Last week, the big, crazy news out of big, crazy America was the Florida Department of Education’s decision to reject 54 school mathematics texts. The reasons? Well, supposedly the rejected texts

*included references to Critical Race Theory (CRT), inclusions of Common Core, and the unsolicited addition of Social Emotional Learning (SEL) in mathematics.*

The claim was immediately undermined, however, by the FDOE’s declining to provide any such references, or to even identify the rejected texts. FDOE’s excuse, that the textbooks “contain confidential and proprietary content” and that the publishers could still “appeal any non-adoption decision and substitute or revise their submitted bids”, was widely recognised to be utter nonsense. So, a few days after FDOE’s nonsense didn’t fly, FDOE released the list of rejected textbooks, but still without any references to supposedly egregious content. Of course this was still nonsense and it still didn’t fly.

Finally, yesterday, FDOE published four images from the rejected textbooks. Four images with no provided context, out of 54 rejected texts. This is, of course, still utter nonsense. But, at least we can now pretend to discuss this. One of the released images is above, and the other three are below. The reader is invited to meaninglessly judge for themselves.

So, what is this kerfuffle about? Should the texts have been rejected? Who are the Good Guys for whom we should be cheering? Here are our brief thoughts:

*) This is indeed about Critical Race Theory. The Critical Race in question is the race for the 2024 Republican Presidential Nomination. And, Florida Governor DeSantis’s Theory about this Critical Race is that if he wages enough ludicrous Trumpian culture wars then he’ll get the nomination.

*) It is almost certain that the texts should have been rejected. It is quite probable that they should have been rejected because they contain manipulative, social engineering twaddle of the type of which has been claimed. But, more probably, the texts should have been rejected because, like almost all modern school maths texts, they are mathematical garbage.

*) There are no Good Guys here. DeSantis, as is his Education Minister henchman, Richard Corcoran, is an utter slimeball. But the textbook companies are undoubtedly swill merchants, without an ounce of genuine concern for the quality or integrity of their publications.

What a country.

### UPDATE (25/04/22)

The *New York Times *has a (semi-paywalled) article on Florida’s textbook rejection. The article is telling, and hilarious.

Education reporter Dana Goldstein and politics reporter Stephanie Saul looked at the online resources/versions of twenty-one of the rejected textbooks and fished around for what might have pissed off the Florida thugs. Obviously one cannot do justice to twenty-one out of fifty-four texts in one article, but it’s something. So what did they find?

The reporters claim that they found “little that touched on race, never mind an academic framework like critical race theory” (while making no comment on the crazy bar graph image that FDOE released). They did apparently find, however, a lot of other stuff:

*But many of the textbooks included social-emotional learning content, a practice with roots in psychological research that tries to help students develop mind-sets that can support academic success.*

OK, so lots of touchy-feely SEL crap. And how do the reporters report on this touchy-feely SEL crap? Well, they quote a Harvard education professor, “a developmental psychologist and expert on social-emotional learning”, to the effect that the touchy-feely SEL crap is not crap. And, they quote a Northwestern education professor, “a director of teacher leadership”, to the effect that the touchy-feely SEL crap is not crap.

Is that it? Of course not. This is the *New York Times*, so of course they will balance the “touchy-feely SEL crap is not crap” opinions from the declared experts with an at least one opposing view. To this end, they quote “a right-wing activist”, some culture warrior fruitcake from a libertarian nutjob institute, to the effect that the touchy-feely SEL crap is, indeed, crap. Way to do the balance, guys.

It’s not so much the reporters putting their fingers on the scales as their entire idiot asses. It is exactly the kind of manipulative and tone-deaf crusading that convinces people, wrongly, that the Florida thugs are The Good Guys. Of course the true hilarity is that the reporters’ crusading is immediately defeated by the very evidence that they provide:

LOL there was no way you would not have mentioned this if you pardon the double negative!

Uh, did I double-negative somewhere, or have you just pigeon-holed me (correctly) as That Kind of Guy?

I am more critical of exercises that I set my students than I used to be. If I frame a problem in some context, I think about how that context might affect my students. I would not set a problem about cancer (even though I worked with cancer statistics for some years), or body image (e.g. estimate the surface area of your body) anymore. I would not even set a problem along the lines “A class has 20 boys and 13 girls….”. There are plenty of other problems to choose from.

Setting the problem in some unrealistic context does not seem helpful – although I did borrow an idea (with appropriate acknowledgment) for a problem about the seven dwarfs from Tony Gardiner.

The book by Ole Skovsmose entitled “An invitation to critical mathematics education” contains a dreadful example of a problem set in Italy during WW2.

Using only pure mathematical problems avoids the issue.

BTW, we lived in Florida between 1970 and 1974. It was a long time ago, but the movie “Hidden figures” was a realistic depiction of circumstances in that part of the world.

