Sagetex: Definite Integrals


I've added two definite integrals to the Sagetex: Integrals page. The first problem creates two random parabolas in different directions and the area between the two curves must be calculated. This requires them to find the intersection points as well to set up the integral properly. The second integral gives a random exponential in e along with (random) endpoints of integration.


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

  • USA Today reports "Texas is decriminalizing students' truancy": "Gov. Greg Abbott has signed into law a measure to decriminalize unexcused absences and require school districts to implement preventive measures. It will take effect Sept. 1. Reform advocates say the threat of a heavy fine — up to $500 plus court costs — and a criminal record wasn't keeping children in school and was sending those who couldn't pay into a criminal justice system spiral. Under the old law, students as young as 12 could be ordered to court for three unexcused absences in four weeks. Schools were required to file a misdemeanor failure to attend school charge against students with more than 10 unexcused absences in six months. And unpaid fines landed some students behind bars when they turned 17."
  • There's a wrinkle in a story from my last post. A teacher who was reported to have been removed from his position because he read from Mark Twain was actually removed for making an inappropriate joke (relating to a Mark Twain passage). LA Times has the details: "In his first interview since he was pulled from his fifth-grade class, Esquith told The Times on Monday that controversy stemmed from a joke he made in the classroom. He said he quipped with students that if he could not raise enough money for the annual Shakespearean play, they would all have to perform their parts naked like the king in Mark Twain's "The Adventures of Huckleberry Finn." After another teacher complained, he said he explained the context of the joke to his principal at Hobart Boulevard Elementary. The principal, he said, told him he had nothing to worry about. Nonetheless, Esquith was removed from the classroom in April."
  • EducationWeek reports on the L.A. Unified budget has reduced the spending on police. This was a victory for The Dignity in Schools Campaign which, "..demanded that the school district, which is the second largest in the country, redirect $13.1 million in funds it had planned to spend on policing practices during the 2015-16 school year into jobs and programs aimed at improving school climate. (The district is still budgeting about $54 million for school police from other parts of its budget.) Though the district school board adopted the revised budget, campaign organizers don't yet know how much of the redirected money will go toward their specific funding recommendations, which include using $8 million for restorative justice measures like technical assistance and staff training, as well as $5 million for hiring prevention and intervention staff in alternative schools to create counselor-student ratios of 1 to 50. Such investments have been proven to positively transform school climate, whereas school-based policing has not, said Ruth Cusick, an education rights attorney at Public Counsel."
  • Huffington Post's piece "Meet the 63rd Black Woman in American History with a Physics Ph.D." provides a glimpse into "the challenges faced by marginalized communities in science".
  • Put this on your radar: has an update on a case making its way through the legal system: "A little over a year ago, a group of nine California students with the help of the activist group Students Matter won an amazing victory in California Superior Court in the case of Vergara v. California.As I reported at the time:

    Judge Rolf M. Treu reasoned that the challenged teacher rules—regarding permanent employment status, dismissal procedures, and a "last in first out" rule for layoffs—do indeed damage California children's constitutional right (on the state level) to an education. He wrote that the challenged statutes "cause the potential and/or unreasonable exposure of grossly ineffective teachers to all California students" and "to minority and/or low income students in particular, in violation of the equal protection clause of the California constitution."

    Naturally, the losers appealed, and Judge Treu stayed actual enforcement of his ruling pending appeal. Today, the Students Matter side filed their brief in the appeal process in the Court of Appeal for California, 2nd appellate district....In a press conference call this morning announcing the brief, lawyers on the Students Matter side say they still need to wait for the teachers side to file its response brief and then await an actual court date. Once the hearings are over, though, a decision must come within 90 days, but that could still be a very long time away--more's the pity for California public school students.". There's a decent video that's posted on the page.

  • The Norway Chess Tournament 2015 ended with victory for Topalov. The tournament was marred by some blunders and a short draw between Anand and Topalov in the final round. But most newsworthy is what Chessbase reports here,"...this is easily the worst tournament ever played by Carlsen after obtaining his GM strength."
  • The 43rd Sparkassen Chess Meeting Dortmund 2015 has begun; it features players such as Kramnik, So, Hou Yifan, Naiditsch.
  • American chess lost an icon recently. The NY Times has a piece on Walter Browne who passed away in Las Vegas at the age of 66.
  • Michael Krieger posts on "Salt “Black Markets” Emerge in Indiana School System as Students Seek to Avoid Bland Michelle Obama Lunches"

Resource: SymPy Gamma


It's not considered important enough to be implemented in Sage but I think every teacher sees the educational value if Sage were able to show the steps of its calculations. SymPy Gamma shows how it could be implemented for (some) derivative and integration problems. I've typed in the command integrate(ln(x)) which results in the screenshot above (where it annoyingly writes ln(x) as log(x)). In addition to that information it plots the graph of the solution and even finds the root.


But the explanation for how it got the answer was most impressive:


The main problem is that there were plenty of times in my experimentation that the steps weren't given--as I said already, it shows the solution for some problems. Before you rush out and try it I need to mention I that while most of the output is provided quickly, some of the information (usually the plot) can take a lot more time to show up-maybe a minute or so. And sometimes it just "times out" without giving all the output. So if you're willing to put together problems that result in a solution you've got a great teaching tool for calculus. I've added SymPy Gamma to the links on sidebar.

Here are some issues that caught my eye this week:

  • There's growing opposition to the growing budget for police protection in Los Angeles schools. Southern California Radio has the story: "Superintendent Ramon Cortines proposed growing the school police budget by about $2 million, bringing the department's total funding to $59 million for the 2015-2016 school year. The district runs the largest school police department in the country with more than 350 officers. The armed staff supervise students who walk to and from school under a safe passage program and perform other duties related to campus security....Last fall, school police estimated they would need 80 new officers to protect students walking home from school with iPads. The department later retracted the statement....Students living in communities such as Watts are more likely to feel harassed than protected by police, according to Ruth Cusick, an attorney for Public Counsel, a legal advocacy group....The school police department drew scrutiny last fall after reports that it owned an armored tank, grenade launchers and more than 60 assault rifles from the military surplus program. The district later returned some of the weapons.". While police protection sounds great, the harassment mentioned above hearkens back to 2012 when police were issuing citations to kids as young as 6 for fighting and, for example, "...two boys who were stopped by officers near their school, minutes late, and were searched, handcuffed and allegedly intimidated inside a squad car before officers took them into school and wrote them curfew tickets.". As covered in more detail here, "Students at schools with some of the highest dropout rates have reported staying home if they were running late — rather than risk meeting up with police and getting tickets that can rise to $400 once court fees are tacked on.". The vote on the budget is set for Tuesday.
  • Connie St Louis, one of the women who led the campaign to oust Tim Hunt from his job explains her side of the story to Scientific American. Her agenda goes even deeper: "I didn’t just call out Hunt in that first tweet, however, but also the Royal Society, the U.K.’s national academy of science, where he is a fellow. Sexual inequality in the STEM fields continues in part because the Society continues to take very little action....I felt it would be a waste if the uproar ignored the forest for trees—rebuking only Hunt and not higher orders of power as well—so my next action was to present a framework for systemic change:...The Royal Society was founded in 1660 there has never been a female president, so I went to and set up a petition called, “Its time to elect a female president to lead the Royal Society.” So far there have been only 68 signatures .... Condemning one mans’ sexist remarks is not enough. It is important that this episode also affects change for women in science.". Racism and sexism will always exist--but is the playing field so unfair when the targeted group can bully the system to remove a former Nobel Prize winner and use that issue to push for a female president of the Royal Society? It seems like "the system" is on her side. Indeed, in her own article (link above) she recalls a "disturbing" dream where she's confronted by reporters: "They are all shouting the same question: “How did you think you would get a way with publically calling to account a prominent white male scientist?”". No such problem in the real world.
  • In an earlier post, Jerry Seinfeld expressed his displeasure with the extreme PC environment on college campuses. A college student wrote in to Huffington Post to explain comedy to Jerry Seinfeld. Comedian Bill Maher takes aim at these 'idiots' and dispenses his verbal beat down of the college student as only a comedian could. It can make you laugh or maybe it will offend you--view at your own discretion.
  • LA Times reports on a "nationally recognized" teacher who was removed from his post for reading a passage from Mark Twain's book "The Adventures of Huckleberry Finn". The PC climate, again. Great literature forces can force you confront some uncomfortable questions whether it's "Lord of the Flies", "1984", "To Kill a Mockingbird" and other numerous books that are targeted for banning. The American Library Association's website notes "Each year, the ALA's Office for Intellectual Freedom records hundreds of attempts by individuals and groups to have books removed from libraries shelves and from classrooms.". How many of those classic books have you read?
  • The French government is warning it's citizens about the US attitudes/culture. From the article,"Along with warnings about slower speed limits, higher drinking ages and hurricanes in Texas, the French foreign ministry adds a note of warning against being too “Latin.”“It’s recommended to adopt a reserved attitude toward those of the opposite sex,” it says. “Comments, behavior, and jokes, which might be harmless in Latin countries, can lead to criminal cases,” the ministry’s website says....Reinforcing French views of American prudishness, the website notes that even minors can be accused of sexual harassment, and asks that children use toilets reserved for their sex in the U.S....Among other advice to the French in America: “keep calm in all circumstances” since some states authorize the carrying of weapons. It asks visitors to avoid raising their voice or making sudden or aggressive gestures at the police."
  • With 4 out of 9 rounds down, the Norway Chess Classic 2015 is drawing attention for Carlsen's poor showing. As Chessbase notes, "This disaster, however, is simply unprecedented.". Round 1 started with magnificent play by Magnus to achieve a winning position. But he lost on time because he didn't know the time control for the tournament(!!!). It's been downhill from there. He was outplayed by Caruana and Anand. You can follow the games at the tournament site here.
  • The Daily Caller reports on the "fiasco" while implementing Common Core in Nevada: "Under No Child Left Behind, states are supposed to test children in grades 3-8 each year in mathematics and reading. At least 95 percent of students must take the tests, or else a state can face federal sanctions such as a loss of millions of dollars in funds. Nevada, on the other hand, was only able to test 37 percent of the 213,000 students it was supposed to, thanks to a cascade of glitches and computer problems that left students unable to complete their exams. In Clark County, which contains the Las Vegas metro area and over half the state’s students, only 5 percent were successfully tested. Because so few were tested, Nevada’s department of education says it will be unable to issue grades for individual schools based on performance, like it is supposed to. The failure means Nevada is at risk of losing millions in federal funding, but such sanctions are unlikely in this case because the state made an honest effort that simply undone by technical shortfalls.". There is, of course, a scramble to assign blame.
  • WND has a piece on author Alex Newman calling for a debate with Huffington Post writer "...Rebecca Klein over her June 4 article, “5 of the Most Extreme Claims Made Against Common Core In The Last 5 Years.”One of her claims was Newman’s contention in March 2014 that Common Core was part of a global agenda to “transform American children, and students around the globe, into what globalists refer to as ‘global citizens’ ready for the coming ‘green’ and ‘sustainable’ world order.” He is asking for her to investigate the claim for herself. For example, in a 2010 speech at the Sustainability Summit, Duncan bragged that his Education Department was “taking a leadership role in the work of educating the next generation of green citizens and preparing them to contribute to the workforce through green jobs.” In a separate 2010 speech given to UNESCO, Duncan proclaimed the U.S. must partner with foreign countries to tackle global challenges. Newman also addressed another one of Klein’s five “extreme” claims: that Common Core will turn kids into communists and/or socialists. She accused Glenn Beck and Rep. Jim Bridenstine, R-Okla., of making those assertions. However, as Newman pointed out, that’s not exactly what Beck and Bridenstine said." . Two very different perspectives that should give a lively debate. Will she rise to the challenge or give the other side "bragging rights" by refusing. Stay tuned!


Sagetex: plotting templates


The plotting templates that are posted on the Handouts page should be good enough for most of your plotting needs--they're convenient because you don't need sagetex and Sage to use them. But lately I've found myself graphing functions that can't be done with those templates, such as the Cantor function, and decided to make sagetex driven versions of those 2 templates. The image above shows the version with the magnifying glass--the zeta function, Weierstrass function, and a Fourier series have been plotted simultaneously. I've made the main tick marks thicker but the important change is seen in the circular magnified portion. The templates incorporate comments by reader Lazza posted on the Plotting with Sagetex page to get around a problem of having enough points to make the graph look good but not too many that it won't compile. The complicated functions would look like this (step size .01):

SagetexSPYorigThe Fourier plot doesn't look smooth and the Weierstrass function looks too smooth. Lazza's comments apply to the regular template as well.


Note that for the zeta function above, the red circle shows that the zeta function doesn't go to the bottom of the screen with step size .01. This issue, which was previously mentioned on the Plotting with Sagetex page, can sometimes be solved by increasing the number of points. But if there are too many points, the code doesn't run. Lazza's improvement allow for decreasing the step size in just the areas where more points are needed. For the zeta function, the problem area is before 1, so the x coordinates could be calculated as:

x2_coords = srange(LowerX,.8,.001)+ srange(1.2,UpperX,step)

Without step of .001 the function doesn't make it to the bottom but .01 is adequate for the right hand piece. Also, starting at 1.2 avoids all the non-plotted points in between the two pieces. And of course, you could break this into 3 intervals so that the step size of .001 is only used closer to .8, say .75 to .8, eliminating even more points. Once the x coordinates are determined the y coordinates follow easily with a simple statement:

y2_coords = [(zeta(t2)).n(digits=6) for t2 in x2_coords]

The two templates can be found on the Plotting with Sagetex page along with more information, such as how the graph paper feature can be turned off or having a frame instead of axes. With these templates you can have the same look and feel for whatever you're graphing plus the additional power of Sage.

So many stories that caught my eye over the past week!

