SageTeX: First Derivative Test


This week I've added another problem to the SageTeX: Derivatives page. The screenshot is above. Given a polynomial students need to create a table to show when the function is increasing or decreasing. Then they have to determine the local extrema.

Filling out the table makes use of Sage's ability to calculate derivatives. Here's a small snippet of the code. Note the indentation has been lost.

if df(0)>0:
a13 = '+'
a14 = "increasing"
a13 = '-'
a14 = "decreasing"

Depending on whether the derivative is positive or negative we can fill out the chart. And the same logical reasoning that allows you to fill out the chart by hand is the same logical flow that the Python code goes through--but without the errors we humans are prone to make. And of course, recompiling can generate lots and lots of problems with an answer key, faster and more accurately than any human could.

Here are some stories that caught my eye this week:

  • ZeroHedge has the latest on the Chicago Pension Scandal, "Take the example of two union lobbyists who substitute taught for one-day in the public schools and then started collecting over $1 million of lifetime public ‘teacher’ pension payout – despite a state law expressly designed to stop them. And now take all the other 7,499 educators. The retirees in question paid so little into their own retirement (breaking even on their cost basis within the first 20 months of retirement) that taxpayers now face a $900 million bill just to keep the pension payments flowing!...The fraud appears to be focused on the city of Chicago. Some examples:
    • Northern Illinois school districts are driving the majority of $100,000 pensions. In fact, 6,706 pensions for over $800 million in annual payouts were conferred by districts in the Chicago metropolitan suburban area. Only 793 six-figure pensions totaling $95 million in annual payouts were conferred by school districts in the rest of the state. Yet, income-taxpayers across the whole state guarantee the retirement annuities for everyone.
    • The Top 100 All-Time pensions: #1 $302,991 (Lawrence Wyllie at Lincoln-Way CHSD) to #100 $200,812  (Michael Radakovic at Aurora East USD 131). Read the Top 500 All-Time IL teacher pension list.
    • The Top 5 school districts conferring six-figure pensions are Palatine TWP HSD 211, Palatine (449); Township HSD 214, Arlington Heights (419); Consolidated HSD 230, Orland Park (196); Northfield TWP HSD 225, Glenview (188); Maine TWP HSD 207, Park Ridge (180)."
  • You thought hoped her 15 minutes of fame were over. But it isn't--she's baaaack! Melissa Click was interviewed, shamefully enough, by the Chronicle of Higher Education. dissects it all: "More:

    While Ms. Click acknowledges that she was certainly frustrated that day, she says she was simply trying to protect the black student protesters. Everything she has come to stand for since the video came out—intolerance, anger, mouthiness, and dismissiveness—is exactly the opposite of who she says she really is. Focusing on her behavior, she says, is a way to take attention away from the demands of Concerned Student 1950, the group of protesters. 

    "I’m not a superhero," Ms. Click says. "I wasn’t in charge." But she’s taken the fall. "When it got out of control," she says, "I was the one held accountable." 

    And not by accident. Click was held accountable because she committed assault. If her behavior is drawing attention away from the student activists, that's entirely her own fault. 

    The Chronicle story also includes some biographical details that uncritically accept Click's I-am-a-hero narrative....Is this the profile of a woman who has overcome great adversity, or the profile of an intolerant ideologue firmly convinced of her own greatness?.....But she doesn't deserve sainthood, either. She did a very bad thing, and her revisionist attempts to explain away her criminal behavior should be rejected. Assault is wrong, even if the person committing it has a minor in women's studies."

  • An article in the Tennessean says, "Police handcuffed multiple students, ages 6 to 11, at a public elementary school in Murfreesboro on Friday, inspiring public outcry and adding fuel to already heightened tensions between law enforcement and communities of color nationwide.The arrests at Hobgood Elementary School occurred after the students were accused of not stopping a fight that happened several days earlier off campus. ....Murfreesboro police didn't say what state law the kids violated, but parents of several of the arrested children say the kids were charged with "criminal responsibility for conduct of another," which according to Tennessee criminal offense code includes incidents when a "person fails to make a reasonable effort to prevent" an offense."
  • NPR reports on the latest report card of public high schools, "This tiny downtick was statistically significant in mathematics, but not for the reading test....NAEP scores are comparable across decades — back to 2005 for math and all the way back to 1993 for reading....According to research by Ho and others, just under 40 percent of students score at college and career ready levels on NAEP....One is that in 2015 the nationwide high school graduation rate was 82 percent, not 40 percent. That leaves a potentially large group of kids who got diplomas but who weren't ready to succeed in college. Who is right: their high schools or NAEP?
    ...On the other hand, he says, "the less-than-charitable view would be that graduation is just a lower standard than college readiness. If you get right down to it, the reading and math required by NAEP, the ACT, the SAT, colleges and careers is much greater than what high schools are saying is sufficient." High schools with dumbed down standards to increase graduation? Shocking!
  • Most of us aren't particularly excellent at what we do, but imagine if we could compete against high school students. We'd look really good then. Vice News continues "A few weeks ago, Jonathan Nicola was the star player on his high school basketball team, with a coach who believed he had a shot at going pro. But now that it's come out that the 17-year-old is actually a 29-year-old man, his ambitions — whatever they may have been — have been put on hold, and he's begging the Canadian government to send him back home to South Sudan."
  • The Huffington Post looks at standardized testing, "Turns out, academic conformity sells, and business is booming: As of 2011, Gaston Caperton, the president of the College Board,nonprofit owner of SAT, was paid $1.3 million. Richard Ferguson, formerexecutive officer of ACT Inc., made roughly $1.1 million. Meanwhile, The National Board on Educational Testing and Public Policy at Boston College reported that the value of the standardized testing market was anywhere between $400 million and $700 million........Standardized testing isn’t just about every student meeting the same standards. It is about every student, school, and administrator paying for the same product." So, so true. And public education means there companies have less people to persuade. Give an incentive for those at the top and a lot of money flows to the company. A good article which is worth reading very carefully.
  • Chessbase reports on Fabiano Caruana winning the US Chess Championship. The US Women's Chess Championship was won by Nazi Paikizde after the favorite to win, Irina Krush, had an uncharacteristically bad tournament and the tournament leader, Tatev Abrahamyan, lost the final round. Some very ugly chess by the women but fighting chess that kept me riveted as never knew who would make the final mistake to lose. The tournament was followed by the Ultimate Blitz championship which featured Kasparov, Nakamura, So, and Caruana. Nakamura won, Kasparov was only .5 points behind but the highlight was a So-Kasparov brilliancy. The Chessbase report quotes Yasser Seirawan as saying "Wesley's game against Kasparov will go down in history as one of the greatest blitz games ever played. I will remember that game for the rest of my life." and Kasparov said "It reminded me of games Morphy played against amateurs.". It's that brilliant. Make sure you check out the game at the Chessbase link.
  • It looked like Carlsen was going to easily win the Altibox Norway Chess tounament. A loss in the penultimate round kept the issue in doubt but winning the final round gave Carlsen first place. Chessbase has the story here.
  • The Atlantic looks at "Why would a Teacher Cheat?" I can think of some reasons but back to the article, "The prevalence of test-score manipulation in the United States is well-documented. In fact, with the help of the same researchers who authored the Regents Exams study, The Wall Street Journal in 2011 revealed a significant spike in the number of exams in all the main subjects with scores of 65 points out of 100—the minimum passing grade....There’s good evidence that score manipulation does harm kids, particularly when teachers are falsifying their responses outright for the sake of avoiding sanctions. But there’s also good evidence to suggest that score inflation—teachers grading a bit more leniently, often because they think the student underperformed on the exam—may have positive effects as well. While inflating an individual student’s test score doesn’t magically inject her with more knowledge, the two aforementioned studies indicate it significantly boosts her odds of overcoming an obstacle increasingly critical to future success: high-school graduation." WTF? Schools cheat but hey that may be a good thing because kids graduate. Isn't it obvious that increasing inflating a students grade would increase the chance of their graduating? And, news flash, it's probably likely that some of the inflation is done precisely to get that failing senior out of the school system. But when about 40% of the graduating classes are college ready perhaps high school graduate as an indicator of future success will lose its value as a high school degree is no longer proof that you can read and write. This is an absurd article on a lot of levels. And the nonsense continues, "Indeed, a growing body of international research suggests that the prospect of a raise—or the threat of sanctions—seldom induces teachers to fudge their students’ test scores. Altruistic motivations appear to be at play." And I've got a bridge in Brooklyn to sell you. The school system is so broken and most of the people in charge aren't interested in fixing it.
  • Yet another Common Core defector wanna-be: Michigan. Truth in American Education says, "Michigan’s Common Core Repeal Bill just made it over a a major hurdle. The Senate Education Committee voted to pass SB 826, a bill that would repeal Common Core and replace them with Massachusetts pre-Common Core standards."

