Sage Interact: Taylor Polynomials


I've added another Sage Interact to the Python/Sage page. The text can be copied into any Sage Cell Server, like the three that are on the Sage Sandbox page. Just press "Evaluate" and the Sage Interact appears; This Interact allows you to generate Taylor polynomial approximations for a function about some center. It's a little unpolished because you set the function to graph, the center of the expansion, the width (xrange shown is 2*width) and the minimum and maximum y values for the figure in the code itself. The resulting Sage Interact is programmed to handle the Taylor polynomials of degree 1 through 7. Simply click the boxes to display which  the polynomials you want to see. The screenshot above shows the function e^{x} with center 1 having a dot on it. Of course you can modify the size or not plot the point if you find it too distracting.

Don't overlook the "TaylorPoly.pdf" in the bottom left.TP2

Right click on the link to download a pdf of the figure for your own use. This is a quick and easy way to generate examples for, say, a Powerpoint beamer presentation.

I also need to mention that Detlef Reimers, the author of the lapdf package for LaTeX, left some comments. One is on the Common Core Questions page where he shares his philosophy behind the lapdf package which and states, "The audience for such a packet full of math, programming utilities (loops) and many complex drawing commands - directly based on the fore runner of PDF, PostScript - would generally be the scientific orientated people.". I agree. If you haven't tried the package then you definitely need to. My complaint at the time was the lack of good documentation--the package has a lot to offer but you have to be willing to puzzle through the details on how to make things work. The good news is that the package is currently undergoing an update which will provide some more documentation and fix the problems I noticed with ellipses. In a second comment, at the bottom of the lapdf packge post, Mr Riemers mentions that lapdf has some ability to draw chess diagrams--you can go to the links and check out some of what he's working on. I'll be looking forward to seeing the the new version of lapdf show up on CTAN.

Here are some stories that caught my eye over the last week.

  • Hikaru Nakamura won the 2016 Tradewise Gibraltar Masters chess tournament on tiebreaks over MVL; both players had 8/10. Nakamura bested MVL 3-2 in speed chess.
  • John Cleese of Monty Python fame was in a ZeroHedge article, "John Cleese says political correctness has gone too far, especially on America's college campuses, where he will no longer go to perform...Cleese, having worked with psychiatrist Robin Skynner, says there may even be something more sinister behind the insistence to be always be politically correct.
    "If you start to say we mustn't, we mustn't criticize or offend them then humor is gone. With humor goes a sense of proportion. And then as far as I'm concerned you're living in 1984.""
    Serious words from a funny man.
  • EAGNews with headlines that over 15,000 Chicago school employees make over $100,000 a year. "So what is the overall record of student learning and achievement in the Chicago district? Absolutely awful. “Four out of ten CPS freshmen don’t graduate,” reported in 2014. “Ninety-one percent of CPS graduates must take remedial courses in college because they do not know how to do basic math and other schoolwork. Only 26 percent of CPS high school students are college-ready, according to results from ACT subject-matter tests.“Education should be the great equalizer; but in Chicago, public education is more of a holding cell than a launch pad.”" Bad education+expensive price tag+ lack accountability =waste of money.
  • The Washington Post reports there is a noticeable performance difference between students taking Common Core with a computer versus those using pencil and paper, "...about one in five took the exam with paper and pencil, and those students — who tested the old-fashioned way — tended to score higher than students who took the tests online...It’s not clear whether the score differences were due to the format of the testing, or due to differences in the backgrounds of the students who took the two different types of test, according to the Feb. 3 Education Week report. But the publication reported that in some cases the differences were substantial enough to raise concerns about whether scores on the exam — the Partnership for Assessment of Readiness for College and Careers test — are valid and reliable enough to be used for teacher evaluations or school accountability decisions." Did you catch that? The differences are, apparently, valid and reliable enough to gauge the student but not the teacher or school.
  • I'd been ignoring this story until the The Columbian piqued my interest with a flashier headline (linking the Babylonians with calculus) for a reprint of a Washington Post piece, "The astronomers of Babylonia, scratching tiny marks in soft clay, used surprisingly sophisticated geometry to calculate the orbit of what they called the White Star — the planet Jupiter. These tablets are quite incomprehensible to the untrained eye. Thousands of clay tablets — many unearthed in the 19th century by adventurers hoping to build museum collections in Europe, the United States and elsewhere — are undeciphered." Until a key breakthrough, "... The calculations merely describe Jupiter’s motion over time as it appears to speed up and slow down in its journey across the night sky. Those calculations are done in a surprisingly abstract way — the same way the Oxford mathematicians would do them a millennium and a half later. “It’s geometry, which is itself old, but it’s applied in a completely new way, not to fields, or something that lives in real space, but to something that exists in completely abstract space,” Ossendrijver said. “Anybody who studies physics would be reminded of integral calculus.”Which was invented in Europe in 1350, according to historians.""

Sagetex: Rational Functions 2


I've added another problem to the Sagetex: functions page. This is a rational function with two vertical asymptotes, a horizontal asymptote and no holes. In the coming weeks I'll work on putting a problem together that has a hole in it.

Here are some stories that caught my eye this week:

  • It's not math and it's not chess--but if you play chess you probably will have some interest in's story on a Google designed artificial intelligence based computer, called AlphaGo, crushing the "...reigning three-time European Go champion Fan Hui....However, AlphaGo is not going to stop. Next time it will face one more Go guru – the legendary Lee Sedol, “the top Go player in the world over the past decade.". Some decent videos are posted on the page and don't skip the link to Google's official blog posting on the event.
  • The Tata Steel Chess Championship is almost over. Magnus has assured himself with at least a tie for first. Caruana is the only player to have a chance to catch him but he's losing against Tomashevsky on move 61.
  • According to, a federal judge took aim at some policies at Iowa State University, "As far as Iowa State University President Steven Leath was concerned, censoring the T-shirts of a campus group advocating the legalization of marijuana was simply good politics, a way of maintaining friendly relations with state officials. It was also clearly unconstitutional, according to a federal judge who last week told Leath and his subordinates to cut it out....."We are gratified that the court understood that ISU bowed to political pressure when it imposed special restrictions on NORML ISU," said First Amendment lawyer Robert Corn-Revere, who represented Gerlich and Furleigh. "This violated the most basic First Amendment requirement that the government cannot discriminate against a student group or its members because it disagrees with their viewpoints. This decision vindicates the right to freedom of expression not just for the courageous students who brought this case, but for the students of all public universities.""
  • The inspiring words of Martin Luther King were under attack recently. From the Daily Emerald, "“I have a dream that my four little children will one day live in a nation where they will not be judged by the color of their skin, but by the content of their character. I have a dream…".....The quote is not going to change, but that decision was not made without some hard thought by the Student Union Board." Maybe next year?!?
  • USAToday on "...a new study made public Tuesday scratches beneath the surface to pin down just how many students in major U.S. metropolitan areas can actually read or do math proficiently. The results: Startlingly few. If all of Detroit’s fourth-graders took the well-respected National Assessment of Educational Progress (NAEP) tests, just 120 African-American fourth-graders across the entire city, by researchers’ estimates, would score “proficient” or above in math.“This is not a misprint,” the authors warn.....In Atlanta, just 60 Hispanic fourth-graders and 40 Hispanic eighth-graders would score proficient or above in reading." More depressing stats can be found in the article.
  • The USAToday link above might get you thinking why public schools are so shockingly bad. Truth in American Education has presidential candidate Carly Fiorina weighing in: "...all these programs, some of them have come out under Republicans too – Common Core, No Child Left Behind, Race to the Top, they are all bad ideas. Because guess what they are? They are big bureaucratic programs coming out of Washington and, by the way, there are a bunch of interests who helped write those programs.  In the case of Common Core guess who helped write it? Text book companies and the testing companies it’s all crony capitalism folks. It’s alive and well under Republicans and Democrats. We have to take our country back,” Fiorina answered." According to a spokesperson for Ms Fiorina, "As she has said, there is absolutely no evidence that the work of a big, centralized bureaucracy in Washington makes things better. In fact, there’s loads of evidence to the contrary. The Department of Education has been growing in size and budget for 40 years and the quality of our education continues to deteriorate." Sounds on the mark to me.
  • reports on the teachers union protecting their turf from charter schools. "Nebraska is one of seven states without charter schools. Previous attempts to authorize them under state law haven’t gotten far, in large part because of stiff opposition from the union representing public school teachers: the Nebraska State Education Association...There are no charter school bills in the current session of the Legislature, but Sen. Bob Krist’s Legislative Bill 26, carried over from last session, would allow donors to receive tax credits for contributing to scholarships that allow low-income students to attend private schools." Why not stick to education and stop working towards eliminating school choice? Perhaps if unions there would work on teacher quality and get rid of poor teachers there would be no demand for charter schools.
  • has a piece responding to the recent call to ban chess by Saudi Arabia's grand mufti. "Far from being a waste of time, chess can be of great benefit to children's minds. Several academics have looked into this extensively. Chesshas been persuasively linked with improving children's concentration, problem-solving, critical, original and creative thinking - and even mathematical abilities. It is also said to help with memory storage and how young brains manage information - and should not only be perceived as a game for gifted children. Children with special educational needs can improve their abilities to learn and interact with other children if they become involved in school chess programmes and chess clubs. Children are also equal in a chess match regardless of things that might divide them. Their age, gender, ethnic backgrounds and religious affiliations are of no significance. Chess can cross socio-economic and cultural boundaries and give otherwise disadvantaged children a chance to compete on equal terms."

