Polling: statistics isn't really math

I've said it before: statistics isn't really math. It's an application of math like engineering,  mathematical economics, mathematical finance, predicting the weather, etc that uses math to claim respectability. Sure, theoretical statistics is math--akin to analysis--but actually applying statistics to numerous problems when there is no certainty that underlying assumptions (such as the data being random) are true is just wrong. In a previous post, "Statistics Isn't Really Math" I looked at some of the problems with statistics. In particular, I cited the post at AMSTAT News, (The Membership Magazine of the American Statistical Association) saying  "Statistics, however, is not a subfield of mathematics. Like economics and physics, statistics uses mathematics in essential ways, “but has origins, subject matter, foundational questions, and standards that are distinct from those of mathematics” (Moore, 1988, p. 3). David Moore, statistics educator and former president of the American Statistical Association, gives the following four compelling reasons why statistics is a separate discipline from mathematics:

  • Statistics does not originate within mathematics
  • The aims and foundational controversies of statistics are unrelated to those of mathematics
  • The standards of excellence in statistics differ from those of mathematics
  • Statistics does not participate in the inter-relationships among subfields that characterize contemporary mathematics

Statistics exists because of the need for other disciplines to examine and explain variation in their data."

That's a nice, clean authoritative explanation by statisticians as to why statistics isn't really math.

I followed that post up later with "Brexit: because statistics isn't really math" when virtually all the hacks statisticians made a horrendous call on Brexit. The bad prediction wiped out trillions in market cap when the vote went against what almost every public poll believed would happen.

Now with the US election coming up, I figure I should highlight a couple of new pieces that caught my attention. The first is a link that was brought to my attention by a reader, courtesy of the NY Times: "When you hear the margin of error is plus or minus 3 percent, think 7 instead". Now margin of error is a key term in polling statistics; except, according to this article, prepare to have your knowledge challenged: "In a new paper with Andrew Gelman and Houshmand Shirani-Mehr, we examined 4,221 late-campaign polls — every public poll we could find — for 608 state-level presidential, Senate and governor’s races between 1998 and 2014. Comparing those polls’ results with actual electoral results, we find the historical margin of error is plus or minus six to seven percentage points. (Yes, that’s an error range of 12 to 14 points, not the typically reported 6 or 7.)". Yes, throw out everything you learned about confidence intervals. But wait, it gets worse. A link off of that article takes you to here, an article entitled: "We Gave Four Good Pollsters the Same Raw Data. They Had Four Different Results" which is about just what the title indicates. Four pollsters were given exactly the same set of polling data and 4 different predictions. This is NOT what you'd get in a math course. The reason?: "Polling results rely as much on the judgments of pollsters as on the science of survey methodology. Two good pollsters, both looking at the same underlying data, could come up with two very different results.How so? Because pollsters make a series of decisions when designing their survey, from determining likely voters to adjusting their respondents to match the demographics of the electorate. These decisions are hard. They usually take place behind the scenes, and they can make a huge difference....Pollsters usually make statistical adjustments to make sure that their sample represents the population – in this case, voters in Florida. They usually do so by giving more weight to respondents from underrepresented groups.". Got that? Pollsters tamper with adjust the data as they feel like.

In fact, ZeroHedge has this post where polls contradict the margin error of others, and another post looking at the methodology behind a recent Washington Post poll: "Of course, like many of the recent polls from the likes of Reuters, ABC and The Washington Post, something curious emerges when you look just beneath the surface of the headline 12-point lead."METHODOLOGY – This ABC News poll was conducted by landline and cellular telephone Oct. 20-22, 2016, in English and Spanish, among a random national sample of 874 likely voters. Results have a margin of sampling error of 3.5 points, including the design effect. Partisan divisions are 36-27-31 percent, Democrats - Republicans - Independents."As we've pointed out numerous times in the past, in response to Reuters' efforts to "tweak" their polls, per the The Pew Research Center, at least since 1992, democrats have never enjoyed a 9-point registration gap despite the folks at ABC and The Washington Post somehow convincing themselves it was a reasonable margin."

Finally, there is this somewhat humorous post "Here's The 30 Seconds After The Last Debate That CNN Would Rather You Didn't See" where CNN polling has a 52% to 39% win for Clinton in the 3rd debate "So when the CNN focus group was asked "did this debate help anyone make up their mind or possibly change their vote", the results did not turn out how Goebbels they expected...

  • 5 Clinton
  • 10 Trump
  • 0 3rd Party
  • 6 Undecided

A much, much different result than there poll. Polling data is not the same coin flip data and the situation is even worse with respect to the integrity of the data---Stanford University called attention to Election Fraud here. By now it should be even more obvious that statistics isn't really math: the margin of error doesn't mean what it should and qualified statisticians with exactly the same data come up with different answers.

Here are some events that caught my eye lately.

  • Poor Nigel Short can't really catch a break. After getting into trouble with PC police for his comments on women which got twisted and blown way out of proportion, he had a 6 game match with Hou Yifan, the highest rated woman chess player in the world. The match was actually less close than the score would indicate with Short winning the match after 5 games in which he was never really in trouble--before losing badly in the final game. Was it a gift?--after all, he'd won the match, the last game wouldn't be rated, and it would be good gesture. Whatever the reason for the one game in which Short played badly, he got punished yet again. Chess.com has a report which states, "Well, Short had secured match victory after the fifth game, and later that day, he discovered that according to official regulations the last game should not be rated. Paragraph 6.5 of the FIDE Rating Regulations says:"Where a match is over a specific number of games, those played after one player has won shall not be rated." Short had an email discussion with tournament director Loek van Wely late Friday night. Van Wely wasn't immediately convinced. In fact, two years ago, when Anish Giri had won his match before the last game with Alexey Shirov, that sixth game was rated." So Short showed clear dominance throughout the first 5 games, never being in any danger, knew the last game wasn't going to be rated before it was played and "finished" the match with a bad loss, only to find the game WAS rated, which violated FIDE rules. Now he's not happy. And check out the footnote like reference to Short winning the match at Chessbase. Had he lost there would have been a BIG story on woman beats man in grudge match.
  • American Thinker with a piece on  precious snowflakes scared of Halloween: "College offers round-the-clock counseling for students 'troubled' by Halloween costumes"
  • EAGNews on the high school principle who told a student to remove his headphones in school, and  "When the student refused, Tossman attempted to remove the headphones, which allegedly sent Penzo into a rage. “ … (T)he 18-year-old student cold-cocked the principal,” according to the news site. “Penzo continued to pounce on Tossman, socking him several times in the face, causing swelling and lacerations around both the principal’s eyes.”A prepared statement released by the school contends “The NYPD immediately responded” and took Penzo into custody.""
  • FiveThirtyEight reports "A new study shows that first-grade teachers consistently rate girls’ math ability below boys’ — even when they have the same achievement level and learning style. The study out today in the journal AERA Open from researchers at New York University and the University of Illinois at Urbana-Champaign seems to represent a setback for gender equity in math. A widely reported 2008 study found that girls score as well as boys do on standardized state math tests. But the latest study suggests that early in their math education, many girls run into a teacher who perceives them as being worse at the subject than they are — which could discourage some of them from heading down a path that could lead to a career in math, science or engineering.". This is surprising to me because I have the impression that most math teachers at that level are women. Unfortunately I don't have the data to back that up. Is anyone aware of the data for this?
  • A powerful image of education winds up in a story on Sott.net.  Take a look at the school in Afghanistan halfway down the page. I've got to believe that some teachers would find that useful in their class.
  • Geekwire with a piece "Meet the minds behind Axiomatic: An art project based in theoretical mathematics"
  • Carlsen versus Nakamura in a blitz match today. Chess.com tells you how to watch it online.

