More than half of Americans oppose the use of Arabic numerals!

December 29, 2021 • 1:30 pm

Just a bit of fun, but the headline below is true. The survey on which it’s based is reported in this article in from the Independent, which you can see by clicking on the screenshot:(you can register for free with email and a password if it’s blocked; there’s no paywall)

So, here are some results given in the article:

More than half of Americans believe “Arabic numerals” – the standard symbols used across much of the world to denote numbers – should not be taught in school, according to a survey.

Fifty-six per cent of people say the numerals should not be part of the curriculum for US pupils, according to research designed to explore the bias and prejudice of poll respondents.

The digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are referred to as Arabic numerals. The system was first developed by Indian mathematicians before spreading through the Arab world to Europe and becoming popularised around the globe.

A survey by Civic Science, an American market research company, asked 3,624 respondents: “Should schools in America teach Arabic numerals as part of their curriculum?” The poll did not explain what the term “Arabic numerals” meant.

Some 2,020 people answered “no”. Twenty-nine per cent of respondents said the numerals should be taught in US schools, and 15 per cent had no opinion.

John Dick, who happens to be the head of Civic Science, issued this tweet with the data in graphic form, which I’ve put below as well:

Now Dick thinks this is an example of bigotry—”Islamophobia,” I suppose. I’m not so sure. Although I am sure that many of us know that Arabic numerals are the numerals we use every day, some people don’t, and, this being America, it’s possible that nobody has told children that they are learning “Arabic numerals.” The 56% figure could thus represent ignorance rather than bigotry, although both could play a role.  But Dick seems wedded to the latter explanation. Regardless, if it is ignorance, it’s pretty appalling. After all, everyone knows what Roman numerals are!

But wait! There’s more. There was so much doubt about this survey’s results that Snopes had to investigate it.

In its headline Snopes says “It’s difficult to answer survey questions if you don’t fully understand the meaning.” I’m pretty sure, from following them, that Snopes is woke,but their assumption that there’s no anti-Arabic bigotry involved is just a guess.

You can read their analysis, in which they reluctantly admit that the claim is true, by clicking on the screenshot below.

But wait! There’s still more! You get this special grapefruit-cutting knife if you read on—for free!

Snopes:

Those were the results of a real survey question posed by the polling company Civic Science. John Dick, the Twitter user who originally posted a screenshot of the survey question, is the CEO of Civic Science.

The full survey doesn’t appear to be available at this time (we reached out to Civic Science for more information), but Dick has posted a few other questions from the poll, as well as some information regarding the purpose of the survey.

Dick, who said that the “goal in this experiment was to tease out prejudice among those who didn’t understand the question,” shared another survey question about what should or shouldn’t be taught in American schools. This time, the survey found that 53% of respondents (and 73% of Democrats) thought that schools in America shouldn’t teach the “creation theory of Catholic priest Georges Lemaitre” as part of their science curriculum. Here are the results:

33% of Republicans, a whopping 73% of Democrats, and 52% of independents thought that Lemaître’s theory should NOT be taught.

Now this question is more unfair, because, really, how many Americans know what the “creation theory of Georges Lemaître” was? If you read about science and religion, or have followed this site for a while, you’ll know that, although he was a Catholic priest, Lemaître held pretty much the modern theory of the Big Bang and the expanding Universe. As Wikipedia notes:

Lemaître was the first to theorize that the recession of nearby galaxies can be explained by an expanding universe, which was observationally confirmed soon afterwards by Edwin Hubble. He first derived “Hubble’s law”, now called the Hubble–Lemaître law by the IAU, and published the first estimation of the Hubble constant in 1927, two years before Hubble’s article. Lemaître also proposed the “Big Bang theory” of the origin of the universe, calling it the “hypothesis of the primeval atom”, and later calling it “the beginning of the world”.

Yes, and Lemaitre did other science, including analyzing cosmology using Einstein’s theories of relativity. He was a smart dude, and should have gone into physics instead of the priesthood. There’s a photo of him with Einstein below.