  • The NY Post tells us that a Brooklyn high school was caught giving students science credits they needed to graduate by taking math classes. "The scheme was engineered following the February transfer of the only 12th-grade science teacher at Lafayette HS, where most of about 350 students are immigrants, the source said...Principal Jon Harriman didn’t return a call seeking comment — and on Friday sent out an e-mail instructing school faculty not to speak with reporters.". Seems likely this story will continue to evolve.
  • ProPublica has an audio interview with theJohannes Bohannon, Ph.D., mentioned in an earlier post, about how he was able to convince the world that chocolate can help you lose weight.
  • I used to have tissues and antibacterial lotion for students to use, if they wanted, when they came into class. IFLScience explains "Why You Should Never Use Hand Sanitizer".
  • has the crazy story of a Thomas Jefferson high school student at the center of controversy: "The Korean media dubbed Sara Kim the “Genius Girl.” A young math whiz so brilliant that two elite universities, Harvard and Stanford, offered her dual admissions. Her father, an exec at Korean game company Nexon, must have been proud! Other people, however, were suspicious. ..., which ran the original story, received similar denials from both Harvard and Stanford in afollow-up report published today. In this latest update, Kim allegedly still says she is not lying and is sticking with her story that she has been accepted into both universities....While reporting this story, today writes it received an email on Monday signed by Harvard Public Affairs and Communications official Anna Cowenhoven, stating that Sara Kim had been accepted by the Ivy League university. The following day, Cowenhoven told the paper that the email was also a forgery.".
  • Do you let kids eat in class or give out food to them? The NY Post also reports, "A Harlem boy allergic to peanuts died after school staff inadvertently gave him a nut-based candy bar and then failed to immediately administer an antidote or call an ambulance, his devastated mother charges...The tragedy was compounded by the fact that Brandon, the eldest of three kids, was due to be a bone-marrow donor for his younger brother, Tyler, who suffers from sickle cell anemia, ...."
  • The Washington Post writes, "A Woodbridge teenager admitted in court Thursday that he was the secret voice behind a pro-Islamic State Twitter account, which once counted more than 4,000 followers, and that he helped another teen travel to join the Islamic State in Syria. Ali Shukri Amin, 17, a former student at Prince William County’s Osbourn Park High School who was arrested earlier this year, pleaded guilty to conspiring to provide material support to a terrorist organization. As part of a deal with prosecutors, he admitted that he helped arrange a successful trip to Syria for an 18-year-old Prince William County man who wanted to fight with the Islamic State."
  • The tragic story of high school student Kalief Browder, first mentioned here,  who spent 33 months in prison without a trial before charges were dropped has a tragic end: he committed suicide recently. The damage of torture and starvation haunted him after he was freed. "At Rikers, Browder spent two of his three years in solitary confinement. There, as he frequently recounted later, Browder was routinely brutalized and starved by guards and subjected to virtually unrestrained violence by other prisoners....After a visit with Browder in the psych ward at St. Barnabas Hospital in January, Gonnerman described him as “gaunt, restless and deeply paranoid.”She added: He had recently thrown out his brand-new television, he explained, “because it was watching me.” Condolences to his family on their unnecessary, tragic loss.
  • ZeroHedge posts on BioMed Central: "A major publisher of scholarly medical and science articles has retracted 43 papers because of “fabricated” peer reviews amid signs of a broader fake peer review racket affecting many more publications."
  • A school in Idaho is arming staff to protect students. According to the Guardian, "A tiny school district in Idaho far removed from law enforcement has purchased firearms and trained a handful of staff to use them should the same school shooting rampage that has occurred across the country take place. It takes at least 45 minutes for officers to reach the Garden Valley School district – a district made up of less than 300 students all taught in the same building – where limited funds have prevented the school from being able to afford hiring police officers to patrol the building during school hours."
  • The NY Times reports on the crippling education budget problems in Arizona: "In the rural Saddle Mountain Unified School District 50 miles west of Phoenix, three new libraries have been locked since last year. In a neighboring county, an elementary school closed last month because there was no money to keep it open, even after the district agreed to shift to a four-day week....In Peoria, a suburb northwest of Phoenix, Curtis J. Smith, the principal at Peoria Elementary, said he had about $42,000 to pay for toilet paper and printing paper; athletic equipment and arts materials; and light bulbs, small repairs and cleaning materials for the school year that ended May 22. It amounts to only $68 for each of his 620 students over the school year. Next year, Mr. Smith will have roughly $32,000, or about $52 per student."
  • There's plenty of buzz for this story which is continues the PC theme in schools mentioned in the last post--but this time it's in the UK. Several articles stand out from the rest: Huffington Post gives one woman's harsh, sarcastic perspective on the tone deaf statements by former Nobel Prize winner Tim Hunt which led to his in "The Illiberal Persecution of Tim Hunt" provides my view: "In a normal world, a world which valued the freedom to make a doofus of oneself, that should have been the end of it. Seventy-two-year-old man of science makes outdated joke, tumbleweed rolls by, The End. But we don't live in a normal world. Certainly we don't live in a world where people are allowed to make off-color comments. And so with tedious, life-zapping predicability, Hunt fell victim to the offence-policers, to the machine of outrage being constantly cranked up by self-styled guardians of what we may think, say, and even joke about....What is truly alarming, what should really send a shiver down every liberal's spine, is not the words that came out of Hunt's mouth but the haranguing of him that followed, the shunning of him by the academy and possibly by the scientific elite itself...The response to Hunt is way more archaic than what Hunt said. Sure, his views might be a bit pre-women's lib, pre-1960s. But the tormenting and sacking of people for what they think and say is pre-modern. It's positively Inquisitorial...The Hunt incident is quite terrifying. For what we have here is a university, under pressure from an intolerant mob, judging a professor's fitness for office by his personal thoughts, his idea of humour. Profs should be judged by one thing alone: their depth of knowledge. It shouldn't matter one iota if they are sexist, stupid, unfunny, religious, uncouth, ugly, or whatever. All that should matter is whether they have the brainpower to do the job at hand. UCL and the mob's hounding of Hunt echoes the university of the pre-Enlightenment era, when only those who were 100 percent Good Catholics had a hope in hell of getting a job. Only now, academics must be unflinchingly in accordance with the commandments of PC rather than with Biblical thinking." Missing from most accounts is provided by one woman who, thankfully, has come to his defense. Sarah Vine of the Daily Mail writes, "His so-called sexist remarks were actually, it turns out, more a veiled mea culpa. His wife (an equally eminent scientist, immunology professor Mary Collins, who, ironically, has done much to further the standing of women in science) was once his student. She was already married when they met over the roaring flame of a Bunsen burner. They had an affair, she divorced her first husband — and she and Sir Tim have been together for the past 20 years. ‘I have fallen in love with people in the lab and people in the lab have fallen for me, and it’s very disruptive to the science,’ he said yesterday, trying in vain to calm the story and explain why he’d said what he’d said. ‘These emotional entanglements make life very difficult.". And after reminding the reader of other cases where men have been taken down for their not being sensitive enough (such as atrophysicist Matt Taylor reduced to tears for wearing "...a shirt emblazoned with scantily clad women of the comic-book variety...") continues, "Don’t get me wrong. I wouldn’t die in a ditch to defend any of these three men as being entirely innocent. You might say they were all a bit silly, or you might say they were just being men. But I would argue that the enraged response from women in all cases was wildly disproportionate...But the feminists aren’t prepared to cut them that slack. They spot a potential target, zone in on their off-the-cuff remark, or their lurid shirt, or their ill-advised joke, and harry away until they achieve their goal: emasculation, defenestration, prostration or gibbering apologies. But what does this tactic actually do for the feminist cause?". But there's an interesting side story from the Huffington Post piece (above): "In a recent article posted on the Science Magazine website, Alice Huang, herself a very successful scientist, dispensed advice to a young female researcher wondering how to cope with the perceived unwelcome advances of a senior male colleague. Dr. Huang's recommendation: put up with it. She went on to say that it was likely that the male colleague likely couldn't help himself and as such, should be forgiven. Following substantial (and in my view, highly warranted) backlash on social media, this article was quickly removed.". Bloomberg Business has that report under the prurient headlines "Academic Journal Deletes Article Telling Woman to Let Adviser Ogle Her Breasts". Like Nigel Short, notice the comments getting twisted in the headlines by a "journalist". Dr Huang, a woman, gets some heat for her advice which isn't PC enough. The original question and answer are posted; no information on whether she'll lose her job. But recognize that a man giving the same advice starts with an extra strike of being a many--so he can be freely labelled and abused (in a way a woman can't) by a reactionary mob. Unfortunately the younger generation has a much different set of acceptable standards than their parents. Check out "The Most Whiney, Thin-Skinned, Easily Offended Society In The History Of The World" posted on ZeroHedge which explains the thinking of today's younger crowd and the  "microaggressions" they are taught to see, such as opening the car door for a woman. Microaggressions and people's need to make the perceived offender pay the price, regardless of the intent behind the comments get taken very seriously by today's schools and, in the US, by more and more businesses and individuals. If you don't have the proper opinion then, man or woman, the situation can get spin out of control very quickly.
  • You can feel relieved now that the family which cheered too loudly at their daughter's graduation is no longer facing arrest warrants and jail time for cheering too loudly. WREG in Mississippi has the original coverage--with video for you to judge just how disruptive they were. Local channel KOAT has a more recent story telling us the school superintendent (Foster) dropped the charges: ""Our purpose in filing the complaints was not to place a hardship of any kind on the four individuals who disrupted the ceremony, but to protect the rights of the class of 2015," Foster said to WHBQ just minutes after dropping the charges.".
  • American Radio Works has some nice podcasts. Here's one: "What Can Japan Teach Us About Teaching?"
  • The NY Post again: "Reading? Math? Nah- let's teach kids to put on a condom". The article beginning sets the tone: "Can anyone spare a banana? New York City public schools are now offering demonstrations of how to put on a condom. Because, you know, they’ve already mastered teaching kids math and reading. So let’s move on to the important stuff. Well maybe not. Thirty six percent of students in the city were proficient in math and 31 percent were proficient in reading. With these teachers in charge of condom demonstrations, I think we’re headed for a lot of unintended pregnancies."

