Homeschooling Corner: Math Philosophy

Music is a hidden arithmetic exercise of the soul, which does not know that it is counting.–Gottfried Leibniz

Fibonacci Spiral

You may have noticed that I talk a lot more about math than reading or writing. This is not because I dislike the language arts, but because they are, once learned, not very complicated. A child must learn to decode symbols, associate them with sounds, and then write them–tricky in the beginning, but most children should have the basics down by the age of 6 or 7. For the next several years, the child’s most important task is simply practice. If a child has a book they love to read, then they are already most of the way there and will probably only need some regular instruction on spelling and punctuation.

Math, by contrast, is always advancing. For every new operation or technique a child masters, there is another waiting to be learned.

I don’t hold with the idea that mathematical concepts must be taught in a particular order or at particular ages–I introduced negative numbers back in preschool, they’ve learned about simple logarithms in elementary, and they seem none the worse for the unusual order.

Count on Math gives the logic behind Particular Order:

Developmental sequence is fundamental to children’s ability to build conceptual understanding. … The chapters in this book present math in a developmental sequence that provides children a natural transition from one concept to the next, preventing gaps in their understanding. …

When children are allowed to explore many objects, they begin to recognize similarities and differences of objects. When children can determine similarities and differences, they can classify objects. When children can classify objects, they can see similarities and difference well enough to recognize patterns. When children can recognize, copy, extend and create patterns, they can arrange sets in a one-to-one relationship. …

This developmental sequence provides a conceptual framework that serves as a springboard to developing higher level math skills.

This logic is complete bollocks. (Count on Math is otherwise a fine book if you’re looking for activities to do with small children.)

Humans are good at learning. It’s what we do. Any child raised in a normal environment (and if you’re reading this, I assume you care about your children and aren’t neglecting them) has plenty of objects around every day that they can interact with, observe, sort, classify, etc. You don’t have to dedicate a week to teaching your kid how to tell “similar” and “different” in objects before you dedicate a week to “classifying.” Hand them some toys or acorns or rocks or random stuff lying around the house and they can do that themselves.

Can you imagine an adult who, because their parent or preschool skipped straight from”determining similarities and differences” to “making patterns,” was left bereft and innumerate, unable to understand fractions? If the human mind were really so fragile, the vast majority of people would know nothing and our entire civilization would not exist.

More important than any particular order is introducing mathematical concepts in a friendly, enjoyable way, when the child is ready to understand them.

For example, I tried to teach binary notation this week, but that went completely over the kids’ heads. They just thought I was making a pattern with numbers. So I stopped and switched to a lesson about Fibonacci numbers and Pascal’s triangle.

Then we went back to practicing addition and subtraction with regrouping, because that’s tricky. It’s boring, it’s not fun, and it’s not intuitive until you’ve really got base-ten down solid (base 10, despite what you may think, is not “obvious” or intuitive. Not all languages even use base 10. The Maya used base 20; the Babylonians used base 60. There are Aborigines who used base 5 or even 3; in Nigeria you’ll find base 12.) Learning is always a balance between the fun stuff (look what you can do with exponents!) and the boring stuff (let’s practice our times tables.) The boring stuff lets you do the fun stuff, but they’re both ultimately necessary.

 

What else we’ve been up to:

Fractions, Decimals, and Percents, by David A. Adler. A brightly-colored, well-written introduction to parts of numbers and how fractions, decimals and percents are really just different ways of saying the same thing.

It’s a short book–28 pages with not much text per page–and intended for young children, probably in the 8 to 10 yrs old range.

I picked up Code Your Own Games: 20 Games to Create with Scratch just because I wanted to see what there was outside the DK Workbooks (which have been good so far, no complaints there.) So far it seems pretty similar, but the layout is more compact. Beginners might feel less intimidated by DK’s larger layouts with more white space, but this seems good for a kid who is past that stage. It has more projects than the shorter DK Workbooks but they’re still pretty simple.

I also happened across a Singapore Math Workbook, which seems fine. Sample problem:

Emily and Jasmine had the same number of stamps. After Emily gave Jasmine 42 stamps, Jasmine had twice as many stamps as Emily. How many did Jasmine have at the end?