Irrational Numbers with Patterns

img_20160919_163743715I'm not really posting anymore but I had to make an exception. The bad quality picture above is from a student's math class and the worksheet says: "Decimals that never end and have no pattern, think MUMBO JUMBO NUMBERS" in describing irrational numbers. Some context: the student had prealgebra last year where they learned that rational numbers were numbers that can be written as an integer divided by a nonzero integer and that irrational numbers were real numbers that weren't rational. More importantly, the student had learned the decimal characterization of rational and irrational numbers: rational numbers are terminating or nonrepeating and irrational numbers are nonterminating and nonrepeating.

So when the student, now in algebra, went through the beginning of the school year review of the real number system with this worksheet you have to cringe. First, the algebra class has learned the important definitions for rational and irrational numbers, so why not review those terms? That SHOULD be the goal. Second, the characterization of irrational numbers as "have no pattern" is wrong and she uses pi as an the only example to back up her claim. The teacher has given the class a worksheet with wrong information and doesn't know it. Welcome to a quality public school.

So let's give some quick examples to of irrational numbers which have decimals that never end BUT have a pattern.


Yes, ... is ambiguous, so let's describe the pattern. Just count the positive integers and put them together after the decimal. Understanding the pattern you know the next digits are ....161718192021..... and you can calculate whatever place after the decimal you want if you need to because there is a pattern. Here's another example:


The pattern is to have separate one "1" from two "1"s from three "1"s from...using a 0. Under that pattern, you know the next digits are 11111110111111110..... and so on. Both of these decimal numbers are nonterminating and nonrepeating. You can't shouldn't make up your own math, especially when it's wrong. It causes unnecessary confusion.

Here are some stories that caught my eye recently:

  • From the Daily Mail, "Meet the boy geniuses who developed a math theorem that calculates problems faster than a COMPUTER - despite still being in high school"
  • Russian chess announces the passing of chess trainer Mark Dvoretsky. As someone fortunate enough to have attended some of his training sessions, I appreciate just what a tragic loss this is for chess.
  • Poor Chicago teachers! Well, not poor exactly. ZeroHedge reports they are ready to strike yet again. "Chicago teachers have a 13% raise (over four years) offer on the table, but that is not enough. They set a strike date of October 11 because the city wants the union to contribute more than 2% for their underfunded pensions, among the worst funded pensions in the nation. The Chicago public school system is bankrupt. Its bonds are deep in junk status....an affiliate of the American Federation of Teachers, is gearing up for a strike. It would be the union’s second in four years, despite the fact that the median salary for a teacher in Chicago is $78,169. When you add another $27,564 for various benefits, the total compensation for a teacher – good, bad or middling – becomes almost $106K per annum. (Please keep in mind teachers work 180 days a year, while employees in other professions typically work for 240 to 250 days.) In retirement, the average Chicago teacher receives a hefty $50,000 a year.
  • Truthdig with a sobering look at the status of adjunct teachers. With the hurdles to teach at public high school too onerous they are the working poor.
  • Sott.net with a well covered story on a Michigan student who, "...noticed nasty discolored water coming from the sink in her school, so she took a picture and shared it with social media. Hazel Juco was hoping that she could raise awareness about the potentially dangerous issue, and perhaps get the problem fixed. Unfortunately, the school was not impressed with the student's whistleblowing and actually suspended her for violating the school's policy of taking photos in the bathroom."
  • Propublica on "Education Department Terminates Agency That Allowed Predatory For-profit Colleges to Thrive"
  • Daily Mail with a viral image. You can't trust your senses.
  • Remember the poor Yale professor who was screamed at by hysterical brats? The Federalist has more video of what led up to the incident. "Altogether, the footage is nearly 25 minutes long — during which Nicholas manages to keep his cool in an attempt to rationally discuss his wife’s email with a cluster of impassioned students. The scene is chaotic — students verbally attack Nicholas, demanding he apologize for his wife’s “racist” comments. Ultimately, he does not decry the content of Erika’s email, but he emphatically and repeatedly apologizes for any pain her words caused....Based on this footage, it’s clear the students at Yale were incapable of having a rational discussion with another individual who dared to push back against their hasty accusations of racism. Despite what others have tried to claim, it’s plain as day many of those students who loudly disrupted the campus with their protest really were crybabies that threw tizzies over an email about Halloween costumes."
  • Lew Rockwell with a nice video on the value of a college degree.
  • American Thinker has some thoughts on reforming higher education: "We need to increase by 40% over the next ten years the number of people with college degrees, a state official once lectured us. Sitting in the audience, I thought, we know how to give people degrees. We no longer know how to give them a college education...."
  • Quartz with a piece on "Seven Rhode Island universities, including Brown and Rhode Island College, will move to open-license textbooks in a bid to save students $5 million over the next five years, the governor announced Tuesday"
  • The Federalist spotlights just how worthless a PhD in education is in reporting on  a PhD candidate who claims "Science Is Sexist Because It’s Not Subjective". "Throughout her dissertation, Parson assumes and asserts that women and minorities are uniquely challenged by the idea that science can provide objective information about the natural world. This is an unfair assumption, she says, because the concept of objectivity is too hard for women and minorities to understand."


Odds and Ends: Aug 30, 2016

Just a quick post. As I'm no longer teaching I won't be working on the website as much.

Here are a few stories that caught my eye since the last update. A lot of links for you science teachers:

  • RT with an entertaining video from a finalist in the Best Illusion of the Year Contest 2016. Science teachers, take note!
  • Listverse has "10 Reasons Academic Journals Are Filled With Junk Science". Number 9 is a good one, related to bogus journals: "A pair of computer scientists, frustrated with unwanted spam from a pay-for-publication journal, submitted a joke article. It was 10 pages of the same seven words repeated over and over: “Get me off your f—king mailing list.”"
  • Reason adds its voice on junk science, "Sarewitz cites several examples of bad science that I reported in my February article "Broken Science." These include a major biotech company's finding in 2012 that only six out of 53 landmark published preclinical cancer studies could be replicated. Researchers at a leading pharmaceutical company reported that they could not replicate 43 of the 67 published preclinical studies that the company had been relying on to develop cancer and cardiovascular treatments and diagnostics. In 2015, only about a third of 100 psychological studies published in three leading psychology journals could be adequately replicated.....Sarewitz also notes that 1,000 peer-reviewed and published breast cancer research studies turned out to be using a skin cancer cell line instead. Furthermore, when amyotrophic lateral sclerosis researchers tested more than 100 potential drugs reported to slow disease progression in mouse models, none were found to be beneficial when tested on the same mouse strains. A 2016 article suggested that fMRI brain imaging studies suffered from a 70 percent false positive rate. Sarewitz also notes that decades of nutritional dogma about the alleged health dangers of salt, fats, and red meat appears to be wrong."
  • Signs of the Times with "Madam Marie Curie's research papers still radioactive 100+ years later".
  • Signs of the Times again with a piece on "The first computer programmer was a woman - Ada Lovelace"
  • Salon with an article: "The State College of Florida recently scrapped tenure for incoming faculty. New professors at this public university will be hired on the basis of annual contracts that the school can decline to renew at any time."
  • Reason on generation obnoxious: ""We have spoken. We are speaking. Pay attention." Nothing captures the attitude of the modern college activist as perfectly as this statement, made by Yale University students petitioning the English department for changes to the curriculum (they wanted to read fewer white male poets).It's the constant refrain of the far-left social justice student: Our minds are made up. The time for discussion is over. We aren't here to be educated. We are here to educate you."
  • Huffington Post on the US winning the math olympiads for the 2nd year in a row.

SageTex: Polynomial Interpolation 1


Vacation! But before it's time to go I've added a problem to the SageTex: Matrices page. It's not enough to have a lesson on polynomial interpolation like was mentioned earlier so I've put together a problem. Given what starts out as the Fibonacci sequence, students will have to find a polynomial to justify the sequence continuing with a term which breaks the pattern that people think is there.

