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."