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Calculus Is the Peak of High School Math. Maybe It's Time to Change That

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For more than 30 years, calculus has been seen as the pinnacle of high school math—essential for careers in the hard sciences, and an explicit or unspoken prerequisite for top-tier colleges.

But now, math and science professionals are beginning to question how helpful current high school calculus courses really are for advanced science fields. The ubiquitous use of data in everything from physics and finance to politics and education is helping to build momentum for a new path in high school math—one emphasizing statistics and data literacy over calculus.

"We increasingly understand the world around us through data: gene expression, identifying new planets in distant solar systems, and everything in between," said Randy Kochevar, a senior research scientist at the Education Development Center, an international nonprofit that works with education officials. Statistics and data analysis, he said, "is fundamental to many of the things we do routinely, not just as scientists but as professionals."

He and other experts are still debating the best way to integrate a new approach in an already crowded high school curriculum. One of the most difficult philosophical challenges: how to prevent a statistics path from replicating the severe tracking and equity problems that have long existed in classical mathematics.

"There's a sense that calculus is up here and statistics is a step below," said Dan Chase, a secondary mathematics teacher at Carolina Day School in North Carolina, adding that he often struggles to suggest to students that, "if you are interested in engineering, that might be a good reason to go to calculus, but if you are interested in business or the humanities or social sciences, there are different paths you might go, even if you are a top-achieving math student."

On face value, new expectations for students already seem to be moving toward statistics. Both the Common Core State Standards, on which many states' math requirements are based, and the Next Generation Science Standards call for teaching data analysis and statistics, both on their own and in the process of learning other concepts.

But Kochevar warned: "There's a huge disconnect; if you look closely at the science standards, they are expecting students to have tremendous faculty with using data by middle school, but if you look at the courses, it's really not clear where those skills are supposed to be filled."

Both sets of standards need more integration of data and statistics, he and others argue, because they were developed in the early years of the big data boom. Studies tracking data worldwide through the years have found people produced 1.5 exabytes of new data in 1999—or roughly 250 megabytes of data for every person alive—but by 2011, when states were adopting and implementing the math standards, people produced more than 14 exabytes a year. Today, people worldwide produce 2.5 exabytes of data every day, and the total data have doubled every two years.

Ironically, the rapid expansion of big data and statistics use in the broader society and economy comes at the same time American students seem to be struggling with those concepts. From 2007 to 2017, 4th and 8th students' scores on the National Assessment of Educational Progress in mathematics fell significantly on problems related to data analysis, statistics, and probability—a decline that helped drive overall dips on the math test in 2017.

In part, experts say, that's because statistics and data analysis have traditionally taken a back seat to calculus in high school math, and most students already have difficulty completing the classical path.

"The idea that statistics is hard is grounded in that fact that if you took statistics 10 years ago, you had to take calculus first, and the statistics used formal probability ... with theorems that built on calculus," said Uri Treisman, a mathematics professor and the executive director of the Charles A. Dana Center at the University of Texas at Austin. He's been working with K-12 and university systems to develop a statistics pathway as an alternative to classical calculus.

It's an idea that others have pushed back on, by situating a high school statistics pathway as either advanced material only suitable for students who have already passed calculus—or a less-rigorous path for students who can't hack it in classical math.

"Any time you have multiple pathways, the advantaged will capitalize on one and that will become the 'real' one," Treisman said. "If we are going to create data science pathways, they had better be anchored in things that lead to upward social mobility and have a rigor to them. We have to make sure new pathways have at least equal status as the traditional one—and ensure everyone has access to them. If we allow [statistics and data] to be the easy or weaker path, we relinquish the commitment to equity we started with."

Mixed Signals in Calculus

For a picture of how severe that inequity can get, one only has to look at calculus.

Until about 1980, calculus was seen as a higher education course, primarily for those interested in mathematics, physics, or other hard sciences, and only about 30,000 high school students took the course. That began to change when school reformers glommed onto calculus as an early example of a rigorous, college-preparatory course, said David Bressoud, a mathematics professor at Macalester College and a former president of the Mathematical Association of America, who has examined the evolution of calculus studies.

"The more schools did this, the greater the expectation that they would do it" from parents, and district leaders—and in particular from colleges and universities, Bressoud said. "It's not just math majors or engineering majors; this has become an accepted requirement for admission to top universities. You are not going to get into Duke if you haven't taken calculus, even if you plan to major in French literature."

Today, some 800,000 students nationwide take calculus in high school, about 15 percent of all high schoolers, and nearly 150,000 take the course before 11th grade. Calculus classes have been and remain disproportionately white and Asian, with other student groups less likely to attend schools that offer calculus or the early prerequisites (like middle school algebra) needed to gain access to the course.

