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Further Dispatches From the War on Math

Discussions of social policy where math is relevant can be useful. But a student who does not understand how an equation works will fail at both math AND social policy

Earlier this year, I reposted an article that originally ran at Salvo on the war on the teaching of mathematics as a discipline in publicly funded schools in North America. The war continues so here are some updates: Recently, three mathematicians who immigrated to the United States weighed in: The United States has been dominant in the mathematical sciences since the mass exodus of European scientists in the 1930s. Because mathematics is the basis of science—as well as virtually all major technological advances, including scientific computing, climate modelling, artificial intelligence, cybersecurity, and robotics—US leadership in math has supplied our country with an enormous strategic advantage. But for various reasons, three of which we set out below, the United States is Read More ›

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Closeup of unrecognizable little girl using smartphone, focus on hands scrolling through internet, copy space

Drawing a Line: When Tech To Keep People Safe Seems Dangerous

A dispute at the Washington Post about tech aimed at detecting child sex abuse highlights some of the issues

Princeton computer scientists Jonathan Mayer and Anunay Kulshrestha thread that needle:: Earlier this month, Apple unveiled a system that would scan iPhone and iPad photos for child sexual abuse material (CSAM). The announcement sparked a civil liberties firestorm, and Apple’s own employees have been expressing alarm. The company insists reservations about the system are rooted in “misunderstandings.” We disagree. We wrote the only peer-reviewed publication on how to build a system like Apple’s — and we concluded the technology was dangerous. We’re not concerned because we misunderstand how Apple’s system works. The problem is, we understand exactly how it works. Opinion by the Editorial Board: Apple’s new child safety tool comes with privacy trade-offs — just like all the others Read More ›

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Joke

Why Animals Can Count But Can’t Do Math

A numerical cognition researcher outlines the differences between recognizing numbers and doing math

At The Conversation, psychology professor Silke Goebel offers some perspective on the differences between the way animals and small children process numbers and the way adults do. As a researcher in numerical cognition, she tries to focus on how brains process numbers. Her research shows that Humans and animals actually share some remarkable numerical abilities – helping them make smart decisions about where to feed and where to take shelter. But as soon as language enters the picture, humans begin outperforming animals, revealing how words and digits underpin our advanced mathematical world. Silke Goebel, “Why animals recognise numbers but only humans can do maths” at The Conversation (July 28, 2021) Essentially, she says, there are two different types of counting Read More ›

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No, the Surveillance State isn’t Better in the Hands of the Public

Matt Walsh's suggestion that cameras be installed in every classroom is understandable, but it won't teach children to live in a free society

In the modern era, cameras are everywhere. Nearly every person — man, woman, or child — carries a high-end video camera with them everywhere they go on their cell phone. This proliferation of cheap surveillance equipment has caused society to largely re-think the ethics of surveillance. In previous generations, sound and video recording devices were expensive. While recording equipment in general was not out of the reach of ordinary people, miniaturized equipment was, and having enough of it to actually “surveil” someone or something was quite expensive. Today, I can have nondescript cameras set up in each room in my house for just a few hundred dollars. This ability for ordinary people to engage in constant surveillance of their own Read More ›

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Red and green men meet for a treaty. Candidates Political Debate. civilized resolution of conflicts and disputes, search for compromise. Networking in business. Negotiation platform.

Will Florida’s Law for Diversity of Thought at Universities Work?

In an internet-linked global society, protecting diversity of thought becomes even more important

A new Florida law, which took effect July 1, asks universities to survey “intellectual freedom and viewpoint diversity” annually on their campuses, to find out how free students, faculty, and staff feel “to express their beliefs and viewpoints.” Ohio Northern University law professor Scott Gerber explains, The problem DeSantis has identified is not unique to Florida — Indiana’s Republican governor signed a similar bill last month — and it traces directly to the political biases of the processes by which faculty are hired. Many of the same colleges and universities that tout tenure as a way to encourage free thought censor it by not allowing conservative and libertarian faculty candidates who think freely to get in the door. I once Read More ›

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The War of Logic vs Creativity

Are You Left-Brained? Right-Brained? That’s Nice. Now Forget It.