Graph Theory, Sage, and LaTeX page


I've added another page to the website. It's still in the beginning stages but it will cover graph theory, $latex \LaTeX$ and Sage. You can find it here and it's listed on the sidebar or click here. From this documentation at the Sagemath website you can see the way Sage works with $latex \LaTeX$ to produce graphs. This method is quite different than what you'll find in the Altermundus tkz-berge package despite the fact that Sage uses that package. The information I just posted has to do with the creating a graph in the simplest and cleanest way. I opted for the 'Normal' representation of graphs to allow for a choice of labels inside or outside. A vertex is created as follows:


where R1 is what the vertex will be referred to by the program and the factors which determine the label are handled in the options:

LabelOut to put the vertex label outside the vertex. Lpos is the label position. It's the angle of rotation around the center of the vertex (0 is east of the vertex, 90 is north of the vertex, etc). L= will be the label, and x=, y= handle the placement of the vertex. Simple and efficient. You can read more on the new page where I've posted the code for two 'Normal' graphs, with labels out and with labels in.

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

  • 11alive covers Tennessee phasing out Common Core. "Common Core standards ignited a political brawl last year when state lawmakers, who saw the standards as federal overreach, pushed to scrap them. In response to cries for state-specific standards, Gov. Bill Haslam authorized a review of the state's English and math standards."
  • St Louis Post Dispatch reports "Missouri became the latest state to adopt a new set of education benchmarks to replace the national Common Core standards, ditching the benchmarks Tuesday following conservative backlash.". Common Core is not so common anymore.
  • EAGnews has a piece on  Tennessee students "Parents and community leaders in Murfreesboro are fuming after police arrested numerous elementary students at school over a fight that occurred off campus several days prior....Several students at Hobgood Elementary School, ranging in age from about 6 to 13 years old, were then handcuffed and arrested, and hauled to a juvenile detention center before their parents were even notified, WKRN reports.....“Here’s the catch, the girls were just bystanders in the video. They were not fighting, they were not instigating it, they were just standing in the video. And there was actually no technical fight in the video,” he said. “But the claim and the accusation is that they didn’t stop the fight, so they should be arrested.”"
  • RT has a piece where the title says it all: "Teacher tackles pupil to the ground in ‘deeply disturbing’ classroom attack".  A violent, profanity laden assault that will hopefully lead to jail time.
  • But it's better overseas, right. Not all the time. RT has video footage of  "A teacher in China bore the brunt of a vicious classroom uprising after he tried to forcibly collect a student’s exam paper in a shocking case of school violence caught on camera."
  • Don't even think about messin' with Colorado schools. ABC news reports, "A suburban Denver school district is arming its security staff with military-style semiautomatic rifles in case of a school shooting or other violent attack, a move that appears unprecedented even as more schools arm employees in response to mass violence elsewhere."
  • Chalkbeat reports  "Facing widespread backlash after years of controversies and testing glitches, one of the world’s largest testing companies is taking an unusual approach to quieting critics: It’s opening its doors." The Washington Post covers some of the problems here.
  • The Altibox Norway Chess 2016 tournament has 4 rounds in  the books. Magnus in first but with Kramnik, Giri, and MVL lurking around the tournament is wide open. You can follow it here. Click on the "Live Streaming" button at the top of the page to follow it live.
  • There are just 2 rounds left in the US Chess Championship. You can watch it live here. Caruana leads for the championship section, and Abrahamyan for the women. Irina Krush doesn't control her fate anymore as she competes for another title.

Altermundus: circle-circle intersections


I've added information on getting the intersection of 2 circles using the tkz-euclide package. The tkz-euclide package gives a macro \tkzInterCC to find the intersection of 2 circles. As there are multiple ways to input a circle, the macro can be used in different ways.

\tkzInterCC(D,B)(A,C) \tkzGetPoints{M}{N}

finds the intersection of circle centered at D containing point B along with the circle centered at A containing point C. The two intersection points are recovered with \tkzGetPoints macro. Likewise

\tkzInterCC[R](A,1 cm)(B,1 cm) \tkzGetPoints{M1}{N1}

finds the intersection of circle centered at A with radius of 1 cm along with the circle centered at B with radius 1 cm. Note the R option.

You can download the code, with comments, here.