For example, in 2015-16, black students were 9 percentage points less likely than their white peers to attend a high school that offered calculus and half as likely to take the class if they attended a school that offered it. And if black students did get into a class, their teachers were also less likely to be certified to teach calculus than those of white students, according to an Education Week Research Center analysis of federal civil rights data.

And despite the rapid growth of calculus as a gold standard, university calculus experts argue it is a much weaker sign that a student is actually prepared for postsecondary math in the science fields than it appears.

In fact, a new report by the Mathematics Association of America and the National Council of Teachers of Mathematics found many students who took Advanced Placement Calculus AB still ended up retaking calculus in college—and 250,000 students end up needing to take even lower-level courses, like precalculus or algebra.

In the end, the report found taking calculus in high school was associated with only a 5 percentage point increase on average in calculus scores in college—from 75 percent to 80 percent. Rather, the best predictor of earning a B or better in college calculus was a student earning no less than As in high school Algebra 1 and 2 and geometry.

So if high school calculus isn't the best indicator of a student prepared for college-level math, what does it signify in college admissions? In a word: Money.

More than half of students who take calculus in high school come from families with a household income above $100,000 a year, according to a study this month in the Journal for Research in Mathematics Education. By contrast, only 15 percent of middle-income students and 7 percent of those in the poorest 25 percent of families take the course.

"Math is even more important to upward mobility now than it was 20 or 30 years ago, because ... it's seen as related to your general ability to solve problems quickly," Treisman said, adding that as a result, "there's general anxiety and panic about equity issues for anything new, even though the current [calculus] pathway is a burial ground for students of color."

Forging a New Path

Statistics and data literacy advocates hope diversifying the field of interesting and rigorous math courses could broaden students' path to STEM and other careers. As of 2017, the U.S. Bureau of Labor Statistics estimations showed that jobs that require data literacy and statistics are among the 10 fastest-growing occupations in the country.

"We have two paths forward," said William Finzer, a senior scientist at the Concord Consortium, which works with school districts to improve their math curricula. "The easier one—like the path computer science took—is to develop a course or a subject area and get schools to give it time. ... The problem of that is, it doesn't spread the opportunity very widely. It becomes concentrated in the small group of kids who elect to take the course—and it's just one more subject to take."

EDC’s Oceans of Data Institute is building learning progressions for statistics and data literacy at different grades. Randy Kochevar, who directs the institute, said they are based on the acronym CLIP, meaning students learn how to use:

Complex, multi-variable data (“We’re not just looking at hours of sunlight and heights of bean plants,” he said);

Larger data sets than students need to answer any one question, so they are forced to sort and understand relevance;

Interactively accessed data, rather than sample graphs just written out on paper; and

Professionally collected data that forces students to think about how and why it was collected—and what biases may exist in the samples.

Finzer instead envisions a more holistic approach in which at least one class a year—be it math, biology, or even civics or history—asks students to grapple with making sense of large data sets. Such an approach, he said, "would make a huge difference, because it would mean when you came out of high school, data would not be foreign to you."

EDC's Oceans of Data Institute is building learning progressions for statistics and data literacy at different grades. The progression would include concepts in statistics and data literacy, but also computer science—to be able to use common programming and tools used by data professionals—and more philosophical concepts, such as the ethical use of statistics and privacy protections.

Vol. 37, Issue 32, Pages 12-13

Published in Print: May 23, 2018, as Move Over, Calculus. Statistics Is on the Rise

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satadru
10 hours ago
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As a person who took calculus in high school, I really do wish I had actually gotten a good grounding in statistics.
New York, NY
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sarcozona
1 hour ago
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The most useful math class of my education was discrete

Ex-worker at Karnes immigrant detention center says she saw unethical behavior

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Molly Hennessy-Fiske is a staff writer for the Los Angeles Times, where she has spent a dozen years covering foreign, national, metro and business news, including reporting rotations in Afghanistan, Egypt, Iraq and Lebanon. She won an Overseas Press Club award in 2015, a Dart award from Columbia University in 2014, was a finalist for the Livingston Awards and Casey Medal and won state awards for her work in California, Florida, New York and North Carolina. She completed a Thomson Reuters fellowship in Lebanon in 2006 and a Pew fellowship reporting from Mexico in 2004. She has reported for newspapers in Boston, Miami, Raleigh, Schenectady, Syracuse, Washington and West Palm Beach. Hennessy-Fiske grew up in Upstate New York before attending Harvard College, graduating with a bachelor’s degree in social studies in 1999. She spent last year as Middle East bureau chief before returning to cover foreign/national news as Houston bureau chief.