tkz-euclide: tangents to circles


I've added some more material to the Circles page on Altermundus tkz-euclide package. As I've already mentioned the documentation is in French and having the important information posted in English is both a convenience and necessity when you don't use the package frequently. The material relates to drawing the tangent lines to a circle; there are 2 main cases: Case 1 is to plot the tangent to the circle at a specific point on the circle. The point can be given explicitly, e.g. (-1,1) or chosen at random with one of the macros from the package. Case 2 is to draw one or two tangents to a circle given a specific point outside the circle. That case is shown above; from point C in the picture both tangents have been drawn. You can find the details and the sample files with commentary to walk you through it.

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

  • Chicago public school chief executive resigns from her position," ...amid a federal investigation into a $20.5 million no-bid contract.". Guilt/innocence has not been determined but it highlights yet another problem with a heavy top down educational system: layers of bureaucracy (which drain money from schools), lots of money (so it's easy for a bit to go missing), and the power for people in key positions to direct that money.
  • Caffeinated Thoughts blog has a decent post. From the blog, "Once again, the Common Core Standards are another federal policy which discourages students from memorizing multiplication facts and other basic math theories and formulas.These policies are in place to justify the emphasis on student-centered, discovery, and inquiry methods of instruction which fail because they are laborious, error-ridden, discouraging methods for introducing new concepts to young learners according to research.". My experiences have been similar. Too many people without math backgrounds have too much of a say. They question the need for learning multiplication tables, algebra, homework, and proofs and push for everything to be student centered. There's a time and place for discovery learning as well as drilling. It shouldn't be either/or but both. As classes get more challenging the problems are more complex and you need to be able to finish off the "pieces" of the problem in a reasonable amount of time.
  • reports, "The Farrington Elementary School principal, named a National Distinguished Principal of the year in 2013, resigned within two weeks of the disclosure that mathematics assessment results for 106 students there will be thrown out because of testing irregularities....The school superintendent wrote recently in a letter to parents that two rooms where the tests were administered “inappropriately” contained math “reference sheets and posters.”". Two testing rooms were compromised.
  • King5 news in Washington state reports, on school sexting and blackmail, "The investigation involves two junior high schools, Canyon Park and Skyview. Police say over the past several months, boys were pressuring girls to send nude photos of themselves. In some cases they even threatened to make the pictures public if the girls didn't send more, according to a letter sent home by the district....Sexting with minors can be considered trafficking in child pornography, and police say this case will be referred to prosecutors for possible charges."
  • In California, LAschoolreport informs us of a new educational report which found, "“While most new math textbooks are advertised to be ‘Common Core–aligned,’ few actually are, differing little from their previous editions,” the report stated. “In fact, of the 31 instructional programs formally adopted by the California State Board of Education in January 2014, 10 were reviewed by EdReports, and only one partially met the non-profit organization’s expectations for Common Core alignment.”". It makes me wonder 1. Who determines what material can legitimately be advertised as Common Core? and 2. How come the state didn't have a list of California approved textbooks?
  • Both's piece on a self-described liberal professor who is afraid of his students and conservative commentator George Will's video commentary posted on ZeroHedge mention the power that students have to avoid dealing with speech they don't like. You can even find Jerry Seinfeld and Jay Leno talking about the chilling PC culture on videos here. It all seems to be an extension of a general problem at the high school level as well. Students in the U.S. have a tremendous amount of power and aren't afraid to use it as a weapon. This makes education in the US even more challenging in today's world. I have yet to find a teacher with 2+ years of experience who hasn't felt the unfair power/wrath of kids in the classroom. I've seen some of that overseas as well but the US takes it to a "higher level".  For example, more recently I discovered 2 students (quietly) quizzing each other for some test they were taking later that day. I stopped it and reduced their participation scores for the day. Upon seeing the lower  participation scores posted online, I was told by 1 student it was unfair and they'd tell their parents if the score wasn't changed. I said I'd be happy to talk with the parents. Perhaps the parents agreed with me (I hope so) but it didn't matter: the next day I had admin telling me to change the scores. The student "is a good kid" and admin "had better things to do". This sort of thing would never happen when I taught overseas. The admin would not cave into a student wanting to not pay attention; I doubt the students would even think to approach admin. But not in the US. The above articles and videos indicate this problem is more widescale than you might think.
  • Two California teens arrested for hacking into school computers to change grades. ABC news reports, "The grade-changing incident comes just a few weeks after a senior from Dixon High School in northern California was also arrested for gaining access to his school's computer network, according to police. The student, 18, was arrested on May 13 after school officials learned that over 200 grades of 32 students had been changed, a Dixon Police Department spokesperson told ABC News today. He was charged with unauthorized access of a computer network operated by the government, a felony."
  • reports that presidential hopeful Chris Christie no longer supports Common Core, "Navigating New Jersey interests and a likely presidential campaign, Gov. Chris Christie on Thursday proposed dropping national Common Core education standards he once supported but have since become a lightening rod issue for Republican voters."