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

  • What happens in Vegas may stay in Vegas, but in Mexico---not so much. RT has a piece on "A prestigious fee-paying school in Mexico has failed to separate twerking from working, allegedly forcing a 24-year-old teacher to resign after she participated in a dance competition while on spring break. The primary school teacher, known only as Clarissa, was in the popular Mexican holiday spot Cabo San Lucas when she decided to channel her inner Miley Cyrus and grind on one of the judges."
  • Listverse has "10 Strange Cold War Tales Left Out Of The History Books"
  • RT on "Flint, Michigan has become the epicenter of the lead water crisis in the United States, but hundreds of schools across the country have tested positive for unsafe lead levels in their water over the past three years, according to a new report."
  • Reuters on "Meet the Thai math prof whose copyright case is headed for SCOTUS – again"
  • Technology review looks at  "A chip that can’t guarantee that every calculation is perfect can still get good results on many problems but needs fewer circuits and burns less energy, he says...A chip that can’t guarantee that every calculation is perfect can still get good results on many problems but needs fewer circuits and burns less energy, he says....In a simulated test using software that tracks objects such as cars in video, Singular’s approach was  capable of processing frames almost 100 times faster than a conventional processor restricted to doing correct math—while using less than 2 percent as much power."
  • The US Chess Championship (closed) has begun. Caruana, Robson, and So are tied for first after 3 rounds of the scheduled 11 rounds. Follow it live here.
  • IndyStar's Russ Pulliam looks at who won common core, and with the number of states using common core down to 21 you get the idea that failure has been achieved.
  • WTHV11 has a report and video on one of those states that has moved away from common core , "In nine days, 85 Arkansas teachers across the state revised 65 percent of the Common Core Math Standards. They hope these revisions turn confusion into a statewide understanding."
  • looks at the teacher shortage in Detroit, "Two moms want answers. How can it be that in public schools in this country - kids can go months without a math teacher?" Answer: The priority of the system isn't about providing a good education for the kids. If they'd remove the numerous hoops to jump through requiring money and time they'd have plenty of people. Certified does not mean qualified. And many qualified teachers are denied certification. Until they fix the Orwellian double-speak you won't have meaningful change.
  • A cougar in LA might not be uncommon, but a mountain lion at an LA high school is. RT has the the details and video that led to a school lockdown.

Sage Interact: Generate Continuous Data


We already know it's not math, but like (physics, engineering, chemistry, etc) it's an important application of math. But we've seen, "David Moore, statistics educator and former president of the American Statistical Association , gives the following four compelling reasons why statistics is a separate a.discipline from mathematics:......

  • The standards of excellence in statistics differ from those of mathematics"

Truth be told, the standards of the pseudo-science of statistics differs from real science as well. Data analysis is, as my graduate analysis teacher used to say, more of an art than a science. Now there's an understatement! As statistics infects the high school math curriculum you might find yourself having to teach it, in which case you'll find the pseudo-math field of statistics needs data---lots of data.

Luckily, the brief foray into statistics at the high school level doesn't get too involved. A lot of the descriptive statistics in high school doesn't venture into the BS dubious areas of statistics; they tend to focus on mean/median/mode/standard deviation and plotting a bunch of graphs by hand even though in the real world they'd use Excel to process the data and put out charts. To eliminate some of the drudgery I've put together a Sage Interact that generates data for some continuous probability distributions (normal, exponential, gamma, beta). As you can see from the screenshot above, you can pick how many items to include in your data set as well as specify the number of digits shown. Finally you can specify the number of bins to use in the histogram. Be aware that the figure might be cut off (as below) and to see the rest of it you'll need to find and use the scroll bar underneath the histogram.


The total output is a histogram, the data set, and some common statistics (sample mean and standard deviation, mode, minimum, and maximum). A simple copy and paste will get you data for a test/quiz/example along with the answers to prevent any mistakes.

You can find the code on the Python/Sage page. Copy and paste the code into a Sage Cell Server (such as on the Sage Sandbox page), press "Evaluate" and generate the data sets you need quickly and easily.

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

  • The NY Post has a story on teachers taking a public stand: "Renegade city public school teachers have been sending emails to parents the past week encouraging them to boycott the state English and math Common Core exams being administered citywide starting Tuesday,...some teachers at the Earth School on the Lower East Side emailed a four-page letter to parents slamming the exams and applauding the 73 percent of parents who opted out last year,...A city Department of Education official warned that teachers “may be subject to discipline” if they cross the line in prodding parents to opt out. Teachers complained DOE has imposed a gag order."
  • The New Scientist has a piece on the knew movie on Ramanujan's life and it's not positive: "Ramanujan’s journey is the subject of a new film, The Man Who Knew Infinity, based on a book of the same name....the film attempts to give us a glimpse of an unknowable mind traversing the realm of abstract thought, while also humanising its subject. And frankly, the formula is starting to wear thin....The Man Who Knew Infinity isn’t bad, it’s just safe, cramming Ramanujan’s colourful life into a well-established, sellable format."
  • Common Core is dead, according to the Federalist. It's not official yet, though: "The big postmortems will roll out in a year or two, but it’s already clear this education monstrosity is eking out its last gasps....Common Core has by now not only failed academically, it has failed operationally. This is a horrific outcome...Common Core’s failure should indict every single Common Core cheerleader and prompt a revival of genuine education reforms we’ve known for decades would actually help children but aren’t sexy to the consultant class that makes a living as “education innovators” (i.e. experimenting on children for fun and profit)...Researcher Ze’ev Wurman looked at several other indicators of student achievement and found none have improved since Common Core went into effect. In fact, SAT and ACT scores are slightly down....Common Core tests’ rapid (and predictable) disintegration has negated politicians’ central justification for the (unconstitutional) federal requirement that states give annual math and reading tests: “public accountability.” That’s because it’s impossible to compare Common Core test results to those that came before them. It would have been possible had educrats cared enough about accountability to require the proper testing translations, but they didn’t. Common Core test results cannot even be compared to themselves yet because they have not generated enough reliable data....Obama’s dictatorial flourishes of the pen have forced tens of thousands of people to spend hundreds of millions in tax dollars and millions of man-hours essentially shuffling paperwork. It’s trickle-down bureaucracy. (That’s why half of school employees are not teachers, but instead mostly paperwork shufflers. Thanks, feds!) " A good piece with a lot of information. Why does every educational plan fail after 5-7 years time and time again so the educational experts people can spend a lot of money to come up with another plan? That's rhetorical, of course
  • EAGnews on reports on "Parents are removing their children from Bear Branch Elementary School after the principal allegedly banned them from school grounds and threatened violators with arrest....District officials issued a prepared statement to Fox 26 about the situation that supported Ray’s supposed goal of a safe dismissal....Parents said they do not believe the old dismissal process was unsafe, and believe the principal is on a power trip.
  • ZeroHedge hosts a piece by Jim Quinn: "The Department of Education was created in 1979 and now has an annual budget of $73 billion, with 5,000 government bureaucrats roaming its hallways. When you include all Federal, State and Local spending on public education it totals about $700 billion per year, or $13,000 per student. ...According to the 2007 California Academic Performance Index, research show that 57% of students failed the California Standards Test in English.... 50% of the unemployed between the ages of 16 and 21 cannot read well enough to be considered functionally literate" If doctors or lawyers had such poor results they'd be sued for malpractice.