Altermundus: More triangles

AltTri2I've added more content to the Altermundus: triangles page. Last time the content was mostly about various triangles that can be created using the documentation. This week I've expanded on that with examples that illustrate features you'll almost certainly want in your triangles such as (marked) congruent angles and (marked) congruent sides.

Here are some stories that caught my eye over the last week:

  • Smithsonian has a piece on the latest and biggest prime number to be discovered: "M74207281, as mathematicians are calling the new prime, is 5 million digits longer than the previous record holder, which was also discovered by the GIMPS program. The new prime is too long to write out in full here, but it was found by multiplying 2 by itself 74,207,281 times, and then subtracting one."
  • with a comment by a professor of mathematics at Stanford University annoyed by Mr. Zimba's comments covered in a previous post. "...Zimba addressed nationwide parental frustration at nonsensical math assignments by warning parents to do what he does with his children -- basically shut up and let the teacher follow the standards. “The math instruction on the part of parents should be low,” Zimba said. “The teacher is there to explain the curriculum.”" The concerned parent/math professor writes, "Just a few weeks ago, my son had been working with a child for whom he’s the guardian, a fourth-grader, to make sure she understood some basic math concepts about place value and how they work in the standard algorithm for long (stairstep) multiplication. Her fourth-grade teacher would not let her use it. Instead, she was required to draw pictures of lines, points, and squares, and then laboriously count them up to achieve the product of two whole numbers, each less than 100. She complained to my son, understandably, that she was totally confused and didn’t understand why she wasn’t allowed to use the standard method that she both understood and realized was tremendously more efficient....It’s critical that children understand what actually matters and what is supposed to be happening. If they waste a year ensnared in mathematical idiocy, they won’t be able to pick up what they need when they need it later....Zimba can do what he wants with his own kids. But he needs to understand that it is almost criminal to try to prevent other parents from doing what they think necessary with theirs.". The whole article is worth reading in full. Whenever I hear some teacher talk about the deep concepts of common core to "really understand" what's going on I want to barf. Those people give it away--they don't know what they're talking about.
  • Gens Una Sumus? The Daily Mail reports that Saudi Arabia is banning chess-or maybe that's trying to ban chess. "Saudi Arabia's top religious cleric has ruled that chess is forbidden for Muslims because it is a 'waste of time' and promotes gambling. Grand mufti Abdul Aziz bin-Abdullah issued the fatwa ahead of a major chess tournament in Mecca tomorrow....Musa Bin Thaily, president of the law committee at the Saudi Chess Association, said a tournament would go ahead as planned tomorrow despite the fatwa, which he said was issued last month."
  • with the story: "A [C]onnecticut high school called the cops on a teenager for allegedly uttering the word "ISIS" during the Pledge of Allegiance... The student was cleared of any criminal wrongdoing but was removed from classes at Ansonia High School and is now attending alternative schooling".
  • The Federalist writes that the undercover videos by James O'Keefe (last week) are just the tip of the Common core iceberg: "While rants about bad curriculum surface regularly, almost nobody talks about why we are stuck inside a decades-long cycle of curriculum that a) feeds kids politically correct pablum, outrageous examples of which we see pouring over social media constantly and b) insiders can arrange through taxpayer-funded sweetheart deals that never benefit children....A big tip-off to a distorted market is a lack of competition.....Whenever you see economic oligarchy, you should suspect cronyism: where businesses get contracts not by demonstrating how good their products are, but by schmoozing with politicians....Concentrating the power in the hands of a few people exacerbates special-interest control because it makes it easier for a highly motivated faction to dominate everyone else simply by capturing the few regulators. A tiny faction can’t convince the majority to do what it wants. But government-run central planning means it doesn’t have to. The faction only has to convince a few key regulators the rest of us don’t even know exist.This is why a free market is better for everyone, because it requires textbook companies to go school by school and convince a hundred thousand principals individually rather than having to just convince a few dozen unelected bureaucrats somewhere. Those principals then can pick materials that better fit local sensibilities....Common Core itself is a regulation that favors the big guys at the expense of the little guys. Textbook publishers have massive standards compliance databases, which are basically searchable documents that ensure every product of theirs at least mentions the things the myriad state and now national curriculum regulations demand. Does any of this correlate with better instruction for kids? Absolutely not.". Excellent Part 1 article that deserves several readings.
  • Part 2 of the Federalist article "Because of several basic realities of U.S. education, such as the ineptitude of all central planning, Common Core could never work. It was doomed from the beginning (it didn’t “fall apart during implementation,” which is the new narrative now that the problems are too big to hide)....Regulating curriculum through “standards” is just a futile exercise in box-checking, former textbook editor Beverlee Jobrack told me: “You [publishers] have your math program, and new standards come out, and you look to see if you’re covering those topics, and you check it off. You don’t really revise your materials.” No wonder quality research has found thatstandards do not improve student achievement....The more education regulations change, the more business these companies and government officials will have. They make more money from instability. And it’s probably not a coincidence that research has found essentially all professional development in the education field is a massive waste of time and taxpayers’ money.....Education schools—the colleges and graduate schools that have state monopolies on providing coursework and other hoop-jumping anyone must perform to receive a teaching license—are utter failures, if you consider their mission to be training effective teachers. Arecent report, for example, finds that they teach almost nothing science indicates about how children learn or how to effectively teach reading, that core academic skill upon which all others rest.Even more damning is decades of evidence showing that teachers who are certified are no more effective than teachers who are not. Research shows that education schools recruit the least-qualified students, give them the highest grades, and teach them very little that is practically helpful to their eventual careers.". Another excellent article!
  • EAGNews with the latest from Milwaukee Public Schools. If you've been reading this blog then you've seen how they use their position and influence to weaken the competition from other schools rather than raise their poor standards. "Means was recently selected by the Milwaukee County Executive to lead the Opportunity Schools and Partnership Program (OSPP), a state-mandated initiative that will identify, manage and improve some of the worst schools in the Milwaukee Public Schools (MPS) district....Some MPS supporters are already describing the program as an attempted “takeover” of public schools...The OSPP is even having trouble arranging its first public “listening session.” It was supposed to take place at Destiny High School, but had to be moved to another location due to complaints from MPS supporters. They complained because Destiny is a private school that participates in the Milwaukee Parental Choice Program, which allows low-income MPS students to attend private schools through state-provided vouchers. Many public school supporters, particularly within MPS, hate the voucher program because it “competes with Milwaukee Public Schools for students,” according to the Journal Sentinel. Each of those students has a certain amount of state money attached to them. Every time one leaves MPS for a voucher school, the money leaves as well. That’s not good news for MPS employees who count on the district for jobs...The union has long been hostile to choice schools and many of the city’s charter schools, because they don’t hire union teachers. Perhaps they fear that schools selected for the OSPP will also hire less expensive non-union teachers, so they can funnel more money directly toward student programs.". So much time, effort, and money spent is not spent on education; it's more about protecting money and influence.
  • FiveThiryEight says that a new planet may have been found. It hasn't actually been found but the math indicates it's there. "This isn’t the first time scientists have found a new planet before reallyfinding it, but this technique also has produced outright blunders. This time, though, astronomers say there’s reason to take the new potential planet seriously....There are still many ways that the scientists could have made an error or overlooked some subtle source of bias, or there could be another explanation for their data. “I’d be willing to bet about 50/50 odds, maybe better, that there’s another planet out there,” said Scott Tremaine, an astronomer at the Institute for Advanced Study in Princeton. He said he places the claim “somewhere between prediction and speculation.”" Another victory for math or just a mistake? Time will tell.
  • Round 8 is under way at the Tata Steel Chess Tournament. Caruana and Carlsen are tied for first with 5 out of 7. The tournament streams live here.

Sagetex: Evaluating Logarithms

EvaluateLogsI've added a worksheet on Evaluating Logarithms to the Basics page. It creates random logarithms and has the solutions attached at the end. I've also added some piecewise  defined functions to the Graphics page. These are meant to used as problems in Precalculus BC/Calculus where you determine the limit from the right and left. Of course, you can use them as you see fit. I've included the file that created them since it's convenient to have open/closed circles built in to the LaTeX code if you want to create additional diagrams.