At a movie, 1/4 of the people in the theater were men, 5/8 were women, and the rest were children. If there were 100 more women than children, what was the total number of people in the theater?

Our recorders arrived, so now we can play music.

Finished reading The Secret Garden, planted seeds, collected and identified rocks. Nature walk: collected fall leaves and pressed flowers. Caught bugs and observed squirrels for Ranger Rick nature workbook. Read about space and worked with cuisenaire rods. Etc.

 

Cathedral Round-Up #26: Philosophy

In sob stories about just how hard it is to be one of the most privileged people in the world, 21 Harvard and Oxford Students Share Their Experiences of Racism They Face Everyday [sic]:

I, Too, Am Harvard is a powerful photo campaign highlighting the faces and voices of black students at Harvard College. Fed up with the institutional racism they face everyday [sic], the students are speaking speaking out against it by sharing their heartfelt stories in a series of portraits.

“Our voices often go unheard on this campus, our experiences are devalued, our presence is questioned,” they say. “This project is our way of speaking back,of claiming this campus, of standing up to say: we are here.”

The students from Oxford University have also begun a similar campaign.

Examples of nefarious racism keeping down Harvard and Oxford students include people asking if they’re listening to rap music on their headphones and jokes abut Somali pirates. Several complaints also center on the fact that whites believe that blacks and Hispanics get an admissions boost due to Affirmative Action, which Blacks find terribly offensive. (Of course, as the NY Times notes, Harvard has been acting affirmatively since 1971:

The university has a long and pioneering history of support for affirmative action, going back at least to when Derek Bok, appointed president of Harvard in 1971, embraced policies that became a national model.

The university has extended that ethos to many low-income students, allowing them to attend free. Harvard has argued in a Supreme Court brief that while it sets no quotas for “blacks, or of musicians, football players, physicists or Californians,” if it wants to achieve true diversity, it must pay some attention to the numbers. The university has also said that abandoning race-conscious admissions would diminish the “excellence” of a Harvard education.

This is why Harvard is now getting sued by Asians, whose excellent SAT scores result in a significant admissions discrimination at top schools.)

Why do students at such elite schools indulge in such petulant whining? For that matter, why do these schools allow inanities like students yelling at faculty members about Halloween costumes (Yale, I’m looking at you)?

They say the Devil’s best trick was convincing people he doesn’t exist; perhaps the Cathedral’s best trick is convincing people that it’s oppressed. If Cathedralites are oppressed, then you can’t complain that they’re oppressing you.

Or perhaps people who get into top schools develop some form of survivor’s remorse? How do you reconcile a belief that “elitism” is bad, that intelligence isn’t genetic, that no one is “inherently” better than anyone else nor deserves to be “privileged” with the reality that you have been hand-selected to be part of a privileged, intellectual elite that enjoys opportunities we commoners can only dream of? Perhaps much of what passes for liberal signaling in college is just overcompensation for the privileges they have but can’t explicitly claim to deserve.

Over at Yale, the Philosophy Department is very concerned that too many white males are signing up for their courses:

But not all departments draw evenly across Yale’s many communities — some will be more demographically homogeneous than others, such as Yale’s Philosophy Department, which has historically been majority white and male.

Philosophy has struggled as a discipline to attract students from diverse backgrounds, and faculty and students within Yale’s Philosophy Department told the News that while the department is not as diverse as it could be in terms of racial and gender makeup or curricular offerings, ongoing efforts to remedy the problem are a cause for optimism.

Yalies seem lacking in basic numeracy: if some departments–say the African American Studies and Women’s, Gender, and Sexuality Studies–attract disproportionately high numbers of blacks and women, then there won’t be enough blacks and women left over to spread out to all of the other departments to get racial parity everywhere. Some departments, by default, will have to have more whites and men.

“[Lack of diversity] has inspired a lot of soul-searching in the discipline in recent years,” said Joanna Demaree-Cotton GRD ’21, co-coordinator of Yale’s chapter of Minorities and Philosophy which works to combat issues faced by minorities in academia. “Lots of departments, including ours at Yale, have started asking tough questions about the cause of this drop-off in the representation of women and racial minorities, and how we might go about ameliorating the problem.”