Handout: counting factors


If you teach some combinatorics in your classes you're probably familiar with the Fundamental Principle of Counting, otherwise known as the Multiplication Rule, and the typical problems (how many ways to roll a 7 with a pair of dice, how many outfits to where, how many different pizzas given specific topping choices). Some of that is fine, but I also like to link it to things they should already know: factoring numbers. I've created a handout on determining the number of factors of a number. For example, there are 9 factors of 100 (1, 2, 4, 5, 10, 20, 25, 50, 100).  Typically schools teach students to try dividing the the numbers 1,2,3, ....n into the number n and pairing the factors along the way but that's certainly not the way a math person would do it, especially as the numbers get bigger. For a number with a lot of factors, such as 6!, it's too easy to miss some factors unless you have a methodical way of finding them. Getting the prime factorization of the integer will let you use the Fundamental Principle of Counting to quickly get the answer: no trial and error. You can find the details in the PDF is posted on the Handouts page. Most students don't know the basics, which is a good enough reason to combine it with combinatorics, so factors and primes and other basic concepts need to be reviewed.

I've added a link to OER Commons, covered in the last post, to the sidebar.

Here are some stories that caught my eye this week:

  • Let's call this now. This is one of the most interesting educational stories you'll read for 2016. It's a lengthy Reuter's article, two parts in fact, on the cheating on the SATs taking place in other countries, while the College Board (the organization that owns the SATs) does nothing. PART 1 and PART 2. From part 1: "A confidential PowerPoint presentation reveals that College Board officials had documented widespread security problems in June 2013...Even so, College Board officials confirmed that some portions of those tainted tests were later administered overseas. And the College Board took no steps to restrict testing in China, the SAT's largest market by far, even as it tightened security in smaller countries where exams had leaked." There is literally too much to quote and I'd strongly urge you to read both articles. There's even a video in PART 1.
  • I've mentioned the corruption in education many times. RT reports "A dozen current and former principals from Detroit Public Schools were among those hit with bribery and conspiracy charges by the federal government regarding a scheme to score kickbacks from school supplies that were rarely, if ever, delivered....Flowers and the 12 principals have been accused of submitting fraudulent invoices for school supplies to DPS that were either never delivered or only partially delivered, according to complaints filed in the US District Court. In exchange for inaccurately reporting the delivery of these goods to DPS, Allstate Sales would receive payments from DPS, while the company owner Norman Shy would deliver kickbacks to the principals as well as Flowers, according to court documents....The charges come as officials in Lansing continue to debate the future of DPS, which currently suffers from a crushing debt in excess of $500 million, in addition to crumbling infrastructure. " Large pools of money and lax oversight is a tempting target for educational professionals crooks.
  • Chess is taken pretty seriously in other parts of the world; RT tells us "A chess duel at a major competition in Ukraine evolved into a fist-fight after a coach became incensed by the way his pupil was being treated....The young woman’s trainer, Mikhail Gerasimenyuk, hurried to help his pupil, but in a way that nobody had expected: he slammed Sakun twice...Sakun had his eyebrow and nose cut, and vessels in his eye ruptured."
  • Students behaving badly, EAGnews reports, "Numerous Glenn Hills High School students face murder charges after a massive 50-person brawl that ended with the death of an 18-year-old man.....Police allege Demajhay Bell, 18, died from being stabbed in the neck during a large street fight involving as many as 50 people, many Glenn Hills students, in Augusta, Georgia March 18. The melee was caught on cell phone video and posted online, providing a harrowing look at a very violent clash involving pipes, bats, and a vehicle barreling through the fracas..."
  • More students behaving badly. Once again from EAGnews, "An Alaska charter school suspended three first-grade girls for plotting to kill a classmate with “poison.” Anchorage police told KTUU three first-graders at Winterberry Charter School planned to poison a classmate with a silica gel packet they believed to be toxic in hopes of killing the young girl."
  • Yet more students behaving badly from EAGnews: "A 16-year-old Syracuse high school student faces two felony assault charges after police allege he punched two teachers in the face for attempting stop him from using his phone in class..The problem stems from a “restorative justice” approach to school discipline that’s designed to reduce punishments for minority students. Large inner-city school districts adopted the approach at the behest of the federal government as a means of reducing suspensions for minority students.....In Syracuse, a December survey of 830 district teachers revealed the vast majority of teachers don’t feel safe in their own classroom, with a third reporting to have been physically assaulted by students, WSTM reports.." Because when admin have caved into students doing what they want, students will do what they want. Do you think that makes it easier for schools to attract qualified people into the teaching profession?
  • The lack of certified teachers is a problem in Arizona. KVOA tells us, "Arizona is simplifying its test for prospective math teachers, in order to help solve its teacher shortage crisis. The State Board of Education has opted to only test teachers on math up to Algebra 2. Teachers will no longer have an exam on trigonometry or calculus, which many educators believe is better than the current alternative."Now a lot of those classes, Algebra 1, geometry, or calculus... Those are being taught by long-term substitutes," said Melissa Hosten, co-director of the Center for Recruitment and Retention of Mathematics Teachers." Certification drives down quality by keeping qualified people out of the classroom. The result is a lousy education run by "experts" who have shown an inability to educate for decades.
  • Some good news. The Federalist has a piece "8 Great Women of Science History".
  • And back to reality. Michael Snyder on just how stupid Americans have become.
  • Do you ever give out candy or snacks to your class? A VERY BAD IDEA if some new regulations get approved. on the consequences: "The federal government is taking steps to fine schools that do not comply with first lady Michelle Obama's school lunch rules....The regulation would punish schools and state departments with fines for "egregious or persistent disregard" for the lunch rules that imposed sodium and calorie limits and banned white grains. A West Virginia preschool teacher was threatened with fines for violating the rules by rewarding her students with candy for good behavior in June 2015. The teacher ultimately did not have to pay, but the school had to develop a "corrective action plan" with training on the policies. The government now seeks to make fines enforceable by regulation. Section 303 of the law requires that the federal government "establish criteria for the imposition of fines" for all the Department of Agriculture's child food programs...The Food and Nutrition Service is targeting schools that refuse to comply with Mrs. Obama's lunch rules and said monetary penalties are a "useful tool" to get noncompliant cafeterias in line...The proposed rule would also apply to private organizations participating in federal childcare nutrition programs, including "institutions, sites, sponsors, day care centers, and day care providers." ." One more problem for those in public schools.

Resources: OER Commons


Good resources are so important to teaching. OER Commons is a good resource to have. I've added the link to the sidebar. According to the website, "Open Educational Resources (OER) are teaching and learning materials that you may freely use and reuse at no cost. Unlike fixed, copyrighted resources, OER have been authored or created by an individual or organization that chooses to retain few, if any, ownership rights. In some cases, that means you can download a resource and share it with colleagues and students. In other cases, you may be able to download a resource, edit it in some way, and then re-post it as a remixed work. How do you know your options? OER often have a Creative Commons or GNU license to let you know how the material may be used, reused, adapted, and shared." Now THAT'S the type of support that teachers need. Why don't these education departments support their teachers like this? They could save so much money on books as well.