Here are some some stories that caught my eye over the last week.

  • EAGNews has a story with the explanatory title, "Teacher arrested for buying meth -- from student!".
  • Sports Illustrated weighs in on PC idiocy: "The Wisconsin Interscholastic Athletic Association has banned high school students from chanting certain words and phrases at basketball games, and none of them are remotely close to being hurtful or inappropriate.....• “Fundamentals”
    • “Sieve”
    • “We can’t hear you”
    • “Air ball”
    • “You can’t do that”
    • “There’s a net there”
    • “Scoreboard”
    • “Season’s over” (during tournament play)
  • The 2016 Tata Steel Chess Tournament has begun, featuring such 2700 players like Carlsen, Caruana, Giri, Ding Liren, So, Karjakin, Eljanov, Adams, Mamedyarov, Tomashevsky, Navara, Wei Yi, Hou Yifan, Van Wely. You can follow the live games, along with GM Seirawan's commentary, here.
  • Education Next on "School teachers are much more likely to use a private school than are other parents. No less than 20% of teachers with school age children, but only 13% of non-teachers, have sent one or more of their children to private school. Teachers are also just as likely to make use of a charter school or to homeschool their child as other parents. As insiders, teachers presumably know the truth about the level of education that is being provided. One expects employees to be loyal to the employer who sends them a regular paycheck, especially if the product being produced is of high quality. How many Apple employees are using a Samsung? How many Yankee employees root for the Mets?....That teachers are no more loyal than other educated parents suggests that the commitment to the traditional public school is neither uniform nor unqualified....One public school teacher, Michael Godsey, has confessed publicly on the internet that he has chosen a private school for his children, even though he says he “superficially loathe[s]” the school for its elitism. The private school, he says, “promotes ‘personal character’ and ‘love of education,’ and the tangible difference between this environment and that at the public school in the area was stunning to me—even though I’m a veteran public-school teacher.” Presumably, many other school teachers feel the same way."
  • EAGNews reports that "In the 2013-14 school year, for instance, an amazing total of 1,272 MPS employees had salary and benefit packages worth more than $100,000. By comparison, the Seattle school district had only 313 employees receiving compensation packages worth at least $100,000 in 2014-15. The San Francisco district had 769 that year....More than half of the employees in the “six-figure club” – 744 – were teachers. While they made out well, they were certainly not clustered at the top of the compensation chart. Out of all those teachers, only two made the list of the top 200 compensation packages in the district.The rest of the top 200 were school district administrators, with the vast majority having the title of central office administrator, principal or assistant principal.Compensation for the top 10 on the list was staggering. The top earner that year was Superintendent Gregory Thornton, who made $265,000 in straight salary and $78,847 in benefits for a grand total of $343,847."
  • It was bad enough when We Up It posted the comments of a Houghton Mifflin Harcourt  employee disparaging the textbook industry but now the New Boston Post has come up with a second video "...The latest video shows a woman, Amelia Petties, identified as a Houghton account executive, saying that education initiatives like Common Core are “never about the kids” and that they present lucrative business opportunities for companies that produce textbooks, training and other curriculum materials.” Both employees were fired. Educational movements such as Common Core provide a great opportunity to put "old wine in a new bottle" and force schools to spend lots of education dollars that would be better spent in other places."
  • ZeroHedge on the dire problems facing the Chicago public school system, "Borrowing and trimming the proverbial fat helped close some of the $1.1 billion hole but once the board reached the point where “further cuts would reach deep into the classroom” (to quote system chief Forrest Claypool), the schools asked Springfield to make up the difference which amounts to $480 million. The Chicago Public School (CPS) system has nearly 400,000 students and more than 20,000 teachers. Around 1,400 jobs were eliminated in an effort to save money and more layoffs may be just around the corner if Springfield - which is mired in budget gridlock - doesn’t step in...With no viable options, the base case is now that described by Chicago Democrat John Cullerton last year: the system will lose 3,000 teachers and will be forced to shorten the academic year."
  • TheCollegeFix with the latest on the modern day educational version of McCarthyism: "The public university is in the midst of a massive campaign that encourages students not only to watch what they say, lest they offend someone, but also to report any and all biased statements to campus officials....Lisa Powers, director of Penn State’s strategic communications office, said in an email to The College Fixthat an act of intolerance includes microaggressions. “An act of intolerance can be identified as any forms of microaggressions, verbal assaults, and/or racial subjugation,” Powers said."
  • TulsaWorld reports on the reality of our broken education system for Oklahomans, "When they don their caps and gowns, nearly nine out of 10 of them will be handed a diploma certifying they meet Oklahoma’s “College Preparatory/Work Ready Curriculum Standards.” Months later comes a reality check: They are told they aren’t ready for college after all, at least until they take and pass one or more remedial courses....Scores on the ACT exam show only 22 percent of Oklahoma’s test-takers were considered proficient, or ready for college, in math, reading, English and science, compared with 26 percent nationally...Oklahoma City Public Schools and Tulsa Public Schools. In 2014-15, out of a combined 2,654 graduating seniors in the two districts, only 269, or 10 percent, enrolled at the University of Oklahoma or Oklahoma State University, the state’s flagship research institutions. The percentage would be lower if students who didn’t graduate were counted. Both districts have large low-income populations.."

Sagetex: Rational Functions 1


I've added a problem on graphing rational functions (in this case, hyperbolas) to the Sagetex: Functions page. The problem asks the student to sketch a randomly generated transformation of a hyperbola along with the horizontal and vertical asymptotes and then give the domain and  range. Of course, you can easily modify the problem to best suit your class.

Here are some stories that caught my eye this week:

  • The News & Observer writes, "De-emphasizing memorization when teaching math is wrong-headed, a group reviewing academic standards agreed in an email exchange last fall as they discussed how to declare the value of rote learning in their report recommending changes to Common Core...The final report does not include a full argument for memorization, but one of the group’s conclusions is “models are over-emphasized at the expense of standard algorithms.”"
  • The Libertarian Republic writes, "Asian-American students are outperforming other students; now some want to change the rules so others aren’t left behind– that has many feeling like Asian-Americans are being punished.....Asian-American students make 65% of the student population at West Windsor-Plainsboro Regional School District in New Jersey. They make up 90% of the accelerated math and enriched math studies courses. The district has a competitive instrument music program. In the last three graduating classes, sixteen students were admitted to M.I.T., while also constantly showcasing Science Olympiad winners, classically trained musicians, and students with perfect SAT scores. According to the New York Times, the school district has become popular “bedrock communities for technology entrepreneurs, pharmaceutical researchers and engineers.” Many of the students attending the school district are children of immigrants from countries such as China, Korea, and India and are often the first-born in America.". Success! This is what we want, right? Depends on who you talk to: "However, the school district has canceled the accelerated math and enriched math studies courses. The district Superintendent, David Aderhold, has also canceled high school mid-terms and finals. He has made entrance into the instrument music program easier, adding that there is a “right to squeak.” He stresses that he doesn’t want to make the district a Palo Alto where two clusters of teen suicides happened due to academic stress. Most Asian-American parents have been up in arms against the changes.".
  • Education hijinks in Florida: myPalmBeachPost writes, "Imagine playing a game of football where you set the score after the game....Sounds preposterous. But that’s pretty much how standardized testing is handled for Florida’s public school children....The problem for Florida is that a significant performance gap has occurred between the grades on the NAEP that Florida students have scored last year and the anticipated scores they would receive on the Florida Standards Assessment tests they also took....Some say that Florida shouldn’t be setting “cut scores” — the grading scale that redefines passing and failing — in a way to paint a rosier picture than the national test results. Others argue that the two tests and their scoring scales are dissimilar enough to ignore the gap and make sure that most Florida school children receive passing grades....“If nearly 70 percent of Florida students are declared non-proficient in Grade 10 this would result in unconscionable harm to students and their ability to graduate,” the Florida Association of District School Superintendents wrote. “Such an outcome would also create negative impacts to the Florida economy.”".  Note the difference in approach of the educational experts professionals employees. Some, rightly, want to let the chips fall where they may and face the problem while the other group wants to obscure it so that the average person is unaware of the problem--sweep it under the rug and CYA. Which brings up another point to remember: the lousy state of education is actually worse than it looks thanks to these sorts of practices and all the tutoring that students get in order to make up for what students can't learn in school.
  • EAGNews on how the Seattle Public School system was going to lose teachers (for the second year in a row) due to underenrollment in the school district. "District officials argued that they lacked the funds to leave the teachers in the classrooms where they were already teaching, and hire a few more to fill holes in schools with shortages. But as Seattle Times columnist Danny Westneat recently noted, the district increased its central staff budget by 16 percent this year, and the superintendent’s office budget by 16.4 percent. So perhaps there was some money available after all, but it was spent in the wrong places...In the 2014-15 fiscal year, an astonishing total of 275 employees, mostly administrators, made at least $100,000 in straight salary. They were paid a combined $31.9 million....Then there was the district’s 2014-15 travel budget....the district spent nearly $1 million on travel in 2014-15."
  • The Hechinger Report cites Jason Zimba, a designer of Common Core's math standards, as telling parents to keep out of their children's math life as much as possible:"“The math instruction on the part of parents should be low. The teacher is there to explain the curriculum,” said Zimba.".  Put your trust with teachers, many with no real math background, and a typical track record of around 40% passing Common Core exams. Sure, what could go wrong with that approach?
  • with some good news: "Recently the Office of Educational Technology of the United States Department of Education stated that it believes "creating an open education ecosystem involves making learning materials, data, and educational opportunities available without restrictions imposed by copyright laws, access barriers, or exclusive proprietary systems that lack interoperability and limit the free exchange of information."...The CK-12 Foundation is a California based non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Key benefits include: access to free textbooks; access to high-quality, educator-created content; support for publishing tools that make content creation easy; and licensing via Creative Commons CC-BY-NC....CK-12 founder Neeru Khosla and her husband Vinod had a vision: to revolutionize the way students interface with textbooks. According to Neeru Khosla, "The publisher's textbook model was getting to be really, really expensive, especially when there is only one type of one-size-fits-all content. So I thought technology might be a good way to solve that problem by giving free textbooks and allowing people to customize them."". There are a lot of hardworking, dedicated professionals trying education better. Unfortunately, there is a corrupt, bloated, ineffectual bureaucracy that throws up roadblocks in their way. Open source educational content is the way to go but vested interests will almost certainly stand in the way.
  • Bullying is a nasty part of high school and can invoke the images of a kid who wants to beat someone up for lunch money---or perhaps the cyber-bullying of today through social media. But as reports, "A social media storm erupted after administrators at a New Jersey high school accused a student of bullying because of anti-Israel comments that she posted on Twitter. They say that the tweets may have violated the state’s broad anti-bullying laws.". I'm not exactly sure how admin thinks that Israel is being bullied by "a 16-year-old Israeli Jew" but look at what follows next "In addition to rebuking her and warning her about legal consequences, the administator searched Koval’s phone to make sure that he had not recorded their conversation. The student could be sued if she had, he told her.The administrator was correct in their assumption; Koval posted videos of the meeting on Twitter. In one recording, Koval can heard telling the administrator that her tweets may have been controversial, but she didn’t think they were “problematic.”“Well that’s your interpretation,” the administrator said. “There’s a state law that might interpret it differently.”"". Seems like there are 2 issues here: first, if admin is correct and the law could be interpreted in such a twisted manner to charge her with bullying. In that case, the law seems messed up and admin has done what they legally had to. But it seems like a legal stretch that seems to infringe on constitutionally protected free speech. I'm no lawyer, but this seems to bring up the second issue of the bullying of a teen by admin. I suspect there will be more lawsuits in the future to sort this out. But according to, "Being written up as a bully then kick-starts a bureaucratic process that could end up leaving a black mark on a student's permanent record, which may leak out to colleges". The Gothamist writes, "...Koval plans to return to school tomorrow, but she is researching online schools because she said she no longer feels safe on campus....As for the alleged search of Koval's phone and lawsuit threat, he said that any search without a warrant would be a clear Fourth Amendment violation. Her recording of the conversation, on the other hand, is protected by the state's wiretap law....". Stay tuned!
  • StopCommonCore NC has a piece on Kentucky trying to eliminate Common Core.
  • NY Times takes a look at the upcoming landmark court case I mentioned last week on the legality of mandatory dues for teachers to unions. "The court’s decision, expected by June, will affect millions of government workers of all kinds and may deal a sharp financial and political blow to public unions. (The ruling is unlikely to have a direct impact on unionized employees of private businesses, as the First Amendment restricts government action and not private conduct.)". This would be a major blow to unions but a good first step to fixing California's messed up educational system.

Altermundus: Triangles


I've added a new page to the website which you can find on the sidebar; it covers some of basics of the Altermundus packages with respect to tkz-euclide and triangles. Remember the original documentation is in French--I'm trying to learn the package myself so I'm posting some explanation as I try to understand them in an order that fits with how I use the package. Any mistakes are almost certainly mine--please let me know if you find anything which is wrong.  Ultimately I hope to have most of the information online for quick reference--templates/examples will make it easier to modify the code for to suit your particular use. Click on the sidebar link or here to see the new page.

Here are some stories that caught my eye over the last week.

  • Storypick has 13 One-Liner jokes for math lovers. Get your geek on!
  • Qatar Masters 2015 ended with a tie for first between Carlsen and Yu Yangyi. Carlsen took the title easily on a tiebreak match. Chessbase has this report.
  • EAGNews on the problems RTW (right to work) is causing for teaching unions. "Wisconsin, Michigan and Indiana, having  become “right-to-work” (RTW) states over the past several years, have given teacher freedom a big boost".Wisconsin, which also limits teachers’ collective bargaining activities via Act 10, has seen its National Education Association affiliate’s numbers cut by more than half...In Michigan, the teachers unions have lost 20 percent of their membership since becoming a RTW state in 2012, but this number will grow. Many unions, sensing the inevitability of RTW legislation in the Wolverine State, signed long-term contacts with their school districts. However, once those contracts expire, more teachers will be liberated from paying forced union dues....Of course freedom from forced unionism could greatly accelerate in 2016 courtesy of the Friedrichs v California Teachers Association case. If the litigants are victorious, no teacher – or public employee – in the country will be forced to pay any money to a union as a condition of employment. With oral arguments in just 13 days, the ruling will be finalized in six months.". This will be an important case for 2016. Since unions have put kids last and have stood in the way of teacher accountability any weakening of their power could allow actual meaningful education reform.
  • Tenth Ammendment Center notes, "A bill prefiled in the Maine House for the 2016 legislative session would withdraw the state from Common Core standards, an important step toward nullifying nationalized education in the state. Rep. Will Tuell (R- East Machias) along with a bipartisan group of nine cosponsors prefiledLD1492 on Dec. 23. The legislation would void Common Core standards at the end of the 2016-2017 school year and create a framework to establish state standards to replace them."
  • Forbes looks back at math in 2015.
  • Michael Krieger  of Liberty Blitzkrieg looks at a Washington Post piece Google collecting information on students. Quoting from the Washington Post, Krieger's column reads, "Google is a major player in U.S. education. In fact, in many public schools around the country, it’s technically a “school official.” And that designation means parents may not get a chance to opt out of having information about their children shared with the online advertising giant.". So go to a public school and forfeit your privacy; if you have enough money you can "opt out" (by going to private school) and if you don't you're stuck. But the questions in my mind are "Who decided that 'school official' was the proper description of Google" and "How much did it cost" to get that classification. Public school is big business and decisions will not always be made for educational reasons.
  • The Atlantic, which usually has some excellent articles, has an AWFUL article by an education expert person which doesn't read so well; I could practically feel her trying to put the square pegs into the round holes to make a lame argument about Common Core. She mentions how one sixth grader had a test on her first day of class. "But why does this only happen in math? Teachers in history or English don’t give tests on the first day to find out what students know.". It's called a pretest. Math is cumulative and if students haven't mastered basics then the teacher will need to get the class up to speed before covering the new material.  I don't think that history has the problem of cumulative knowledge needed like math does. Seems like English math but the question should be directed at the English teacher. She writes, in another article, "This summer I taught a course through Stanford’s open online platform explaining research evidence on ability and the brain and on good mathematics teaching, for teachers and parents.". So clearly her background indicates she should know what a pretest is and shouldn't be critical of a math teacher for giving one. A typical school has plenty of math students who are weak in math (about 40% pass Common Core math) and a teacher really needs a better idea of what the class is weak in. This education expert teacher also points (in both articles) to scientific research papers which she says prove that there is no such thing as "math people". The"scientific article" to prove her case doesn't (by my reading) and even her link to "math people" says, "Is math ability genetic? Sure, to some degree...Essentially none of us could ever be as good at math as Terence Tao, no matter how hard we tried or how well we were taught....For high-school math, inborn talent is much less important than hard work, preparation, and self-confidence.". Read the drivel that follows and you get the distinct impression they've never seen naturally talented math students. Virtually every field from sports to music, math, language, chess, etc will have people that are naturally gifted. Take a look at Terry Tao's Wikipedia page "Tao exhibited extraordinary mathematical abilities from an early age, attending university level mathematics courses at the age of 9.".  And I've certainly encountered students who have worked hard to get better in math but haven't been successful--that's life. People like Terry Tai illustrate clearly there is a math tye--extend that and you'll conclude there can be varying degrees of math types and that innate skill makes math easier to some at the high school level than others. The author continues by writing about Field's Medal Lawrence Schwartz to make the valid point that speed is not important for success in math. She slowly makes her way to the main point she wants to make: "Although news sites are filled with opposition to the Common Core, the new curriculum is at least a step in the right direction, as it asks students to engage in in the most mathematical of acts—reasoning. Mathematicians prove ideas by reasoning and justifying their thinking. Those who oppose the Common Core often do so because they want to keep the traditional mathematics approach in classrooms, even though this has turned off millions of students.". These assertions are backed up with just her opinion--no link to what a mathematician thinks, for example. So let's remind ourselves of Dr James Milgram, professor emeritus of mathematics at Stanford University, who has worked on the Common Core standards and refused to sign off on them. His letter is worth reading and, as he says here, "..., there are a number of extremely serious failings in Core Standards that make it premature for any state with serious hopes for improving the quality of the mathematical education of their children to adopt the end of fifth grade the material being covered in arithmetic and algebra in Core Standards is more than a year behind the early grade expectations in most high achieving countries. By the end of seventh grade Core Standards are roughly two years behind...ore Standards in Mathematics have very low expectations. When we compare the expectations in Core Standards with international expectations at the high school level we find, besides the slow pacing, that Core Standards only cover Algebra I, much but not all of the expected contents of Geometry, and about half of the expectations in Algebra I. ...Realistically, the most likely outcome of the Core Mathematics geometry standards is the complete suppression of the key topics in Euclidean geometry including proofs and deductive reasoning. Also, there is no discussion at all of topics more advanced than these.... .". Such a poorly presented article, with a non-"proof" that there are no math types and a string of BS along the way and  I had to look a bit further---only to find this post off of Dr. Milgram's school webpage. This pdf off his site says, in reference to some of her work in California, "As is the case with much education research of this nature, Prof. Boaler has refused to divulge the identities of the schools to qualified researchers. Consequently, it would normally be impossible to independently check her work. However, in this case, the names of the schools were determined and a close examination of the actual outcomes in these schools shows that Prof. Boaler’s claims are grossly exaggerated and do not translate into success for her treatment students. We give the details in the following article.". Given the awful article from the Atlantic, I'll give a LOT more credence to Dr. Milgram's views. A math education expert person is not, in general, an expert in math it shows. And Dr Milgram is someone who has given lots of specifics on what's wrong with Common Core math.
  • Oped News has a piece on the LA Unified School District--the poster child of what's wrong with public education. Public education at its worst takes enormous sums of money from hard working taxpayers, gives it to the public school system where it's likely to be mismanaged (or stolen, misappropriated, etc). And with no real accountability there's no incentive to fix what is broken. Much of the money gets funneled to creating more administration positions that do NOTHING for improving student education. But when the pile of money is huge it's easy to get "Zuckered" out $100 million by the education professionals crowd. The end product: students who are ill prepared for college--like, for example, Camden, NJ (mentioned last week). From the article: "The LAUSD's continued refusal to abide by the California Public Records Act in a timely manner is only one example of how the District often seems to be an unyielding behemoth of a bureaucracy that is incapable of change. ..Although facing a $1 Billion lawsuit, the District continues to bully teachers through the use of Teacher Jail."

