# Polling: statistics isn't really math

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

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

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

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

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

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

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

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

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

Here are some events that caught my eye lately.

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

# Irrational Numbers with Patterns

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

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

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

.123456789101112131415......

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

.101101110111101111101111110.....

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

Here are some stories that caught my eye recently:

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

# Sage: Polynomial Interpolation

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

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

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

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

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

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

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

• Decades ago, a high school degree was normal and few people had college degrees. Yet people could get jobs that allowed them to provide for a family. Now the quality of high school education has been watered down, graduation rates are higher and a college degree is "necessary" to get a job. And that means people are some $30,000 in debt after college (which is more likely to be 5 years now) and too many students have taken courses in topics that lack rigor and meaning. And while I've taught algebra to many young students outside the US, somehow in the US algebra is too complicated for 18-22 year old students to master--it's actually standing in the way of people graduating. How can you get horribly educated students through college with a pesky math course in the way? Simple--water down standards at the college level. Now Wayne State University leads the charge in dumbing down education, "Up until now, students had to take one of three different math classes before they could earn their degree. Now, depending on their major, students may be able to squeak through college without taking math. The university is leaving it up to the individual departments to decide whether math will be a required part of a degree's curriculum." So in the future, students can graduate high school and college and still not have the math skills of someone who only graduated from high school 50 years ago...and pick up a lot of student loan debt along the way. But at least more people are graduating from college! Progress? • Now compare the American drive to banish math with this clip from NextShark called "Watch Korean Students Take the American SAT Math Section For the First Time". You'll hear some people talk about Americans as "exceptional"--that probably shouldn't be taken as a compliment. Even the weak Korean students are feeling better about their math now.... • The Columbus Dispatch reports "The State Board of Education is expected to lower minimum proficiency standards on two new high school math tests after results came in lower than expected.The move raises questions about whether benchmarks for new assessments will accurately gauge a student’s readiness for college or a career" Somehow I doubt they care about college readiness... • Wired.com with an article on "deep learning" that underpins AlphaGo and other computer programs. • He's gone viral! ABC News with a video on "8TH GRADER GRABS BELLY LAUGHS FOR CANDIDATE IMPERSONATIONS" • Mental Floss with "15 Observational Facts About Isaac Newton" • The bit-player blog has a fascinating post on the non randomness of the prime numbers. "These remarkably strong correlations in pairs of consecutive primes were discovered by Robert J. Lemke Oliver and Kannan Soundararajan of Stanford University, who discuss them in a preprint posted to the arXiv in March. What I find most surprising about the discovery is that no one noticed these patterns long ago. They are certainly conspicuous enough once you know how to look for them...For the past few weeks I’ve been noodling away at lots of code to analyze primes mod m. What follows is an account of my attempts to understand where the patterns come from. My methods are computational and visual more than mathematical; I can’t prove a thing. Lemke Oliver and Soundararajan take a more rigorous and analytical approach; I’ll say a little more about their results at the end of this article." • A May 18th, 2016 interview with graph theorist Maria Chudnovsky on anthonybonato.com. Looking for a female mathematician to inspire the girls in your classes. Look no further; she's even been in 2 commercials. # SageTex: Complex Numbers It's been a very busy week as schools wind down for the year. I've added a new page Sagetex: Complex numbers to the sidebar. I will, of course be adding problems to the page in the coming weeks. Here are some stories that caught my eye this week: • Mathematician Dr. Ken Ono has been written about in Quanta Magazine. • Dr. William Stein is leaving academia to start a company around Sagemath. His pdf slideshow can be found on this Reddit thread. He has a talk about this in a video posted here. • Ars Technica reports, "Google's DeepMind AI division will face off against humanity's number one Go player, Ke Jie, according to Chinese state news agency Xinhua. Ke Jie is currently the top-ranked Go player in the world." • DurhamLocalNews has a piece on how "Legislation recommended Wednesday by a Senate committee would require North Carolina schools to offer traditional high-school-level mathematics classes alongside newer “integrated” classes that arrived with Common Core...If the bill were to become law, districts would have to offer both math class sequences to students starting in the 2017-18 school year." • Click2Houston tells us a creepy story about a math teacher who enjoys being with kids a little too much: "The video shows Gregg Gustafson wrestling and tickling minors at a student's home when the parents were not around...One of the students told the police Gustafson gave him several wedgies that broke his underwear. The boy said he was wrestling with Gustafson and that he would not let him tap out.The student posted two videos of his broken underwear. Gustafson allegedly asked the boy to get rid of the evidence." • Washington Post on the new school report "Many people in education and the workplace don’t think some of the English Language Arts and math standards — which are being used in most states — are what students and workers need to be successful in college and career." One of the findings is that calculators are prevalent in math class. That's exactly what I'm seeing--but you'll see the teacher teaching how to work a problem and then they jump to using a calculator, so that the students quickly forget the skills they were supposed to learn. Whose "best practice" is that? More disturbingly, "There may be disagreement across K-12, college, and workforce about which mathematics topics are important to success in postsecondary STEM coursework and STEM careers. In K-12, there may also be disagreement about when these topics should be introduced in the mathematics curriculum." Shouldn't these issues have been worked out before forcing them upon everyone? • Ars Technica with an interesting article on "That ’70s myth—did climate science really call for a “coming ice age?”" • EAGNews on how "For a mere$6.5 million, New York City’s School Construction Authority renovated a former clothing store on Fifth Avenue into a “state-of-the-art” facility for 18 students to participate in its new, free pre-K program....The renovations cost the city about $362,222 per pupil, which was about$160,000 per seat more than the next most expensive renovation in Staten Island, for creating partitions, pouring concrete slabs, adding sprinkler systems and HVAC, and other upgrades." It's easy to spend public money.
• ZeroHedge on the embarrassment that is the new generation. But it's not just America. "In the western world, political correctness is often taken to absolutely ridiculous extremes in attempt to keep people from being exposed to anything that could remotely be considered “offensive”.  For instance, just consider a couple of examples from the United KingdomThis hyper-sensitivity has prompted the University of East Anglia to outlaw sombreros in a Mexican restaurant and caused the National Union of Students to ban clapping as “as it might trigger trauma”, asking youngsters to use “jazz hands” instead. Could you imagine banning clapping? But this is actually happening.  Anything that might make someone feel the least bit “uncomfortable” is now being labeled as a “micro-aggression”, and at schools all over America “safe spaces” are being set up where young people can avoid anyone or anything that may make them “feel uncomfortable, unwelcome or challenged”.And this is not a fringe movement at all.  These “safe spaces” are being established at some of the most prestigious universities in the entire country, and in at least one case a “safe space” included “calming music, cookies, Play-Doh and a video of frolicking puppies”
At Brown University – like Harvard, one of the eight elite Ivy League universities – the New York Times reported students set up a “safe space” that offered calming music, cookies, Play-Doh and a video of frolicking puppies to help students cope with a discussion on how colleges should handle sexual assault. A Harvard student described in the university newspaper attending a “safe space” complete with “massage circles” that was designed to help students have open conversations.Are you kidding me?...Now that we have defined “safe spaces” and “trigger warnings”, I am going to define a term that I used in the title of this article.