But I digress. Even better, the resources are easily searchable based on criteria such as grade level, resource type, common core, and so. You can see below there are groupings by the area of mathematics and, in some cases, the resources have a description and rating.


Of course, with any site, it has its share of junk. But there are plenty of decent resources as well. By searching the material you also get an idea of other sites that are creating the materials that have been hosted. From CK-12 books (sign-in required) to NASA, and to one of my favorite, OpenStax, you should be able to find something useful.

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

  • The Candidates Finals are almost over. Round 13 is underway. After an exciting round 12, Caruana and Kajarkin are in the lead, with Anand right behind them. You can follow the games live on ChessBomb, located on the sidebar.
  • ZeroHedge has the latest on America's shame: the next generation. "The Daily Mail reports, the president of Emory University has spoken to demonstrators who said they were frightened after someone wrote 'Trump 2016' in chalk around campus.
    Students at the Atlanta school, which has an enrollment of more than 14,000 claim their 'safe space' was violated when the messages appeared on sidewalks and buildings. ...the students viewed the messages as intimidation, and they voiced 'genuine concern and pain' as a result. ...Now administrators want to track down those responsible for the controversial markings."
  • ClickOrlando reports "A 12-year-old was arrested and facing misdemeanor battery charges after pinching a boy's butt in school....According to the report, after the initial incident, the boy told the school resource deputy he didn't want to press charges and Evans was suspended. Evans said she didn't know the boyBut last week, the boy's mother got involved, calling deputies and saying that she wanted to prosecute Evans for battery."
  • Minnesota, like other states, is facing problems due to teacher "shortages". reports, "Teacher shortages in Minnesota have reached critical levels, and there’s no easy fix. The issue is not confined to just one part of the system; unsustainable trends in teacher recruitment, licensure areas and increased retirements have worked together to create a school environment in which students either do not have the right teachers in the classroom or schools can’t find enough applicants for the positions they need to fill.". Creating an artificial shortage through the licensing hoops which require time and money to get into a school system that is fundamentally broken isn't working. Since there's no evidence that certified teachers are better and teacher performance in some areas is so poor (eg 2% math proficient in Camden) you have to wonder how good is that certificate, anyway. But that's not the point: the certificate is for job security and not quality.
  • And here's one of those certified teachers in action: reports, "A Georgia special education teacher has resigned after disturbing surveillance video emerged, allegedly showing her slamming a boy to the ground...The boy doesn't notice his teacher behind him when she slams her knee into his back, sending him sprawling face-first to the ground, according to the boy's mother, Sarah Patterson. The boy had just turned 4 years old Wednesday, .". Check out the video. Disturbing, to say the least.

Altermundus: Line-Circle Intersections


I've added some more information to the Altermundus: Circles page. The new information is related to the finding the intersections of circles and lines. The tkz-euclide package has a macro to find the 2 points of intersection that occur when a line crosses a circle. This allows you to make diagrams, such as the one shown above, more quickly. The .tex files of two examples are posted along with comments. You can download them and experiment on your own.

Here are some stories that caught my eye this week:

  • The Verge has wraps up the AlphaGo match, looks at its impact and talks about what is next for AI.
  • looks at a bill working its way through the Mississippi legislature that would, "....require teachers to grade parents on how involved they are with their kids' education...According to

    The legislation, by state Rep. Gregory Holloway (D-Hazlehurst), would mandate a section be added to each child’s report card on which the parents are graded on their responsiveness to communication with teachers, the students’ completion of homework and readiness for tests, and the frequency of absences and tardiness.

    What's more, adds the Parent Herald, parents would also be required to volunteer—an oxymoron at best:

    [P]arents will be required to participate in at least one supportive function for the school. This includes holding position in the Parent Teacher Association, working at concession stands during sports games or helping kids at bus stops.


  • NPR reports "This week, British professor Andrew Wiles, 62, got prestigious recognition for his feat, winning the Abel Prize from the Norwegian Academy of Science and Letters for providing a proof for Fermat's Last Theorem....The Abel Prize carries a cash award of 6 million Norwegian kroner — around $715,000 at today's exchange rates. Wiles will formally receive the prize from Crown Prince Haakon of Norway on May 24 in Oslo."
  • The Washington Post reports, "More than 100 education researchers in California have joined in a call for an end to high-stakes testing, saying that there is no “compelling” evidence to support the idea that the Common Core State Standards will improve the quality of education for children or close the achievement gap, and that Common Core assessments lack “validity, reliability and fairness."" Wouldn't it make more sense for experts to determine this prior to spending lots of money to implement Common Core?
  • ZeroHedge posts "Illinois College Will Stop Arresting Students For Passing Out Constitution". With such repressive, unconstitutional conduct by admin, it's not surprising that student behavior is so poor.
  • Quanta magazine with the interesting piece for the week: "Two mathematicians have uncovered a simple, previously unnoticed property of prime numbers...Kannan Soundararajan and Robert Lemke Oliver of Stanford University present both numerical and theoretical evidence that prime numbers repel other would-be primes that end in the same digit, and have varied predilections for being followed by primes ending in the other possible final digits...This conspiracy among prime numbers seems, at first glance, to violate a longstanding assumption in number theory: that prime numbers behave much like random numbers.."
  • The 2016 Candidates matches to determine a challenger for Magnus Carlsen are in the 8th round. After 7 rounds, Karjakin and Aronian are tied for first with 4.5 points. Topolov is in last place with 2 points. With 7 more rounds the tournament is still wide open. You can follow it on ChessBomb (side link). The tournament site is here.


LaTeX: Letter template


Well, I lost. As I already mentioned, I ran into problems when I moved states. It seems that not having a teacher training program which ended with hours of student teaching was enough deny my application for a regular license, despite the fact that I had 3 years full time teaching experience as a public school teacher. Go figure. And if you knew just how bad some of the certified teachers are in this state (any state) you would understand what a farce the educational system is. From one side of their mouth they say they want qualified STEM teachers but from the other side of their mouth they put up barriers to disqualify them. Want to be qualified according to them then pay some fees and jump through their hoops. But I don't have a lot of patience for this sort of institutionalized stupidity; rather than be classified as a rookie teacher and be forced to pay thousands of dollars to attend hundreds of hours of training on to eventually prepare myself so I'll be officially qualified by this state to teach in a classroom (something I've been doing for years) it's time to give up on being a public school math teacher. That means my job search has been in high gear for the last two months as I write letters--lots of letters-- to apply for jobs. I designed a simple template that you can see in the screenshot above. There is some code that has been commented out to produce a line at the top and the bottom, if you want. I've posted it on the LaTeX page; I call it ClassicLetter as it is inspired by the Classic thesis design.

