Curios of the week #70

Clippings, endnotes and other ephemera

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This week, we have been on our term break. I decided to start the week with a full English breakfast, but there was a snag. I could not find any black pudding in the supermarket, even though I was sure I had bought it there before. Undaunted, I went on a quest and eventually found a butcher’s shop in Sebastopol that not only sold black pudding, but also some very tender lamb chops.

Other than that, I have been working on my weird fiction project, posting another short story that about three people will read. I know, I know, but it makes me happy. And please don’t feel any obligation to follow that link if you are not interested. I don’t want to be the text-based version of that guy at Glastonbury with the ukulele.

This week’s Curios include the unsurprising, the absurd, something about exam halls and much more.

General election of the week

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On Thursday, the UK held a general election. In an extraordinary turnaround, a large Conservative majority in 2019 was turned into a much larger Labour majority. There are many reasons for this, not least a growing fickleness among voters and the effects of Covid and lockdowns. I would also argue that there is an element of incompetence, where voters are increasingly aware that politicians seem incapable of effecting meaningful change. A Conservative government with a mandate to lower taxes and reduce immigration has done precisely the reverse.

And despite the landslide, there is no palpable enthusiasm for Labour. The vote seems more of a punishment of the incumbent Conservatives, not least because the Labour Party pursued a ‘Ming vase’ strategy, giving little away. In terms of education, we do know that they want to extend the UK’s 20% sales tax to independent schools fees, proposing to spend the revenue on more teachers in the government sector. We shall see how that works out. They have also nodded to more progressivist education policies, talking about ‘oracy’ and listening to Peter Hyman who founded School 21, the grooviest free school to have opened over the last 15 years.

This has caused a lot of old Twitter progressivists to become rather excited. I think this may be premature. Keir Starmer, the Labour leader, appears to believe in nothing so much as he believes in pragmatism. It is impossible to know whether he is a leftist pretending to be a moderate or whether, under Jeremy Corbyn’s leadership, he was a moderate pretending to be a leftist. Perhaps he’s just changed his mind? Nevertheless, in this context, the private school tax, inherited from his predecessor, may represent the extent of his radicalism.

Silly mathematics article of the week

This week, a number of folks posted to my timeline an article from EdSurge by Dr Nicola Hodkowski, first published on 5 June. Hodkowski is a senior maths researcher at an education nonprofit and in essence, her article is exactly what we should expect. However, there has been much gaslighting in recent times. Advocates who once argued that teachers should ‘be less helpful’ have started to deny the existence of a debate between teaching methods, suggesting it is the domain of cranks and obsessives.

Why do people do this? They know they are on shaky ground. Rather than concede the argument, they pretend there is no argument. We went through something similar on EduTwitter around ten years ago when progressivists attempted to deny the existence of progressive education.

In the case of mathematics education, we are told that everyone believes in explicit teaching and everyone does it where appropriate. We are told that everyone sees mathematical procedures as being of equal value to conceptual understanding.

Hodkowski did not get this memo. Instead, she said the many quiet parts out loud. There is a whole section on, ‘why concept matter more than procedure.’ This is quite at odds with evidence that shows that procedural and conceptual knowledge develop in tandem.

After incorrectly asserting that teachers tend to focus on students with the right answer, Hodkowski suggests students with the wrong answer but the right reasoning are closer to conceptual understanding. Needless to say, this seems to involve lots of verbal explaining and hand waving — precisely what we invented the formalism of mathematics to avoid.

Hodkowski is opposed to direct instruction (explicit teaching) on the grounds that it leads to no conceptual understanding:

“Direct instruction, the gradual release model, or “I do, we do, you do,” is a teacher-led type of instruction in which teachers model procedures and processes for students to then memorize and follow — the opposite of developing concepts.”

This would be news to all those whose understanding of maths has been aided by a good explanation.

What do we need to do instead? You’ve guessed it:

“Inquiry-based instruction, which tends to be more student-centered, helps students develop conceptual understanding instead of simply copying the teacher’s modeled steps. For example, the perception-action cycle allows students to develop mathematical reasoning, understanding, justifications, and their own solutions and strategies, which can result in positive math identities beyond the classroom.” [My emphasis]

Procedures, where they feature at all, should, ‘evolve from conceptual understandings over time.’ Some people get upset when this is labelled ‘discovery learning’ but what else is it if students are developing their own solutions and strategies?

Curriculum choice of the week

On the subject of mathematics education, there is some worrying news from the U.S.