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

  • The Daily Caller has noted "The University of North Carolina at Chapel Hill issued a guide this week which instructs students that Christmas vacations and telling a woman “I love your shoes!” are “microagressions.” The taxpayer-funded guide — entitled “Career corner: Understanding microaggressions” — also identifies golf outings and the words “boyfriend” and “girlfriend” as microagressions...Christmas vacations are a microagression, the public university pontificates, because “academic calendars and encouraged vacations” which “are organized around major religious observances” centralize “the Christian faith” and diminish “non-Christian spiritual rituals and observances.”"
  • NJ1015 with a tragic story, "The 17-year old Robbinsville High School student who fatally ran over this district’s beloved schools superintendent in April was talking on her cell phone at the time of the crash, prosecutors said Thursday.The student, who is now 18 but is not being named by authorities because she was a juvenile at the time of the crash, has been charged with second-degree death by auto and leaving the scene of a motor vehicle accident resulting in death.She also was ticketed for reckless driving, improper use of a cell phone while driving and leaving the scene of an accident, the Mercer County Prosecutor’s Office said."
  • ZeroHedge with a piece on Randi Weingarten and teacher unions, "Weingarten instructed investment advisers at the federation's Washington headquarters to sift through financial reports and examine the personal charitable donations of hedge fund managers, focusing on those who want to end defined benefit pensions, and entities backing charter schools and the overhauling of public schools. In early 2013, the union federation published a list of roughly three dozen Wall Street asset managers it says donated to organizations that support causes opposed by the union, and the federation wanted union pension funds to use the list as a reference guide when deciding where to invest (or not invest) their money. Said otherwise, if asset managers don't support unions, the unions won't invest with the funds." You'll have to go to the link to see what happened next.
  • Philly.com with a story that's gotten a lot of coverage, "On June 16, police were called to an unlikely scene: an end-of-the-year class party at the William P. Tatem Elementary School in Collingswood. A third grader had made a comment about the brownies being served to the class. After another student exclaimed that the remark was "racist," the school called the Collingswood Police Department, according to the mother of the boy who made the comment....The boy's father was contacted by Collingswood police later in the day. Police said the incident had been referred to the New Jersey Division of Child Protection and Permanency. The student stayed home for his last day of third grade."
  • Campus Reform has a story on "Donald Trump’s campaign slogan is a “racialized, targeted attack” according to Skidmore College’s Bias Response Group (BRG). Three white board messages with the phrase “Make America Great Again” were included in the BRG’s annual report and classified as “written slur[s] or graffiti” because they had been written on the white boards of female faculty of color." These Bias Repsonse Groups provide flimsy cover to assault free speech.
  • WGBH news reports on the Harvey Silvergate's Muzzle Awards for 2016. First place went to Yale over "...a string of events that started with an email about Halloween costumes, Nicholas and Erika Christakis, two well-respected professors at Yale University, resigned their administrative posts as faculty of Silliman College (a dormitory) amid student protests."

Brexit: because statistics isn't really math

A last minute change in my post due to Friday's historic day that wiped out 2 trillion off of the worlds equity markets. The cause? Virtually all the experts predictions were wrong on Brexit: the pollsters got it wrong, the betting line was wrong, and the markets got it wrong-- thank the statisticians for another job well done! CNN reports, "Ahead of the 2012 U.S. elections, Nate Silver, from the website FiveThirtyEight, correctly predicted who would win all 50 states, even as pundits were saying the race was "too close to call." In 2008, he had also correctly projected all but one state. As this year's British election results started trickling in, Silver tweeted that the world "may have a polling problem." "Polls were bad in U.S. midterms, Scottish referendum, Israeli election and now tonight in UK," Silver said....In a commentary on FiveThirtyEight, Silver suggested that forecasters had been overconfident. "Polls, in the UK and in other places around the world, appear to be getting worse as it becomes more challenging to contact a representative sample of voters. That means forecasters need to be accounting for a greater margin of error," he said....Prediction models for the U.S. elections had also become more reliable, Parakilas said, something he didn't believe had happened yet in the UK...." And while they tell you NOW that the models in the UK are less accurate, the Nate Silver that CNN trumpeted as the expert is the same Nate Silver I mentioned here, who performed so badly.

The great thing about statistics is you can explain why you were wrong after you learn that you were wrong. Here are some other explanations floating around as to why the results were so wrong:

  • there was a lot of rain in London and that could impact the turnout of city dwellers who tended to support Bremain.
  • Brexit voters were criticized as racists and not too bright, as all the "experts" came out for Bremain. As a result, Brexit voters were not honest when polled. I think this is a big factor, and a reason why applied statistics is more of an art than science.
  • the inability to predict how many people would turn out to vote
  • Bremain is what the establishment wanted to win so the dissenting voices were minimized. This seems unlikely given how genuinely surprised the establishment was.
  • From Reuters, "Predicting the outcome of Thursday's referendum was harder than that of a national election because there was virtually no historical data to draw on, said David Rothschild, an economist at Microsoft Research. He said pollsters also did not pay enough attention to working class and less educated voters....Rothschild, who also is a fellow at Columbia University’s Applied Statistics Center, said he expected forecasting to improve with a transition from polls using small, random representative samples to large Internet-based ones with rich demographic data. "If I have one million respondents with a large amount demographic data, I should be able to predict outcomes better, or I'm not a very good statistician," he said." OK, but right up to the end statisticians were confident of the result even though many polls were based on only a few thousand people. How representative were the samples they claimed were representative and why were so many experts wrong.
  • Statsblog.com gives their 5 reasons, including "Survey respondents not being a representative sample of potential voters (for whatever reason, Remain voters being more reachable or more likely to respond to the poll, compared to Leave voters)". Hard to argue with the samples not being representative of the whole AFTER you've been proven wrong. But aren't statisticians supposed to be guarding against this happening?

Lots of excuses; of course some or all arguments could be right BUT:

  • From NYTimes, "Britain’s decision to leave the European Union on Thursday was a big surprise. As late as 6 p.m. Eastern in the United States, less than five hours before the results became clear betting markets gave “Remain” an 88 percent chance to win the election, but it wound up losing by four percentage points....One could certainly argue that the polls were “wrong” in the sense that they tended to show a slight Remain advantage heading into the vote count. But it was clearly a distinct possibility that Brexit would win, based on the available survey data. So it’s hard to argue that this was a big polling failure, and it’s a bit strange that the financial markets appear to have been caught completely by surprise." The American Thinker responds to this stupidity,  "Sure it wasn't.  Once you are done rolling around on the floor in laughter at claims that this wasn't a massive polling failure, read on....Not a single one of the well known polling aggregators/predictors picked Brexit in their last-minute final projections...Thus, we had a systematic bias in the aggregated polling data that ranged from 4% to almost 11%.Individual polls leading up to the vote were publishing ridiculous results.  In the week prior to the vote, 9 of the 13 polls predicted a victory for Remain ranging from 1% up to 10%.  Just three polls had Leave in the lead, but just by 1% to 3%– i.e., still below the actual margin of victory – and one poll had a tie.  Not a single individual poll got the result correct, or overpredicted a Leave win....The overall bias in favor of Remain was effectively uniform, which is statistically impossible if the bias was random.  The bias was systematic."
  • In region after region the Brexit numbers were consistently underestimated by several percentage points.

The Telegraph has a lot more analysis with charts and graphs as to what wrong, "Professor Curtice was cautious throughout the campaign, saying that“some of the polls are definitely wrong” in “a cloud of uncertainty”. There were also clear distinctions between phone and online polls - phone polls invariably scored higher results for Remain compared to online." [Comment: Aren't you glad you know this now, after the fact?] "Interestingly, the Leave vote remained constant across both phone and online - it was the “don’t know” score that decreased for phone polls, and Remain seemed to be securing most of these. This was falsely encouraging for the final result. According to YouGov’s analysis, the reduction of don't knows for phone polls was because people were more likely to give an opinion when in conversation with someone, rather than admitting they didn’t know what they thought about such an important choice.Analysts dismissed the idea that different methods would reach different demographics.." So they got it wrong again. But at least their hindsight is 20/20.