Here are some stories that caught my eye this week:

  • Tomorrow is Pi Day and CNBC tells us "Want to earn 3.14 years of free pizza from Pizza Hut? All you have to do is answer three math questions. There's a catch. The questions have been devised by famed Princeton mathematics professor John H. Conway and range in difficulty from high school to PhD level....."Pi may be irrational, but free pizza is anything but," Conway, an award winning mathematician, said in a statement. "I'm eager to challenge America with these problems and find the next great pizza-loving mathematician that can solve them.""
  • with an article by Dr William Stein, on Sagemath Cloud in the classroom, "Before SageMath, we were using clunky, expensive, and incomplete tools (like, Mathematica) that were closed source software, so we couldn't see how they worked and modify them to do what we really needed them to do....I wanted SageMath to be a powerful tool for my students. It wasn't initially intended to be something hundred of thousands of people used! But as I began building the project, and as more professors and students started contributing to it, I realized these were problems many others were striving to solve as well....To solve the problem, I created SageMathCloud, a web-based and collaborative way for people to use SageMath and other open source software solutions, like: LaTeX, Jupyter Notebooks, command line terminals, the full scientific Python stack, Java, Julia, Fortran and more....For the first time, teachers can easily use Python and R in their courses, which are industry standard and mainstream open source programming tools...Teachers can also collaborate in real time to manage their online courses with the same cutting edge software used by top mathematicians at the best universities in the world. For the first time, students can use a full suite of open source math-related software programs to learn, experiment, and collaborate with others to improve their skills and gain a better understanding of math." Note there is a video as well.
  • The Daily Beast tells us, "Students at Western Washington University have reached a turning point in their campus’s hxstory. (For one thing, they’re now spelling it with an X—more on that later.) Activists are demanding the creation of a new college dedicated to social justice activism, a student committee to police offensive speech, and culturally segregated living arrangements at the school, which is in Bellingham, up in the very northwest corner of the state....WWU must meet the needs of this new “College of Power and Liberation” by immediately hiring 10 faculty members—subject to the approval of student-activists. Finding the money to do all this is solely the responsibility of WWU’s administration, “whose accountability to students should be expressed through their fervent advocacy for students’ needs at both the local and state levels,” according to the activists, who want an extra $50,000 to throw a kick-off party for the new college....At the heart of this effort lies a bizarrely totalitarian ideology: Student-activists think they have all the answers—everything is settled, and people who dissent are not merely wrong, but actually guilty of something approaching a crime. If they persist in this wrongness, they are perpetuating violence, activists will claim."
  • The latest in educational "research". From, "For elementary-aged children, research suggests that studying in class gets superior learning results, while extra schoolwork at home is just . . . extra work. Even in middle school, the relationship between homework and academic success is minimal at best. By the time kids reach high school, homework provides academic benefit, but only in moderation. More than two hours per night is the limit. After that amount, the benefits taper off. "The research is very clear," agrees Etta Kralovec, education professor at the University of Arizona. "There's no benefit at the elementary school level."". 
  • Wisconsin takes the lead in real educational reform. From EAGnews, "On Tuesday Gov. Scott Walker signed a bill during a visit to Brown Deer High School, allowing K-12 school districts to hire vocational education teachers who have not earned traditional teacher licenses, according to the Milwaukee Journal Sentinel. The teachers can now be awarded “experience-based licenses,” so they can share their knowledge and help guide young people into the workplace....Critics of the legislation, “including the state Department of Public Instruction, the state’s largest teachers union and university schools of education have raised concerns, saying the measure will lower the bar on teacher standards and create an uneven licensing system around the state,” according to the Journal Sentinel. Of course the university schools of education crank out most of the traditional teachers, many of whom join the union. The Wisconsin Department of Public Instruction is led by state Superintendent Tony Evers, a loyal Democrat with strong ties to the union.
    ...Meanwhile, on the most recent Badger Exam, taken by Wisconsin students in grades 3-8 across the state, only 51 percent tested proficient or advanced in reading, and only 44 percent hit the mark in math.They all have conventionally trained teachers, and a lot of them aren’t doing very well at all.Can it really hurt to trying something different, using people with practical experience in their fields who want to share what they’ve learned with youngsters?". This is a great idea. It opens up teaching to private school teachers and adjunct college professors working for poverty level wages and if Wisconsin is reasonably selective as to what experiences it accepts, would increase the quality of teachers. There is no research that shows a teaching certificate means a better teacher and given how badly certified teachers have performed, this reform is long overdue.
  • The NY Times has an article on the tenured professor fired for his views on Sandy Hook: "James F. Tracy, 50, a tenured associate professor of communications at the Boca Raton university, has repeatedly called into question the authenticity of recent mass shootings, including the slaying of churchgoers in Charleston, S.C., and office workers in San Bernardino, Calif. In his blog postings and radio interviews, Mr. Tracy has said the Newtown massacre may have been carried out by “crisis actors” employed by the Obama administration....Florida Atlantic University ultimately dismissed him on grounds that have nothing to do with his theories or his feud with the Pozners. They said Mr. Tracy, who because of his tenure could not be easily fired, had failed to submit paperwork for three years in a row that listed any other jobs or similar activities that he performed outside the university. "
  • Crushed in the first three games of the historic match of AlphaGo versus Lee Se-dol, the Garry Kasparov of the game Go, the human has found a weakness. He managed to win game 4 and has asked for, and received, a change in the match rules. But first, The Verge has an account after Alpha Go defeated Lee Se-dol, "A huge milestone has just been reached in the field of artificial intelligence: AlphaGo, a program developed by Google's DeepMind unit, has defeated legendary Go player Lee Se-dol in the first of five historic matches being held in Seoul, South Korea. Lee resigned after about three and a half hours, with 28 minutes and 28 seconds remaining on his clock. The series is the first time a professional 9-dan Go player has taken on a computer, and Lee is competing for a $1 million prize." The GoGame Guru comments on the computer winning the second game,"After losing the first game of the match to the computer Go player AlphaGo on the previous day — something that the majority of the world’s top players had thought to be practically impossible just months ago — Lee’s play exhibited a sense of calm patience and steadiness, which was not evident the day before. But somehow it wasn’t enough. AlphaGo met Lee’s solid, prudent play with a creativity and flexibility that surprised professional commentators, eventually consolidating its advantage in the endgame.Finally, after a tightly fought contest which left spectators on the edge of their seats, Lee was left with no better move than to resign...Lee Sedol was full of praise for AlphaGo, remarking that, “Yesterday I was surprised, but today, more than that, I’m quite speechless.”He added, “. . . there was not a moment in time where I felt that I was leading the game.”." The LA Times has an article after AlphaGo's second win and the Korean reaction was mixed: "Google DeepMind, he said in a Yonhap News Agency report, was nothing less than guilty of “insulting the 2,600-year history of Go.”...But for the most part, more than bristling over the struggles of their native son, South Koreans have marveled at the proficiency of AlphaGo." KoreaTimes has the most recent piece with Lee Se-dol finally smiling, "Lee said he has seized on the AI’s weaknesses in the game. AlphaGo seemed to feel more difficulties playing with black than white,” he said. “It also revealed some kind of bug when it faced unexpected positions.”...During the post-game interview, the go grandmaster asked the Google DeepMind team if he could play with black stones in the final round. According to Chinese go rules, which this competition follows, the player playing with black stones yields 7.5 compensation points to his opponent at the end of the game for playing first, and thus this considered as a disadvantage.“As I won the game with white stones, I would like to play with black stones because winning with them will be more valuable,” Lee said.
    DeepMind CEO Demis Hassabis accepted Lee’s request." With Go essentially conquered, ten years ahead of schedule, what's next: Skynet?!?
  • Corruption or stupidity or something else? IdahoEdNews notes "A report tracking $16.7 million in teacher “leadership premiums” — compiled by the State Department of Education and presented to two legislative committees — is fraught with math errors....The premiums are designed to reward teachers who mentor colleagues, assume hard-to-fill teaching jobs or perform other leadership roles....In some cases, the report contains grossly inaccurate data about district staffing....In nine cases, the report offers no data at all about district or charter leadership premiums. ...The report lists the total amount of premiums awarded by a district or a charter, and the number of teachers who received a premium. ...But in many cases, this math does not line up with the averages listed in the report...In numerous other cases, the report’s math simply doesn’t add up... For example, the West Jefferson School District reported an average premium of $847.55, a maximum of $1,007.48 and a minimum of $850. This is mathematically impossible — and not the only error of this type." Public education means large quantities of money are available for skimming. Who will lose their job over this? Probably nobody? Stay tuned.
  • on the horrid state of American education, "The US Department of Education just released the results from the Program for the International Assessment of Adult Competencies (PIAAC), and they are perilously disappointing....When it comes to basic technological skills like using email, buying and returning items online, using a drop-down menu, naming a file on a computer or sending a text message — Americans rank dead last. But it's not just daily technology tasks that Americans fail at accomplishing, they also scored terribly in math and literacy.
    According to study, Americans with a high school diploma performed about the same as high school dropouts in other countries. So what's the problem? Is it lack of spending in the education department? No. The United States spends more money on education than any other country in the world, yet the average high school graduate can't even compete with dropouts in other countries. In spite of the ever increasing DOE expenditures, US students continue to trail their rivals on international standards tests."
  • The Candidate matches to determine a challenger for the World Chess Championship have begun. The games can be followed here. Unfortunately, you're forced to login to watch the games. You're better of going to ChessBomb--the link is on the sidebar.