Basics: LCM and GCF

LCMI've added 2 worksheets to The Basics page--one on finding the greatest common factor (greatest common divisor) and the other on the least common multiple. You should change the teacher name and it would be a good idea to experiment with the random numbers being generated to make sure the level is appropriate for your class.

Here are some stories that caught my eye this past week:

  • The always interesting EAGNews has the provocative article title "2% of Camden, NJ high schoolers ‘proficient’ in math — despite spending $26,000 per student". Read further to find, "EAGnews last year pointed out that despite a 14-to-1 student to teacher ratio, and much higher spending than other districts at $26,000 per student – about $8,000 per student more than the state average – less than half of the Camden’s students graduated high school. That’s likely because much of the spending went to unnecessary expenses that have little to nothing to do with improving academics...“Camden students enjoyed jaunts to various performing arts theaters ($57,587); professional sporting events ($10,112); amusement parks ($20,427); movies theaters, bowling alleys and arcades ($23,759); the Medieval Times dinner theater ($13,668); museums, zoos and aquariums ($120,174).“School officials told the Board of Education that the bowling outings improved student’s ‘hand eye coordination.’ … They told the board that roller skating outings helped students ‘expand muscle coordination, balance and rhythm,’ … (and) trips to amusement parks are meant to improve students’ ‘math and physics skills.’” The needless field trips, however, were dwarfed by the cash administrators spent on themselves or other staff members, including nearly $1 million in legal fees, $394,818 in professional conferences and workshops, $708,817 on consultants, $86,989 on restaurants and catering and $160,666 on drug and alcohol treatment."". Public education puts massive amounts of money under the control of people with no good accountability. What will happen to those who mismanage funds? Almost certainly, nothing.
  • The Qatar Masters Open 2015 is almost over. After 7 rounds Mamedyarov, Carlsen, and Sjugirov are tied for first with 5.5. You can follow the games, with commentary, here.
  • This week marked the 128th birthday of the late, great Ramanujan. IndiaToday has "...some facts on his genius".
  • on the scrooge behavior at an Idaho school. "A cafeteria worker at an Idaho middle school was fired for giving lunch to a 12-year-old student who said she was hungry and had no money for food. The worker said she tried to pay for the lunch, but the school rejected her attempt...the student had told her she had no money for the $1.70 lunch. Bowden then asked her supervisor if she could purchase the meal for the girl. When the offer was denied, Bowden gave out the lunch for free...she was first placed on leave last week, then summarily fired, by the Pocatello/Chubbuck School District for the theft of school district property and inaccurate transactions in her duties". In your own words, figure out how you would describe the problem here (rigidness of gov't rules, bureaucratic incompetence, etc) and ask yourself how such a rotten system is going to produce good educational results. Shameful.
  • If you check the last two posts you'll find the remarkable lengths that the Milwaukee Public Schools (MPS) is going to in order to keep students from getting a better education by bypassing MPS--even when it costs taxpayers a lot of money to do so. EAGNews has news on a change in policy: "...the MPS board has stubbornly resisted applications for new charter schools – particularly those that do not want to be staffed with MPS-hired union teachers – even though such schools often produce significantly better academic results than regular MPS schools. But the board changed direction last week, officially chartering the new Milwaukee Excellence Charter School, a “no excuses” school that promises to establish and uphold high academic expectations for students, as well as a strict disciplinary policy, according to the Milwaukee Journal Sentinel....Why did the school board suddenly change its mind about the school, after giving it a lukewarm reception last spring?Apparently because the founder of the school, former Teach for America executive and MPS graduate Maurice Thomas, promised to aggressively recruit students away from private voucher schools and independent charter schools and lure them back into MPS.". This story has a lot more chapters in it. How much money will MPS be willing to waste on weakening competition that exposes how badly the schools are run? Since it isn't their money, the answer is going to be "a lot".
  • Remember the student in SC who was manhandled by a police officer? has a follow up: "Officer Ben Fields, the cop guilty of the assault, was fired from his position, but he has faced no legal consequences as a result of his actions, as any normal person would in the same situation.". With respect to the girl who was assaulted and the girl who filmed the assault, "Both girls face misdemeanor charges of disturbing schools, which could result in a $1,000 fine or 90 days in jail if they are found guilty.". It's a legal system and not a justice system.
  • with an interesting piece on the recruitment of teachers from the Phillipines to teach in Mississippi schools. There are a couple of angles here. First is that Mississippi has a shortage of public school teachers. Like many states, the certification requirements needed to become "qualified" in the eyes of the state are not actually about getting qualified teachers but serve the interests of unions, teaching colleges, and even the state for raising revenue by fees to ensure "standards". Mississippi decides to solve the DOE created problem by hiring teachers from the Phillipines. Are they certified? No. Second angle, "Once the interviews were complete and the school board approved the hires, Avenida began working on the visa process for the employees, who often pay her company a fee of about $10,000 to cover visa fees, transcripts, airfare and housing, among other expenses.". Does this seem like it could be a conflict of interest?!? Third angle, "However, the Mississippi Department of Education’s recent policy change requiring teachers be certified by an American program poses a challenge, according to Avenida.“By changing the licensing requirements where they do not accept teaching coursework, academic coursework from the Philippines … It slows down or doesn’t encourage teachers to come to Mississippi because of that,” she said....Foreign teachers in Mississippi must now obtain an expert citizen’s license, one-year teaching licenses issued by the Mississippi Department of Education to people witcertain business and professional experience. They must then go through a Mississippi teacher certification program to obtain a valid license.". So Mississippi has changed certification rules to allow teachers from the Phillipines to be allowed to teach (rather than US citizens), an education official uses her company to find those noncertified teachers (making money in the process) who are classified as "expert citizens" (what does that mean?!?) and those new recruits will have to spend a chunk of their salary to the state to become "certified". Education is a racket.
  • The stupidity continues, this time at Oberlin. reports, "What's eating students these days? Inauthentic sushi, it seems. Some offended diners at Oberlin College are accusing the dining halls of disrespecting Asian culture by preparing dishes so bad, they practically count as microaggressions....But cultural appropriation in the cafeteria isn't the only thing on the minds of Oberln students. Activists recently released a lengthy list of demands—many of them reminiscent of the demands made by students at dozens of other universities. Perhaps most notable: Oberlin students want blacks-only safe spaces and allowance money for black student leaders.". Can you really solve racism by giving one group extra perks?
  • The New York Times on a trend any teacher will confirm. "It is a pattern repeated in other school districts across the state and country — urban, suburban and rural — where the number of students earning high school diplomas has risen to historic peaks, yet measures of academic readiness for college or jobs are much lower. This has led educators to question the real value of a high school diploma and whether graduation requirements are too easy....But “the goal is not just high school graduation,” Arne Duncan, the departing secretary of education, said in a telephone interview. “The goal is being truly college and career ready.”.The most recent evaluation of 12th graders on a national test of reading and math found that fewer than 40 percent were ready for college level work. College remediation and dropout rates remain stubbornly high,...The first results, from the ACT college admissions tests, showed that only about a quarter of students statewide were ready for either college-level math or reading. Just 6 percent of black students and 15 percent of Hispanic students scored ready for college in math, with only slightly higher rates for reading. In one poor rural district where most of the students are African-American, graduation rates have risen to more than 85 percent, yet not one student scored high enough on the ACT to be deemed ready for college in reading or math."