Some lessons according to the Washington Post,

  • "First, we did not see this coming. For some weeks now, Stephen Fisher and Rosalind Shorrocks have been tracking referendum forecasts. They consider a wide range of sources, from forecasting models based on polls, to citizen forecasts, to betting markets. None of these methods saw a Leave outcome as the most likely outcome."
  • "Second, this was not a systematic polling failure of the same magnitude as last year’s U.K. general election, where opinion polls badly underestimated the Conservatives’ chance of victory." So the defense is: the failure isn't as bad as when they REALLY messed up last year. That should inspire confidence.
  • "Third, we learned something about campaign dynamics in referendums — and we went wrong by believing too firmly in a claim about how voters decide. Part of the disparity between relatively close polls and relatively confident betting markets was due to the belief in status quo reversion — the idea that undecided voters will be more likely to choose the status quo option (in this case, Remain) than the alternative."
  • "Fourth, given the types of areas that voted to Leave, and given the available polling evidence, it seems likely that a majority of Britons have traded economic benefits for restrictions on people from the European Union coming to live and work in Briton. The areas which voted Leave were older, whiter, and less likely to have a university education."

Another black eye for statistics and statisticians but you can't expect statistics to have the accuracy of mathematics--it isn't math any more than mathematical economics is.

Here are some stories that caught my eye last week:

  • ZeroHedge reports "The percentage of new doctorate recipients without jobs or plans for future study climbed to 39% in 2014, up from 31% in 2009according to a National Science Foundation survey. Those graduating with doctorates in the US climbed 28% in the decade ending in 2014 to an all-time high of 54,070, but the labor market - surprise surprise - has not been able to accommodate that growth. "The supply of PhD's has increased enormously and the demand in the labor market has increased but not nearly as fast. When you can import an international workforce or outsource research, you have a buyer's market" said Michael Teitelbaum, senior adviser to the Alfred P. Sloan Foundation."
  • Wow! RT notes "Around one in 10 of the students attending the largest four-year public university system in the US is homeless, while one in five cope with food insecurity, according to a new study by the California State University system."
  • I've got nothing against unions, my issue is against the terrible decisions/policies they (or anyone) support. Case in point. ChicageCBSlocal reports "He crossed the line – the CPS teachers’ one-day strike — out of his love for the classroom. Joseph Ocol stuck with his kids and brought home a chess championship. Tonight, he’s expelled from the union and wonders if he’ll even have a jobCBS 2’s Brad Edwards reports.The union’s decision came via certified mail, in a letter signed by Chicago Teachers Union President Karen Lewis.....the CTU said in a statement: “Mr. Ocol has been informed of his member privileges and is talking to us through media, which is unfortunate. All members are well aware of what happens to strike breakers and are informed by their own peers of the process for both suspension and reinstatement. CTU is a democratically led member-organization.”"
  • CounterPunch explains how Common Core helps bust the unions.
  • HeatStreet looks into how colleges are letting students censor speach, "For many students and professors, one of the great appeals of college life is being exposed to new and different ways of thinking. But that age-old process is now under threat at schools around the country. Take the University of Northern Colorado. After two of the school’s professors asked their students to discuss controversial topics and consider opposing viewpoints, they received visits from the school’s Bias Response Team to discuss their teaching style. The professors’ students had reported them, claiming the curriculum constituted bias. These incidents, both in the 2015-2016 academic year, reflect a growing trend in higher education. College students increasingly demand to be shielded from “offensive,” “triggering” or “harmful” language and topics, relying on Bias Response Teams to intervene on their behalf. Such teams are popping up at a growing number of universities....To date, more than 100 U.S. public colleges and universities have established Bias Response Teams."
  • HeatStreet again with "Kayla-Simone McKelvey will serve 90 days in jail, five years of probation and 100 hours of community service for her role in a racially charged hoax threat issued to Kean University students. McKelvey, who is black and the former president of the New Jersey college’s Pan-African Student Union, used a fake Twitter account to send a message threateningto kill a group of black students at an on-campus rally in NovemberThe Twitter account, @Keanuagainstblk, claimed that the anonymous user would “kill all male and female black students” at Kean and issued a bomb threat against the school. The account was quickly suspended from Twitter, but not before causing an uproar on social media. Supporters of #BlackLivesMatter across the country called on the university to take action to protect protesting students, and demanded that Kean President Dawood Farahi resign. They tried to use the threat to demonstrate that Farahi had not done enough to diffuse racial tension on campus....McKelvey told the court she was sorry she issued the threat, and that she still believes her actions helped expose racism on campus...But if McKelvey’s excuse sounds a bit strange, she’s not alone, even at Kean, in thinking that her clearly illegal actions “helped” fellow social justice warriors to bring Kean’s “systemic racism” to light. Some Kean students said that the threat’s author didn’t matter that the threat was still evidence of strong racial bias on campus."
  • LA Times reports that Pat Haden used an educational foundation to enrich himself and his family, "Under Haden's leadership as board chairman, however, the $25-million foundation became a lucrative source of income for him and two of his family members -- even as its scholarship spending plunged to a three-decade low and the size of its endowment stagnated, a Times investigation has found.Haden, his daughter and sister-in-law together collected about $2.4 million from the foundation for part-time roles involving as little as one hour of work per week, according to the foundation’s federal tax returns for 1999 to 2014, the most recent year available. Half of that, about $1.2 million, went to Haden. His annual board fees have been as high as $84,000; the foundation paid him $72,725 in 2014....Many foundations do not pay their board members, philanthropy experts say. The $1.5-billion California Community Foundation, for example, does not pay board members. Foundations that do compensate board members, those experts say, typically pay far less than the amounts received by Haden and his relatives. The $12.5-billion Ford Foundation paid its board chairman about $30,000 less than the Mayr foundation paid Haden in 2014. Mark Hager, an associate professor of philanthropic studies at Arizona State University, said in an email the Mayr payments to the board would be high “even for a foundation that was giving out more than $50 million in grants each year.”“I’ve never heard of fees that large,” said Adam Hirsch, a law professor at the University of San Diego who specializes in trusts."

Sage: Polynomial Interpolation


In an earlier post I mentioned that it's not that uncommon for math teachers and even education professionals making up academic resources to mess up badly on sequences. For example, the IXL site, which is, in general, an excellent resource for teachers and students makes a common error with sequences both here and here. Experiment with the problems that are randomly created at those 2 links. Try entering a "wrong" answer and you'll get an explanation of what the "right" answer is. But the "logic" they're using is that here's a formula that describes the sequence, therefore the next term is... The problem is that if you follow the same logic you can justify the missing terms of the sequence to be whatever you want. Therefore those problems have no correct answer and should not be given. Moreover, they shouldn't mark other answers as wrong.

Whenever teachers and math professionals are wrong on the math, you've got a teachable moment. This lesson would be for someone teaching about matrices who has gotten through reduced row echelon form. I'll suggest that you start a class by working through the material on the IXL website and have them figure out what the terms of the sequence are. Write the various sequences on the board to refer to later. When they've gotten comfortable ask them what will happen if you put in a term that doesn't seem to fit the pattern. They'll predict that you will be marked wrong. After showing them that you are indeed marked wrong by IXL figure out a formula to justify your answer and have students confirm that it works. You now have a formula that justifies a sequence that IXL was marking you wrong for. Get the class to discuss what it must mean for an answer to be correct (you can find a formula) and for what it means to be incorrect (it's impossible for anyone to find a formula).