Problem: "Puzzle math"


I've added the following puzzle to the Problems page: For the 8 squares below (corners aren't included) squares are adjacent up/down/left/right/diagonally. Fill in each square with a number from 1 through 8 (one time each) so that adjacent squares don't contain consecutive integers. I found the problem here. You can reason it out logically but I ended up using graph theory to get the answer.

Lots of stories this week:

  • A MUST READ article by John Bohannon: "I Fooled Millions Into Thinking Chocolate Helps Weight Loss. Here's How". From the article, "It was, in fact, a fairly typical study for the field of diet research. Which is to say: It was terrible science. The results are meaningless, and the health claims that the media blasted out to millions of people around the world are utterly unfounded." and the key to generate bad conclusions from good data is "...If you measure a large number of things about a small number of people, you are almost guaranteed to get a “statistically significant” result. Our study included 18 different measurements—weight, cholesterol, sodium, blood protein levels, sleep quality, well-being, etc.—from 15 people. (One subject was dropped.) That study design is a recipe for false positives.". And the p-value is instrumental in the deception, "It’s called p-hacking—fiddling with your experimental design and data to push p under 0.05—and it’s a big problem. Most scientists are honest and do it unconsciously. They get negative results, convince themselves they goofed, and repeat the experiment until it “works”. Or they drop “outlier” data points.". This article is a great resource if you teach statistics.
  • Magnus Carlsen won a 3 board blindfold (with clock) exhibition. The video is posted on Chessbase.
  • Caruana and Nakamura earned their place in the upcoming Candidates tournament to determine the next challenger for the World Chess Championship by taking the top two places at Khanty-Mansiysk 2015.
  • The editor in chief of the Lancet, one of the world's most prestigious medical journals has stirred up some controversy. "Dr. Horton recently published a statement declaring that a lot of published research is in fact unreliable at best, if not completely false. “The case against science is straightforward: much of the scientific literature, perhaps half, may simply be untrue. Afflicted by studies with small sample sizes, tiny effects, invalid exploratory analyses, and flagrant conflicts of interest, together with an obsession for pursuing fashionable trends of dubious importance, science has taken a turn towards darkness.. Yes, statistics isn't really math.
  • Forbes has one of those REALLY annoying posts by someone who really lacks basic knowledge about what they're writing about--something all too common in mainstream media where even robots now generate worthless content. Although posed as a question "Should We Stop Teaching Calculus in High School?" the author is clearly saying "yes". "The list of high school math courses in the U.S. hasn’t changed for decades. My daughters are taking the same courses I took long ago: algebra, geometry, trigonometry, and calculus. These are all fine subjects, but they don’t serve the needs of the 21st century.". But the author goes on to say, "...the vast majority will never use calculus again. And those who do need it – future engineers, physicists, and the like – can take it in college.". So the courses do serve the needs of the 21st century. The author makes the point that we are awash in data today so the author asks, "What math courses do young people really need? Two subjects are head-smackingly obvious: computer science and statistics.". Huh? Who believes computer science is math? And anyone reading this blog knows (e.g. see here and here) that statistics isn't math either. Yes, theoretical stats is basically analysis but the statistics he's talking about (confidence intervals, p-values, etc) isn't. Whether (see the links) you want to look at schools having a "department of math and statistics", or that bigger schools have a separate statistics department, or that AMSTAT news says statistics isn't a subfield of math, or as is mentioned in the second link that statistics books and teachers have been presenting p-values incorrectly. If you believe stats is math then please explain what other branch of math teaches you the wrong way to do something as has been done with p-values? There is a different reasoning process for stats. But back to the article. With respect to statistics, "Most high schools don’t offer either one. In the few schools that do, they are usually electives that only a few students take.". Let's mention that statistics is covered in Common Core. The Common Core Standards are posted here and this government site notes, "The recently adopted Common Core State Standards for Mathematics (CCSSM) contain a large amount of statistics in the middle and high school grades and some at the elementary school level.". Not being a math teacher, this author is unaware how much things have changed: more statistics, mathematical proofs in geometry have been largely removed (I even had to teach probability(!) in my geometry classes), and 4 ways to subtract (which has confounded parents) are some noticeable changes. Assuming that because his daughters are taking the same courses he took decades ago means there hasn't been any change in content is, at best, sloppy journalism. To be clear, let me agree that computer courses in high school would be great. Python is such a natural choice that could be useful--but you don't sacrifice core math classes for that; you eliminate or consolidate less relevant courses to make room for it. The removal of most proof content from geometry is tragic because proofs are the essence of mathematics. As Alfred Renyi said, "A mathematician is a device for turning coffee into theorems". The author opting for computer science and stats as math classes while neglecting discrete math is, I suspect, based in the ignorance of not knowing discrete math is the math of computer science. The author continues, "Convincing schools to give up calculus won’t be easy. I imagine that most math educators will scream in protest at the mere suggestion, in fact. In their never-ending competition to look good on a blizzard of standardized tests, schools push students to accelerate in math starting in elementary school, and they offer calculus as early as the tenth grade. This doesn’t serve students well: the vast majority will never use calculus again.". There's some truth in here but since he hasn't taught high school he can't properly interpret what's happening. High schools get awarded numerical scores according to a formula for "performance" (which often get translated into star ratings for the school). Admin look at how they can increase scores (to make their performance look better). More students taking AP exams means a higher score is given, regardless of how poorly the students do. That's why school admins get teachers to encourage students to sign up for AP classes and that's why schools often pay for the student to take the AP exam--it's an easy way to raise the school's score. The consequence is that it's commonplace for students who struggle with fractions to be taking AP Calculus. But no matter, just require a graphing calculator to give students a chance. The child feels smart, the parents feel proud, admin performance improves, and some business makes a lot of money selling expensive calculators when you can buy a laptop computer for $200. The only problem is the child still has poor math skills that they'd be put to shame by a typical student from another country at a lower grade level that has a fraction of the resources but has parents making sure kids learn multiplication tables and basics and not giving them a calculator to use as a crutch at lower levels. But the issue isn't about producing quality in the US, so it's no surprise we never get it. They're looking to maximize performance under the rules they've been given so wasting taxpayer money on improving the school's score gets the admin credit for improving school quality even though no real quality has taken place. Same thing with attendance. Some schools have poor scores due in part to poor attendance. Since that poor attendance is, in cases, predictable (before Christmas break) schools often have incentives (such as a drawing for a free computer) for students who attend. This expenditure of taxpayer money has nothing to do with quality. There's so much to criticize in this article but you get the idea. His argument that "here’s a simple fix: get rid of high school calculus to make way for computer programming and statistics" is nonsense.
  • The controversy of why women don't perform as well as men in chess, which I first raised here, continues with a new study (authored in part by women). The data itself is interesting: "“Hard” sciences such as physics and statistics on average have a larger gender gap than social sciences and humanities – no surprise there. However, this is only part of the story. According to 2013 data from the National Science Foundation in the United States, there is large variation within each category: whereas women earned only 19% of PhDs in physics and 18% in computer science, they earned no less than 54% of PhDs in molecular biology – amounting to gender parity. Within the humanities and social sciences, those numbers ranged from 78% in art history and 72% in psychology to a dismal 27% in philosophy and 28% in music theory and composition.". I think the conclusions drawn off the data are suspect, to put it lightly. "The key claims of Leslie and Cimpian’s paper are: 1. that fields vary in the degree to which its practitioners believe that innate ability (“genius” or “brilliance”) is required for success; and 2. that society often promotes the notion that men have greater innate abilities than women.". If women were doing well in those fields then I don't see how they would be "bluffed" out of continuing. It makes more sense to me that they weren't doing well, didn't like it, found their "passion" somewhere else (as jobs opened up in other more desirable fields), etc.. The fact is that women used to hold a large percentage of computer science job. The claim that women would somehow give up pursuing a job in these lucrative white collar fields  because  society has told them men have greater innate abilities seems demeaning to women and contrary to the general rise of women in the workforce over the past 40 years. Women have faced harassment in many areas and haven't quit. More believable to me is that the radical change in the field took computer science out of their comfort zone: computer science today is so much different than back in the 80's. Note also that the study separates Statistics from math (as it should) and the resulting percentages for the two are quite different.
  • The chronotope blog comments on the (included) recent John Oliver video on student test in high schools. Make sure to check out the video!
  • Ravens guard John Urschel analyzes the extra point rule change in football.
  • The Hindu notes on the passing of chess legend Anand's mother. Grandmaster R.B. Ramesh has a fitting quote, "Without Anand it’s tough to imagine Indian chess. Without his mother, it’s tough to imagine Anand”.
  • CinemaBlend posts on a Tobey Maguire starring as former World Chess Champion Bobby Fischer in "Pawn Sacrific". Check out the movie trailer.
  • Hundreds of SATs go missing. If they aren't found soon the teenagers will have to take them again. Let's hope nobody has their college plans derailed.
  • reports  "Wisconsin may be the first state in the country to certify teachers who don't have bachelor's degrees under a provision put in the state budget....Under the change, anyone with relevant experience could be licensed to teach non-core academic subjects in grades six through 12. They would not need a bachelor's degree and they could even be a high school dropout.". This doesn't sound like a good idea.


