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I’m confused about math

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I was interested in this map that purports to rate the quality of math teaching. It’s from the National Council on Teaching Quality, and at first I thought it explained a phenomenon I’ve noticed.

Minnesota grade schools aren’t doing a good job preparing students with math skills. It’s the #1 obstacle to young people coming into science and math majors, especially biology (if they aren’t strong in math in the first place, they aren’t going to even try physics; everyone wrongly thinks you don’t need math to do biology.) We get students who fail the algebra requirement*, which surprises me every time. What are the schools doing? Back in my day, the high schools had a college prep track which told you that you at least needed pre-calc (trigonometry, etc.) to get into a good college. How do you get through middle school without algebra and geometry?

They have a state-by-state breakdown of their evaluation. I looked at Minnesota’s. It expresses a lot of sentiments I agree with: we should “require districts to adopt and implement high quality math curricula,” but they say we fail on that. We should “require elementary programs to address math specific pedagogy,” and again they say we don’t, but I don’t have any experience working directly with grade school math programs, so I’m taking their word on it. Then I notice that the way NCTQ assesses schools is with checklists of various aspects of teaching, and it’s all yes/no stuff. What are “high quality math curricula”? It seems to me that there ought to be something a little more quantitative about that.

Then I looked at their evaluation of our universities’ math teacher prep, and we get low marks, but again there’s a lack of specificity. All they score is how many hours of instruction math education students get in 4 areas, and the only evaluations are “does not meet” or “fully meets” their quota for instruction hours. And the variation is wild! On “Numbers & Operations+Algebraic Thinking,” for instance, some of our colleges provide 0 hours of instruction, while others provide 100 hours. I think the assessment is a bit inconsistent, and maybe not aligned with the goals of the specific programs.

I’m not trying to make excuses for the schools. I’ve been looking at their products, the students, for years and have been unsatisfied with their end result.

They declare that “13% of Minnesota programs earn an A or A+ by dedicating adequate instructional time to both math content and pedagogy” where again, they’re scoring them by this single metric. 26% of our colleges fail by that metric. Also, to get an A, the “program requires at least 135 instructional hours across the five topics and at least 90% of the recommended target hours for each topic,” but there are only four topics listed. I guess someone failed arithmetic, or copy editing.

I had to look at Alabama‘s evaluation. The South in general is scoring very well on math education, so good for them. They get lots of checkmarks in the binary metrics, for instance Alabama does “require elementary programs to address math specific pedagogy” where Minnesota doesn’t, but now I’m wondering what that means. “16% of Alabama programs earn an A or A+ by dedicating adequate instructional time to both math content and pedagogy,” but 24% fail.

I think we could all improve the quality of math education, but I didn’t find any of their reports particularly useful, and they seemed almost arbitrary. So I looked up the NCTQ, and discovered that it was the product of a conservative think-tank, and was associated with the US News & World Report, the magazine that publishes scores for colleges every year (I do not like them, even if my university scores well in their assessments). Then I read this review:

Now, to be candid, I am fed up with our nation’s obsession with data-driven instruction, so I don’t share the premises of the report. The authors of this report have more respect for standardized tests than I do. I fear that they are pushing data-worship and data-mania of a sort that will cause teaching to the test, narrowing of the curriculum, and other negative behaviors (like cheating). I don’t think any of this will lead to the improvement of education. It might promote higher test scores, but it will undermine genuine education. By genuine education, I refer to a love of learning, a readiness to immerse oneself in study of a subject, an engagement with ideas, a willingness to ask questions and to take risks. I don’t know how to assess the qualities I respect, but I feel certain that there is no standardized, data-driven instruction that will produce what I respect.

And then there is the question that is the title of this blog: What is NCTQ?

NCTQ was created by the Thomas B. Fordham Foundation in 2000. I was on the board of TBF at the time. Conservatives, and I was one, did not like teacher training institutions. We thought they were too touchy-feely, too concerned about self-esteem and social justice and not concerned enough with basic skills and academics. In 1997, we had commissioned a Public Agenda study called “Different Drummers”; this study chided professors of education because they didn’t care much about discipline and safety and were more concerned with how children learn rather than what they learned. TBF established NCTQ as a new entity to promote alternative certification and to break the power of the hated ed schools.

I should have read that before wasting all that time trying to interpret the data in the report. And now I understand how Texas and Florida did so well in the NCTQ evaluations.

We still have a problem in poor math preparation. I don’t think turning a bunch of conservative ideologues loose on the schools will solve it.


*I should mention that my university invests a lot of effort in remedial instruction to bring students’ math skills up to the level they need to succeed in our majors.

