Sagetex Basics: Factoring Quadratics

I've added another worksheet to the Sagetex Basics page on factoring quadratics. This worksheet creates 10 random quadratics on the first two pages. The line

while r1 == -r2:
r2 = Integer(randint(-10,10))

prevents any quadratic from being factorable by the difference of squares formula. If you want to allow quadratics of the form x^2-a^2 then comment those 2 lines out.

The variables outputP and outputA are the strings that contain the text for the Problems and for the output, respectively. This avoids having multiple sagesilent environments and allows a loop to take care of the repetition. The answers are printed out on the third page:

Here are some stories that caught my eye:

  • Oregon man fined $500 for using math to challenge red light cameras: "Mats Järlström learned this first-hand last year when the state of Oregon fined him $500 for publicly suggesting that yellow lights should last for slightly longer to accommodate cars making right turns....."
  • ZeroHedge with a post "Intellectual Intolerance - Stunning Speech From Stanford University Provost Exposes "The Threat From Within"" which says, "...But I’m actually more worried about the threat from within. Over the years, I have watched a growing intolerance at universities in this country – not intolerance along racial or ethnic or gender lines – there, we have made laudable progress. Rather, a kind of intellectual intolerance, a political one-sidedness, that is the antithesis of what universities should stand for. It manifests itself in many ways: in the intellectual monocultures that have taken over certain disciplines; in the demands to disinvite speakers and outlaw groups whose views we find offensive; in constant calls for the university itself to take political stands. We decry certain news outlets as echo chambers, while we fail to notice the echo chamber we’ve built around ourselves.""
  • Listverse has "10 Strange Facts About Pythagoras: Mathematician and Cult Leader"
  • Orrazz with a piece "There Are 5,000 Janitors in the U.S. with PhDs"
  • Shame on the AMS for hosting a racist piece on their website. The post "Get Out of the Way" drew enough comments to get the comments section closed. I suspect that had the comments been praise they'd have kept it open. The criticism isn't too surprising with an opening like this: "Not to alarm you, but I probably want you to quit your job, or at least take a demotion. Statistically speaking, you are probably taking up room that should go to someone else. If you are a white cis man (meaning you identify as male and you were assigned male at birth) you almost certainly should resign from your position of power. That’s right, please quit. Too difficult? Well, as a first step, at least get off your hiring committee, your curriculum committee, and make sure you’re replaced by a woman of color or trans person. Don’t have any in your department?  HOW SHOCKING....What can universities do? Well, that’s easier. Stop hiring white cis men (except as needed to get/retain people who are not white cis men) until the problem goes away. If you think this is a bad or un-serious idea, your sexism/racism/transphobia is showing. It is worth considering your complaints. Are you worried it’s unfair to men? Are you concerned the quality if your institution would plummet? Are you worried about all the brilliant minds you’d be missing? List your reasons and ask yourself which ones you’d value over your own freedom. Women are not free, and even our allies tend to only want us equal-ish. As long as we get there on their terms, as long as they lose nothing.If you are on a hiring committee, and you are looking at applicants and you see a stellar white male applicant, think long and hard about whether your department needs another white man. You are not hiring a researching robot who will output papers from a dark closet. You are hiring an educator, a role model, a spokesperson, an advisor, a committee person. When you hire a non-marginalized person, you are not just supporting this one applicant whom you like, you are rewarding a person who has been rewarded his whole life. You are justifying the system that makes his application look so good. You are not innocent. You are perpetuating a system that requires your participation if not your consent. When your female students of color have no role models in your department, that’s not “meritocracy”; that’s on you. Again, if you think the “great mathematicians” are disproportionately male because of meritocracy, then your sexism is showing...Not to alarm you, but statistically speaking you are the problem. Your very presence. I can’t tell you what is the best strategy for you to stop blocking my path. I can just ask that you please get out of my way." Absolutely disgusting. Could you imagine the furor and screams of racism if "white cis males" was replaced with some other ethnic group? Some of comments are interesting, in particular Math Colleague who notes "We are all painfully aware of the inequalities in faculty composition and trying hard to fix it. *Every* math department I know of is trying really hard to hire every qualified minority and female applicant out there (and by qualified I mean: a *very* generous ballpark within the hiring range of each department). The real problem is that there are not enough such candidates, and most departments end up making offers to the same few that are available in the market each year.". Math Colleague's explanation jibes with everything I saw in graduate school as well as out in the world where a woman and/or minority is highly sought after even when they are the weaker candidate. I know some minorities who were given a chance and were grateful for it.. Math Colleague sums up with "And all I can say is that if you did not get a tenure-track offer already, it is because you didn’t apply to enough places. If you what you want is a job at a top research institution, then you’ll need to prove that you are in the ‘generous ballpark’ of the research level you aspire to. I’ll be blunt: you have no grants, one publication, and the one paper is co-authored with your advisor. Write more papers, and we will hire you.You have great potential to make a difference for minorities and women in mathematics. Come up with a reasonable plan to help minorities, and NSF will fund it. But this post is unnecessarily destructive, discriminatory, inflammatory, and counterproductive to our inclusion efforts.". With a little more digging you'll find Piper on another blog where she says "They asked how many years spent on coursework (3), how many years spent on dissertation (10).  TEN YEARS?! WHAT KIND OF PERSON SPENDS TEN YEARS ON ONE DOCUMENT AND STILL HAS TO BUILD UP COURAGE TO DISCUSS IT OPENLY?... Oh, am I here because of Affirmative Action? Oh, am I here because I’m a woman? Oh, am I here because of a mistake? Okay, haha, I get it. Oh, do my friends think I took the spot of someone who deserved it more? That’s okay. It’s okay if my friends think that. Then there was the actual math. Funny story, I was exceptionally behind my peers when I got to Princeton. I’m tired of talking about it. I should have made myself a Tshirt that said “I only took 7 math classes before coming here, and my peers took 20 – 30, so that’s great.”". These comments appear to demonstrate she understands, at least to some degree, that she didn't get into Princeton for purely academic measurements-- she was "exceptionally behind" her peers. Princeton gets geniuses like Terry Tao if they want so there is lots of reason to suspect affirmative action has given her a chance. This, combined with 10 years work on a thesis which has led to one paper isn't awe inspiring. So Piper has gotten a chance to go to a prestigious university but that isn't enough. Remember the quote: "Stop hiring white cis men (except as needed to get/retain people who are not white cis men) until the problem goes away. If you think this is a bad or un-serious idea, your sexism/racism/transphobia is showing". Again, substitute any minority in for white cis male and ask yourself how that sounds. That would be grounds for someone losing their job; do you think it will happen to her? I don't. Or how about, "You are not hiring a researching robot who will output papers from a dark closet. You are hiring an educator, a role model, a spokesperson, an advisor, a committee person." Actually, the schools are trying to hire people qualified in math and producing research is part of the job description but regardless, white cis males are not incapable of being  a role models, spokespersons, advisors, and all the rest, are they? Contrast this Piper's situation with the piece above at Orazz with 5,000 PhDs working as janitors--I suspect they would be jealous of the chances she is getting. Piper's been given a chance that many lots of people haven't gotten and, invariably that means some have been the victims of reverse discrimination. Again, shame on the AMS post for hosting a piece that dismisses other people on the basis of being white males and white females, because "Remember having white cis women run the world is no kind of solution.". You can read a little more about Piper and her thesis by going to her blog.
  • The College Fix reports "After black student activists issued a demand list to American University in response to the racist-banana incident two weeks ago, the administration agreed to three demands.One of them is a ban on whites using a new “student lounge” for the rest of the spring semester."