Why did so many people answer that Lemaître’s theory, which is, as I said, is pretty much the current theory of the Universe’s origin, NOT be taught? Surely it’s because the question identified Lemaître as a “Catholic priest”. That means that people probably thought his “theory” was the one expounded in Genesis chapters 1 and 2—God’s creation. So they didn’t want a religious theory taught in school.

Two points: most Republicans didn’t mind as much as Democrats of Independents, and that may be because more Republicans are creationists than are Democrats. But why did so many Democrats not want Lemaître’s theory taught? Are they that much less creationist than are Republicans? Perhaps that’s one answer. Another is that they are more anti-Catholic, but that seems less likely. But underlying these data—as perhaps underlying much of the data about Arabic numerals—is simple ignorance. I, for one, wouldn’t expect the average Joe or Jill (oops!) to know what Lemaître said.

One final remark: Accommodationists sometimes use the fact that Lemaître got it right as evidence that there’s no conflict between science and religion. I’m not sure if Lemaître thought God created the Universe, but if he did, he might have thought that the Big Bang was God’s way of doing it. (He was surely NOT a Biblical literalist). So yes, religious people can and have made big contributions to science. But that doesn’t mean that religion and science are compatible—any more than Francis Collins’s biological work shows that science and Evangelical Christianity are compatible. I’ve explained what I mean by “compatible” before, and it’s NOT that religious people can’t do science.

In the case of Lemaître, Francis Collins, or other religious scientists, they are victims of a form of unconscious cognitive dissonance: accepting some truth statements based on the toolkit of science, and other truth statements based on the inferior “way of knowing” of faith. And that is the true incompatibility: the different ways that we determine scientific truth as opposed to religious “truth.”

But I digress, and so shall stop.

George Lemaître (1894-1966), photo taken in 1930:

From Wikipedia:

(From Wikipedia): Millikan, Lemaître and Einstein after Lemaître’s lecture at the California Institute of Technology in January 1933.

h/t: Phil D.

“Everybody has won and all must have prizes”: The drive to end merit-based schooling

November 9, 2021 • 12:15 pm

There are two articles you can read that show how quickly merit-based educational assessment is vanishing in the U.S. The first, from the New York Times, discusses California’s downgrading of math instruction, turning it as well into an instrument for teaching social justice. The second, from the Los Angeles Times, describes the move to eliminate grading, or at least the lower grades of D and F so that everyone must have the prize of a “C” (required to get into the Cal State system of colleges).

Click on the screenshot to read the pieces. I’ll give a few quotes from each (indented):

NYT:

If everything had gone according to plan, California would have approved new guidelines this month for math education in public schools.

But ever since a draft was opened for public comment in February, the recommendations have set off a fierce debate over not only how to teach math, but also how to solve a problem more intractable than Fermat’s last theorem: closing the racial and socioeconomic disparities in achievement that persist at every level of math education.

The California guidelines, which are not binding, could overhaul the way many school districts approach math instruction. The draft rejected the idea of naturally gifted children, recommended against shifting certain students into accelerated courses in middle school and tried to promote high-level math courses that could serve as alternatives to calculus, like data science or statistics.

The draft also suggested that math should not be colorblind and that teachers could use lessons to explore social justice — for example, by looking out for gender stereotypes in word problems, or applying math concepts to topics like immigration or inequality.

No matter how good the intentions, math—indeed, even secondary school itself—is no place to propagandize students with debatable contentions about social justice. The motivation for this, of course, is to achieve “equity” of achievement among races, since blacks and Hispanics are lagging behind in math. (Indeed, as the article notes, “According to data from the Education Department, calculus is not even offered in most schools that serve a large number of Black and Latino students.”)

Everything is up for grabs in California given the number of irate people on both sides. Some claim that school data already show that the “new math” leads to more students and more diverse students taking high-level math courses, while other say the data are cherry-picked. I have no idea.