The rise and fall of a really Cool myth about the brain

If you have a few minutes waiting in line, you can try various tests on the internet to help you “figure out the huge dilemma”: Are you left- or right-brained? Or, at least, “Which side of your brain is more dominant?” (in 30 seconds). Buzzfeed, more elaborately, offers a Triangle Test to reveal the dominant side. This stuff is fun (maybe). But should we take it seriously? No. Many of us have heard one version or another of the pop psych myth that the brain functions as two separate departments, logic (left) vs. creativity (right). The myth carries conversations and sells workshops, books and TV shows. In reality, the brain’s two hemispheres work together for most jobs, the degree of Read More ›

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IQ test Result, Very Superior Intelligence Quotient.

If IQ Is Inherited, Is the Intellect Simply Material?

A reader writes: I was reading your writings about mind and brain, and I was wondering about how IQ relates to all of this. Since IQ seems to have a large heritable component to it, and the only thing that can be inherited genetically is physical traits, does IQ and its heritability pose a threat to mind-body dualism? It seems to me that someone with an IQ of 75 would have a very different mental experience than someone with an IQ of 145, and that they would also make decisions very differently, which, to me at least, would pose a threat to free will as well, since wouldn’t a certain level of intelligence be required to make decisions freely in Read More ›

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Collage of portraits of young emotional people on multicolored background in neon. Concept of human emotions, facial expression, sales. Listening to music, delighted, winner, shocked. Flyer for ad

AI Prof Sounds Alarm: AI “Emotion Detectors” Are Faulty Science

An industry worth over $30 billion uses emotion recognition technology (ERT) on school children and potential hires

Kate Crawford, a principal researcher at Microsoft, and author of Atlas of AI (2021), is warning at Nature that the COVID-19 pandemic “is being used as a pretext to push unproven artificial-intelligence tools into workplaces and schools.” The software is touted as able to read the “six basic emotions” via analysis of facial expressions: During the pandemic, technology companies have been pitching their emotion-recognition software for monitoring workers and even children remotely. Take, for example, a system named 4 Little Trees. Developed in Hong Kong, the program claims to assess children’s emotions while they do classwork. It maps facial features to assign each pupil’s emotional state into a category such as happiness, sadness, anger, disgust, surprise and fear. It also Read More ›

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The concept of opposites, hand choose wood blog with plus and minus on blue background, copy space.

The Human Mind Adds Better Than It Subtracts

Getting control of the tendency might be a key to better decision-making skills, researchers say

When trying to solve a problem, a recent study showed that it is much easier for us to add things than to subtract them: In a new paper featured on the cover of Nature, University of Virginia researchers explain why people rarely look at a situation, object or idea that needs improving — in all kinds of contexts — and think to remove something as a solution. Instead, we almost always add some element, whether it helps or not. Jennifer McManamay/University of Virginia School of Engineering and Applied Science, “Why our brains miss opportunities to improve through subtraction” at ScienceDaily The paper is closed access. In a sense, we all know this. When we want to make something look better, Read More ›

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Side view of a woman playing with her infant child. Smiling woman talking to her baby sitting on a couch.

Babies Can Understand Whole Sentences Before They Can Speak

Before uttering their first word, a new study suggests, children can understand what groups of words mean together

In a recent study of 11–12 month olds published in Cognition, researchers found that infants on the verge of saying single words themselves can already process complete sentences such as “Clap your hands.” The research sheds light on the difficulties adults have learning second languages if they focus too intensely on single words: Dr Barbora Skarabela, of the School of Philosophy, Psychology and Languages Sciences, said: “Previous research has shown that young infants recognise many common words. But this is the first study that shows that infants extract and store more than just single words from everyday speech. This suggests that when children learn language, they build on linguistic units of varying sizes, including multiword sequences, and not just single Read More ›