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satadru
11 hours ago
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New York, NY
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Plants repeatedly got rid of their ability to obtain their own nitrogen

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Plants, like all living things, need nitrogen to build amino acids and other essential biomolecules. Although nitrogen is the most abundant element in air, the molecular form of nitrogen found there is largely unreactive. To become useful to plants, that nitrogen must first be "fixed," or busted out of its molecular form and linked with hydrogen to make ammonia. The plants can then get at it by catalyzing reactions with ammonia.

But plants can't fix nitrogen. Bacteria can.

Some legumes and a few other plants have a symbiotic relationship with certain bacterial species. The plants build specialized structures on their roots called nodules to house and feed the bacteria, which in turn fix nitrogen for the plants and assure them a steady supply of ammonia. Only 10 families of plants have the ability to do this, and even within these families, most genera opt out. Ever since the symbiosis was discovered in 1888, plant geneticists have wondered: why? If you could ensure a steady supply of nitrogen for use, why wouldn't you?

A global consortium of geneticists sequenced and compared the genomes of 37 plants—some symbiotic, some not; some that build nodules, some not; some agriculturally relevant, some not—to try to find out what was going on. The group's genetic analysis of the conundrum was reported in Science.

The authors considered three possible influences on the presence of the plant-bacterial partnership: (1) an ancestor underwent a predisposition event that allowed the symbiosis to evolve; (2) symbiosis independently evolved multiple times; and (3) symbiosis was also independently lost multiple times.

They figured that any genes required for a predisposing event would be present in all of the nodulating species, and found only in them and their clade—the other plants descended from the same forbears. They found zero genes meeting this criterion. So if a predisposing event did happen, it did so by coopting extant genes instead of via new ones.

Then they looked for the expansion of a gene family in symbiotic plants, since this is one method by which a trait can evolve multiple times. They didn’t find genes like this either.

To see if genes governing symbiosis had been lost—which seems weird, since nitrogen fixation is so vital—they looked for genes found only in nodulating species and plants outside their clade but not in most non-nodulating species within their clade. The existence of such a gene would imply that an ancestor would have had it but the non-modulating species would have lost it along the way.

Lo and behold, a gene called NIN (named for its function, Nodule Inception) fit the bill. The non-nodulating species had the same genes surrounding NIN as their nodulating cousins, but eight different deletion events had erased the NIN gene from different species. One other gene, also required to house the symbiotic bacteria, followed a similar pattern.

"Use it or lose it" applies to genes as much as (or maybe even more than) anything else. Genes involved in biological processes are lost if the trait they confer is unused or unnecessary. For most of the time that plants have lived on this planet, nitrogen has been limiting, so symbiosis should have been favored. But it was jettisoned at least eight different times. Maybe it was too energetically costly for most plants to keep: maybe housing and feeding the bacteria wasn't worth it, or non-nitrogen fixing bacteria took advantage and moved in.

Synthetic biologists are currently working to engineer nitrogen fixation into crops—it's a worthy goal, as it could decrease the use of fossil fuels to manufacture nitrogen fertilizer and prevent the runoff of said fertilizer into water sources. But they should bear in mind that, when left to their own devices, plants got rid of their ability to fix nitrogen time and time again.

Science, 2018. DOI: 10.1126/science.aat1743 (About DOIs).

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satadru
11 hours ago
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Fascinating.
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ACLU Report: Detained Immigrant Children Subjected to Widespread Abuse by Officials

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Richard Gonzales, reporting for NPR on a new report from the ACLU:

Among the allegations, U.S. officials are said to have:

  • Denied a pregnant minor medical attention when she reported pain, which preceded a stillbirth.
  • Subjected a 16-year-old girl to a search in which they “forcefully spread her legs and touched her private parts so hard that she screamed.”
  • Left a 4-lb. premature baby and her minor mother in an overcrowded and dirty cell filled with sick people, against medical advice.
  • Threw out a child’s birth certificate and threatened him with sexual abuse by an adult male detainee.
  • Ran over a 17-year-old with a patrol vehicle and then punched him repeatedly.

Customs and Border Protection said the ACLU report “equates allegations with fact” and ignores reforms that have been made recently.

Widespread abuse of children.

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satadru
13 hours ago
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ICE needs to be eliminated and if necessary rebuilt from the ground up with all new people, under heavy oversight, and not by Trump appointees, who have shown a cavalier disregard for the rights of people of color.

And therein lies the problem.

As an aside, leaving a 4lb premature baby in a cell, regardless of ANY OTHER AGGRAVATING FACTORS, is mind-boggling. 4 lbs is 1.8 kg. One commonly used weight cut-off for babies to be sent to a neonatal intensive care unit is 2 kg, or 4.4 lbs. If your newborn is under 2kg at birth, they aren't going home with you until they've gone to the NICU and been cleared for discharge after we know that they're eating ok and gaining weight ok. If that baby was born in the US, and that baby died in custody, that would be the death of a US citizen through actions under the color of authority of the US government.