Complicating matters is that even if the draft becomes policy, school districts can opt out of the state’s recommendations. And they undoubtedly will in areas of affluence or with a high percentage of Asian students, who excel in math. This is not a path to equal opportunity, but a form of creating equity in which everybody is proportionately represented on some low level of grades. I wish all the schools would opt out! There has to be a way to give every kid equal opportunity to learn at their own levels without holding back those who are terrific at math. I don’t know the answer, but the U.S. is already way behind other First World countries in math achievement. This will put us even farther down.

From the L. A. Times:

 

This issue is a real conundrum, more so than the above, because it’s not as easy to evaluate.  Here are a few suggestions of what teachers are doing to change the grading system—the reason, of course, is racial inequity in grades that must be fixed.

 A few years ago, high school teacher Joshua Moreno got fed up with his grading system, which had become a points game.

Some students accumulated so many points early on that by the end of the term they knew they didn’t need to do more work and could still get an A. Others — often those who had to work or care for family members after school — would fail to turn in their homework and fall so far behind that they would just stop trying.

“It was literally inequitable,” he said. “As a teacher you get frustrated because what you signed up for was for students to learn. And it just ended up being a conversation about points all the time.”

These days, the Alhambra High School English teacher has done away with points entirely. He no longer gives students homework and gives them multiple opportunities to improve essays and classwork. The goal is to base grades on what students are learning, and remove behavior, deadlines and how much work they do from the equation.

But I had always assumed that grades were based on what students were learning: that’s what tests do. You ask students questions based on what you’ve taught them and what they’ve read, and then see if they’ve absorbed the material.  I have no objection at all to basing grades on “what students are learning” so long as you don’t grade them on the basis tht you have different expectations of what different students can learn. (In fact, as you see below, that may be the case.)

As for behavior, well, you have to conduct yourself in a non-disruptive manner in class; and as far as deadlines and quality of papers and work, those are life lessons that carry over into the real world. You don’t get breaks from your employer if you finish a project late.  I always gave students breaks if they had good excuses, or seemed to be trying really hard, but can you give a really good student a lower grade because she’s learning the material with much less effort than others? Truly, I don’t understand how this is supposed to work.

There is also much talk about “equity” in grading, and I don’t know what that means except either “everyone gets the same grade”, which is untenable, or “the proportion of grades among people of different races must be equal”, which, given the disparity in existing grades between whites and Asians on one hand and blacks and Hispanics on the others, means race-based grading. That, too, seems untenable.  But of course this doesn’t negate my own approval of some forms of affirmative action as reparations to groups treated unfairly in the past. Nobody wants a school that is all Asian and white, and nobody wants a school that is all black or all Hispanic.

Again, I don’t know the solution except to improve teaching while allowing everyone to learn to the best of their ability. And that means effort must be judged as well as achievement. Here’s a statement from L.A. Unified’s chief academic officer:

“Just because I did not answer a test question correctly today doesn’t mean I don’t have the capacity to learn it tomorrow and retake a test,” Yoshimoto-Towery said. “Equitable grading practices align with the understanding that as people we learn at different rates and in different ways and we need multiple opportunities to do so.”

Somehow I get the feeling that this refers not to different individuals‘ capacity to learn, but on assumptions about the capacity of members of different races to learn—assumptions that are both racist and patronizing. This is supported by the fact that San Diego’s school board said this:

“Our goal should not simply be to re-create the system in place before March 13, 2020. Rather, we should seek to reopen as a better system, one focused on rooting out systemic racism in our society,” the board declared last summer.

Similar to Los Angeles, the San Diego changes include giving students opportunities to revise work and re-do tests. Teachers are to remove factors such as behavior, punctuality, effort and work habits from academic grades and shift them to a student’s “citizenship” grade, which is often factored into sports and extra-curricular eligibility, said Nicole DeWitt, executive director in the district’s office of leadership and learning.

It seems to me that you can’t solve the problem of unequal achievement by adjusting grades based on race. In the long term, that accomplishes very little. You solve the problem by giving everybody equal opportunities in life from the very beginning of life. Since minorities don’t have that, we should be investing a lot of time and money in providing those opportunities. In the meantime, some affirmative action is necessary to allow more opportunity than before, and because we owe it to people who have been discriminated against and haven’t had equal opportunity.