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child hands showing a colorful 123 numbers agains wooden table. Concept of Child education, learning mathematics and counting

The Fundamental Problem With Common Core Math

Intuition relies on skill, not the other way around

In 2010, a bold effort to reform math curriculum was adopted by the majority of the United States. Known as “Common Core Math,” the goal of this endeavor was to establish a common foundation of mathematics education across the country, and to help bolster not only students’ mathematical abilities, but also their mathematical intuition. The goal was to help students think about math more deeply, believing that this will help them work with mathematics better in later years. Before discussing problems with this approach, I want to say that I appreciate the idea of helping students think more deeply about mathematics. After years and years and years of mathematics education, many students wind up thinking about mathematics as merely a set Read More ›

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group of school kids raising hands in classroom

Practicing the Basics: Teaching Math Facts in the Classroom

How to help students make deeper connections within mathematics with creative games.

Many people learn to hate math early on. One of the places where people learn to hate math first is in high-stakes speed testing for math facts. This has caused quite a bit of angst in mathematics education for people on both sides of this issue. On the one hand, some have advocated for getting rid of math facts memorization altogether. On the other hand, others have doubled-down, saying that we need speed tests in order to make sure that the cognitive load of arithmetic is limited for later mathematics work. While I fall more into the latter camp than the former, I do think that a more balanced approach to mathematics education may help students in the long run.  Read More ›

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The Paradox of the Smallest Uninteresting Number

Robert J. Marks sometimes uses the paradox of the smallest “uninteresting” number to illustrate proof by contradiction — that is, by creating paradoxes

In this week’s podcast, “The Chaitin Interview IV: Knowability and Unknowability,” Walter Bradley Center director Robert J. Marks interviewed mathematician Gregory Chaitin on how he proved that the number that determines whether computer programs are elegant (in the sense of maximally efficient) is “unknowable.” As Dr. Chaitin explained in the segment published yesterday, any solution would be contradictory. Thus, his proof is a proof by contradiction. By way of illustrating the concept of proof by contradiction, Dr. Marks then offered his proof by contradiction that “all positive integers — numbers like 6 or 129, or 10 100 — are interesting.” This portion begins at 19:45 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: If [some Read More ›

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Serious african american student in headphones studying foreign language online

Researchers: We Learn Better Using Paper Than Laptops and Phones

Writing on paper involves more of our whole minds and even more of our bodies — and that aids retention

It doesn’t sound like good news in a digital society but at least hear the reasoning: A study of Japanese university students and recent graduates has revealed that writing on physical paper can lead to more brain activity when remembering the information an hour later. Researchers say that the complex, spatial and tactile information associated with writing by hand on physical paper is likely what leads to improved memory. “Actually, paper is more advanced and useful compared to electronic documents because paper contains more one-of-a-kind information for stronger memory recall,” said Professor Kuniyoshi L. Sakai, a neuroscientist at the University of Tokyo and corresponding author of the research recently published in Frontiers in Behavioral Neuroscience. The research was completed with Read More ›

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Schoolchildren writing on chalkboard in classroom during math lesson

Antiracism In Math Promotes Racism and Bad Math

If you are scratching your head over how math might be racist, you are not alone

Recently, a conglomeration of California education associations got together to work on a series of resources for mathematics teachers. The goal? Eliminate racism in mathematics classes by promoting Equitable Math. If you are struggling to imagine how mathematics could be racist, you are not alone. I am certain there exist racist teachers, and probably teachers who exhibit racist expectations of their students. I would support any reasonable action to get rid of or reform such teachers. But that is not the primary goal of these resources. The website, equitablemath.org, instead believes that the very way that mathematics is commonly taught is not just racist, but is specifically white supremacist. While I consider myself to be somewhat of a mathematics reformer Read More ›

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Educational kids math toy wooden board stick game counting set in kids math class kindergarten. Math toy kids concept.