Thanks, Terry. Generally, I agree and would put it more strongly: the idea that these real-world scenarios, independent of any contentiousness, are somehow value-added is absurd. Having said, that what the hell is wrong with “20 boys and 13 girls”? I fear I know your answer, but if you’re crazy enough for that to be the answer, I’d like to have you write it.

The scenarios should encourage students to see potential applications of mathematics outside the mathematics classroom. Many examples in textbooks are contrived and not particularly interesting. I try to create examples that are, in my view, realistic and interesting – but not controversial. There are plenty to choose from, but to develop them takes time and thinking on my part. Sometimes I have to make simplifying assumptions. One of the challenges in applied mathematics is to find a mathematical model to fit the situation, perhaps approximately.

Thanks for, yet again, not answering my question.

Is part of the issue (and I am guessing here a bit more than usual…) that a significant number of students have difficulty grasping the link between and “Terry borrowed 3 dollars from from Marty and then paid 2 dollars back, how much does Terry now owe to Marty?” hence some level of “worded” problem is required.

The “real world” (I have a number of issues with this phrase, as I’m sure do many commenters here, possibly for different reasons) is not the objective, but may be claimed as such. Of course, this leads to all sorts of issues when the “real” world is so obviously fake (polynomial cheese, anyone?) or is used to push other agendas.

On this last point, the University of Melbourne Mathematics Competition was quite well known for using politicians names in their contrived stories about numbers of beds in hospitals, a bottle of Grange even made a mention one year. Thankfully though, the problems themselves in these cases were actually good, which makes up for (some, not all) the other rubbish.

One colleague was very interested in cars; so all his exercises involved cars; I found this tedious. Another colleague liked to make his exercises humorous; I found this distracting. As for me, I can’t drive a car and have no sense of humour.

Yes. Usually gimmicks are distracting rather than charming, my own included.

Even though contexts of the University of Melbourne Mathematics Competition were probably invented as a bit of fun, it is possible that many students would not understand the contexts.

I suspect that some dedicated mathematics students at UM would not have a working knowledge of the names of Australian politicians. Do students drink Grange these days? And who really understands what is meant by a bed in a hospital? I do because I used to work in one, and, in a hospital context, a bed does not mean a bed.

One study of education in regional and remote areas was critical of a test question that was set in a crowded railway station. The author argued that many candidates would have never seen a crowded railway station and be at a disadvantage in the test.

I have told this story before, but when I did the LANTITE test, we had questions to assess our level of comprehension. We were given some text and questions about the text. In the middle of this text was a string of words in Latin – 6 words as I recall. I know enough Latin to see that this was not particularly important for answering the questions. However, some candidates might not know any Latin. And how would I have reacted if these words had been in Japanese?

I wholly suspect the UoM stories were for the teachers (and for the writers’ own) entertainment more than anything else.

My core point remains though: write a GOOD problem and I will (to the extent that my opinion matters) forgive a horrible framing scenario.

The “cheese problem” was not a good problem to begin with, the framing just made it so funny it had me wondering if the writer didn’t do it deliberately (as in, they were told to write a “real world” problem and really didn’t want to so they came up with something so horribly fake that for some reason the publisher didn’t veto…) Probably not, but I can imagine…

RF, I strongly agree.

First and foremost the issue is whether a problem/exercise/passage/test-question is good mathematically. Time spent on worrying if Group X might be offended or if Group Y might be a little confused takes precious time and attention away from worrying if the material has any intrinsic mathematical worth.

Which is exactly what happens. No one in authority cares about the intrinsic mathematical worth.

I agree that the question should be sound mathematically. But it is important that students should be able to read, and comprehend, the question, in the time available.

I recall a text book question that involved reporting the results of a survey on capital punishment. A few of my Year 11 students did not know the meaning of “capital punishment”.

Although knowing the meaning of these words was not relevant to the mathematical issue, it did interfere with the abilities of those students to comprehend the question. To realise that the meaning of these words is not relevant is a skill in applied mathematics. It is part of process involved in isolating the mathematical aspects of the problem; separating the wheat from the chaff.

Yes, Terry, and I know you would put proper time into considering the soundness and worth of your problems. Others do not. Others use these other, valid but very secondary concerns, to avoid entirely thinking about mathematical worth.

VCAA could take note…

EAL students had some difficulty one year with “find the volume of the vessel”

And probably lots of other examples as well.

But… I would also argue that if a suitable exam/exercise/competition question setter was used in the first place we would be having a lot less of these discussions.

The Cambridge ICE-EM series of books have worded problems and that series has not been the subject of a WiTCH, in stark contrast to a series with the same publisher but different authors.

A coincidence, perhaps.

I was working with colleagues the other day to set a question for a test. The question involved the phrase “neither A or B”. I suggested “neither A nor B”. My colleagues suggested that many students would not understand the word “nor”. Eventually a re-wording that satisfied everyone was found.