The new math in Toronto

November 5, 2021 • 1:30 pm

A graduate of the University of Toronto called my attention to this mathematics course as a harbinger of the decline of that great university. I have no idea what “liberated” mathematics is, and can’t find out anything about it, or the course, on the Internet. Several other people have tweeted this course, and I note that the only requirement for it is “high school level algebra.” I gather, therefore, that this course, taught by the mathematics department, is more about ideology than math.

I’ve put the transcript of the course description below, or you can click on the screenshot.

Currently, mathematics is at a crossroads between tradition and progress. Progress has been led in large part by women mathematicians, in particular Black women, Indigenous women, and women from visible minorities. Intertwined in their studies of mathematics is a daring critique of traditional mathematics, re-imagining of mathematics culture, and more. This course will compare and contrast new forms of accessible mathematics with standard sources that draw dominantly on the experiences and narratives of men. Restricted to first-year students. Not eligible for CR/NCR option.

The solution to this morning’s puzzle

September 20, 2021 • 2:39 pm

I haven’t yet looked at the comments about the puzzle I reported this morning that had been proposed by Russian Prime Minister Mikhail Mishustin when visiting a science-oriented “sixth form” class.

Here’s the puzzle again:

Construct a perpendicular from the (red) point on the circle to the diameter, without using any measuring devices.

In other words, given a circle with a diameter marked on it, and a point on the circle, can you find a way to draw a line from the point that hits the diameter at a right angle. (As marked in green above.)

The beauty of this question is the seemingly outrageous restriction not to allow measuring devices, which means that you cannot use a compass or a marked ruler. All you are allowed is an unmarked ruler to draw straight lines.

 

The Guardian has now published the four-step solution (there may be others); go to the preceding link to see it. Below you can see the PM drawing the solution (he must know his math).

A geometry puzzle from Russia’s prime minister

September 20, 2021 • 8:00 am

In lieu of Readers’ Wildlife today, we have a puzzle, one posted (as the Guardian reports) by Russian Prime Minister, Mikhail Mishustin when he was visiting a science-oriented “sixth form” (what age of kids are these?) school. Matthew sent me a link.

Here’s the problem, and there’s a clue in both the photo below and in the Guardian article:

Construct a perpendicular from the (red) point on the circle to the diameter, without using any measuring devices.

In other words, given a circle with a diameter marked on it, and a point on the circle, can you find a way to draw a line from the point that hits the diameter at a right angle. (As marked in green above.)

The beauty of this question is the seemingly outrageous restriction not to allow measuring devices, which means that you cannot use a compass or a marked ruler. All you are allowed is an unmarked ruler to draw straight lines.

Matthew couldn’t solve it and, as I haven’t had my coffee, I’m not even going to try.

Here’s, a picture of Mishustin posing the problem (and giving a bit of a solution):

Russia’s Prime Minister Mikhail Mishustin draws on a chalkboard while visiting the Kapitsa Physics and Technology Lyceum in the town of Dolgoprudny earlier this month. Photograph: Dmitry Astakhov/TASS

Scientific American (and math) go full woke

August 29, 2021 • 12:15 pm

As we all know, Scientific American is changing from a popular-science magazine into a social-justice-in-science magazine, having hardly anything the science-hungry reader wants to see any more. I urge you to peruse its website and look for the kind of article that would have inspired me when I was younger: articles about pure science.  Now the rag is all about inequities and human diseases.

In the past couple of months, there have been some dire op-eds, and here’s another one—not as bad as some others, but (especially for a science magazine) riddled with unexamined assumptions. Click on the screenshot to read it. Apparently the “racial reckoning” that began last year has now crept into mathematics.

After reading it, I have two questions: Is mathematics structurally racist? And why has Scientific American changed its mission from publishing decent science pieces to flawed bits of ideology?

The article, of course, claims that mathematics is a hotbed of racism and misogyny, which explains why there are so few women and blacks in academic mathematics.