Sagetex: Indefinite Integrals 3/4


I've added two more indefinite integrals to the Sagetex: Integrals page.

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

  • The NY Times posts on the tragic death of Nobel prize winning mathematician John Nash and his wife on the NJ Turnpike.
  • The Khanty-Mansiysk 2015 chess tournament continues here with Caruana leading the pack with +1 and only two rounds to go.
  • reports on how a principal was "released" after making racially charged comments during graduation exercises. The posted video lets you judge for yourself.
  • Al-Jazeera reports on how Texas is punishing students for skipping school. From the article (video posted, too): "In Texas, truancy is a Class C misdemeanor that carries a possible $500 fine and the threat of jail time if fines go unpaid when a child turns 17. The law has captured the attention of advocacy group Texas Appleseed, whose research found disabled, poor, and black and Latino students are most often sent to truancy court.".  The poor mom is working 2 jobs and now has extra financial stress trying to pay for her truant son. After watching the video this story describes the pathetic state of many of today's kids and their parents who want to be their friends. Why does the child decide whether he goes to school?!?
  • Stitz Zeager Open Source Mathematics has a variety of free, good quality math ebooks as well as the LaTeX source files.

LaTeX: PDF and tex file output


In an earlier post I mentioned how the output from a Sage session could be saved to a file--you just needed to know the path. As I alluded to, it's possible to do the same through Sagemath Cloud using sagetex, too. That means you can create a pdf and tex file at the same time. But why?

If "because it's fun" doesn't make your list, I've come up with a more plausible scenario. The original Sage Test Template provided a starting point for designing a randomized test. The result was a test along with the answer key in a 3 page pdf. But suppose you don't want the PDF to contain the answer key? It's possible to create a PDF for the test while at the same time producing the tex file for the answer key. Although cumbersome, it can be done. You'll need to create a file

f = open(r"SMCtestAnswers.tex",'w')

As with the earlier post, the file is created if it doesn't exist already. Unlike the that example there is no path given. Once the file is created it's just a matter of filling it with the preamble in order to run and then the answers using the choice of random variables from compilation. So the setup and first solution looks like this:

f.write(r"\usepackage{amsmath, amsfonts, amssymb}")
f.write(r"{\large Answers}")
f.write(r"$x=%s$, and $x=%s$"%(a,c))

And you can see why cumbersome is a kind description. Each line followed by a newline character (it didn't work as one line) and when it's time for the solution we insert the appropriate variables. After compiling you get a pdf for the test and you'll have to go check your files to find the newly created SMCtestAnswers.tex. Compile that file to create a pdf just for the answers.


Mission accomplished. I've posted the "proof of concept" file on the Handouts page.

Here are some issues that caught my eye this week.

  • The Khanty-Mansiysk 2015 chess tournament will seed the top two finishers to be in a tournament which will select the next challenger for World Champion Magnus Carlsen. As such you can find many top players competing. Caruana leads after 4 rounds. Tomorrow is a day off. The tournament can be followed at the site here or through Chessbomb (sidebar).
  • Tragedy in Jacksonville where according to this article in the St. Augustine Record, "A girl was left with a gunshot wound through both cheeks. Another girl was struck in the head by a shot. Both survived, but for a moment Thursday, a routine school bus ride home turned into a ride of terror on Jacksonville’s Westside.".
  • Students behaving savagely: ZeroHedge has the story of 50 teenagers beating an adult into the ground: "Richard Fletcher was beaten by a gang after asking two girls to stop fighting on his truck in Dundalk, Maryland. Man, 61, left with horrific injuries and facing $400,000 medical bills after near fatal attack by pack of FIFTY teens, including girls, when he tried to break up a fight. A 17-year-old boy has been charged as an adult for his role in beating a 61-year-old alongside a group of approximately 50 other teens in Baltimore, Maryland, on April 22.". Five students arrested at the time of the story.
  • In a post on Thomas Jefferson high school we saw people suing the school because "...the numbers [of black students] could surely be higher than they are now.". Now from the Washington Post we have, "More than 60 Asian American organizations filed a complaint (see below) with the federal government on Friday alleging that Harvard University discriminates against Asian Americans in the admissions process and calling for an investigation.". The complaint is posted at the link above. Sputnik news has these statistics: "A coalition of 64 organizations is citing research indicating that Asians need to on average score 140 points higher than white students on the SAT, 270 points higher than Hispanic students and 450 points higher than African-American students to equal their chances of gaining admission to Harvard. The exam is scored on a 2400-point scale.". It seems like the reverse discrimination laws to help "level" the field for Asian-Americans is now legal policy to discriminate against them for performing better than other racial groups.