LaTeX: inserting Sage Code

SageCodeSage and \LaTeX---a great combination! So a natural question is how to put that Sage code into your latex document.  Now the CTAN documentation, specifically sagetex.pdf, gives (starting on page 9) two verbatim like environments for inserting code that isn't meant to run:

  • sageblock: Any text between \begin{sageblock} and \end{sageblock} will be typeset sageblock into your le, and also written into the .sage file for execution.
  • sageverbatim: The text goes only to your latex document and not into the .sage file.

That's probably good enough for most people but suppose you want the latex document to look like the documentation put out by the outstanding people working on Sage? Well Dr. William Stein has been kind enough to post the source files of one of his papers here. Just download the tar.bz2 file, extract the files, and process the .tex file to see how the Sage wizards roll. Here's the view using Gummi:

SteinPaperNote the Sage prompt and commands in the bottom right hand corner. To create a template from it I've ripped out most of the code and and text and then changed the environment to be an article, rather than an academic paper. The resulting template has been added to the LaTeX page; the output is the first picture at the top of the post.

Here are some stories that caught my eye over the last week:

  • MarketSanity has a South Park song on college safe spaces.
  • Get out your calendar and mark off January 7, 2016. Seattle Times reports "When 6,500 mathematicians converge on Seattle for a convention early next year, a Redmond 11th-grader will be a star of their show. Abishek Hariharan, a 16-year-old junior at Tesla STEM High School, will compete against nine other high-school students in a national contest called “Who Wants to Be a Mathematician.”The event, staged like a game show, has become a highlight of the American Mathematical Society’s annual meeting, which the society claims is the largest gathering of mathematicians on Earth.". 6,500 mathematicians, a game show, lots of money at stake--can you say major PARTY?!?
  • Quick! Which country has more than 70% women for its science and engineering students? Forbes takes a look at Iran, "Ansary and others point out today’s culture of gender equality in families is a result of women entering the workforce during the Iraq-Iran war of the 1980s. It’s not uncommon  for men to tend to children while women in managerial positions, or in roles such as doctors, lawyers or judges work late...."
  • The Big Lie in education is the use of the term "qualified" to replace the term "certified". That gives the impression that there aren't enough qualified people looking to teach even as the state turns away qualified teachers for not meeting their certification requirements--which don't have much to do with being qualified. That's good news for teaching colleges, unions, and even the states which can then make money by getting teachers qualified certified. But how do you keep the illusion that the purpose of all the BS is to get teachers qualified? Eliminate the competition. Last week we saw how charter school teachers were doing a much better job teaching rying to students than private school teachers. The unions were not pleased and are trying to eliminate the threat. This week there's another dirty trick on display; from EAGNews: "St. Marcus is an academically successful private school that serves a mostly low-income, African-American student base. It has been looking for more space for several years, to accommodate hundreds of students on its waiting list." The school is just too big now so they approached "...Milwaukee Public Schools (MPS), which has been losing a lot of students in recent years and has approximately two dozen empty schools.St. Marcus has made numerous attempts to purchase two different vacant MPS buildings, but the district has consistently refused to complete a transaction.The reason is that MPS doesn’t want competition for students....The problem for MPS is that it loses a percentage of state money for every student that leaves and enrolls in a voucher or charter school. So MPS officials have been stubborn about selling empty buildings to other schools, particularly those in the voucher program, depriving many students the opportunity to receive better instruction, and forcing Milwaukee taxpayers to maintain several dozen empty buildings.". Rather than make money by selling the shuttered building and help a charter school, the MPS decided to waste taxpayer money to keep St. Marcus from getting bigger. MPS tried selling the school buildings to someone else and rather than make 1 million dollars, they lost $500,000 dollars. Apparently teaching quality isn't the only problem at MPS. "The Malcolm X building, which has been vacant since 2007, remains so today. Taxpayers have forked out more than $200,000 on maintenance for the unused structure since 2012, according to the report. In 2014, tSt. Marcus officials tried to purchase the vacant Lee school building from MPS for its appraised value of $1.4 million, according to the report, but negotiations ended when Milwaukee Mayor Tom Barrett demanded that St. Marcus pay an extra $1.3 million as a “school choice tax.”". The good news is that St Marcus has found a place to grow their school. When you don't really care about spending other people's money and there's no accountability for being incompetent and/or vindictive a lot of resources get squandered: $500,000 of taxpayer money lost on the building sale, $200,000 a year spent to maintain vacant buildings, and a fair offer of $1.4 million for a building turned down. That's millions of education dollars squandered just to stick it it to the competition. Think anyone will lose a job for this "performance"?
  • on Emory University students trying to get end-of-semester course evaluations to allow them to indicate "...whether their professors had committed “microaggressions” against them." According to a statement by students, "We demand that the faculty evaluations that each student is required to complete for each of their professors include at least two open-ended questions such as: “Has this professor made any microaggressions towards you on account of your race, ethnicity, gender, sexual orientation, language, and/or other identity?” and “Do you think that this professor fits into the vision of Emory University being a community of care for individuals of all racial, gender, ability, and class identities?” These questions on the faculty evaluations would help to ensure that there are repercussions or sanctions for racist actions performed by professors. We demand that these questions be added to the faculty evaluations by the end of this semester, Fall 2015."
  • You might not think that Godel's Incompleteness Theorem has much to do with physics. But you'd be very, very wrong. reports, "Cubitt and his collaborators focused on calculating the ‘spectral gap’: the gap between the lowest energy level that electrons can occupy in a material, and the next one up....The team started with a theoretical model of a material: an infinite 2D crystal lattice of atoms....Cubitt and his colleagues showed that for an infinite lattice, it is impossible to know whether the computation ends, so that the question of whether the gap exists remains undecidable....But the undecidability ‘at infinity’ means that even if the spectral gap is known for a certain finite-size lattice, it could change  abruptly... And because it is “provably impossible” to predict when — or if — it will do so, Cubitt says, it will be difficult to draw general conclusions from experiments or simulations....Cubitt says that the team ultimately wants to study a related problem in particle physics called the Yang–Mills mass-gap problem, which the Clay Mathematics Institute in Peterborough, New Hampshire, has named one of its Millennium Prize Problems. The institute is offering $1 million to anyone who is able to solve it."
  • It's over! on the guilty verdict for Philip Chism, "Chism, 16, was convicted of one count of first-degree murder, which carries a mandatory sentence of life in prison. Because he’s a juvenile, the judge will have to consider parole after 15 or 25 years. Chism was also found guilty of one count of aggravated rape and one count of armed robbery. Each of those counts carry the possibility of up to life in prison, though he will also be eligible for parole because of his age."
  • EAGNews on the poor performance of Illinois students, "A recent report shows nearly half of Illinois students enrolling in community college must pay for remedial classes to catch up on lessons they should have learned in high school....Our state literally cannot afford to invest additional time and money for students to acquire the skills and knowledge they should have received during their preK-12 journey,” Smith said.". How do you turn around the miserable performance of Illinois public schools when there is no accountability for failing schools? Answer: You don't.
  • Book smarts but no common sense?: on how eager Yale students sign a petition to get rid of freedom of speech. "In the video, filmmaker and satirist Ami Horowitz is the guy getting students to sign his petition, and reportedly a solid majority was all for it. Even more sad, not a single one of them seems to realize the irony of signing a petition to do away with a freedom that includes the right to petition!...Sure, it's Fox News and sure, it's edited, but as someone who has done plenty of man-on-the-street interviews myself including this one about giving up freedom, it really is horrifying to realize not only are these people serious, but for every single one you see in this video, there are many, many more out there who agree with them and would sign that petition in a heartbeat. Yeah. In summation, it's barf-inducing. Watch at your own risk."
  • The Atlantic has an article on the effects of education on young children, "The researchers also reported more time spent with workbooks and worksheets, and less time devoted to music and art. Kindergarten is indeed the new first grade, the authors concluded glumly. In turn, children who would once have used the kindergarten year as a gentle transition into school are in some cases being held back before they’ve had a chance to start. A study out of Mississippi found that in some counties, more than 10 percent of kindergartners weren’t allowed to advance to first grade....A child who’s supposed to read by the end of kindergarten had better be getting ready in preschool. As a result, expectations that may arguably have been reasonable for 5- and 6-year-olds, such as being able to sit at a desk and complete a task using pencil and paper, are now directed at even younger children, who lack the motor skills and attention span to be successful...A major evaluation of Tennessee’s publicly funded preschool system, published in September, found that although children who had attended preschool initially exhibited more “school readiness” skills when they entered kindergarten than did their non-preschool-attending peers, by the time they were in first grade their attitudes toward school were deteriorating. And by second grade they performed worse on tests measuring literacy, language, and math skills."
  • Detroit Free Press with stunning news: "Detailed results from Michigan's tough new standardized exam paint a worrisome picture for many schools in Detroit and will likely boost state efforts to fix what many see as a broken educational system in the city. Just one fourth-grader in schools run by the Education Achievement Authority — a state district created to turn around the worst-performing schools in the state — passed the math portion of the examaccording to results released this morning. Overall, only 1.2% of the students in the district passed in math and 5.6% passed in English language arts. In some grades and subjects, not one student passed." If they can get 2 people to pass next year they'll have a 100% improvement record to "brag" about.