In case you’re wondering, Demaree-Cotton is a white lady. When the push comes to get some professors to give up their spots in favor of women-of-color philosophers, will Demaree-Cotton get pushed out for being white, or will she be saved because she’s female?

Unfortunately for Yale, they recently lost their only black philosophy professor, Chris Lebron, author of The Making of Black Lives Matter: The History of an Idea and The Color of Our Shame: Race and Justice In Our Time, to Johns Hopkins U.

Yale has a second problem: very few people major in philosophy, period. For example, in 2016, only 20 undergrads received degrees in philosophy or philosophy of mathematics (data is not broken down for each department.) Of these, 13 were men and 7 were female. These are the kind of numbers that let you write hand-wringing articles about how “philosophy is only 35% female!” when we are actually talking about a 6-person gap. The recent “drop-off” in women and racial minorities, therefore, is likely just random chance.

“For example, although over the last four years women have represented less than 25 percent of applicants to our Ph.D. program, they represent about 40 percent of students currently in our program,” Darwall said.

Sounds like Yale is actually giving women preferential treatment, just not enough preferential treatment to make up for the lack of female applicants.

Deputy Dean for Diversity and Faculty Development Kathryn Lofton said that Yale is working hard to “rethink diversity” across the University…

Each academic department and program, not just philosophy, must engage with this topic, Lofton added.

“The protests in the fall of 2015 showed that our students believe we have work yet to do to achieve this ambition,” she said. “The University has responded to their call with a strong strategic vision. But this work takes time to accomplish.”

Kathryn Lofton is also a white woman. Besides lecturing people about the importance of Halloween Costume protests, she is also a professor of Religious Studies, American Studies, History and Divinity and chair of the Religious Studies department. Her faculty page describes her work:

Kathryn Lofton is a is a historian of religion who has written extensively about capitalism, celebrity, sexuality, and the concept of the secular. … Her first book, Oprah: The Gospel of an Icon (2011) used the example of Oprah Winfrey’s multimedia productions to evaluate the material strategies of contemporary spirituality. Her forthcoming book, Consuming Religion offers a profile of religion and its relationship to consumption and includes analysis of many subjects, including office cubicles, binge viewing, the family Kardashian, and the Goldman Sachs Group. Her next book-length study will consider the religions of American singer-songwriter Bob Dylan.

Apparently writing about Oprah and the Kardashians now qualifies you to be a Yale professor.

Back to the Philosophy Department:

For instance, [Jocelyn] Wang said that many undergraduate introductory philosophy classes are history-based and focused on “dead white men,” which is not necessarily as accessible to students from varied backgrounds.

“I think the way that the undergraduate philosophy curriculum is structured contributes partially to the demographic composition of the major,” Wang said.

In other words, Miss Wang thinks that Yale’s black and Hispanic students are too dumb to read Socrates and Kant.

This is really a bullshit argument, if you will pardon my language. Any student who has been accepted to Yale is smart (and well-educated) enough to “access” Socrates. These are Yalies, not bright but underprivileged kids from the ‘hood. If language is an issue for Yale’s foreign exchange students, all of the philosophy texts can be found in translation (in fact, most of them weren’t written in English to start with.) But if you struggle with English, you might not want to attend a university where English is the primary language to start with.

However, if we interpret “accessible” in Miss Wang’s statement as a euphemism for “interesting,” we may have a reasonable claim: perhaps interest in historical figures really is tribal, with whites more interested in white philosophers and blacks more interested in black philosophers. Your average “Philosophy 101” course is likely to cover the most important philosophers in the Western Tradition, because these courses were originally designed and written by Westerners who wanted to discuss their own philosophical tradition. Now in order to attract non-Westerners, they are being told they need to discard the discussion of their own philosophical tradition in favor of other philosophical traditions.

Now, I don’t see anything wrong with incorporating non-western philosophies if they have something interesting to say. My own Philosophy 101 course covered (IIRC) Plato, Aristotle, Kant, Mill, John Rawls, the Bhagavad Gita, Taoism, and Confucianism. I enjoyed this course, and never found myself thinking, “Gee, I just can’t access this Confucius. This course would be a lot more accessible without all of the brown guys in it.”