Sagetex: Rational Functions 4


The latest addition to the website is the sagetex randomized problem on rational functions. It's posted on the Sagetex: Functions page. This one involves functions of the form f = ((a*x^2+abs(d))*(x-b))/((x-b)*(c*x+d)*(x-d)) where a,b,c,d are random integers. Unlike the previous rational function problems you'll see that (x-b) cancels so there will be a hole in the graph, as shown in the picture above.

$latex \LaTeX$ god Alain Matthes, designer of the Altermundus packages, left a comment on this page. It sounds like providing an English version of his documentation is on his mind but, admittedly, no time frame is given. Keep your eye on the CTAN feed....

Here are some things that caught my eye this week:

  • The always entertaining Kevin Knudson of Forbes on a new type of puzzle called Sweet 16.
  • Who could miss the NY Times clickbait "The Wrong Way to Teach Math"? At first I was going to ignore the trashy article, and then after seeing how a hack was given a forum to sell/hype a book I figure I should probably say something. But let's give mathematician Dr. Keith Devlin a standing ovation for stepping in to inflict a brutal beat down: he's got 2 pieces, one on the Huffington Post and the other on Devlin's Angle. The pieces are similar but there are some important differences. From the Huffington Post article he's a bit more restrained: "Since Hacker clearly has a valuable connection to the nation's premier national newspaper, it is then a pity he pitched his article the way he did....There is always a danger in setting oneself up as an advocate for change in a discipline one does not know. Hacker is not a mathematician. He is a retired college professor of political science, who has taught some courses in mathematics to non-majors....Unfortunately, since Hacker plainly does not understand what algebra is, or more generally what mathematical thinking is, he instead proposes we throw away the healthy but neglected baby along with the depressing pool of lukewarm, dirty bathwater it currently hides in....In reading an advance copy to write my review, I annotated 20 pages (out of a total of 200) where he makes significant errors due to a lack of knowledge of, or a misunderstanding of, mathematics. That's an error rate of 10%; way too high for significant errors.". In the Devlin's angle piece you'll see a recap of Huffington Post along with his analysis. But here he gives a couple more blows to the head followed by a $latex \pi$ to the face: "Not only does Hacker give no indication he is familiar with the Common Core—the real one, not the azimuth-strewn, straw-man version he creates—he gives every indication he does not understand mathematics as it is practiced today. (He also does not know that pi is irrational, but I’ll come to that later.) will be jolted by Hacker’s fundamental lack of knowledge of mathematics. He writes, “Along with phenomena like earthquakes and cyclones, nature also has some numbers that control or explain how the world works. One of them is pi, whose 3.14159 goes on indefinitely, at least as far as we know.” Yes, you read that last part correctly." Oooooooh...SNAP! Isn't it great to find out someone with a lack of basic prealgebra knowledge on the irrational number $\atex \pi$: writes a book on removing algebra from high school, has a forum to voice his ignorance at the NY Times, and teaches math at the college level. Shame on the the NY Times for giving this cr@p a forum and  to Queens College, City University of New York for having someone with a "fundamental lack of knowledge of mathematics" teaching math. THANK YOU DR. DEVLIN!!!
  • EAGNews on how "School officials in Huntsville plan on tracking students’ social media accounts as part of a new system that will also levy punishments based on posts, regardless of whether they’re private or public....The “procedure” involves tracking the social media posts of violent students or any school officials deem to be a risk to school safety. The superintendent can then use the social media posts – regardless of whether they posted publicly or privately – to take action against students. "
  • The kids really are different these days: with the story that "A 16-year old Nashville resident is accused of shooting his grandmother, sister and nephew because he did not want to leave his bed to head to school. He also tried to shoot his mother, but she managed to escape."
  • Those kids start young, too. EAGNews on "Police recently busted a drug dealer inside Marlin Elementary School – a 9-year-old who brought in several prepackaged bags of marijuana to hawk to classmates."
  • with a piece on how Denver Public Schools are using district wide credit cards. "The Problem Solvers focused on purchases totaling around $2 million that appeared to contradict school policy but were approved by the finance department anyway.....Auditors sampled 197 employee credit card transactions and found something wrong with 154 of them -- a 78 percent fail rate....That also made it easy to question certain purchases that were culled from a computer database that was built that contained all the credit card purchases in the past couple of years.
    • Party City: $23,511
    • Flowers: $7,806
    • Jewelry: $3,900
    • Gift cards: $110,638

    Putting nonstudent-related food on credit is supposedly under tight control, but when we searched for receipts linked to "BBQ" or "Famous Dave's," there were $73,917 in credit card purchases by school employees. Einstein Brother’s Bagels came out to $174,222. Pizza restaurants were at $451,658."