I hope the discussion about “nor” is resolved before said teacher is asked to teach the new Boolean Logic material in Specialist…

And thus the World gets a little dumber.

RF, on the ICE-EM books, yes, it is not by chance that they haven’t been WitCHed. I think they’re pretty lousy, but the Essential books are at least two orders of magnitude lousier.

I sincerely apologise for not answering your question in my earlier post.

In many debates about social issues, including education, the distinction between male and female participants is not helpful. My cynical view is that questions based on this distinction are “low hanging fruit”; that is, it is very easy to say that there is a difference in the responses between male and female participants, especially in these days of the ubiquitous spread-sheet. Questionnaires nearly always ask you if you are male/female because questionnaires nearly always ask you if you are male/female!

So, in exercises that I set, I would not begin with “A class has 20 boys and 13 girls….”. The mathematical point of the question could be assessed if I put a little bit of effort into finding another context.

Please accept my apologies for not answering your question earlier.

Thanks for the answer. I think you’re probably making a mistake.

Meaningful context, even and especially if successfully meaningful, is more likely than not going to swamp the simple mathematical ideas that should be the proper focus of school mathematics instruction. The history of mathematics and of mathematics teaching is abstraction and idealisation. There is a reason for that.

I see your point. When teaching calculus to science students at university, I also attended their chemistry lectures so that I could find useful ideas for my classes. Eventually a few students told me that they preferred mathematics to chemistry – so my idea was not working as well as I had hoped.

On the other hand, coming to grips with a non-mathematical scenario is an important aspect of applying mathematics. See attached.

2021-Minecraft

Just this week, I was assisting a Year 9 student with a question about simple interest; she had no idea of the meaning of “interest” in this context; I asked her if she had a bank account; evidently not; when I explained to her that the bank adds interest to your account, you could see the amazement from the expression on her face.

The mathematics is trivial; the context is complicated.

Interesting. (So to speak.) I guess no one has had bank interest of note for quite a while.

Frankly, I don’t know enough about race relations in the US to comment in an informed manner on racial prejudice or critical race theory (although I think that having social issues be used as examples in mathematics textbooks is perfectly fine, and these textbooks should not be rejected on this reasoning).

However, the questions in the first image are crap (specifically, the question on the right). In what sense can this set of data, which is grouped into various categories labelled by words and not numbers, be described by that polynomial? Even if you assume that the political identification labels are first converted into numbers (not explicitly stated in the picture, though maybe it’s been cut off further down), there is no way that that graph shows a cubic function; graphing that function confirms that it looks nothing like the actual graph there. This is literally the textbook writers making stuff up.

And why are they writing this cubic as a sum of two separate cubics? This seems like pseudocontext, unless they explicitly explain that e.g. the two separate cubics are models for two different parts of the Race Implicit Association Test, or give some other explicit reason as to why one might ever write this as a sum of two cubics. In any case, having simplified the sum of two cubics, we find that it’s identical to the second cubic in the second image. So the first two pictures evidently show two different parts of the same textbook, both of which refer to the same topic.

The third image appears to be on a topic about counting to 5; given the Common Core Standards, which state that children are expected to be able to “count to 100 by ones and by tens” by the end of kindergarten, I’m assuming this is from a very early part of a teaching guide for kindergarten teachers. Assuming my guess is correct, I don’t see an issue here except that maybe the unit should cover more material (e.g. on counting to 10). I will admit, though, that I don’t have any actual experience with elementary and preschool mathematics education, so perhaps someone more knowledgeable on this front can weigh in.

As for the fourth one, I can’t glean any information about who this particular paragraph is aimed at. I can only guess, due to the font similarity, that this is also part of the teaching guide in the third image, and thus would refer to the “SEL Objective” in the third image. We aren’t even told what these “five competencies” are, although, given that they were established by the Collaborative for *Academic*, Social, and Emotional Learning, I should hope that at least one of them is “competency at the subject matter” (i.e. mathematics, in this case). From the face of it, though, it seems like this is instructing teachers to play a role in social and emotional development of young children, which frankly is what I would expect a kindergarten teacher to do. So it’s unclear what is objectionable about this.

So the FLDOE is really only showing at most three examples, and quite probably only two, of textbooks containing “inappropriate” material (namely, usage of social issues as examples; and instruction aimed at teachers, who are supposed to be well-equipped to handle social and emotional development). Certainly these textbooks need review (though not for the reasons the FLDOE is claiming), but the FLDOE needs a bigger review to weed out whichever bozos decided that this was the hill they wanted to reject these textbooks on.

Thanks, edder. To be honest, I couldn’t get the energy to try to decipher the images. I simply assumed that the mathematical awfulness would be much greater than than the claimed CRT/whatver awfulness.