Look, some people like talking about what a “chair” is and what “is” is, and some people like talking about police brutality against black bodies, and if one group of people wants to get together in the Philosophy department and talk about chairs and the other group wants to go to the African American Studies department, that’s fine. We don’t all have to hang out in the same place and talk about the same stuff. Sometimes, you just need to sit down and acknowledge that the thing you’re interested in isn’t 100% interesting to everyone else on the planet. Some subjects are more interesting to women, some are more interesting to men. Some are more interesting to whites or blacks or Asians, married or single people, young or old, city or country dwellers, etc. We are allowed to be different. If different people have different interests, then the only way to get people with different interests into the philosophy department is by changing the department itself to cater to those different interests–interests that are already being better served by a different department. If you turn Philosophy into Gender + Race Studies, then you’ve just excluded all of the people who were attracted to it in the first place because they wanted to study philosophy.

Speaking of which:

[Wang] added that in her experience, students can create a “culture of intimidation” by making references to philosophers without explaining them, thus setting up a barrier for people who are not familiar with that background.

I know some people can be cliquish, reveling in overly-obtuse language that they use to make themselves sound smart and to exclude others from their exclusive intellectual club. Academic publications are FILLED with such writing, and it’s awful.

But Miss Wang is criticizing what amount to private conversations between other students for being insufficiently transparent to outsiders, which rubs me the wrong way. Every field has some amount of specialized knowledge and vocabulary that experienced members will know better than newcomers. Two bikers talking about their motorcycles wouldn’t make much sense to me. Two engineers talking about an engineering project also wouldn’t make much sense to me. And I had to look up a lot of Jewish vocabulary words like “Gemara” before I could write that post on the Talmud. Balancing between the amount of information someone who is well-versed in a field needs vs the amount a newcomer needs, without actually knowing how much knowledge that newcomer already has nor whether you are coming across as condescending, simplistic, or “mansplaining,” can be very tricky.

This is something I worry about in real life when talking to people I don’t know very well, so I’m sensitive about it.

Still, [Rita Wang–a different student with the same last name] noted several classes that delved into questions of race and gender, such as a class on American philosophy that included the writings of Martin Luther King, Jr. and another course on G.W.F. Hegel that discussed his interpretation of the Haitian Revolution.

I was curious about Hegel’s interpretation of the Haitian revolution. A quick search of “Hegel Haiti” brings me to Susan Buck-Morss‘s Hegel, Haiti and Universal History. According to The Marx & Philosophy Review of Books:

The premise of Susan Buck-Morss’s Hegel, Haiti and Universal History is the arresting claim that Hegel’s renowned ‘master-slave dialectic’ was directly inspired by the contemporaneous Haitian Revolution. Commencing with a slave uprising on the French colony of Saint Domingue in 1791, the victorious former slaves declared Haiti’s independence from Napoleon’s France in 1804, three years before Hegel published his Phenomenology of Spirit, which contained the earliest published (and still the best known) rendition of the master-slave dialectic. …

However, if Buck-Morss is right to claim that Hegel was alluding to the Haitian Revolution when writing his master-slave dialectic, then Hegel’s seemingly callow optimism was not mere fancy but drew directly on lived historical experience: the achievement of Haitian slaves not only in overthrowing a savage and comprehensive tyranny but also in establishing their own modern state. Buck-Morss only hints at this possibility, however. Her aim, she says, is different: she wants to ensure that the great German philosopher is forever linked to the greatest of Caribbean revolutions (16)….

Bridge made of trash, Haiti

Ah, yes, Haiti, such a great revolution! And such a great country! Say, how have things been in Haiti since the revolution?