  • The Periodic Table of Elements in Pictures would be useful for any chemistry teacher.
  • PC zealots are alive and well at Kansas University where the Daily Beast reports that another faculty member has been removed. "You would think that Quenette must have perpetrated an egregious act of harassment or obvious discrimination to provoke her students to publish an open letter demanding her immediate termination. The letter, written by five of Quenette’s students—some, but not all of them, black—alleges that Quenette violated the university’s policies prohibiting racial discrimination...We students in the class began discussing possible ways to bring these issues up in our classes when COMS 930 instructor Dr. Andrea Quenette abruptly interjected with deeply disturbing remarks. Those remarks began with her admitted lack of knowledge of how to talk about racism with her students because she is white. “As a white woman I just never have seen the racism… It’s not like I see ‘Nigger’ spray-painted on walls…” she said....But she did not use inappropriate language to describe any of her students—or to describe anyone else. She was describing her own blindness to racial animus. Could she have used different language? Sure. Should she have? Probably. But genuine self-reflection isn’t usually rehearsed. This wasn’t a public address—it was a classroom discussion about a controversial topic. Some imprecision should be expected, and tolerated.". The potential impact of this generation on free speech in America is frightening.
  • John King, President Obama's choice for the new education secretary, is apparently not well liked by a lot of "progressives". According to Alternet, an open letter to the Senate was published in the Washington Post asking for his rejection, "The letter is signed by world-renowned scholar Noam Chomsky, along with journalist Naomi Klein, Chicago Teachers Union president Karen Lewis, Green Party presidential candidate Jill Stein and a host of other prominent scholars and activists, including some of the most established pro-public education voices. A variety of teachers’ and public education organizations signed the letter as well, including New York for Public Education, Save Our Schools and Time Out From Testing. The signatories warn King’s policies “have been ineffective and destructive to schools, educators, and most importantly students.”..."The American public deserves a Secretary of Education who will advocate for their interests, not those of the testing corporations who profit from the Common Core,” the letter reads.""
  • Alternet again, this time warning, "The FBI Has a New Plan to Spy on High School Students Across the Country...The FBI’s justification for such surveillance is based on McCarthy-era theories of radicalization, in which authorities monitor thoughts and behaviors that they claim to lead to acts of violent subversion, even if those people being watched have not committed any wrongdoing...The FBI’s instructions to surveil and report young people not for wrong they have committed, but for violence they supposedly might enact in the future, is likely to promote an intensification of this draconian practice."

Altermundus: Parallel and Perpendicular Lines


I've added some more information on the Altermundus tkz-euclide package; it's posted on the Points, lines, rays and segments page. The new material deals with the macros for creating parallel and perpendicular lines as well as getting the point of intersection for 2 lines. The code for both examples (along with commentary) is posted online for you to download and modify to suit your needs.

Here are some stories that caught my eye this week:

  • ZeroHedge on the desperate financial shape of Detroit public schools. "Case in point: today we learn that Detroit's public schools have officially reached their borrowing limit which means absent some manner of intervention from the state government, the district will run out of cash by April...."DPS is finally on the brink," State Treasurer Nick Khouri told lawmakers today. “When they run out of cash, sometime in the spring or early summer, without legislative interaction, they will have payless paydays," he warned....Each year, the district spends $70 million more than it brings in in revenues, but a bankruptcy would result in 12 months of "chaos," Khouri cautioned."
  • The Herald Tribune has a piece on the educational games that "educators" play, "The vast majority of states have adopted Common Core academic standards, but individual states are still setting different definitions of "proficient" on annual math and reading tests, according to a new study. And in many states, the study says, annual tests set a significantly lower bar for "proficient" than the National Assessment for Educational Progress, or NAEP, a national exam that is administered every two years to a sample of students in the fourth and eighth grades.". Because when "professionals" know they are failing at their job there is always statistics to make it less obvious.
  • TownHall reflects on how Common Core cost Jeb! the election: "Exactly one year ago, before he announced that he would be running for president, Trump was asked on Hugh Hewitt's radio talk show: "What does Donald Trump think about Common Core?" He replied, "Well, first of all, I think it's going to kill Bush."...One year later, it's clear that Trump was right: not only that it's "ridiculous" for "people in Washington" to be setting curriculum and standards for "what you're going to be studying" -- but he was equally right to foresee that Common Core would "kill" any chance of returning the Bush family to the White House....As Common Core became toxic, Jeb Bush made a too-little, too-late attempt to rebrand the same ideas under a new name. "
  • EAGNews on the potential drugging of a teacher at school, "Police are investigating at the school after the teacher developed “unusual symptoms that required him to seek medical attention” last Tuesday....“During a school day last week, one of our employees consumed a beverage that may have been laced with an unknown substance,” Smithville Superintendent Todd Schuetz wrote in a letter to parents." This isn't the world you grew up in.
  • File this under "what's the world coming to?": according to RT, "Teens in the US state of New Mexico have been officially allowed to keep themselves busy sexting – sending or receiving sexually explicit messages, images through e-means, particularly between cell phones – without fear of paying the price and going to jail."
  • TheRegister reports that "The Chicago Public Schools district has become the first in the nation to make computer science training a requirement for high school graduation." Great idea but I'm more than a little surprised that California wasn't able to have a school district accomplish this.
  • NBCnews on the long overdue termination of Melissa Click, "Melissa Click made national headlines when a video of her attempting to kick out a campus reporter during protests at the University of Missouri went viral. In the video, Click can be heard yelling "I need some muscle over here!" as she tries to boot the journalist."The board believes that Dr. Click's conduct was not compatible with university policies and did not meet expectations for a university faculty member," Pam Henrickson, chair of the University of Missouri Board of Curators, said in a statement."...Click was branded a traitor to her profession by some and in January, she was charged with assaulting Schierbecker. She apologized, and cut a deal with prosecutors last month that kept her out of jail"
  • EAGNews reports on a kerfuffle at University of South Carolina: "Student Ross Abbott created an outdoor First Amendment display highlighting kinds of speech that had been subjected to censorship... Abbott even took the extra step of actually obtaining prior approval from administrators. But that did not stop several of his fellow students from filing complaints....Even though administrators had approved the display, Abbott was still given official notice that he was being investigated for discrimination. He was eventually called before the Office of Equal Opportunity Programs and made to answer for each and every poster he had displayed....Since the university did not respond to Abbott's request to have the complaint expunged from his academic record—and because USC gave no indication that it understood Abbott's speech was constitutionally protected—he has filed suit."