WitCH 62: Video Killed the Proficiency Star

It’s not fun, but we gotta do it.

Yesterday, we wrote about Ofsted’s review of mathematics education. We wrote that it is a great review, and it is a great review. It is perfect in its reactionaryism. But, alas, there’s also a video.

Below is Hannah Stoten, one of the review authors and future kidnap victim, launching the review. An excellent review, and a well-spoken author. What could go wrong?


UPDATE (01/06/21)

Well, that’s not good:

Nonetheless, we’re willing to assume that Hannah is innocent here, and plans to kidnap her and bring her to Australia are proceeding apace.

RatS 12: Sit Up and Think of England

Good news. We’re giving ACARA, and our readers, the night off. No painful reading tonight; just painful reality.

Ofsted is the UK’s ACARA-ish organisation, although the “ish” hides the fact that Ofsted appears to be competent. Last week, Oftsed published a review into mathematics education. We’re sure we are missing something, because the review appears to be important, clear and correct.

Reportedly the work of Hannah Stoten,* the document lays out in a clear and methodical manner what a mathematics education entails, and thus the nature of a proper mathematics curriculum. Here is how the review gets going:

How the review classifies mathematics curriculum content

For this review, we have classified mathematical curriculum content into declarative, procedural and conditional knowledge.

Declarative knowledge is static in nature and consists of facts, formulae, concepts, principles and rules.

All content in this category can be prefaced with the sentence stem ‘I know that’.

Procedural knowledge is recalled as a sequence of steps. The category includes methods, algorithms and procedures: everything from long division, ways of setting out calculations in workbooks to the familiar step-by-step approaches to solving quadratic equations.

All content in this category can be prefaced by the sentence stem ‘I know how’.

Conditional knowledge gives pupils the ability to reason and solve problems. Useful combinations of declarative and procedural knowledge are transformed into strategies when pupils learn to match the problem types that they can be used for.

All content in this category can be prefaced by the sentence stem ‘I know when’.

When pupils learn and use declarative, procedural and conditional knowledge, their knowledge of relationships between concepts develops over time. This knowledge is classified within the ‘type 2’ sub-category of content (see table below). For example, recognition of the deep mathematical structures of problems and their connection to core strategies is the type 2 form of conditional knowledge.

Summary table of content categories considered in the review:

Category Type 1 Type 2
Declarative "I know that" Facts and formulae Relationship between facts (conceptual understanding)
Procedural "I know how" Methods Relationship between facts, procedures and missing facts (principles/mechanisms)
Conditional "I know when" Strategies Relationship between information, strategies and missing information (reasoning)

Is this perfect? Of course not. It would be easy to nitpick over borderline calls. But as a basic guide to building and analysing a curriculum, it is beautifully simple and clear. As guides should be. And as ACARA’s Wheel of Death most definitely is not.

There’s plenty more we could quote. Like the whole damn thing. But we’ll restrain ourselves, and give just a few more. Here’s a note on “core knowledge”:

Foundational knowledge, particularly proficiency in number, gives pupils the ability to progress through the curriculum at increasing rates later on. The path of learning that begins with a diligent focus on core declarative and procedural knowledge is not a straight line, therefore, but a curve. This is a function of the curriculum’s intelligent design. For example, in countries where pupils do well, pupils are able to attempt more advanced aspects of multiplication and division in Year 4 if they have been given more time on basic arithmetic in Year 1. This may explain why successful curriculum approaches tend to emphasise core knowledge early on.

So, arithmetic skills are kind of important, especially early on. Who would have guessed?

Here’s an early comment on problem-solving:

Problem-solving requires pupils to hold a line of thought. It is not easy to learn, rehearse or experience if the facts and methods that form part of a strategy for solving a problem type are unfamiliar and take up too much working memory. For example, pupils are unlikely to be able to solve an area word problem that requires them to multiply 2 lengths with different units of measurement if they do not realise that the question asks them to use a strategy to find an area. They are also unlikely to be successful if they do not know many number bonds, unit measurement facts, conversion formula or an efficient method of multiplication to automaticity. Therefore, the initial focus of any sequence of learning should be that pupils are familiar with the facts and methods that will form the strategies taught and applied later in the topic sequence.

What’s this? Give the kids the knowledge and skills and techniques before having them embark on problem-solving? Are these people nuts?

One last one, on “positive attitude”:

Pupils are more likely to develop a positive attitude towards mathematics if they are successful in it, especially if they are aware of their success. However, teachers should be wary of the temptation to invert this causal pathway by, for example, substituting fun games into lessons as a way of fostering enjoyment and motivation. This is because using games as a learning activity can lead to less learning rather than more.

Some pupils become anxious about mathematics. It is not the nature of the subject but failure to acquire knowledge that is at the root of the anxiety pathway. The origins of this anxiety may have even been present at the start of a pupil’s academic journey. However, if teachers ensure that anxious pupils acquire core mathematical knowledge and start to experience success, those pupils will begin to associate the subject with enjoyment and motivation.

It’s hard to believe, but they seem to be suggesting that to get a kid to like mathematics you should get them good at it, rather than pretending they’re good at it. Crazy, crazy stuff.

Read the whole damn thing. We haven’t read it all yet, and yeah, we’ll probably find something in there that annoys us (because we’re that type). But we haven’t found it yet. It is a great, great document.

UPDATE (31/05/21)

A couple of colleagues, Simon the Likeable and The Hot Dog Man, indicated that they were puzzled by the Review. They both wondered if perhaps what Hannah Stoten is saying isn’t really simple. Indeed, they are correct. In a nutshell, this is Stoten’s message:

The last 50+ years have been a complete screw up. Forget about them, and start again.