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

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

# 1,1,2,3,5,....

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

# Sagetex and Graph Theory

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

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

• WTVR.com, CBS 6, reports "The mother of a Virginia middle school student said she was angry, frustrated, and mad after her son was handcuffed, suspended from school, and charged with stealing a 65-cent carton of milk from the cafeteria. As it turned out, Shamise Turk's son Ryan was on the school's free lunch program and the milk -- was free.....Police said the larceny charge was because Ryan tried to "conceal" the milk, a claim Ryan's mother denied. The school spokesperson said Ryan was suspended for theft, being disrespectful and using his cell phone in school."
• Money.CNN says, "For years, America's college campuses swelled with more and more students. But enrollment peaked in 2010 at just over 21 million students. Attendance has dropped every year since....The two types of colleges with the biggest declines in enrollment are: community colleges and for-profit universities. Those schools draw heavily from low-income and minority households."
• Science Daily with a piece on titled "40-year math mystery and four generations of figuring" which "So, what is the Kelmans-Seymour Conjecture, anyway? Its name comes from Paul Seymour from Princeton University, who came up with the notion in 1977. Then another mathematician named Alexander Kelmans, arrived at the same conjecture in 1979. And though the Georgia Tech proof fills some 120 pages of math reasoning, the conjecture itself is only one short sentence: If a graph G is 5-connected and non-planar, then G has a TK5."
• Oregonlive reports "Portland Superintendent Carole Smith apologized Friday for allowing students and teachers at two schools to continue to drink tainted water after tests showed unsafe levels of lead...At Rose City Park, that meant students were free to drink lead-laced water for eight school days after district officials knew about the toxic results."
• ZeroHedge reports "Federal investigators revealed another blow to Detroit Public Schools this week. Meet Carolyn StarkeyDarden - the system’s former grant-development director - who has just been charged on suspicion of obtaining nearly \$1.3 million by lying about children’s tutoring services....Carolyn Starkey Darden set up a company and allegedly ran a scheme between 2005 and 2012 in which she submitted fake invoices for tutoring services that were never provided to students, according to charges filed by the U.S. Attorney’s Office in Michigan’s Eastern District." This is so typical of the public school system where huge amounts of money can be easily skimmed by the corrupt. Because it's almost never about the kids.
• RT on the 8 year old who brought a loaded gun to class. "It is unclear to whom the gun belonged and what made the boy bring it to school. The NYPD said there were no arrests made so far. Authorities believe that the boy might have had a dispute with another child, and they suspect his teenage brother had something to do with this incident, WABC reported....This is the sixth time authorities in New York confiscated a firearm inside a city school since March. In one case, a 14-year-old boy brought a loaded 9-millimeter gun to Middle School 61. "
• The Third Shakmir tournament is underway with chess superstars Caruana, Kajarkin, Radjabov, Hou Yifan and more. The games can be followed live here.

# Sage Interact: Generate Discrete Data

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

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

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