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.
  • 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."

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 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 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 " 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, 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. "

Coin Tossing references

The subject of coin tossing keeps coming up, no doubt because it is something the average person can relate to--no abstruse definitions like with limits (in Calculus). And that forces me to go back and find references for some of the basic points in the arguments that should be known but aren't. I've decided it's about time to accumulate the basic points and along with references:

The probability of flipping heads on a coin is not 1/2. The assumption that flipping heads on a coin is 1/2 is a mathematical model and not reality which is akin to using 3.14 for pi. Coin tossing is a deterministic process in physics as demonstrated by a coin tossing machine, "To make his point, Diaconis commissioned a team of Harvard technicians to build a mechanical coin tosser -- a 3-pound, 15-inch-wide contraption that, when bolted to a table, launches a coin into the air such that it lands the same way every single time. Diaconis himself has trained his thumb to flip a coin and make it come up heads 10 out of 10 times. But what he really wanted to know was whether unrehearsed tosses -- by ordinary folk who flip coins with unpredictable speeds and heights and catch them at different angles -- would show that the outcome of the act was, in fact, random." Persi Diaconis, Susan Holmes, and Richard Montgomery are authors of the article "Dyanmical Bias in the Coin Toss" (.pdf). There is a Numberphile video with Diaconis (about 8 minutes) that gives a brief overview and there is a YouTube lecture by Diaconis (about 55 minutes) with more detail. One of the main assumptions is that you start the coiin with the heads side up is

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.