Now it's time for math! Elicit that a sequence is a function from the positive integers into the real numbers (or integers, depending on how you teach it). Remind them that this means the sequence -5, 3, 11, 19, 27, ... corresponds to the function where f(1)=-5, f(2)=3, f(3)=11, f(4)=19, f(5)=27. Give them the mathematics known as polynomial interpolation or Lagrangian interpolation, and using one of the IXL sequences written on your board, set up a Vandermonde matrix. Work through the mathematics to create the polynomial. Get those calculators out to solve the matrix equation. And at the end you'll have a polynomial which they'll need to confirm works to generate the sequence. By the end of class your students will have learned about Vandermonde matrices, seen the math behind polynomial interpolation, used the calculator to power through some of the calculations and construct a polynomial that shows that even the "experts" get things wrong. That's a lesson the class will remember long after they've forgotten how to do the math.

But it's easy to make mistake with calculations so I've constructed a Sage program to go through the steps to create an interpolating polynomial using Vandermode matrices. It's posted on the Python/Sage page. A little warning is necessary, however. Usually you just go to a SageCellServer (or SageSandbox on this site) and copy/paste the code and press "Evaluate" to get the code to run. For reasons I don't understand, sometimes you get some sort of I/O Error such as the one below.


That error can pop up at various stages in compilation. The code runs, sometime it's just a matter of pressing "Evaluate" several times.

In order to set the code for your sequence, you need to alter xvalues and yvalues in the code. For example, if your sequence is 3,2,_,0,-1,-2, _,... and someone says that the pattern is to subtract 1 from the previous terms so the missing numbers are 1 and -3 then you'll need to pick the values you want in your sequence. If you choose to complete the sequence as 3,2,5,0,-1,-2,11,... then you'll need to set xvalues = [1,2,3,4,5,6,7] because you have 7 terms in your sequence and yvalues = [3,2,5,0,-1,-2,11] because those are the terms of your sequence. Press "Evaluate" and you'll get a polynomial that goes through those points. So there is a formula for your sequence--it's just not obvious to most people.

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

  • The74million notes that Common Core lowers standards and that's a good thing. HUH? "Implementation of the Common Core has run headlong into high school exit exams, which many states require students to pass in order to graduate. But now states that have adopted the Common Core are grappling with whether raising academic standards should also mean making it harder to graduate.To supporters, tough graduation requirements are necessary to encourage student effort and ensure a diploma “means something.” Some have even pushed for requiring students to demonstrate “college and career readiness” in order to graduate.But decades of research now show that exit exams have not really raised standards, and have actually harmed disadvantaged students....In other words, the unintended consequence of the Common Core may have been to lower the bar to graduate — and research suggests that this was a good thing."
  • Decades ago, a high school degree was normal and few people had college degrees. Yet people could get jobs that allowed them to provide for a family. Now the quality of high school education has been watered down, graduation rates are higher and a college degree is "necessary" to get a job. And that means people are some $30,000 in debt after college (which is more likely to be 5 years now) and too many students have taken courses in topics that lack rigor and meaning. And while I've taught algebra to many young students outside the US, somehow in the US algebra is too complicated for 18-22 year old students to master--it's actually standing in the way of people graduating. How can you get horribly educated students through college with a pesky math course in the way? Simple--water down standards at the college level. Now Wayne State University leads the charge in dumbing down education, "Up until now, students had to take one of three different math classes before they could earn their degree. Now, depending on their major, students may be able to squeak through college without taking math. The university is leaving it up to the individual departments to decide whether math will be a required part of a degree's curriculum." So in the future, students can graduate high school and college and still not have the math skills of someone who only graduated from high school 50 years ago...and pick up a lot of student loan debt along the way. But at least more people are graduating from college! Progress?
  • Now compare the American drive to banish math with this clip from NextShark called "Watch Korean Students Take the American SAT Math Section For the First Time". You'll hear some people talk about Americans as "exceptional"--that probably shouldn't be taken as a compliment. Even the weak Korean students are feeling better about their math now....
  • The Columbus Dispatch reports "The State Board of Education is expected to lower minimum proficiency standards on two new high school math tests after results came in lower than expected.The move raises questions about whether benchmarks for new assessments will accurately gauge a student’s readiness for college or a career" Somehow I doubt they care about college readiness...
  • Wired.com with an article on "deep learning" that underpins AlphaGo and other computer programs.
  • Mental Floss with "15 Observational Facts About Isaac Newton"
  • The bit-player blog has a fascinating post on the non randomness of the prime numbers. "These remarkably strong correlations in pairs of consecutive primes were discovered by Robert J. Lemke Oliver and Kannan Soundararajan of Stanford University, who discuss them in a preprint posted to the arXiv in March. What I find most surprising about the discovery is that no one noticed these patterns long ago. They are certainly conspicuous enough once you know how to look for them...For the past few weeks I’ve been noodling away at lots of code to analyze primes mod m. What follows is an account of my attempts to understand where the patterns come from. My methods are computational and visual more than mathematical; I can’t prove a thing. Lemke Oliver and Soundararajan take a more rigorous and analytical approach; I’ll say a little more about their results at the end of this article."
  • A May 18th, 2016 interview with graph theorist Maria Chudnovsky on anthonybonato.com. Looking for a female mathematician to inspire the girls in your classes.  Look no further; she's even been in 2 commercials.

SageTex: Complex Numbers


It's been a very busy week as schools wind down for the year. I've added a new page Sagetex: Complex numbers to the sidebar. I will, of course be adding problems to the page in the coming weeks.

Here are some stories that caught my eye this week:

  • Mathematician Dr. Ken Ono has been written about in Quanta Magazine.
  • Dr. William Stein is leaving academia to start a company around Sagemath. His pdf slideshow can be found on this Reddit thread. He has a talk about this in a video posted here.
  • Ars Technica reports, "Google's DeepMind AI division will face off against humanity's number one Go player, Ke Jie, according to Chinese state news agency Xinhua. Ke Jie is currently the top-ranked Go player in the world."
  • DurhamLocalNews has a piece on how "Legislation recommended Wednesday by a Senate committee would require North Carolina schools to offer traditional high-school-level mathematics classes alongside newer “integrated” classes that arrived with Common Core...If the bill were to become law, districts would have to offer both math class sequences to students starting in the 2017-18 school year."
  • Click2Houston tells us a creepy story about a math teacher who enjoys being with kids a little too much: "The video shows Gregg Gustafson wrestling and tickling minors at a student's home when the parents were not around...One of the students told the police Gustafson gave him several wedgies that broke his underwear. The boy said he was wrestling with Gustafson and that he would not let him tap out.The student posted two videos of his broken underwear. Gustafson allegedly asked the boy to get rid of the evidence."
  • Washington Post on the new school report "Many people in education and the workplace don’t think some of the English Language Arts and math standards — which are being used in most states — are what students and workers need to be successful in college and career." One of the findings is that calculators are prevalent in math class. That's exactly what I'm seeing--but you'll see the teacher teaching how to work a problem and then they jump to using a calculator, so that the students quickly forget the skills they were supposed to learn. Whose "best practice" is that? More disturbingly, "There may be disagreement across K-12, college, and workforce about which mathematics topics are important to success in postsecondary STEM coursework and STEM careers. In K-12, there may also be disagreement about when these topics should be introduced in the mathematics curriculum." Shouldn't these issues have been worked out before forcing them upon everyone?
  • Ars Technica with an interesting article on "That ’70s myth—did climate science really call for a “coming ice age?”"
  • EAGNews on how "For a mere $6.5 million, New York City’s School Construction Authority renovated a former clothing store on Fifth Avenue into a “state-of-the-art” facility for 18 students to participate in its new, free pre-K program....The renovations cost the city about $362,222 per pupil, which was about $160,000 per seat more than the next most expensive renovation in Staten Island, for creating partitions, pouring concrete slabs, adding sprinkler systems and HVAC, and other upgrades." It's easy to spend public money.
  • ZeroHedge on the embarrassment that is the new generation. But it's not just America. "In the western world, political correctness is often taken to absolutely ridiculous extremes in attempt to keep people from being exposed to anything that could remotely be considered “offensive”.  For instance, just consider a couple of examples from the United KingdomThis hyper-sensitivity has prompted the University of East Anglia to outlaw sombreros in a Mexican restaurant and caused the National Union of Students to ban clapping as “as it might trigger trauma”, asking youngsters to use “jazz hands” instead. Could you imagine banning clapping? But this is actually happening.  Anything that might make someone feel the least bit “uncomfortable” is now being labeled as a “micro-aggression”, and at schools all over America “safe spaces” are being set up where young people can avoid anyone or anything that may make them “feel uncomfortable, unwelcome or challenged”.And this is not a fringe movement at all.  These “safe spaces” are being established at some of the most prestigious universities in the entire country, and in at least one case a “safe space” included “calming music, cookies, Play-Doh and a video of frolicking puppies”
    At Brown University – like Harvard, one of the eight elite Ivy League universities – the New York Times reported students set up a “safe space” that offered calming music, cookies, Play-Doh and a video of frolicking puppies to help students cope with a discussion on how colleges should handle sexual assault. A Harvard student described in the university newspaper attending a “safe space” complete with “massage circles” that was designed to help students have open conversations.Are you kidding me?...Now that we have defined “safe spaces” and “trigger warnings”, I am going to define a term that I used in the title of this article.