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Long COVID in Young Children, School-Aged Children, and Teens | Pediatrics | JAMA Pediatrics | JAMA Network

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  • Original Investigation

    Characterizing Long COVID Symptoms During Early Childhood

    JAMA Pediatrics

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    More prevalent than asthma
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    I received a 30-month jail sentence for nonviolent resistance. Why so harsh? Because protest works | Indigo Rumbelow

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    The judge wanted us to show remorse, but I can’t apologise for fighting the climate disaster

    Last week, at Minshull Street crown court in Manchester, I was sentenced to two and half years in prison for conspiring to intentionally cause a public nuisance. The prosecution’s case was that I intended to “obstruct the public or a section of the public in the exercise or enjoyment of a right that may be exercised or enjoyed by the public at large” – in other words, that I was part of Just Stop Oil’s plan to obstruct planes at Manchester airport. I did intend that – and I have a defence for my actions.

    The offence of public nuisance – which falls under the Criminal Law Act 1977 and the Police, Crime, Sentencing and Courts Act 2022 – was traditionally and frequently used to prosecute significant environmental offences. It punished big corporations causing real harm to the general public by poisoning water, polluting air, emitting dust and noise or dumping chemical waste. There is no irony lost in the fact that the same offence in statutory form is now being zealously deployed to prosecute environmental protesters.

    Indigo Rumbelow is co-founder of Just Stop Oil. She is serving a sentence in HMP Styal

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    Scientists Find DNA Proof of Swine Feces in North Carolina Homes

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    In Duplin County, North Carolina, there is a pollutant that hangs in the air, the water and the soil. It tumbles in the breeze and into homes through open windows, settling as a thin film of dust on their kitchen tables. It gloops together in masses of sludge in the surface water that feeds their creeks and streams. The fresh, nostalgic smell of seawater along the county coast has dissipated, replaced by a permanent foul smell from nearby swine factory farms, similar to that of a decomposing body, residents say. Policymakers have long ignored their complaints but new research from Johns Hopkins University could finally show scientific evidence of pollution that officials can’t ignore.

    It wasn’t always this way, says Devon Hall, who grew up in Duplin County. Over the past few decades, Hall tells Sentient that he has witnessed the rapid expansion of swine factory farms in the region. Now, hogs generate 10 billion gallons of waste across the state annually, so much so that their pollution can be seen from space. Neighbors not only deal with the pungent smell that emanates from these farms, but are also more at risk of adverse health effects from pollution. Constant exposure to pig waste can lead to lung problems, brain damage and an increased risk of bacterial infections.

    Hall, who co-founded Rural Empowerment Association for Community Help (REACH), says interactions with policymakers and industry are fraught. “Has anyone died?” was one county commissioner’s response to residents presenting their concerns, Hall recalls. “That was a bit cold because that’s what you’re asking for? You want body bags until you believe us? Take some stock in the science,” he says.

    Air pollution from Duplin County farms is linked to 98 premature deaths annually, according to The Washington Post’s reporting. But across the U.S., food production results in 15,900 air quality–related deaths each year, mainly from fertilizer application and livestock waste. Yet a key gap remains in proving pollution exposure and, consequently, harm in Duplin County. Christopher Heaney, associate professor at Johns Hopkins Bloomberg School of Public Health, has been working to close that gap and develop a new tool in collaboration with residents that can be used to identify when air pollution comes from pig waste.

    Using microbial source tracking, Heaney identified a specific bacterial gene sequence called “Pig-2-Bac” that is unique to pig fecal waste. That means that if this bacteria is detected, there is no way the feces could be from a cow, a bird, a human or any other sort of wild animal — which is important, considering the pushback from industry and politicians.

    Although a 2017 report by a former EPA and USDA employee found hog feces DNA particles had reached residents homes, this work goes further. Hall and Heaney developed a diagnostic tool that shows this particular harmful bacteria “Pig-2-Bac” has not only reached residents’ doorsteps, but has actually made its way inside their homes, too.

    “If there’s Pig-2-Bac detected on that swab, on that sample that came from the inside of your house, we know that shouldn’t be, plain and simple. I don’t have hogs inside my house,” Hall tells Sentient. “Most of us don’t have hogs even on our properties…So we know it’s airborne, and that’s how it’s getting into the house.”

    Using a specialized Q-tip, Hall and other residents swab the inside and outside of their homes for the pig dust before Heaney analyzes the sample in the lab to measure both the frequency and quantity of this pig sequence. After examining over 1,400 samples from roughly 300 households, they found the highest concentration of fecal waste in homes of neighbors who lived close to or worked in the industrial farms.