Dessalines was proclaimed “Emperor for Life” by his troops.[63] …Once in power, he ordered the massacre of most whites. … In the continuing competition for power, he was assassinated by rivals on 17 October 1806.[66]

The revolution led to a wave of emigration.[70] In 1809, nearly 10,000 refugees from Saint-Domingue settled en masse in New Orleans.[71] They doubled the city’s population. …

Haitian politics have been contentious: since independence, Haiti has suffered 32 coups.[134]

Cité Soleil in Port-au-Prince, one of the biggest slums in the Northern Hemisphere, has been called “the most dangerous place on Earth” by the United Nations.[138]

Haiti has consistently ranked among the most corrupt countries in the world on the Corruption Perceptions Index.[159] It is estimated that President “Baby Doc” Duvalier, his wife Michelle, and their agents stole US $504 million from the country’s treasury between 1971 and 1986.[160]

Haiti’s purchasing power parity GDP fell 8% in 2010 (from US$12.15 billion to US$11.18 billion) and the GDP per capita remained unchanged at PPP US$1,200.[2] … Haiti is one of the world’s poorest countries and the poorest in the Americas region, with poverty, corruption, poor infrastructure, lack of health care and lack of education cited as the main sources. …

Haiti’s population (1961–2003) from 4 to 10 million

Meanwhile, Haiti’s population has steadily increased from 4 million (in 1961) to 10 million (in 2003).

Sounds great. Who wouldn’t embrace a revolution that brought such peace, prosperity, and well-being to its people?

Interestingly, Wikipedia notes that Susan Buck-Morss is a member of the Frankfurt School. Wikipedia also notes that the idea that the Frankfurt School is a bunch of Marxists–or “Cultural Marxists” is just a “conspiracy theory.” Clearly there is nothing Marxist about the Frankfurt School.

But back to Yale:

This year, new faculty members who have joined the department will teach courses that diversify the curriculum, Gendler said. Philosophy professor Robin Dembroff, who is genderqueer, is teaching a social ontology course next semester that focuses on questions surrounding social construction and the nature of social categories.

Here’s an excerpt from Dembroff’s PhD dissertation summary (Princeton):

Many important social debates concern who should count as belonging to various social categories. Who should count as black? …as a woman? …as married? …it is widely assumed that these questions turn on metaphysical analyses of what makes someone black, a woman, and so on. That is, it is assumed that we should count someone as (e.g.) a woman just in case they satisfy sufficient conditions for having the property `woman’. My dissertation argues that this assumption is wrong: whether someone should count as a woman turns not on whether they satisfy the correct metaphysical analysis of what it is to be a woman, but on ethical considerations about how we ought to treat each other. …

While researching this post, I also came across what I think is Dembroff’s old Myspace account. While looking back at our teenage selves can be ridiculous and often embarassing, the teenage Dembroff seemed a much realer, more relateable human than the current one who is trying so hard to look Yale. Perhaps it isn’t the same Dembroff, of course. But we were all teenagers, once, trying to find our place in this world. I think I would have liked teenage Dembroff.

Dembroff’s dissertation, boiled down to its point, is that all of these debates over things like “trans identity” don’t really matter because we ought to just try to be kind to each other. While I think statements like, “What matters for determining ethical gender ascriptions are normative questions about how we ought to perceive and treat others, and not facts about who is a man or a woman. This claim has an important implication: It may be unethical to make true gender ascriptions, and ethical to make false ascriptions,” are quite wrong, because reality is an important thing and basing an ethics around lying has all sorts of bad implications, I find this at least a more honest and straightforward idea than all of the “gender is a social construct” nonsense.

Still, I question the wisdom of having someone who thinks that social ontology, social construction, and the nature of social categories don’t really matter teach a course on the subject. But maybe Dembroff brings a refreshing new perspective to the subject. Who knows.

Let’s finish our article:

“One thing that I have found really encouraging at Yale is that I have been made to feel as if the graduate student community as a whole — including white men — truly cares about working together to create positive change,” Demaree-Cotton said. “This really makes a big difference. The importance of all students and faculty — not just minorities — taking an active interest in these issues should not be underestimated.”

So much social signaling. So much trying to impress the legions of other privileged, to scrabble to the top, to hang on to some piece of the pie while deflecting blame onto someone else.

I wish people could leave all of this signaling behind.

Has Australia gone Totally Nuts?

Is having a loving family an unfair advantage? from ABC Radio National–the Australian Broadcasting Corporation

Or is it just philosophers?

Western moral philosophy is completely broken because “academics” do not understand the basics of how morality works.