    “Wussification” is the act of turning someone into a “wussy”.  And urbandictionary.com defines “wussy” in the following manner… A person with no guts. A person who whines all day and sits around and cries like a little baby for years over nothing. Will blow anything out of proportion and create drama to forget about their sad miserable lives.If our young people need cookies, Play-Doh and videos of frolicking puppies to deal with the challenges in their lives right now, what in the world are they going to do when the things really start falling apart in America?The real world can be exceedingly cold and cruel, and our young people need to be equipped to handle whatever life will throw at them."

  • RT with the latest on "A breakthrough in the study of a mysterious Hellenistic clockwork device which was found at the bottom of the Aegean Sea more than a century ago has led researchers to conclude it was designed for philosophers to peer into the future.Dubbed the ‘Antikythera mechanism’, after sponge divers hauled the bronze mechanism from a shipwreck off the coast of the Greek island in 1900, the machine has been described as an ancient computer because of its advanced technological design."
  • SOTT has an interesting hour long interview "Stefan Molyneux and Dr. Duke Pesta on the dangers of Common Core"


Contrary to what you might be thinking, this post is not about the Fibonacci sequence; it's about an all too common mistake that teachers and test makers make. I've found this error to be very common at the high school level but what brought it back to mind was when I was exploring the IXL.com website recently. Let me start by saying I actually think the website is an excellent resource for teachers. Just find a skill that your students are deficient in and send them to the IXL site for practice on that very topic. If you get your class registered you can even get a lot of analytical data on how your students are doing. That said, the website has some problems, too. You might not think that an educational site would teach students incorrectly but you'd be wrong. A quick look around the website reveals some problems in probability, irrational numbers, and sequences. I'm going to focus on sequences. Sequences are covered in many grades so there are are many different links that are "teaching" students incorrectly, such as here or here. If you experiment (the problems get randomly generated) you'll have no trouble coming up with the type of wrong answer that I've already talked about in my post "...is Ambiguous". In that post I showed that given a formula for the first k terms of the sequence you can produce a formula to justify whatever real number you wanted to be next. But there are some variations you will see on the IXL site that have a slightly different format:

  • Find the next move of a recursive sequence (e.g. 1,1,2,3,5,...)
  • Find more than one missing term from another sequence (e.g. _, 3, 11, _, 27, 35)

Since neither of those is covered by the previous post (I'm ignoring the fact that recursive formulas can be rewritten as an algebraic formula--because we don't need that formula to create our function, unlike last post) I'm revisiting the issue. If these mistakes are so common then the subject should be the foundation of a lesson--to make sure students learn the correct theory and, hopefully, future teachers and educational sites won't teach students incorrectly. That, by the way, is one reason why I'm so adamant that you can't have teachers without a bachelors degree teaching math in high school. It doesn't mean that they all will know this (many still won't); it's just that there are many such pitfalls that a teacher with a poor math background will make. For example, I've tutored students recently that had a certified and tenured teacher "teach" that there are 6 ways to form a committee from 3 people. Turns out she had taught students about permutations for over a week using a word "committee" that should only be used in talking about combinations. Needless to say, I had to fix what she broke. But I digress.

The first type of problem is illustrated by the sequence 1,1,2,3,5,... which you might recognize as the Fibonacci sequence. Yes, that's AN answer, but it's not THE answer. In fact, THE answer doesn't exist; it's possible to produce a polynomial p(x) such that p(1)=1, p(2)=1, p(3)= 2, p(4)=3, p(5)=5 and p(6)= whatever we want. That is, ... is still ambiguous for reasons beyond what I mentioned in the earlier post.

Similarly, in the second case we can pick whatever missing numbers we want and produce a polynomial to go through them. Like a statistician, we can produce any answer we want. Unlike a statistics there is real math underlying the method. Don't believe me? For the sequence 1,1,2,3,5,.... I'm going to claim that the 6th term is -3 and give you a formula to prove it. Try this:


Notice that I've got some help getting the answer. Sage is going through the calculations to make things quick and avoid mistakes. You can see p(1)=1, p(2)=1, p(3)= 2, p(4)=3, p(5)=5 and p(6)=-3. Also notice I said "the polynomial"; there are other polynomials that would work but in the context used above it's about THE polynomial that comes about by following  a particular sequence of steps. Suppose, instead of -3, I want p(6)=11. No problem:


The same method works with the sequence:_, 3, 11, _, 27, 35. It looks like THE formula is 8x-13, so that the first term is -5 and the fourth term is 19. But it's not THE answer, it's just AN answer. Here's one such polynomial.


And there is no reason that the terms have to be integers; it just makes the polynomial nicer. In this one pi is used as a missing term in the sequence. You can click on the image below to make it bigger.


The bottom line is that an nth degree polynomial can be created to go through any sequence of points [where the x values are different]. As a result, ...is ambiguous and it's a shame that many teachers and even educational websites keep making the same mistake. Going forward, I'll look at how Sage can help us compute these polynomials.

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

  • Truth in American Education reports "Even though the Bill & Melinda Gates Foundation acknowledged that the Common Core State Standards and related assessments have not accomplished what they had hoped they are bringing the standards, assessments and accountability movement to higher education.....Of course we have to have standardized tests to go with the common standards

    “It may be difficult to list everything students should know and be able to do,” the book said, “but when faculty are asked to focus on essential elements they are quite ready, willing and able to define priorities for student learning in their disciplines.”

    One of the project’s goals is for the white papers to be used for the creation of tests, or assessments, that colleges can use in a standardized way. However, those possible assessments must be voluntary, the book said, and based on multiple measures rather than a simple box-checking, multiple choice test.

    College faculty, the article noted, may be forced to adopt measures like these." I get the feeling that success isn't measured by academic performance but by the amount of money spent on standardized testing.