    “It’s not just an indicator of swine fecal filth, which has incredible implications for people’s dignity, their overall health, the ability to live with the absence of a nuisance,” Heaney says, but there are other impacts to consider “within the context of antimicrobial resistance, which represents important health implications for the neighbors.” The presence of Pig-2-Bac is strongly associated with antimicrobial-resistant Staphylococcus aureus strains — of concern, considering the growing prevalence of superbug diseases at the same time that new antibiotic treatments remain scarce.

    Science and community collaboration have long gone hand-in-hand in Duplin County to identify pollution sources. The epidemiological effort was largely led by Steve Wing, a former researcher at the University of North Carolina Chapel Hill and Heaney’s former mentor, who studied how agricultural industries were emitting harmful chemicals like hydrogen sulfides that were disproportionately affecting Black residents and residents of color. Heaney says industry and officials often dismissed their research and community grievances as nothing more than a malodor, rather than evidence of real health impacts.

    Heaney is continuing Wing’s legacy of digging into pollution exposures in Duplin by working in collaboration with residents like Hall. One poignant example of their work was finding evidence of fecal contamination in surface water and drinking water. But Duplin County officials again dismissed it, saying there was no proof that contamination was coming from farmed pigs, as it could just be from wild animals, Heaney says.

    “I remember hearing this and saying, ‘Oh my, this is just such a challenging dynamic for the communities,’” Heaney tells Sentient. The writing was on the wall, he says — there are over “2,000 permitted swine concentrated feeding operations, each with approximately having a football field-sized lagoon containing fecal and urine waste,” and laboratory-based evidence of impaired water quality, but it still wasn’t enough to implicate the industrial hog operations in their eyes.

    Yet Heaney was undeterred, deciding to zero in on specific markers like Pig-2-Bac that would unequivocally link these hog operations to the ongoing contamination issues in Duplin County.

    Industrial hog operations in Duplin County spray pig fecal matter into the air via massive sprinklers, raining down upon locals. Such facilities and their waste (stored in open cesspools) are disproportionately concentrated in Black, Latino and Native American communities — creating a long-standing legacy of environmental racism.

    A 2023 study found that the largest CAFOs in Duplin were located where more than 56 percent of residents were people of color, and that exposures to associated chemicals were 66 percent higher for households where members spoke poor English, and 13 percent higher for low-income households. CAFO stands for Concentrated Animal Feeding Operation; these are more commonly called factory farms or industrial livestock operations.

    Beyond the more obvious physical health impacts, living adjacent to pollutant-heavy and smelly industries brings a mental toll, too. The World Health Organization defines health as not merely the absence of disease, but the ability to achieve a full state of physical, social and emotional well-being. Research indicates that people who live near factory farms have higher risks of respiratory problems and mental health issues.

    In North Carolina, hurricanes regularly wreak havoc and breach manure lagoons, causing them to contaminate local waterways. Beyond that, CAFO owners have also illegally drained their lagoons prior to hurricanes by spraying the waste into the air, posing a serious public health problem for locals.

    Multiple groups have worked to prove environmental racism in court cases about the pollution, the most recent of which REACH is involved in, along with the environmental law organization Earth Justice. Their complaint aims to change the exemption for industrial farms in reporting their air emissions to the Environmental Protection Agency.

    Hall wants to be clear about the intent. “​​I’ve never advocated to put anyone out of business. We’ve learned there’s superior cleaning technology that’s better for the environment, better for human health. So implement it. Don’t tell me that it’s not economically feasible. The [industry] not wanting to change the same method of disposing of swine waste tells me that they really don’t care,” Hall says.

    North Carolina’s laws limit the ability of residents to put forth nuisance lawsuits against the state’s agricultural industry — the bulk of which belongs to Chinese-owned Smithfield Foods. “I think that was shameful on their part, not just because they passed those bills, but because the industry belonged to another country,” Hall says. “I know there’s politics involved, but at the same time, when you hinder your state regulatory agencies from doing their work and it’s proven that these facilities, the way they’re operating, are harming people — then I’m not sure what to say about our North Carolina assembly.”

    Environmental justice lawyers say the data gleaned from Heaney’s diagnostic tool will bolster evidence for filing future complaints against agricultural polluters. The EPA is also due to revise its Clean Air Act standards, which will require factory farms to monitor and report their emissions. But it’s unclear if this will actually happen under the leadership of Lee Zeldin, who plans to deregulate the agency. A recent Senate vote also limited the regulation of air pollutants from industries.

    Duplin County is used to the pushback from politicians and industry, but will continue to fight for clean air and water, Hall says. “It is tiresome. It does take a psychological toll on us. But at the same time, what do you do exactly? I can’t just sit down and do nothing, because I still live here. Because I’m not planning to pack up and move. This is home to me.”