The article begins with stories of thee women mathematicians, all of whom report that they felt discriminated against or at least looked down upon. All of them have academic jobs, two as professors and one as a postdoc. I don’t doubt their stories, but what we have are three anecdotes. At face value, they show that there is some racism or sexism in academic math, but these are cherry-picked anecdotes that demonstrate little except that, like all fields, math is not entirely free of bigotry. I also procured two anecdotes with no effort. First, I asked one of my female math-y friends, Professor Anna Krylov,  a theoretical and computational quantum chemist at USC, who deals extensively with mathematicians, if that had been her experience, and she said what’s indented below. (I quote her with permission; we’ve met Anna before.)

 I was often a single women in a room — but so what? It did not turn me away from the subject I was passionate about.  I experienced some forms of discrimination throughout my career and can tell stories… But — as McWhorter often says — “there was then and there is now”! These anecdotes [from Sci. Am.] are blown out of proportion and completely misrepresent the current climate.

She also worried that these narratives, which don’t resemble her own, cultivate a victim mentality in women. (Anna is no anti-feminist, either: she helped initiate a protest against an all-male speaker agenda at a chemistry conference.)

Anna also mentioned another female math professor in the U.S. who agrees with her own experience. So we have two anecdotes on one side, and three on the other. (I have to add that, as I’ve said before, I myself felt inferior and suffered from “imposter syndrome” for several years in graduate school, constantly thinking about dropping out. But I finally realized that I could find my own niche.)

Author Crowell also gives two examples of undeniable racial discrimination against black mathematicians, but those took place in the early 20th century and in the Fifties, and it’s undeniable that at that time there was academic racism. But, as Anna said, “there was then and there is now”. If we’re to accept that mathematics is now structurally racist and misogynist, with an endemic culture of bigotry that leads to inequities, we need to do better than that.

So beyond the academic data, the article adds this:

Racism, sexism and other forms of systematic oppression are not unique to mathematics, and they certainly are not new, yet many in the field still deny their existence. “One of the biggest challenges is how hard it can be to start a conversation” about the problem, Sawyer says, “because mathematicians are so convinced that math is the purest of all of the sciences.” Yet statistics on the mathematics profession are difficult to ignore. In 2019 a New York Times profile of Edray Herber Goins, a Black mathematics professor at Pomona College, reported that “fewer than 1 percent of doctorates in math are awarded to African-Americans.” A 2020 NSF survey revealed that out of a total of 2,012 doctorates awarded in mathematics and statistics in the U.S. in 2019, only 585 (29.1 percent) were awarded to women. That percentage is slightly lower than in 2010, when 29.4 percent of doctorates in those areas (467 out of 1,590) were awarded to women. (Because these numbers are grouped based on sex rather than gender, that survey did not report how many of those individuals identify as a gender other than male or female.)

This is the Kendi-an idea that inequities in achievement are prima facie evidence of bias. But if you think about it for both women and African-Americans, that need not be true. This is a true case of begging the question: assuming that there is structural racism and misogyny in math and thus the lower representation is simply its result.

The problem with this, as we’ve discussed before, is that there are reasons for these inequities beyond structural racism, so you can’t just assume its existence. (As I said, nobody with any sense would deny that there are racist or sexist mathematicians; the claim is that the field is permeated with bigotry._

Regarding women, we’ve learned that the sexes differ in interests and preferences, with men being “thing people” and women being “people people” (these are of course average differences, not diagnostic traits!). As Lee Jussim points out in a Psychology Today op-ed, on the advanced high school level, men and women do about the same in math, but women do better than men in demonstrating verbal and reading skills.  In other words, women are better than men at everything, but many choose areas that are more word-heavy than math-heavy. That itself, combined with different preferences, causes inequities. As Jussim writes,

This same issue of differing interests was approached in a different way by Wang, Eccles, and Kenny (2013). Disclosure: Eccles was my dissertation advisor and longterm collaborator; I am pretty sure she identifies as a feminist, has long been committed to combating barriers to women, and is one of the most objective, balanced social scientists I have ever had the pleasure to know.

