success of more capable students. What a great system.
I dis-agree. Let ss of 20 go up to 35 and students will be fine. This could encourage students to take up methods and specialist (20-> 42?, why not for a difficult subject and difficult examination?)
Except the study score (in all subjects) is based on a normal curve with a mean of 30 and a standard deviation of 7. So it’s mandated that 24% of students must get an unscaled study score of less than 25, regardless of their quality.
So you’d still have capable students in that bottom 24%. Universities require an *unscaled* score of 25 as a prequisite. So then a follow-up suggestion is for universities to lower this requirement to 20. Or even 15. I could flap my arms and fly before this will happen. Then again, maybe I should start flapping and soar like a bird, because it’s the progressive lowering of entry prerequisites by universities that has contributed to many of the failings in education.
And once you scale a 25 to a 40 (and 20 to a 35 etc), watch even more duds flock to Maths Methods, for all the WRONG reasons.
I think the latter is actually what happens in NSW; at least to a certain extent (the scaling is not simple curve fitting by rank).
Somehow the idea is that some subjects are harder than others.
Indeed. In Victoria we have voodoo mathematics about the ‘strength of competition’ in the subject etc. A fat lot of good the scaling is for a capable Specialist Mathematics student who gets 24 (unscaled), simply because the cheap seats are mandated to be filled up.
Schools might be trying to deter capable students from enrolling in Further Mathematics (FM1) or Foundation Mathematics (FM2) and trying to keep them in Mathematical Methods. For example, they might want to encourage a student who got 70% in Year 10 to choose MM. Still, students will vote with their feet.
If not necessarily their brains.
Terry, I have absolutely no problem with the 70% Yr 10 student doing Maths Methods. If only all students going into Maths Methods from Yr 10 had at least a 70% average. It’s the 30% student … (Which begs the question of how a student can be getting 30% in Yr 10 and what was happening in Yr 9, Yr 8 etc).
Having said this, some schools have a very funny idea of what 70% means. In some schools the meaning is “We don’t want to rock the boat …” There’s genuine 70%, and there’s Kum ba yah 70%.
Many schools encourage their capable Yr 11 students to do Further 3/4. Mainly to inflate their 40+ data. It’s legal, and totally morally bankrupt.
Students don’t vote with their feet. They vote with how best to try and game the system. It’s a broken system that encourages gaming.
@Marty: I agree. Brains is not the whole story. But it’s a few chapters of the story. I actually place most of the responsibility on schools – the political and financial motivations that lead to them making ‘expedient’ decisions that are often not in the best interests of the student (despite schools mewling and bleating the contrary). (Which, of course, leads directly to the Govt. and its spin.
In breaking news, big Govt meeting concludes that water is wet. Bureaucrats will now spend 6 months devising a plan for keeping dry).
Yeah, I know. The students are, in the main, simply the victims.
The students are the victims. The instruments that support the current education system are the serial killers.
I wonder why no one has (dared?) mention the role of the VIT…
Indeed. The VIT …
There is a direct correlation between when the VIT slithered onto the scene and the crisis teaching currently finds itself in. I know, correlation doesn’t mean causation. But that doesn’t mean there is no causation. In my opinion, the VIT bears a lot of responsibility for the decline in the number of students studying to be teachers and the number of graduate teachers who leave teaching within 5 years, including mid-career teachers. In my opinion, the demands imposed on graduate teachers by the VIT are stupid, unreasonably onerous and mostly unnecessary. In my opinion, the VIT exists in order to justify its own existence. And charges us 110 dollars each for doing so.
And let’s not forget that the VIT was and still is a major impediment to getting retired teachers back into teaching to help cover shortages over the last few years (Merlino’s *snort* ‘pool’ of teachers vapid gimmick that was going to save us all was even more shallow as a consequence).
What did the VIT do during 2020 – 2021? Nothing except be absent (but nevertheless still able to leech money off each teacher).
I’ve said this several times – look at the things done over the last 20 years and you will find explanations for the current teaching and education crisis.
This mess was decades in the making, and anyone who thinks there are quick fixes is either an idiot or a politician (others can decide how much overlap exists between the two). Of course, times have never been better for the so-called, self-appointed educational ‘experts’ – only idiots would listen to the people that so capably helped create this mess. Which unfortunately means that these self-appointed ‘experts’ will be closely listened to.
On a tangential note – in my opinion, the current EBA negotiated between the VEU and the Victorian State Govt will inflict huge additional damage on an already broken system. If the Govt was serious about the solving the education crisis, it would never have signed off on the current EBA. It would have done the moral thing and told the Union that it’s shot itself in the foot and to go back and re-think. But instead, the Govt was delighted that it could sign off on an EBA that doesn’t force it to invest additional money into education. Victoria will take decades to recover from the consequences, assuming future Govts even bother to try.
I am fairly new to teaching in secondary schools. However I have no issues with VIT. Most professions have such organisations. Of course that is not a justification in itself, but it is not unusual to have such an organisation. The annual fee is reasonable. After reading the reports on cases where VIT has had to discipline some teachers, I was glad there there is some oversight! Whenever I have had to contact people at VIT, they have been quick to respond and the advice was helpful.
In my personal experience, VIT is thoroughly incompetent and thoroughly dishonest. It was only a threat to take the assholes to VCAT that brought them into line.
The purely hypothetical article has been written and submitted. Thank you all for your ideas. Of course if and when the thing appears, I’ll post on it.
Now, on to a very big backlog of blog topics and life tasks.
Unless mathematics is taught in a plain simple and straightforward way with lots of examples for the student to draw from.FURTHER if the answers provided to problems are not spelt out in worked out answers .YOU WILL CONTINUE TO LOSE PEOPLE. One hundred and ten years ago.A maths teacher Silvanus P Thompson, wrote. .The preliminary terror which chokes off most fifth form boys from even attempting to learn how to calculate, can be abolished what is the meaning- in commonsense terms- the principal symbols that are used in calculating.IF YOU CAN’T EXPLAIN IT SIMPLY .YOUDON’T UNDERSTAND THE SUBJECT WELL ENOUGH! ALBERT EINSTIEN Peter Nowlan
Thanks, Peter. Undoubtedly, school mathematics must be taught primarily in an uncluttered “this is the problem/calculation, and this is the idea/technique” manner, and undoubtedly this is not now being done. The new curriculum, to the extent it is coherent, is advocating the exact opposite.
I’ve always taken issue with that quote. It seems to ignore the (obvious, at least to me) fact that sometimes things are intrinsically complex. Some things can be broken down into simple parts, but still the picture they paint is complex. If students are aware of the quote, or of the teacher’s purported aim (to explain all things simply) then they just feel stupid if they don’t understand what to do immediately. I have seen this happen a lot.
I like it more if we are just honest with students about how complex things are. If something has many moving simple parts, a lot of detail, then we are just honest about that fact and explain methodically, revisiting as appropriate. If a student is lost, that’s OK. Not everything can be explained simply.
I don’t think school mathematics is complex.
Indeed. It’s purely imaginary.
The minute that mathematics becomes complex.Thats when you should create a procedures manual.Index it .Eventually all maths exams will have to be open book with calculators – that is what happens i the real world.
Peter, that’s not making much sense to me.
The solution to complexity is example after example.With a good index so that the student can cross relate quickly between examples and worked solutions.Train them to spot what the questions are getting at by cross relating the questions that they are looking at to examples of work that they have done. Peter Nowlan
Huh. Now I’ll agree with Glen.