Understanding "The Test"


The post Understanding the Prediction explained the mathematics behind Richard Wiseman's brilliant magic trick that's posted on his Quirkology site. It's a great way to introduce graph theory to your class.

Richard Wiseman's video "The Test" is a similar type of magic trick that can be explained using digraphs and, once again, is a great way to introduce a class to digraphs. I've added an explanation of "The Test" to the Other page.

Here are some thngs that caught my eye last week:

  • Discover blog has an article, "The Purpose of Harvard is not to Educate People". From the article, "Don’t believe me? Here is the test: when was the last time Harvard made a senior tenure offer to someone because they were a world-class educator, rather than a world-class researcher? Not only is the answer “never,” the question itself is somewhat laughable.".
  • reports on a "...former interim director of special services for the Brick Township School District, failed to reveal a 1990 conviction on heroin and cocaine charges on his job application with the district, the Ocean County Prosecutor’s Office has confirmed. Morgan, 65, was charged Thursday along with Brick Schools Superintendent Walter Uszenski and Uszenski’s daughter, Jacqueline Halsey, in a scheme that supplied Halsey with full-time day care for her preschool child paid for by the Brick Township schools, with official misconduct and theft by deception, said Al Della Fave, spokesman for the Ocean County Prosecutor’s Office.....According to a 1989 report in the New York Times, Morgan was arrested and charged with selling cocaine on five occasions, in amounts ranging from a half-ounce to more than 3 ounces, to undercover detectives assigned to the Brooklyn District Attorney’s investigation unit.Morgan -- who taught English to 9th and 10th graders in a special education program at Canarsie High School -- also was charged with possession of cocaine, as well as with conspiracy to sell heroin, in which he is said to have agreed to travel to Thailand to buy heroin for undercover agents posing as drug dealers. The heroin was supposed to be brought into this country concealed in disposable diapers, the authorities said.Morgan later was convicted of felony drug charges, though a follow-up article in the New York Times does not specify the exact counts. Morgan, who had worked for the school for 20 years, was fired but later won a civil case against the schools over the firing, despite his conviction.". So you've got a school official arrested and charged with selling drugs multiple instances (and the details are such public knowledge that it made the NY Times) and was teaching kids. So the question becomes "Was a background check ever done?" If it was, "How did it miss such well known information?". Also ask yourself what it says when Morgan was hired at the "request and recommendation" of someone still working in the educational system.
  • (Stephen) "Colbert Fune $800K in Grants for SC teachers".
  • Huffington Post has an interview with 2010 Fields Medal winner Cedric Villani.

Sage Essentials: Writing to a file


I've added some information on writing to a file while using Sage installed on your computer. It's on the Sage Essentials page. Essentially you start with a line like

f = open(r"/home/<rest of path>/MyFile.tex",'w')

while filling in the particulars of your path on your computer and after including some code like that shown above, Sage will create the file for you (regardless of whether it had existed before). If you use Sage, the chances are you can think of some times when you'd want to output data/results to a file. Whereas a text file (or .csv file) is probably what most people are used to, the TeX users amongst us will be more interested in .tex files to get the beautiful typesetting of LaTeX.

But remember, Sage can be run through LaTeX using the sagetex package, so this raises the possibility of running LaTeX and, in addition to creating the PDF file, creating multiple .tex file as well. Is there a use for that? From this TeX Stack Exchange post, the answer is yes. And since multiple PDFs are not an option unless the small changes between documents are "predictable" (e.g. change of names in a letter), .tex file output might prove useful as well. More on that later after I have some time to tinker with the idea. Here are some stories that caught my eye this week:

  • Remember the outrageous charges of sexism against Nigel Short? Peter Long, from the Malay Mail Online has a good opinion piece on this and other chess related issues here. He has a busted link  " a very well-written article by Tarjei J. Svensen entitled Susan Polgar and Nigel Short at War which shows that the underlying (real) issue written about by Short in the New in Chess column is certainly not sexism (let alone race, which was sadly thrown into the mix by some without any thought).". There's so much going on here! You can find that Svensen article posted on Chess24. Also, a reader has found a piece in the Guardian of the study that Short was, most likely, citing.
  • One News Now reports some disturbing news: "South Carolina Education Department Chief Operating Officer Elizabeth Carpentier issued a warning to parents that they could be locked up behind bars for 30 days if their children missed even one day of testing, according to South Carolina Parents Involved in Education member Tamra Hood as stated by Breitbart News.Carpentier didn’t stop there, reportedly threatening any groups or organizations involved in encouraging parents to object to Common Core testing with charges of aiding and abetting a crime.School officials made it loud and clear that students and parents have no say in the matter and must abide by the state’s dictates whether they like it or not."
  • The Washington Post has a piece in which a teacher gives a well articulated argument (backed up with specific examples) of the problems in common core exams: "I want to talk about the test itself. It is a fundamentally flawed tool that will only debase the good work we teachers do in the classroom, the work that districts do in designing and implementing quality curriculum, and the work our students do in learning to become enlightened critical thinkers....First things first, one of the most disturbing trends that I have found examining this year’s and last year’s (released) tests is a shift in thinking toward a kind of intellectual relativism. In other words, any claim that a student makes is correct if he or she substantiates it with some evidence. On the surface this doesn’t sound terribly problematic, but when you start to examine some of the anchor papers, the dilemma with this vein of thinking becomes shockingly apparent. The truth is, not all claims are correct and not all evidence is created equal. Making a feeble claim and using evidence out of context to support that claim is an all too common occurrence on these tests....Another disturbing pattern that emerges as one reads the anchor responses for the ELA is what I call “The Easter Egg Hunt.” When it comes to short answer questions in particular, the question that is actually being posed rarely matches the answer required. The wordier the written response, the more likely it is that the student will stumble upon the correct answer, find the decorative egg. (Strategy!) Time after time there is a clandestine condition that must be met in order for an answer to get full credit – “Magic Words.” As my scoring instructor illustrated, it’s kind of like tossing all of the words into a bucket and looking for certain key phrases or ideas to float up to the top."
  • ZeroHedge has the story of a Texas college teacher who snapped and failed the entire class via e-mail, "While we don’t know if any of the above factored into the following story, what we do know beyond a shadow of a doubt is that Texas A&M Professor Irwin Horwitz was sick and tired of the students in his Strategic Management course and so he did what many a college professor across the country has at one time or another dreamed of doing: he failed the entire class. Here’s an excerpt from the e-mail he sent to his students: "Since teaching this course, I have caught and seen cheating, been told to 'chill out,' 'get out of my space,' 'go back and teach,' [been] called a (DELETED: see the link for the proper description) to my face, [had] one student cheat by signing in for another, one student not showing up but claiming they did, listened to many hurtful and untrue rumors about myself and others, been caught between fights between students. None of you, in my opinion, given the behavior in this class, deserve to pass, or graduate to become an Aggie, as you do not in any way embody the honor that the university holds graduates should have within their personal character. It is thus for these reasons why I am officially walking away from this course. I am frankly and completely disgusted. You all lack the honor and maturity to live up to the standards that Texas A&M holds, and the competence and/or desire to do the quality work necessary to pass the course just on a grade level…. I will no longer be teaching the course, and all are being awarded a failing grade.""
  • MetroUK posts a picture of work submitted by a student trying to put one over their teacher, "The teacher clearly didn’t appreciate the cunning blend of the words ‘true’ and ‘false’.Genius as it is, trying it out on every answer was always destined to fail – although he might have been lucky if he’d only slipped it in just once or twice."