The first assumption isn't always true. The Abstract of paper (by Murray and Teare) mentions the odds of an American nickel landing on its edge is about 1/6000.

The deterministic nature of coin flipping can be found in the article "Heads or tails? It all depends on some key variables" which says:

"But first, here's what the researchers concluded: Using a high-speed camera that photographed people flipping coins, the three researchers determined that a coin is more likely to land facing the same side on which it started. If tails is facing up when the coin is perched on your thumb, it is more likely to land tails up. How much more likely? At least 51 percent of the time, the researchers claim, and possibly as much as 55 percent to 60 percent -- depending on the flipping motion of the individual.In other words, more than random luck is at work."

I've put this post on the Other page for future reference. If you teach probability in school this is a good topic to "go beyond" the basic curriculum. Too many students learn that the probability of flipping heads is 1/2 and not that the probability of flipping heads on a fair coin is 1/2. And the coins around us in the real world aren't fair.

Here are some stories that caught my eye this week:

  • What do you do with your spare time? According to, "A 15-year-old boy believes he has discovered a forgotten Mayan city using satellite photos and Mayan astronomy. William Gadoury, from Quebec, came up with the theory that the Maya civilization chose the location of its towns and cities according to its star constellations. He found Mayan cities lined up exactly with stars in the civilization's major constellations. Studying the star map further, he discovered one city was missing from a constellation of three stars. Using satellite images provided by the Canadian Space Agency and then mapped on to Google Earth, he discovered the city where the third star of the constellation suggested it would be."
  • ZeroHege has an article showing just how deep the economic problems bite, "According to Bloomberg, a new survey by Discover Financial Services found that 48% of parents think their child should pay a portion (if not all) of the cost of attending college, up from 39% four years ago. And just how will potential students pay that portion? Why, student loans of course. 32% of respondents said they would ask the bank for help, while 27% plan to rely on family savings, 4% said they would dip into retirement funds, and 3% even indicated that they may refinance their home to pay for their kids college."
  • USNews has an excellent article on just how badly our schools are letting us down, and there is an economic price. "One in four who enter college immediately after high school graduation must pay college-level prices for high school-level classes....But before you write off inadequate high school preparation as a function of a student's family background or the type of college they attend, know this: Nearly half of first-year remedial students come from middle-class, upper middle-class and wealthy families. Forty percent are enrolled at public and private four-year colleges...We already knew that high schools typically underserve students from low-income families and communities, but apparently they're doing poorly with wealthier students as well. It turns out that all students are susceptible to the leaky K-12-to-college pipeline – no one is immune. This should be a wake-up call for all."
  • Say what? CBS6albany starts an article with, ""Stop for a second and think about the standards that you graduated high school with, it's night and day," said Shenendehowa Central School District Superintendent Dr. Oliver Robinson." and I'm thinking, right! Keep reading some more, though, "Under current state regulations, and in the age of Common Core, there's a real concern among parents about their kids making it to the stage in cap and gown to receive a high school diploma - and it's only getting tougher." Wait, what? The educational system has gotten weaker over the years. Try finding someone under, say, 30 to 35 who can handle decimals, fractions and percents. Whereas taking calculus used to be rare, nowadays "good" math students are taking calculus--and they can't handle fractions. "Parents and educators across the state are expressing worries about the impact on graduation rates. Robinson says data predicts a severe drop."We would go from about 93% graduation rates to barely over 50%, significant," he said...."We'd have a situation where, to be quite frank, districts would not produce graduates," he explained." And THAT is one of the many reasons why the public school system is so messed up. High school is something you have to go through before you go on to a college, enjoy parties, go into debt and come out with a degree that you need to get a job because everybody has a worthless high school degree. Rather than uphold a standard that students who graduate learn math, grammar, spelling, history, etc so that students who graduate are college ready we now have a system where 37% are college ready and "Only 8 percent of U.S. high school graduates complete a curriculum that prepares them well for college and the workplace" all while "The nation's high school graduation rate hit 82 percent in 2013-14, the highest level since states adopted a new uniform way of calculating graduation rates five years ago.". When you make something free, it loses its value. Make students earn a high school degree and some might take it more seriously. College has become the "high school" of 50 years ago except you go into debt and there's still no guarantee you can do basic math when you're finished.

Handout: counting factors


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

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

Here are some stories that caught my eye this week:

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

Sage Interact: Taylor Polynomials


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

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

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

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

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

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

Sagetex: Evaluating Logarithms

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

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

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

Basics: LCM and GCF

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

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

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

The Basics: Solving Linear Inequalities

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

Here are some stories that caught my this week:

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