*) (Update 31/05/21) And Steve Wren. Efforts are already underway to kidnap them both. No one tell them.

RatS 11: Taibbi and The Miserableness of Documenting Censorship

We link a lot to Matt Taibbi. He is smart, he cares (mostly) about  the right things, and he is beholden to no one. Which means that, with the polarising idiocy of our times, Taibbi is hated by pretty much everyone. It’s always a good bet to judge a man by his enemies.

Taibbi has an on-going series, Meet the Censored, to which we link whenever he has a new post. Now, Taibbi has written about that series, and the difficulty bringing people on with what the series is really about. If for example, you were cheering when Trump was kicked off Twitter, you might want to think again. Having thought again, you’re probably still fine to cheer Trump being kicked off Twitter, and maybe that’s ok, but it is not a gimme.

Here is Taibbi’s post on the issue:

On the Miserable Necessity of Doing Censorship Stories in Pairs



RatS 10: Adam Curtis’s CGYOoMH

Well, to be more accurate, this is a WatS, since it’s a BBC series.

Adam Curtis is a unique, brilliant filmmaker, exploring the psychology and politics of modern society like no one else. Two previous series, The Power of Nightmares and The Century of the Self, are musts. Curtis now has a new series, Can’t Get You Out of My Head: an Emotional History of the Modern WorldIt is viewable on BBC iPlayer (with VPN trickery) and, at least for now, here. It is great.

RatS 9: The Campus as Factory

Jacob Howland is an emeritus professor of philosophy at the University of Tulsa. For the last couple of years Howland has been watching the demise of his university, and the perversion of other American universities from the same anti-academic forces. (Of course, Australian universities are entirely immune from such anti-academic perversions.) This has come together in Howland’s article,

The Campus as Factory: corporatist progressivism and the crisis of American education.

RatS 8: Donald McNeil Has His Say

Last month, science writer Donald McNeil got shoved out of the New York Times. McNeil has waited until he was formally out of the Times to have his say. Now, he has done so. The whole thing is insane.

Part One: Introduction

Part Two: What Happened January 28?

Part Three: What Happened in the 2019 Investigation?

Part Four: What Happened in Peru?

RatS 7: Taibbi on Dr. Seuss and eBay

It was big news that the estate of Theodor Geisel – aka Dr. Seuss – had decided to cease publication of six Seuss titles, because of their portrayal of people “in ways that are hurtful and wrong”. Seuss is huge, of course, but in the scheme of it the news shouldn’t have been that huge. Geisel-Seuss wrote plenty of mediocre stuff, and some grotesquely racist stuff. It’s complicated. Books – good and bad – go out of print for all sorts of reasons – good and bad. We were a bit surprised by the discontinuance of Circus and Mulberry Street, but they aren’t great, and it’s not like they’ll be hard to find.

But then, eBay decides it will no longer list the Bad Seusses. And, as Matt Taibbi points out, that is batshit insane. Read it and Scream.


RatS 6: Bipolar Opposites

We’ve never paid particular attention to Scott Alexander (pseudonym) and his blog, Slate Star Codex (now Astral Codex Ten). Long ago, we ran into a few SSC posts and our very vague memory is that we liked them. Then, while reading more on the New York Times‘s crucifying of Donald McNeil, we came across the Times‘s smelly article on SSC, including the gratuitous and sleazy outing of Alexander.* We explored a little, including reading this thoughtful critique of SSC. Still, we didn’t, and don’t, look to have an opinion on SSC, or on the “rationalism” in which it is supposedly immersed. (We did however, come to the opinion, that the New York Times has lost its collective fucking mind.)

A couple days ago, however, and completely by chance, we ran into an old, 2014 post on SSC. Alexander is a psychiatrist, and this post was on his long and futile attempt to conduct a study of a screening test for bipolar disorder, a test that Alexander suspected was of limited worth and knew was being widely misused. From the introduction to Alexander’s saga:

You ask patients a bunch of things like “Do you ever feel really happy, then really sad?”. If they say ‘yes’ to enough of these questions, you start to worry.

Some psychiatrists love this test. I hate it. Patients will say “Yes, that absolutely describes me!” and someone will diagnose them with bipolar disorder. Then if you ask what they meant, they’d say something like “Once my local football team made it to the Super Bowl and I was really happy, but then they lost and I was really sad.” I don’t even want to tell you how many people get diagnosed bipolar because of stuff like this.

Alexander’s post struck a particularly strong chord. Our father was a clinical psychologist, and he saw the worst. The whole Cuckoo’s Nest thing. More importantly, he didn’t think the not-worst was generally all that much better. In general, he regarded his psychologist and, especially, psychiatrist colleagues as arrogant, narrow-minded, drug-pushing quacks. Alexander’s story is from a different angle, but it fits right in.

Alexander’s post is alternately hilarious and horrifying. Read it. And then scream.


*) The kind of thing that a toady like James Massola would do.

RatS 3: The GameStopping of Wall Street

Matt Taibbi has written a great article on the GameStop game: Suck it, Wall Street.

(Subheading: In a blowout comedy for the ages, finance pirates take it up the clacker.)

It’s all really worth reading, but here’s Taibbi’s summary:

[E]verybody “understands” what happened with GameStop. Unlike some other Wall Street stories, this one isn’t complicated. The entire tale, in a nutshell, goes like this. One group of gamblers announced, “Fuck you!” Another group announced back: “No, fuck YOU!”

That’s it. Or, as one market analyst put it to me this morning, “A bunch of guys made a bet, got killed, then doubled and tripled down and got killed even more.”

UPDATE (07/02/21)

Taibbi interviews one of the GameStop gamers.

And, Taibbi responds to a critic.