Yes, There Really Is a War on Math in Our Schools

Pundits differ as to the causes but here are some facts parents should know

The Oregon Department of Education (ODE) recently encouraged teachers to register for training that encourages “ethnomathematics,” an education trend that argues, “among other things, that White supremacy manifests itself in the focus on finding the right answer”: “The concept of mathematics being purely objective is unequivocally false, and teaching it is even much less so,” the document for the “Equitable Math” toolkit reads. “Upholding the idea that there are always right and wrong answers perpetuate objectivity as well as fear of open conflict.” … An associated “Dismantling Racism” workbook, linked within the toolkit, similarly identifies “objectivity” — described as “the belief that there is such a thing as being objective or ‘neutral’” — as a characteristic of White supremacy. Instead Read More ›

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Propaganda and brainwashing of the influential mass media concept. Vintage TV set with hypnotic spiral on the screen.

Contradictory Beliefs Are a Feature, Not Bug, of Critical Theory

As a historian of totalitarianism has pointed out, “The aim of totalitarian education has never been to instill convictions but to destroy the capacity to form any.”

“Intersectionality” is the claim by critical theorists that various kinds of oppression against victim groups intersect, in the sense that all oppression ultimately has the same source — you. In an essay at Substack titled “Intersectionality Has Hit the Stop Sign,” Tom Knighton argues, too optimistically in my view, that intersectionality is falling victim to its own contradictions. I believe he misunderstands the nature of the problem. Let me explain why. He cites the example of women’s rights vs. trans rights. A major victory for women’s rights is all-female sports, which allow women to compete without having to overcome the natural physical advantages of men. A major victory for trans rights is to allow men who identify as women to Read More ›

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The red human figure extends its influence to the neighboring figures. Spreading ideas and thoughts, recruiting new members. Infection of other people, zero patient. Leader and leadership, new team.

To Succeed, Understand Difference Between Influence and Power

Do you wonder why some people are listened to and not others, regardless of the value of their ideas? Well, read on…

At business mag Forbes, some have begun to consider the difference between influence and power: Swarthmore College has been rated the best liberal arts college in the U.S. by Academic Influence, a new college rankings method that uses artificial intelligence technology to search massive databases and measure the impact of work by individuals who’ve been affiliated with colleges and universities throughout the world. Last Monday, Academic Influence released its first-ever ranking of American liberal arts colleges – those four-year institutions that are relatively small in size, focus on bachelor’s level education, emphasize direct engagement with professors, provide an enriched residential experience, and insist on broad grounding in the liberal arts along with focused study in a major. In brief, here’s Read More ›

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Guérilla urbaine

Gödel’s Incompleteness Theorems: The Cause—and Cure—of Wokeness?

Why do so many people today think there are only arguments, not facts?

In modern “woke” ideology, there are no facts, only arguments which express cultural power— based on the acceptance of those arguments by current society. In such ideologies, it is not important whether or not the arguments are logically consistent or if they are true in any real sense. What is important is whether or not they achieve the desired results in politics and society. This is not a criticism. It is a description of their methodology (for a review of the academic literature on the subject, see the book Cynical Theories by Helen Pluckrose and James Lindsay. Many people wonder how we got here. Why do so many scholars actively reject logic as a method of finding the truth, and Read More ›

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Will Machine Learning Disrupt Academic Rankings?

A case study in the best computer science and artificial intelligence programs

Note: Our author, Ross Gulik, an educational consultant who closely follows the academic ranking industry, offers us a look at how such rankings are created and how they might be improved. 1 Introduction to AcademicInfluence.com AcademicInfluence.com is a new website that claims to do academic rankings right. Getting academic rankings right has become a pressing concern for higher education. As AcademicInfluence.com correctly observes on its methodology page, schools face enormous pressure to perform well in the big annual rankings. The big academic ranking organizations (such as US News and Times Higher Education) carry enormous weight. If a school slips in these annual rankings, it can affect student enrolments, the bottom line, and the prestige of the institution. This pressure leads Read More ›