Math Models and a Birthday Problem resource

Mathematical models is one of those ideas that students should know, but don't. Even after they've studied them. Ask your class the following: "A coin is tossed. What's the probability that it lands as heads?".

Most students have are quick to say 1/2 but that's wrong--the correct answer is we don't know the probability for any particular coin. We could use experimental probability to estimate it but even that's an approximate answer. The probability of heads that the students think is reality is actually a based on a mathematical model with a "fair coin". Mathematical models are approximations of reality. Unfortunately most students who have had some probability don't know coin flipping is based on a model and think the number of outcomes determines the probability (not realizing the equally likely assumption is an assumption which could be false). Some of these problems invariably trace back to the teachers who have taught them incorrectly.

Mathematician William Feller was a well known expert in probability who wrote a classic book An Introduction to Probability Theory and Its Applications in which you can find (by click on "Look Inside") the following quote on page 19: "As a matter of fact, whenever refined statistical measures have been used to check on actual coin tossing, the result has invariably been that head and tail are not equally likely. And yet we stick to our model of an "ideal" coin even no good coins exist. We preserve the model not merely for its logical simplicity, but essentially for its usefulness and its applicability.".

The coin flipping model has two assumptions built into it:

  1. There are two outcomes (heads and tails)
  2. The two outcomes are equally likely.

Since its possible for coins to balance on their sides (nickels and quarters more easily than a dime), it's possible (though admittedly remote) for a coin to land on its side. And it seems like most people have had experiences of a dropped coin which lands on its side only to roll away. Heck, it's even happened during a football game. This paper estimates the odds of an American nickel landing on its edge as 1/6000. says that a study (broken link) indicates "...the "randomness" of a toss is actually weighted ever so slightly towards the side of the coin that's facing upwards when a flip begins....The paper, written by statistics and math professors from Stanford and UC Santa Cruz, also points out that a perfect coin toss can reproduce the same result 100 percent of the time.".

So coin tossing is a simple example of a mathematical model that students should learn. Another model is the famous "Birthday Problem". As I mentioned in an earlier post:

Answering the Birthday Problem involves creating a mathematical model. The model rests on two assumptions that aren't true and should be discussed with the class:

  • there are 365 days in a year (Feb 29th is ignored to simplify the model)
  • birthdays are equally likely to be on any given day (Also false. This varies from country to country; in the US birthdays are more towards the middle of the year. Count back 9 months and you've got cold weather. Nothing random there.)

I'm revisiting this post because I ran across a chart showing the distribution of birthdays referred to in the second point above. The Gizmodo post "How Common is Your Birthday" says, "The visualization used data from 1973 to 1999 to chart popular birthdays and figured out when the most popular time to pop out babies were."  So now you have a source to back up my claim and a nice chart to use in the classroom.

If you teach the Birthday Problem then you should get a copy of the chart or bookmark the page above.

Here are some stories that caught my attention this week:

  • In an earlier post I pointed out the case of a high school student accused of stealing a backpack who was in prison for almost 3 years because he had been accused of stealing a backpack and would not plead guilty. The charges were eventually dropped and, because he was able to specify the specific dates on two occasions when he was abused, video has surfaced of these events. Democracy Now! has  "Explosive video obtained by The New Yorker depicts extreme violence inside New York City’s Rikers Island jail complex." and interviews New Yorker staff writer Jennifer Gonnerman, who has reported on the issue.
  • NY Post reports on, "A copy of the state’s English Language Arts test that students took last week was leaked online Wednesday in an apparent act of sabotage by anti-testing activists......“This is a political act and it will be interesting to see whether [test-creation company] Pearson or the state Department of Education understands it as that or goes after them for civil or criminal liability,” said Brooklyn College education Professor David Bloomfield, who called the post an act of “civil disobedience.”"
  • The Washington Post covers the widespread resistance of New York to Common Core testing: ,"Newsday has translated raw numbers into percentages, estimating that over 40 percent of all Long Island 3-8 students refused to take last week’s ELA Common Core state tests. Numbers in some districts reached well over 70 percent, with at least one district exceeding 80 percent. It appears that no more thanseven of the 124 districts on the island will meet the testing threshold of 95 percent. And that is before this week’s math tests, when opt-out numbers are expected to climb, as they did last year...It seems clear that the final 2015 tally will well exceed 200,000 students. New York State will likely not make the minimum 95 percent federal requirement for testing.."
  • Shamkir 2015 has ended in victory for Magnus Carlsen. Chessbase has the report here. Anand took second with Caruana and So tied for third. Anand's second place performance has put him at number 2 in the world with a 2803.7 Live Chess Rating. I never thought he'd get there again. At 45 with his peak years ago and he's still in the hunt: incredible!
  • My sympathies go out to Nigel Short. Not for his 1.5 - 8.5 versus Kasparov (Chessbase only has part 1 out here) but for the savage "beating" the "PC-police" are inflicting on him. The brouhaha, discussed here, starts with Nigel's comment, "“Men and women's brains are hard-wired very differently, so why should they function in the same way? I don't have the slightest problem in acknowledging that my wife possesses a much higher degree of emotional intelligence than I do. Likewise, she doesn't feel embarrassed in asking me to manoeuvre the car out of our narrow garage. One is not better than the other, we just have different skills. It would be wonderful to see more girls playing chess, and at a higher level, but rather than fretting about inequality, perhaps we should just gracefully accept it as a fact.”" which became sensationalized with The Telegraph's article, " Nigel Short: 'Girls just don’t have the brains to play chess".  You can even see Nigel defending his common sense position on Sky News and being given the absurd argument that he's wrong because J Polgar has a plus record against him. Given that there are distinct differences in the hardwiring  of male versus female brains (not to mention the differences between males and between females) and the study Short points out, it's difficult to believe his comments have become so controversial. Sorry Nigel! You deserve better.
  • Huffington Post has an article about Ramanujan whose birthday was April 26th. The brilliant mathematician who was most definitely wired differently than others: "The biggest question is how an untrained teenager, and later young adult who repeatedly flunked out of college in his native south India (generally the area of Madras, today's Chennai), was able to obtain--all on his own--mathematical expressions that later would take some of the world's leading mathematicians years and even decades to ascertain and prove.".
  • I've deleted the CTAN Mail Archive link and replaced it with the updates They were notifying about many changes in LaTeX that never made it to the other link. The link is CTAN announcements, located on the sidebar.