  • The Valley Patriot explains "The Ugly Truth About Common Core Education" with such observations as "Private testing companies and textbook publishers are pushing for spending millions of dollars pushing Common Core because these corporations see the possibilities of hundreds of millions of dollars in profits generated from the new tests, computers, preparation guides, and Common Core-aligned textbooks.... The new ELA texts contain graphic pornographic depictions, which should cause deep concern for every parent. One especially graphic text in the curriculum is Toni Morrison’s The Bluest Eye, which graphically depicts rape, incest, and pedophilia. Is this what we want our students to read and “analyze” in English class? Dr. Sandra Stotsky, who wrote a large part of the ELA Framework for Massachusetts, which made Massachusetts the highest achieving state in the nation, resigned in disgust from the Common Core Advisory Team and is now actively opposing the implementation of Common Core."
  • Graduation is approaching and you might think it's time to reward academically superior students. Not in this Texas school. Kens5 has the story: "National Honor Society (NHS) stoles are frequent sight at high school graduation ceremonies around the country, but one Plano Senior High School student is frustrated that he won't be allowed to wear one when he puts on his cap and gown next month. According to school practices, students are not allowed to wear NHS regalia....KellyAnn Frederick says a National Honor Society sponsor claimed school administrators want everyone to feel included in graduation and not single students out." Since said teenager wants to be singled out for his hard work the issue is apparently that the students who didn't excel will feel badly.
  • The Dayton Daily News reports "Ohio students performed dramatically worse than expected on two state exams this spring according to preliminary results, and state officials want to soften the scoring system so more students pass....An Ohio Department of Education memo leaked by Wagner shows that only 24 percent of students scored proficient or better on the Geometry test, and only 21 percent did so on the other sophomore math option — Integrated Math II. Students had to get roughly half of the questions correct to be proficient....So Jim Wright, director of ODE’s office of curriculum and assessment, on Wednesday proposed softening the scoring system so that 52 percent of students would pass the Geometry exam and 35 percent would pass Integrated Math II." The rhetoric of higher standards sounds great until your numbers look bad. The result? "Wagner calls the system “class warfare,” pointing out that for years, test scores have closely tracked income levels, with poorer students scoring worse." Luckily some educators are actually interested in standards, "“We’re increasing the rigor as we should. We should make sure that every child has the ability to perform at something after high school,” Gunlock said. “Hiding behind the fact that they all got a diploma even if they weren’t qualified doesn’t make any sense to me. … The idea that this is holding back poor kids is baloney.”". The point was to raise the academic bar because student achievement was poor. The fact that the DOE wants to pass them anyway shows you how academic performance is not a priority.
  • A surprising result in Shakmir 2016. Tournament favorite Caruana lost in the penultimate round and drew the final round to tie for first with Mamedyarov--Mamedyarov, having beaten Giri in the last round then beat Caruana in the playoff to win the title. Chessbase has the report here "Tied for first, both Fabiano Caruana and Shakhriyar Mamedyarov faced each other in a Playoff shortly after the end of Mamedyarov's game against Giri. In the first mini-match of games at 10 minutes plus 3 seconds, Fabiano Caruana achieved a decisive advantage in both games, but each time failed to deliver the killing blow and the Azeri managed to escape. With two draws and a score of 1-1, the momentum had to seem to swing to Mamedyarov's side, if only for psycholgical reasons: escaping 'certain defeat' twice in a row had to be a confidence booster, feeling the opponent is just not firing all cylinders at this point. Furthermore, Caruana is not known to be the best blitz player (his FIDE Blitz rating is not a fluke), an area where Shakh might now feel he had he edge.Whatever the truth of it, Mamedyarov won the first game in a very tense battle that had everyone on the edge of their seats. Vishy Anand, watching online, was no less riveted and commented about their great fighting spirit, "We are not worthy!". Game two saw Caruana in a must win situation with black, but being blitz, anything goes. After reaching a clear advantage in a rook and opposite-colored bishop ending, it was the opinion of grandmaster pundits that Fabiano was going to win it and level the score, but everything went south for the American and after a wild scramble he was suddenly worse with no chance of winning whatsoever, and the players shook hands." Hou Yifan had a disappointing last place finish. Playing with the men is quite different when every game is a battle. Judith Polgar's place as a (former) top 10 player in the world still puts her as the best woman ever.
  • Gen Whiny is on the move in Yale University yet again. According to Reason, "Some Yale University students are demanding changes to the English Department curriculum: specifically, they don't think it should feature so many English poets who were straight, white, wealthy, and male. "It is your responsibility as educators to listen to student voices," the students wrote in a petition to the faculty. "We have spoken. We are speaking. Pay attention....Students should feel comfortable challenging the notion that a Shakespeare or a Milton deserves his place in the canon: in fact, that sounds like an excellent subject for a classroom discussion facilitated by a professor. But professors need to actually teach students about these pivotal figures before those discussions can be had....In a brilliant piece for Slate, Katy Waldman eviscerates the idea that non-white students have nothing to learn from dead white poets: ...

    But even if you disagree, there’s no getting around the facts. Although you’ve written that the English department “actively contributes to the erasure of history,” what it really does is accurately reflect the tainted history we have—one in which straight white cis-men dominated art-making for centuries—rather than the woke history we want and fantasize about. There are few (arguably no) female poets writing in Chaucer’s time who rival Chaucer in wit, transgressiveness, texture, or psychological insight. The lack of equal opportunity was a tremendous injustice stemming from oppressive social norms, but we can’t reverse it by willing brilliant female wordsmiths into the past.

    In tangentially related news, Nicholas and Erika Christakis—who declined to protect students from offensive Halloween costumes—have finally resigned their positions at Yale." The adults in the room are now gone. 

  • The Federalist explains how the Gen Whiny came to be, "Forty-five years later: By this time, we had instituted a wildly successful pogrom in higher education, eliminating most of the conservative faculty and driving the rest underground. We ran amok, instituting freethinking, progressive reforms at every level of the system....Gradually, new codes of conduct were instituted to ensure everyone was comfortable at all times. ...The enlightened former freaks who now inhabit these campuses have become increasingly hypersensitive and nasty, spitting tacks at people for all manner of imaginary crimes such as “cultural appropriation.” Recently, a white guy got hammered for wearing dreadlocks. This is deeply ironic because, as I recall, we hippies were masters of cultural appropriation. Hookahs, Nehru jackets, bead curtains, reggae, Eastern religions, sitar music, Tibetan prayer flags, chakras, ethnic food, dashikis, Rasta shoulder bags, ironically worn military apparel, mandalas, henna tattoos, muumuus, hand-woven Guatemalan tunics, pyramid power, Maori tattoos, macramé... Meanwhile, at Emory University, some fascist from outside the perimeter jumped the razor wire and wrote “Trump 2016” on the sidewalk in chalk —a situation that could easily be remediated with a bucket of water. Instead, the student government allocated emergency funding for counseling sessions, and the college administration issued the usual limp apologies and assurances. Students were afraid to attend classes because they might sit near someone with a different worldview.....Today’s outraged, privileged, fragile snowflakes conjure up utterly trivial nonsense to consider as an affront: microaggression. This can include using the wrong one of more than 50 gender pronouns, sideways glances, snort-chuckling, eye rolling, resigned sighing, and even merely existing in proximity to a person with raw sensitivity. "

Sagetex and Graph Theory


I've added some information to the Graph Theory, Sage, LaTeX page. For more complicated graphs, typesetting the placement of each individual vertex is too time consuming. Sage can help us out. Some of the important commands are located here. Many of the named graphs are posted here. SageTeX lets you use the power of Sage in both creating the graph and calculating the various parameters you want. You can find more details posted on that page along with working code to get you started.