    Update: This story has been updated to include a link to the published study.

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    Flat out unfair? A progressive take on taxes | Datawrapper Blog

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    Hi, this is Luc, working in the visualization team. If you like visualizing data and, like me, often procrastinate to do your taxes, I present you here my best tax filing avoidance achievement: visualizing data about taxes!

    When paying income taxes, the rate of taxation often depends on your life circumstances. A common rule is that taxes take a progressively higher percentage out of higher incomes, what's known as a progressive tax rate. In other words, the more you earn, the more of it you pay in.


    The charts above represent the tax rate for a single person without children at various income levels, measured as a percentage of each country’s average income. Columns on the left represent lower-income households, while columns on the right have higher income. The steeper the gradient between them, the more progressive that country's tax system is.

    How progressive are European income tax rates?

    Tax rates in Europe are on average rather progressive, but the situation varies a lot between countries.

    • For Belgium, the difference between the highest and lowest rate is almost 30 percentage points, which makes its system the most progressive in Europe. Most western European countries likewise have a fairly progressive range of at least 20 percentage points. Spain has Europe's lowest tax rate for the poorest households (6.5%), 21.9 percentage points less than its highest tax rate.

    • Countries with a less progressive tax rate than the EU27 average are a diverse group. Germany, Slovenia, or Denmark, all still fairly progressive, have higher-than-average taxes for both their poorest and richest residents.

    • Other countries, notoriously Switzerland, combine a less progressive gradient with low tax rates for all income groups. This is rather to the advantage of the wealthiest residents, who pay just 22.8% of their income, only 10 percentage points more than the lowest earners.

    • The most surprising fact to me was to discover that many eastern European countries have a barely progressive tax rate, below 10 percentage points, or even a totally flat rate like Hungary, where tax is 33.5% for all income groups.

    Whether progressive taxation disturbs the free market, as conservative economists argue, or distributes the fruits of labor more equally and creates a more harmonious society with positive effects on the economy in the long run, is a contentious issue in the political realm. Income tax rates also don’t capture the whole tax situation: The data above doesn’t account for tax exemptions and relates only to income, not investments, which is how the wealthiest persons actually make most of their money.

    I hope you enjoyed this tour d'horizon of the tax situation in Europe. We'll be back next Thursday with another Weekly Chart.

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    Virginia activist charged with vandalism after drawing crosswalk at intersection | Virginia | The Guardian

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    After officials in Charlottesville, Virginia, reportedly ignored his pleas to implement a pedestrian crosswalk at a dangerous intersection, traffic safety activist Kevin Cox drew a crossing with chalk.

    Authorities responded by covering Cox’s handiwork with black paint and charging him with vandalism in a case that evidently demonstrates how acrimonious relations can sometimes get between local government bureaucrats in the US and those who say they are trying to hold them to account.

    As the Charlottesville news station WVIR put it, Cox is well known in the community for his outspoken pedestrian safety advocacy. He had recently focused his efforts on a municipal intersection where a 64-year-old woman was struck by a motorist and killed while trying to cross the road to get to work in October.

    Cox said he had since pleaded with city officials to lay down a crosswalk at that intersection. Those efforts went nowhere, so he said he took a line marker as well as a can of spray chalk to fashion a makeshift crosswalk on 17 May – a Saturday – as a crowd of onlookers cheered him.

    He also reportedly wrote an email to Charlottesville’s city manager which read: “There is a marked crosswalk now [at the intersection in question] in spite of you … It’s chalk[,] not paint[.] Please replace it with a real one.”

    Police subsequently called Cox and accused him of committing vandalism. He soon surrendered and was booked with intentional destruction of property, which carries up to a year in jail as well as a maximum fine of $2,500, WVIR reported.

    A police report that Cox shared with the news station alleged that officers were unable to determine whether his improvised crosswalk had been created with permanent paint. Officials determined the crosswalk could not be removed, so city workers covered it with black paint.

    Cox has gotten a lawyer and was given a trial date tentatively scheduled for 14 July.

    “They have provoked me,” Cox told WVIR. “It’s not going to stop me.

    “This is a common cause for many people in the city. It’s all about our day-to-day quality of life on the streets and the sidewalks, and everyone is affected by that.”

    A Charlottesville municipal spokesperson said on Tuesday that the city would not comment on the case against Cox because it was pending.

    Many know Charlottesville as the site of the unrelated 2017 white supremacist rally objecting to the removal of a statue of the Confederate general Robert E Lee. A demonstrator protesting against the white supremacists was murdered by a neo-Nazi sympathizer who intentionally drove a car into her as well as others.

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