In a national study of over 1,000 high school students, they found that:

1. 70 percent more girls than boys had strong math and verbal skills;

2. Boys were more than twice as likely as girls to have strong math skills but not strong verbal skills;

3. People (regardless of whether they were male or female) who had only strong math skills as students were more likely to be working in STEM fields at age 33 than were other students;

4. People (regardless of whether they were male or female) with strong math and verbal skills as students were less likely to be working in STEM fields at age 33 than were those with only strong math skills.

Thus inequities in academic math may be a matter of differential preferences or other factors not reflecting bigotry. And this may be one explanation for why, although Sci. Am. notes that only 29.1% of doctorates in math were awarded to women in 2019, it looks from Jussim’s bar graph that about 35% of first time graduate enrollees in math and computer science are women. That bespeaks only a slightly higher attrition rate among women than men—something that needs to be addressed. But again, the go-to answer is not automatically “misogyny.”

As for African-Americans, yes, there’s way too few doctorates awarded in mathematics. To me this does bespeak racism, but racism in the past, not necessarily now. The situation is that due to inequality of opportunity, blacks almost certainly lack easy entry now into mathematics studies. This is a narrowing of the pipeline from the outset that needs to be rectified. But again, the figures do not show that the low output at the pipeline’s terminus is due to racism.

As to what happened to Scientific American, well, it’s gone the way of all the science journals. It is doing performative wokeness.

One more item: Have a look at MathSafe, an organization hired by the American Mathematical Society to police meetings like beagles sniffing out impurities. It’s as if we are no longer adults who can police our own behavior at meetings, and need to pay others to do it for us.

h/t: Anna

McWhorter and Loury on the math gap

March 8, 2021 • 2:00 pm

Here’s a 15-minute segment of the latest Glenn Show, featuring Glenn Loury and John McWhorter. (To see the rest requires a Patreon donation). In it, both men take up the issue of the black/white race gap in academic achievement, and both seem to attribute it to the culture of African-Americans. That, of course, is anathema to antiracists like Ibram Kendi, who seems to has a feud going on with McWhorter.

McWhorter refers to Ibram Kendi’s dictum, one that I just read in his How to be an Antiracist book, that black students should be ranked on their “desire to know” rather than what they do know. McWhorter’s characterization of Kendi is correct, as Kendi says that there are “different ways of ranking” appropriate to each race, and that black students should be ranked not by achievement, which is a white criterion, but by things like their spunk and their desire to know. And yet despite that, Kendi also says that the idea of a black culture is an illusion, and that all races are equal in every respect, including culture, though there are some local differences. This is one of the contradictions I found in Kendi’s book. (I recommend that everyone read it, as we all need to know about the bibles of the anti-racist movement. You will learn some stuff, and it’s not all bad, but it’s truly Manichean in its worldview.)

Loury gets particularly exercised at the low performance of black students in mathematics (he’s an economist), and at people who say that math is not a Black Thing. At times Loury looks like he’s going to blow out an artery, almost yelling that the response of people like Kendi is to “denounce the entire corpus that your people are not mastering by saying that it’s somehow alien to, or in fact repressive to the essence of your people.”

McWhorter chimes in, adding that the notion that each ethnic group should be judged by a different set of academic standards is a view that is often raised, but “has never gotten any purchase”.  Loury and McWhorter both suspect that the achievement gap is caused by a subtle cultural factor connected with “what it is to be raised black”. And that view is absolutely opposed to the ideas of Kendi, who doesn’t think that black “culture” operates any differently from white culture. Kendi, I believe, would attribute the math gap to racist policies of the present put in place by the academic power structure.

Loury winds up extolling the universality and beauty of math, using as one example we should admire the fact that “there is no largest prime number.” The universality of mathematical instruction, he implies, means that there is no reason not to teach any group differently from any other, nor hold different groups to different standards.

I hope that Loury doesn’t have high blood pressure, as he’s going to get an aneurism if he keeps getting this exercised. Both men, as usual, are great speakers, uttering long disquisitions without a hitch. Their conversations are a thing to behold.