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

  • WTVR.com, CBS 6, reports "The mother of a Virginia middle school student said she was angry, frustrated, and mad after her son was handcuffed, suspended from school, and charged with stealing a 65-cent carton of milk from the cafeteria. As it turned out, Shamise Turk's son Ryan was on the school's free lunch program and the milk -- was free.....Police said the larceny charge was because Ryan tried to "conceal" the milk, a claim Ryan's mother denied. The school spokesperson said Ryan was suspended for theft, being disrespectful and using his cell phone in school."
  • Money.CNN says, "For years, America's college campuses swelled with more and more students. But enrollment peaked in 2010 at just over 21 million students. Attendance has dropped every year since....The two types of colleges with the biggest declines in enrollment are: community colleges and for-profit universities. Those schools draw heavily from low-income and minority households."
  • Reason.com checks in with today's most whiny generation at Oberlin, which was highlighted in a recent The New Yorker issue. "...activist students not only wanted to abolish all grades below a 'C,' they also thought faculty members should proactively offer them alternatives to taking a written, in-class midterm exam." The New Yorker had a longer piece which went into more detail "For years, a campus café and performance space called the Cat in the Cream had a music-themed mural, painted by an alumnus, that celebrated multiculturalism: it featured a turbanned snake charmer, a black man playing a saxophone, and so on. Students recently raised concerns that the mural was exoticizing. “We ended up putting drywall over it, and painting over that,” Robert Bonfiglio, who had been the chair of the Student Union Board, told me. “They were saying, ‘Students are being harmed. Just do something now.’ ” But if individuals’ feelings were grounds to efface art work, he reasoned, every piece of art at Oberlin would be in constant danger of being covered up, or worse—a practice with uncomfortable antecedents. “The fear in class isn’t getting something wrong but having your voice rejected,” he said. “People are so amazed that other people could have a different opinion from them that they don’t want to hear it.”...Copeland has taught at Oberlin since the nineteen-seventies. He was puzzled by many things about today’s students—“They do not make eye contact! They do not look into your motherfucking eyes!”—but what galled him most was their apparent eagerness to go over their professors’ heads. In the late fall of 2014, during rehearsals for a play he was coördinating, he spoke sharply to a student: a misfire not of language, he says, but of tone. The student ran out of the room. Copeland says that he wanted to smooth ruffled feathers and keep the production on track, so he agreed to meet with the student and his department chair. At the meeting, the student asked that he leave the room, and she and the department head spoke alone for about half an hour.Later, the dean of arts and sciences asked to meet with him. He reported complaints that Copeland had created “a hostile and unsafe learning environment,” and that he had “verbally berated” a student—but said that it must be kept confidential which student or incidents were concerned. Then the dean asked Copeland to sign a document acknowledging that a complaint had been lodged against him....He gave the dean a list of students he thought could confirm that he hadn’t “berated” anyone. He says the list was brushed aside: “They said, ‘What matters is that the student felt unsafe.’ ” Then he was told that, because gender could have been a factor, the issue was being investigated as a possible Title IX violation. That inquiry was later dropped; by then, Copeland had hired a lawyer. In September, 2015, the original inquiry was still going on, and Copeland said that the dean told him that if he wouldn’t meet without his lawyer he would be brought before the Professional Conduct Review Committee. Copeland and his lawyer welcomed that idea: the committee process would bring some daylight. They never heard back."
  • Science Daily with a piece on titled "40-year math mystery and four generations of figuring" which "So, what is the Kelmans-Seymour Conjecture, anyway? Its name comes from Paul Seymour from Princeton University, who came up with the notion in 1977. Then another mathematician named Alexander Kelmans, arrived at the same conjecture in 1979. And though the Georgia Tech proof fills some 120 pages of math reasoning, the conjecture itself is only one short sentence: If a graph G is 5-connected and non-planar, then G has a TK5."
  • Oregonlive reports "Portland Superintendent Carole Smith apologized Friday for allowing students and teachers at two schools to continue to drink tainted water after tests showed unsafe levels of lead...At Rose City Park, that meant students were free to drink lead-laced water for eight school days after district officials knew about the toxic results."
  • ZeroHedge reports "Federal investigators revealed another blow to Detroit Public Schools this week. Meet Carolyn StarkeyDarden - the system’s former grant-development director - who has just been charged on suspicion of obtaining nearly $1.3 million by lying about children’s tutoring services....Carolyn Starkey Darden set up a company and allegedly ran a scheme between 2005 and 2012 in which she submitted fake invoices for tutoring services that were never provided to students, according to charges filed by the U.S. Attorney’s Office in Michigan’s Eastern District." This is so typical of the public school system where huge amounts of money can be easily skimmed by the corrupt. Because it's almost never about the kids.
  • RT on the 8 year old who brought a loaded gun to class. "It is unclear to whom the gun belonged and what made the boy bring it to school. The NYPD said there were no arrests made so far. Authorities believe that the boy might have had a dispute with another child, and they suspect his teenage brother had something to do with this incident, WABC reported....This is the sixth time authorities in New York confiscated a firearm inside a city school since March. In one case, a 14-year-old boy brought a loaded 9-millimeter gun to Middle School 61. "
  • The Third Shakmir tournament is underway with chess superstars Caruana, Kajarkin, Radjabov, Hou Yifan and more. The games can be followed live here.

Sage Interact: Generate Discrete Data


In an earlier post I designed a Sage Interact to generate data for continuous distributions. This week I've added a Sage Interact to generate data for discrete distributions. A screenshot of the Interact is shown above. To use the Sage Interact, copy the code posted on the Python/Sage page and paste it into any Sage Cell Server. Press "Evaluate" to start the interact. Pick the distribution you want to generate data for, adjust the parameters and the Interact will create your data as well as calculate standard statistics for the data. This is a quick way to generate examples for quizzes, tests, and lessons.

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

  • the74million.org has a surprising piece on "Connecticut’s Shame: In One of America’s Richest Counties, a High School Has Been Failing for 50 Years". The school is so bad there isn't really any way to get worse "Even to the jaded, Bassick’s achievement statistics are disturbing. Last year, only 15 percent of students tested proficient in language arts on the new Common Core-aligned state tests. The percentage of students who met that benchmark in math? Zero." Good thing they have certified teachers getting the most out of them.
  • Segregation--it wasn't that long ago. Actually, it's still going on. RT reports, "A northwest Mississippi school district has been ordered by a federal district court to "consolidate its secondary schools" that have long been separated along racial lines some six decades after the US Supreme Court ordered school desegregation.....This decision serves as a reminder to districts that delaying desegregation obligations is both unacceptable and unconstitutional,” said Principal Deputy Assistant Attorney General Vanita Gupta, head of the DOJ's Civil Rights Division. " In what way was the 50 year delay shown to be unacceptable?
  • Sputnik news notes that "A former elementary school paraprofessional in the Atlanta area must report to jail by 6:00 on Friday evening after being charged with reckless endangerment for hanging a five-year-old student by his belt from a classroom blackboard."
  • Reason.com closes the chapter on a teacher who used the N-word in class. "Andrea Quenette, the University of Kansas communications professor subjected to protests and a formal investigation after offending her liberal students, was cleared of wrongdoing. But she is still ultimately out of a job."
  • EAGnews with a horrific tale of student animal behavior that was impossible to imagine decades ago. "South Fort Myers High School officials believe as many as 25 boys had “inappropriate activity” with a 15-year-old female student inside of a bathroom on campus Tuesday. Students told NBC 2 the incident occurred in a girl’s bathroom after classes ended and involved the school’s football team." The NBC 2 link has a video and there's another link here with a little more depth, "While she would not pinpoint why the different students were on campus after hours, she said South Fort Myers students involved in extracurricular activities — athletics or otherwise — participate in a study hall from 1:47 to 2:30 p.m. This is roughly the time frame for when the bathroom activities took place, Chandler said." So about 45 minutes in which we have dozens of students unaccounted for and no adult apparently around the area to see or hear what was happening.
  • The Greeley Tribune on the decline of teachers in Colorado. "Since 2010, UNC has watched enrollment in its teacher preparation programs plummet from a high of nearly 4,000 in 2011 to just 2,900 last year. The state is expected to graduate only 2,000 next year, and it needs twice that amount, education officials say...There are states that are worse off than Colorado (Oklahoma, California). There are states that are doing better (Connecticut). But every state has seen its list of needs increase as the number of people pursuing teaching as a career has decreased." The school system is run by many people who aren't up to the challenge but there is little consequence for mismanagement and poor quality. Take the Connecticut situation above: what will be the consequence for poor performance? Will the school close for having 0% proficiency in math? How did the school get to a 0% proficiency rating with "professionals" running the school? Do teachers still get pay increases (above the rate of industry) for such an awful showing? Money will keep coming in from taxes, and the system will continue on. When there's no consequence for failure, expect more of it.