The Basics: Solving Linear Inequalities

SolveInequalities1Two additions to the website. First is a worksheet on Solving Inequalities which is on the Basics page. Second, I've added a link to a BBC Horizons show on Fermat's Last Theorem. You can find it on the Resources page.

Here are some stories that caught my this week:

  • It seems like the crybullies are in season: TPM Livewire reports "Some students at Lebanon Valley College, a private liberal arts institution in Pennsylvania, have demanded administrators rename the campus' Lynch Memorial Hall because of the "racial connotations" associated with the term "lynching,"...The building was named after Dr. Clyde A. Lynch, the college's 11th president who served during the Great Depression and WWII.". Perhaps they should sue people to legally change their names. The Rebel interviews college students about opposing free speech and microaggressions. Is saying "God bless you" to someone who has sneezed a microaggression? Tune in to find out!
  • Breitbart on student protests at "...73 schools all want the following:1) WE DEMAND at the minimum, Black students and Black faculty to be reflected by the national percentage of Black folk in the country2) WE DEMAND free tuition for Black and indigenous students3) WE DEMAND a divestment from prisons and an investment in communities". Free tuition but just for black and indigenous--sounds like a bit much, don't you think?
  • The Yale Daily News reports Erika Christakis "...whose Halloween email to students sparked conversations about race and discrimination on campus, will no longer teach at Yale." and her husband will take a sabbatical this spring.
  • CTpost with one of those posts that really bother me. If you come here a lot you'll have heard me talk about how departments of education create artificial shortages of certified teachers which they then broadcast as a shortage of qualified teachers even while they prevent qualified people from teaching because of their extra certification requirements that don't have anything to do with real quality (for example here ). Teacher shortages are becoming even more common nowadays and as the article says, "Learning algebra and geometry is hard enough. Try doing it without a teacher. At least 200 freshmen and sophomores at Harding High School have spent the semester doing just that, with their classes staffed with a string of substitute teachers that a number of students say have not taught them a lick of math....Another student, Jadiel Torres, 15, went to the city school board this week, saying he had had enough. ...“I’m mad,” Torres told the board. And worried. How will not knowing geometry impact him next year when he takes Algebra II? Will it hurt his chances to get into a good college?...Torres said his fourth period geometry class has been a wasted 50 minutes, spent on his phone or listening to music. Math books sit uncracked in a stack in the room. He said the class was essentially being graded on attendance....Harding already suffers from some of the lowest math test scores on state standardized tests. Only 2.7 percent of Harding juniors were deemed to be at grade level on the Smarter Balanced Test given last spring.". Absolutely shameful. Students who go to school ready and willing to learn and can't. These students will be unable to stay at grade level as a direct consequence of the school's failure. They'll pass the course for this year based on attendance and then will be totally unprepared for next year. Those in education should take a good look at how they keep the educational system broken.
  • The 2015 London Chess Classic has finished--sort of. Magnus staged a 2.5 out of his final 3 games to catch Giri and MVL. That means playoffs and given the tiebreaks it favors Carlsen, who will play the winner of Giri-MVL. Much more chess is coming after a short break. You can follow the games here. Interview with Kasparov coming up shortly.
  • That cynical use of power to keep education from improving is on display again at EAGNews: "More and more Milwaukee parents are choosing to send their children to schools that are not staffed by teachers employed by Milwaukee Public Schools. In other words, more parents are choosing schools that are not staffed by union teachers.......A recent study conducted by the Wisconsin Institute for Law and Liberty (WILL) determined that students attending Wisconsin charter schools “are exhibiting greater growth on average in those core areas (reading and math) than students at traditional public schools,” according to WILL study determined that Wisconsin’s independent and non-instrumentality charter schools, which are mostly found in Milwaukee, perform better academically than instrumentality charters. In other words, the freedom to hire non-union teachers, and avoid cumbersome rules like having to lay off or transfer teachers based largely on seniority, helps charters meet their academic goals....Perhaps more parents would have stuck with MPS schools over the years if district authorities had demonstrated more flexibility. But they have stubbornly refused to allow many of their charter schools to have more freedom in hiring practices, particularly when it comes to hiring non-union teachers, according to various media reports....Of course some groups continue to oppose the very existence of charter and voucher schools in Milwaukee. The most vocal among them is the Milwaukee Teachers Education Association, the district’s teachers union. But as notes about the MTEA, “It, of course, has an obvious economic interest in supporting only MPS schools which are staffed by union members.”That’s because the union depends on revenue from dues paid by teachers. The more schools with union teachers, the more money the union makes.". There is no evidence that being a certified teacher makes you better. Results of private schools performance and cases like the one above show the opposite is true. But as you can see, the certification of teachers affects unions. Teaching colleges also wouldn't like people becoming teachers without being trained and approved by them.
  • And that same abuse of power is on display in Minnesota where EAGNews tells us, "Administrators and teachers at St. Paul Public Schools have their own ideas about what to do regarding the lack of student discipline, which has led to an alarming spike in violence and unruly behavior, and culminated in the assault of two teachers in the last week. The teachers union wants the district to provide millions of dollars for teacher/parent committees in each building, to spend as they wish on potential remedies to the problem....“The union has asked for a dedicated staff member and $100,000 for each campus’ ‘school climate improvement team’ to implement whatever restorative practices they see fit,” the news story said.“Silva said that plan would cost $11 million. She said she would rather set up a committee of teachers and administrators to come up with solutions for the entire district.”.
  • TruthOut has the best coverage on the Greenpeace sting which " how fossil fuel companies can secretly pay academics at leading American universities to write research that sows doubt about climate science and promotes the companies' commercial interests....Professor Frank Clemente, a sociologist from Penn State university, was asked if he could produce a report "to counter damaging research linking coal to premature deaths (in particular the World Health Organization's figure that 3.7 million people die per year from fossil fuel pollution)".He said that this was within his skill set; that he could be quoted using his university job title; and that it would cost around $15,000 for an 8-10 page paper. He also explained that he charged $6,000 for writing a newspaper op-ed....Professor Happer, who is a physicist rather than a climatologist, told Greenpeace reporters that he would be willing to produce research promoting the benefits of carbon dioxide for $250 per hour....Both Penn State and Princeton University declined to comment.". You have to wonder if there is more fallout to come-selling themselves out makes the universities look bad; for them to not do anything looks even worse.
  • Some people think being good at chess is enough to build your street cred but at Sputnik news we find that the real warriors are going for the "ice chess challenge" in February 2016. Start practicing!
  • on how a high school student Dominick Rowan has "...helped to find a Jupiter-like planet and has calculated that this type of planet is relatively rare, occurring in three percent of stars overall. Their research is has been accepted for publication in the Astrophysical Journal.". Great job Dominick!
  • CTAN has two new packages you should be aware of: Metropolis beamer theme to give your presentation a new look and an ellipse package for drawing ellipses.

