Gonna put all this stuff in one post:

I was at the Aspen Ideas Festival last week, talking about various aspects of outward-facing math. We taped an episode of Science Friday with Jo Boaler and Steve Strogatz, mostly about K-12 teaching, but I did get to drop Russell’s paradox on the audience. I also did a discussion with David Leonhardt, editor of the New York Times Upshot section, about the future of quantitative journalism, and sat on a big panel that debated the question: “Is Math Important?”

The big news from England was that Waterstone’s chose HNTBW as their nonfiction book of the month for June. That was a big factor in the book riding the Times bestseller list for a month (it’s the #5 nonfiction paperback as I write this.) I went to London and did some events, like this talk at the Royal Institution. I also got to meet Matt Parker, “the stand-up mathematician,” and record a spirited discussion of whether 0.9999… = 1 (extra director’s cut footage here.) And I wrote a piece for the Waterstone’s blog about the notorious “Hannah and her sweets problem.” from this year’s GCSE.

I was on Bloomberg News, very briefly, to talk about my love for dot plot charts and to tell a couple of stories from the book. (Rare chance to see me in a blazer.) On the same trip to New York, I sat in on the Slate Money podcast. I also wrote a couple of op-eds, some already linked here: In the New York Times, I wrote about states replacing Common Core math standards with renamed versions of the same thing, and in the Wall Street Journal, I talked about the need for a new kind of fact-checking for data journalism, where truth is not enough.

The book just came out in Brazil this month; good luck for me, I was already invited to a conference at IMPA, so while I was there I gave a talk at Casa do Saber in Rio, talking through a translator like I was at the UN.

I think that’s about it!

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You didn’t mention your post on the viral “Hannah and her sweets” problem!

I was listening to Science Friday on my old Sony Walkman while out walking my dog. I was amused by the “Russell’s paradox” problem, and I laughed out loud about how the real world response to the train problem should be: stop the trains!

Nadia: added!

For stuff like the Hannah column it’s important to actually get all the details right, especially when your point was that the problem is badly composed. I think the writers did a decent job given the constraints of an essay question on a giant national test.

The original GCSE question did not use the ambiguous formulation “choose 2 at random from a bag” quoted in your column. It said that she takes one, eats it, then takes another (and eats that!). This makes it clear that the picking is without replacement and it also gives a hint to the possible majority of students, those who don’t automatically jump to the solution with N(N-1) as the number of pairs, to treat the process into a sequence of two actions, rather than one act of pair-selection as in your solution.

Another interesting thing done by the GCSE writers is to add superficially irrelevant second “eating”. By making the second action clearly parallel to the first action, they avoid the confusion interpretation that there is some mysterious difference between them, or that one selection has replacement and the other not. If nothing else it shows they took care in the phrasing.

As to the specific criticisms you made,

1. The quadratic equation, although partly a red herring, is making it clear that they want a particular derivation and not just any valid analysis of the problem (such as deducing N=10 without using an equation). This is not ideal, and it sounds stupid when characterized that way, but their motivation is understandable on an essay question administered to a million students: to standardize the correct responses. That makes things easier and cheaper to grade, and more likely that correct answers will demonstrate the specific skills that the problem is there to test. Packing some combination of algebra and probability into one problem may have been not only an attempt to sort out the better students, but also because there isn’t enough space on the essay component to test everything separately.

2. Your other criticism, that having the probability as known but N as unknown is unnatural, doesn’t readily translate into better phrasings of problems based on the same idea. From a pure-mathematical point of view the important, intuitive and natural point of the problem is that, as a function of the number of candies of the other color, the probability of the observed selection is strictly increasing from 0 towards 1, so that there will always be an N where this probability is equal to, or nearest to, any given value. But this or its consequences are hard to pose directly as GCSE essay problems in a way that is (all at once) nontrivial, feasible, and free of confusing interpretations.