Normal people understand morality. People who were dropped on their heads as infants generally understand morality. Philosopher Adam Smith, however, thinks,

‘What we realised we needed was a way of thinking about what it was we wanted to allow parents to do for their children, and what it was that we didn’t need to allow parents to do for their children, if allowing those activities would create unfairnesses for other people’s children’.

The test they devised was based on what they term ‘familial relationship goods’; those unique and identifiable things that arise within the family unit and contribute to the flourishing of family members.

For Swift, there’s one particular choice that fails the test.

‘Private schooling cannot be justified by appeal to these familial relationship goods,’ he says. ‘It’s just not the case that in order for a family to realise these intimate, loving, authoritative, affectionate, love-based relationships you need to be able to send your child to an elite private school.’

“I don’t think parents reading their children bedtime stories should constantly have in their minds the way that they are unfairly disadvantaging other people’s children, but I think they should have that thought occasionally,”

Jesus effin’ Christ, this guy is an idiot.

Of course, anyone who studies inequality and sets themselves up as an expert on the issue and says things like, “I had done some work on social mobility and the evidence is overwhelmingly that the reason why children born to different families have very different chances in life is because of what happens in those families,” is an idiot. We have studies on these nifty people called “identical twins” and what happens when they are adopted by two different families and raised in different environments.

What happens is not very much. Within the normal range of parenting (like, not beating your children and locking them in the closet,) measurable life outcomes like criminality, IQ, income, etc., have more to do with the kids’ genes than with their adoptive parents’ parenting.

(Where parenting probably does matter is how much your kids like you. If you’re a jerk to them, they probably won’t call you very often.)

So, no, inequality is not caused by people reading bedtime books to their kids. It’s not caused by sending them to private school, and parents sure as hell don’t need philosophers to come up with complicated theories to justify being nice to their kids, because normal people don’t suffer these delusions.

“According to Swift, from a purely instrumental position the answer is straightforward.

‘One way philosophers might think about solving the social justice problem would be by simply abolishing the family. If the family is this source of unfairness in society then it looks plausible to think that if we abolished the family there would be a more level playing field.’”

Riiiight. Remember, you pay actual money to send your kids to university so they can be taught by these people.

“‘When we talk about parents’ rights, we’re talking about the person who is parenting the child. How you got to be parenting the child is another issue. One implication of our theory is that it’s not one’s biological relation that does much work in justifying your rights with respect to how the child is parented.’

For Swift and Brighouse, our society is curiously stuck in a time warp of proprietorial rights: if you biologically produce a child you own it.”

This is because most humans would knife you before letting you take their children away from them, because the instinct to take care of our children is a basic biological drive honed by thousands of years of evolution. Morality is an evolved instinct for taking care of our children. If you don’t understand that, then you don’t understand morality, though you might get by simply by listening to the collective wisdom of thousands of generations of your ancestors who managed to successfully raise children.

“Then, does the child have a right to be parented by her biological parents? Swift has a ready answer.

‘It’s true that in the societies in which we live, biological origins do tend to form an important part of people’s identities, but that is largely a social and cultural construction. So you could imagine societies in which the parent-child relationship could go really well even without there being this biological link.’”

I am normally a peaceful person, but this guy actually inspires a deep, burning hatred, but that might just be my fear that this guy is going to try to kidnap my children speaking.

Rights are a social construct. Ethnicity is kind of a construct, and kind of a biological reality. Identifying with and getting along with one’s parents is based entirely in reality. It has to do with things like “are my parents jerks?” and “Do my parents understand me?”

So let me tell you a little secret of some relevance: I was adopted. My adoptive family was very loving and very kind. I am now, as an adult, in contact with my biological family, from whom I was, shall we say, unjustly removed. My biological family is also very loving and kind. No one here was jerkfaces; I am grateful to everyone.

I have a much, much stronger connection with the biological family I only met as an adult than I have with the adoptive family that actually raised me. I can’t help it. These people are like me in deep, fundamental ways. They have the same or similar hobbies as I do. They struggle with similar problems. They reason about the world in the same ways. We have instant shortcuts to understanding each other.

So, even though my adoptive family was super-loving and awesome and I love them and so on, the idea of trying to run a whole society like this, the idea of depriving everyone in society of that basic instinctual connection with the people around them that you non-adopted people don’t even realize you have, is kind of horrifying.