Odds and Ends: Basics and Graphics

SolvingEqns1I've added another worksheet to The Basics page; this is a collection of solving equations with one variable--often called 2-step equations. As it runs using sagetex you'll need it installed on locally on your computer or, even easier, open a free Sagemath Cloud account. The link for Sagemath Cloud is on the the sidebar. I've also added two plots to the Graphics page: the first plot is a exponential (growth) versus its logarithmic inverse to see the reflection around y=x (also plotted). The second plot has a exponential (decay) plotted against its logarithmic inverse.

Here are some stories that caught my attention over the last week:

  • The London Chess Classic 2015 has begun and though you won't find Komodo or Stockfish you can find some pretty good carbon based talent including (human) World Champion Magnus Carlsen, Anand, Caruana, Nakamura, Topolov, Grischuk, Adams, MVL, Giri, and Aronian. You can find the games streaming here along with GM commentary.
  • Some follow up on TCEC: Chessdom reports "Komodo also proved dominant in earlier stages of the competition. It won Stage 1a, then easily cruised through Stage 2. In Stage 3 it gave the first warning to its main opponent by winning with a two points difference.With this Season’s victory, Komodo successfully defended its title from TCEC Season 7 and together with the victory from TCEC Season 5 Komodo  is now triple champion of TCEC. That makes it the engine with most titles in Top Chess Engine Championship, together with Houdini which won Seasons 1,2, and 4. Stockfish is the only other engine that has a title from the competition.".
  • has a piece by GM Robert Hess explaining how he played Komodo in a 4 game match shortly before the TCEC matches began., "My two starting positions were as follows: White with an exchange up and my rook on b1 while Komodo's rook on a8 was removed, and White with pawns on e4 and d4 and Black missing the f7 pawn. In all games, I had 45 minutes+25 seconds increment per move, while Komodo had 45 minutes with 15 second increment. I was given greater increment because I was providing commentary while playing, thus ensuring I would be making slower moves." The result was 4 draws.
  • Dr Everett Piper, president of Oklahoma Wesleyan University has had enough of the cry-bullies that have taken over numerous universities and he earned a lot of attention and respect by posting a letter to the school website "This is Not a Day Care. It's a University". TribLive has more of the details, "Mr. Piper is the president of Oklahoma Wesleyan University. He became incensed when a student confronted him after a chapel service to complain that he felt “victimized” by a sermon about not showing love. “In his mind,” Piper wrote in a scathing blog post, “the speaker was wrong for making him, and his peers, feel uncomfortable.” “Our culture has actually taught our kids to be this self-absorbed and narcissistic,” Piper continued. “Any time their feelings are hurt, they are victims. Anyone who dares challenge them and, thus, makes them ‘feel bad' about themselves is a ‘hater,' a ‘bigot,' an ‘oppressor,' and a ‘victimizer.'”And Piper was far from done.". Well done Mr Piper! Other admins take note, please.
  • The Daily Caller reports, "District of Columbia officials released results from a recent citywide elementary school exam Monday, and the scores are abysmal. Less than a quarter of students met expectations in either math or English. Among all eighth grade students who took the test, just 3 percent met expectations in math, while 8 percent of seventh graders met the math expectations, according to Partnership for Assessment of Readiness for College and Careers (PARCC) test results."
  • Google crosses some red lines: RT reports,"The Electronic Frontier Foundation has filed a complaint with the Federal Trade Commission in which they allege that Google has been violating the privacy of students as young as seven years old by mining their data.The EFF’s Tuesday complaint said that Google can track every search term, site, and video students view using a feature that is enabled by default on the Chromebooks that are sold to schools. The data collection is allegedly not used for advertising purposes, but rather to “to improve Google products.”The complaint alleges that the monitoring is in violation of a Student Privacy Pledge that Google signed in 2014, which the EFF said is legally enforceable under the Federal Trade Commission Act."
  • You might remember how, decades ago, corporations got themselves into schools by selling a lot of junk food in vending machines which was followed over time by a rise in child obesity and diabetes. Now CNBC has an in depth piece on corporations in the classroom and Google is winning, "Google, Microsoft and Apple have been competing for years in the very lucrative education technology market. For the first time, Google has taken a huge lead over its rivals.Chromebooks now make up more than half of all devices in U.S. classrooms, up from less than 1 percent in 2012,...Google's major advantage when it comes to wooing cash-strapped school districts — which are expected to purchase more than 11 million devices next year in the U.S. alone — is Chromebook's extremely competitive price...."They set up what's called a blended classroom, so they would have the teacher with only about seven students, but then seven other students would be learning from Khan Academy, seven others would be doing a group project and seven students would be assessing their skills to try to figure out where they are at that point in time."". Note the classroom reference to kids learning from a Khan Academy video  of an uncertified person who isn't a teacher. A little bit ironic given some of the ferocious criticism directed his way.
  • The NY Times takes a look at the quandry of NY education officials, "...If the percentage of students passing the Algebra I exam falls to 63 percent from 72 percent, and the passing grade is scheduled to increase by 9 points in coming years, should the test be made easier?...This fall, they established a committee to study the results on the new exams to determine, among other things, whether the bar for passing, which students would have to meet starting in 2022, had been set too high. (They had originally said the class of 2017 would need the higher scores to pass, but last year decided to push that back)....The city’s Education Department is “in a panic about this,” said Uri Treisman, a professor of mathematics at the University of Texas who has advised the department on plans to improve math instruction in middle and high school.Among the ideas the city is considering: having fifth graders take math with a specialized instructor instead of one teacher for all subjects; teaming up with local universities to get more sixth- and seventh-grade math teachers certified in math instruction; creating summer programs for middle- and high-school students who are struggling in math; and training middle-school and algebra teachers in how to address students’ “math anxiety.”". Quick recap: Common Core would toughen standards and show the soccer moms their children weren't quite as good as they thought. Objective achieved and now, with a higher bar, educators look like they are doing an even worse job and parents and students are not happy. So lets make the test easier. Here's one reason, of many, why education fails. Also take note the "...committee to study the results on the new exams to determine...whether the bar for passing...had been set too high". Given that officials are panicked about the results you have to wonder how independent the committee will be. If the level is determined to be set incorrectly will the company that designed the faulty test be held accountable? Will more money be required to create a test that gives the proper results? Stay tuned!
  • The DailyStatesman has a topic that I think is a winning idea, "The Hour of Code is a world-wide initiative during the Dec. 7-13 Computer Science Education Week, aimed at introducing millions of new learners to computer science....The Hour of Code involves the use of a self-guided tutorial which allows students to learn at their own pace and skill level. The tutorials expose the students to fundamental computing concepts on a level playing field and is intended to inspire today's youth to build technology..."They don't realize it, but when they're learning this and writing in functions, they're basically writing in x-y t-charts, applying algebra skills and again, applying critical thinking skills in the process."They're challenged in this process," Bolin says. "It's not for everyone, but you never know. You see kids with their interest peaked once they get into it."As evidence, Bolin says that a group of students he taught last year were so interested in advancing their coding skills, they continued the process at home. The group went on to compete at the National Jr. Beta competition and placed second in the nation."". Some schools are taking an interesting and innovative approach to education.
  • If you follow chess you know there is always a debate about whether the current chess players are better than great players from the past and, if so, by how much. The issue of chess ratings muddies the water because of chess ratings inflation. It makes some fans think the current crop of players is always best because their ratings are higher. But something unusual has happened:LiveChess12-5-15Notice that of the top 4 players in the world, three are in their forties. This really shouldn't be happening. Has something like this ever happened before?? I  think all of those players (Topolov, Kramnik, and Anand) would admit their "best chess days" (in terms of chess strength and not rating) are behind them. Is the current generation of 20 somethings really better than the last generation of players? It certainly doesn't show from the current rating list. And when you consider that much of the improvements in modern chess players are tied to them growing up with chess engines to spar with and help them get better, it's difficult to believe that the current generation is better. It seems clear that Topolov, Anand, and Kramnik would have been even more fearsome had they grown up  with the chess playing software that we now take for granted. So the question becomes, "Is this evidence that chess is dying as the current generation is not replacing the last one even on the basis of today's inflated ratings?". Chess rating inflation seems to be covering the decline in chess players. What do you think?