Oh yeah, and we're also talking about leaving a pre-term baby in a dirty cell filled with sick people? Infants under about 8 weeks of age are known to have largely immature immune systems where they don't show outward signs of sickness until they are near death. A baby that age will go from looking healthy while actually having a raging septic infection to outwardly decompensating and dying in 8 hours. (This is also why you take a kid that age with a fever > 100.4F to the ER - that kid is in serious trouble. )

That a child would be left in such conditions, against medical advice, that medical advice wouldn't override the concerns of petty bureaucrats with guns... I fear I do not have words which are strong enough.
New York, NY
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Apple Has Rejected iOS Version of Valve’s Steam Link App

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Kyle Orland, writing for Ars Technica:

“On Monday, May 7, Apple approved the Steam Link app for release,” Valve said in a statement sent to Ars. “On Wednesday, May 9, Valve released news of the app. The following morning, Apple revoked its approval citing business conflicts with app guidelines that had allegedly not been realized by the original review team.”

Valve says it appealed that decision on the basis that “the Steam Link app simply functions as a LAN-based remote desktop similar to numerous remote desktop applications already available on the App Store.” That includes an official Windows Remote Desktop app from Microsoft, third-party apps from LogMeIn and GoToMyPC, and many more. There are even streaming apps for iOS which use Nvidia’s GameStream technology to remotely play titles running on a PC, just like the Steam Link app.

There are two parts to this story, both of which make Apple look bad. First, Steam Link is more or less equivalent to a VNC client. It doesn’t stream games from Valve’s servers — it streams them from a Mac or PC on your local network. As Ars points out, there are plenty of other VNC/remote desktop apps in the App Store.

The second part is the yanking of the carpet out from under Valve’s feet, by first accepting Steam Link, leading Valve to announce it officially, before rescinding the acceptance.

Apple hasn’t explained its decision (yet?), but it seems pretty obvious they’re objecting to it on the grounds that it’s a competitor to the App Store for buying games, cutting out Apple’s 30 percent cut of purchases. I think that would be true if Steam Link were a way to stream games from Valve’s servers, but I don’t think it is for a LAN-based app.

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satadru
14 hours ago
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And this friends is why walled gardens (cable television, the iOS ecosystem) are inherently bad - everyone not only wants their cut, but even worse everyone thinks they perpetually deserve a cut.
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tingham
2 days ago
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I can't even tell if this is a hot take or not.
Cary, NC
steingart
2 days ago
gruber-fuego!

Today in Uber Autonomous Murderbot News

jwz
1 Comment and 3 Shares
The Uber executives who put this software on the public roadways need to be in jail. They disabled safety features because they made testing harder. They disabled safety features because they made the ride rougher.

NTSB: Uber's sensors worked; its software utterly failed in fatal crash:

The National Transportation Safety Board has released its preliminary report on the fatal March crash of an Uber self-driving car in Tempe, Arizona. It paints a damning picture of Uber's self-driving technology.

The report confirms that the sensors on the vehicle worked as expected, spotting pedestrian Elaine Herzberg about six seconds prior to impact, which should have given it enough time to stop given the car's 43mph speed.

The problem was that Uber's software became confused, according to the NTSB. "As the vehicle and pedestrian paths converged, the self-driving system software classified the pedestrian as an unknown object, as a vehicle, and then as a bicycle with varying expectations of future travel path," the report says.

Things got worse from there.

At 1.3 seconds before impact, the self-driving system determined that an emergency braking maneuver was needed to mitigate a collision. According to Uber, emergency braking maneuvers are not enabled while the vehicle is under computer control, to reduce the potential for erratic vehicle behavior. The vehicle operator is relied on to intervene and take action. The system is not designed to alert the operator.

Deadly Accident Likely Caused By Software Set to Ignore Objects On Road:

The car's sensors detected the pedestrian, who was crossing the street with a bicycle, but Uber's software decided it didn't need to react right away. That's a result of how the software was tuned. Like other autonomous vehicle systems, Uber's software has the ability to ignore "false positives," or objects in its path that wouldn't actually be a problem for the vehicle, such as a plastic bag floating over a road. In this case, Uber executives believe the company's system was tuned so that it reacted less to such objects. But the tuning went too far, and the car didn't react fast enough, one of these people said.

Previously, previously, previously, previously, previously, previously, previously, previously, previously, previously, previously.

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satadru
14 hours ago
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And this is why Uber shut down its autonomous vehicle project in AZ.
New York, NY
mareino
1 hour ago
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Washington, District of Columbia
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