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. Sott.net 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 HuffingtonPost.com 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".
  • RT.com 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? Sott.net 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.
  • CBS19.tv 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. Reason.com 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 Watchdog.org....The 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 UrbanMilwaukee.com 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 "...exposed 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!
  • Phys.org 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.

Odds and Ends: Basics and Graphics

SolvingEqns1I've added another worksheet to The Basics page; this is a collection of solving equations with one variable--often called 2-step equations. As it runs using sagetex you'll need it installed on locally on your computer or, even easier, open a free Sagemath Cloud account. The link for Sagemath Cloud is on the the sidebar. I've also added two plots to the Graphics page: the first plot is a exponential (growth) versus its logarithmic inverse to see the reflection around y=x (also plotted). The second plot has a exponential (decay) plotted against its logarithmic inverse.

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

  • The London Chess Classic 2015 has begun and though you won't find Komodo or Stockfish you can find some pretty good carbon based talent including (human) World Champion Magnus Carlsen, Anand, Caruana, Nakamura, Topolov, Grischuk, Adams, MVL, Giri, and Aronian. You can find the games streaming here along with GM commentary.
  • Some follow up on TCEC: Chessdom reports "Komodo also proved dominant in earlier stages of the competition. It won Stage 1a, then easily cruised through Stage 2. In Stage 3 it gave the first warning to its main opponent by winning with a two points difference.With this Season’s victory, Komodo successfully defended its title from TCEC Season 7 and together with the victory from TCEC Season 5 Komodo  is now triple champion of TCEC. That makes it the engine with most titles in Top Chess Engine Championship, together with Houdini which won Seasons 1,2, and 4. Stockfish is the only other engine that has a title from the competition.".
  • Chess.com has a piece by GM Robert Hess explaining how he played Komodo in a 4 game match shortly before the TCEC matches began., "My two starting positions were as follows: White with an exchange up and my rook on b1 while Komodo's rook on a8 was removed, and White with pawns on e4 and d4 and Black missing the f7 pawn. In all games, I had 45 minutes+25 seconds increment per move, while Komodo had 45 minutes with 15 second increment. I was given greater increment because I was providing commentary while playing, thus ensuring I would be making slower moves." The result was 4 draws.
  • Dr Everett Piper, president of Oklahoma Wesleyan University has had enough of the cry-bullies that have taken over numerous universities and he earned a lot of attention and respect by posting a letter to the school website "This is Not a Day Care. It's a University". TribLive has more of the details, "Mr. Piper is the president of Oklahoma Wesleyan University. He became incensed when a student confronted him after a chapel service to complain that he felt “victimized” by a sermon about not showing love. “In his mind,” Piper wrote in a scathing blog post, “the speaker was wrong for making him, and his peers, feel uncomfortable.” “Our culture has actually taught our kids to be this self-absorbed and narcissistic,” Piper continued. “Any time their feelings are hurt, they are victims. Anyone who dares challenge them and, thus, makes them ‘feel bad' about themselves is a ‘hater,' a ‘bigot,' an ‘oppressor,' and a ‘victimizer.'”And Piper was far from done.". Well done Mr Piper! Other admins take note, please.
  • The Daily Caller reports, "District of Columbia officials released results from a recent citywide elementary school exam Monday, and the scores are abysmal. Less than a quarter of students met expectations in either math or English. Among all eighth grade students who took the test, just 3 percent met expectations in math, while 8 percent of seventh graders met the math expectations, according to Partnership for Assessment of Readiness for College and Careers (PARCC) test results."
  • Google crosses some red lines: RT reports,"The Electronic Frontier Foundation has filed a complaint with the Federal Trade Commission in which they allege that Google has been violating the privacy of students as young as seven years old by mining their data.The EFF’s Tuesday complaint said that Google can track every search term, site, and video students view using a feature that is enabled by default on the Chromebooks that are sold to schools. The data collection is allegedly not used for advertising purposes, but rather to “to improve Google products.”The complaint alleges that the monitoring is in violation of a Student Privacy Pledge that Google signed in 2014, which the EFF said is legally enforceable under the Federal Trade Commission Act."
  • You might remember how, decades ago, corporations got themselves into schools by selling a lot of junk food in vending machines which was followed over time by a rise in child obesity and diabetes. Now CNBC has an in depth piece on corporations in the classroom and Google is winning, "Google, Microsoft and Apple have been competing for years in the very lucrative education technology market. For the first time, Google has taken a huge lead over its rivals.Chromebooks now make up more than half of all devices in U.S. classrooms, up from less than 1 percent in 2012,...Google's major advantage when it comes to wooing cash-strapped school districts — which are expected to purchase more than 11 million devices next year in the U.S. alone — is Chromebook's extremely competitive price...."They set up what's called a blended classroom, so they would have the teacher with only about seven students, but then seven other students would be learning from Khan Academy, seven others would be doing a group project and seven students would be assessing their skills to try to figure out where they are at that point in time."". Note the classroom reference to kids learning from a Khan Academy video  of an uncertified person who isn't a teacher. A little bit ironic given some of the ferocious criticism directed his way.
  • The NY Times takes a look at the quandry of NY education officials, "...If the percentage of students passing the Algebra I exam falls to 63 percent from 72 percent, and the passing grade is scheduled to increase by 9 points in coming years, should the test be made easier?...This fall, they established a committee to study the results on the new exams to determine, among other things, whether the bar for passing, which students would have to meet starting in 2022, had been set too high. (They had originally said the class of 2017 would need the higher scores to pass, but last year decided to push that back)....The city’s Education Department is “in a panic about this,” said Uri Treisman, a professor of mathematics at the University of Texas who has advised the department on plans to improve math instruction in middle and high school.Among the ideas the city is considering: having fifth graders take math with a specialized instructor instead of one teacher for all subjects; teaming up with local universities to get more sixth- and seventh-grade math teachers certified in math instruction; creating summer programs for middle- and high-school students who are struggling in math; and training middle-school and algebra teachers in how to address students’ “math anxiety.”". Quick recap: Common Core would toughen standards and show the soccer moms their children weren't quite as good as they thought. Objective achieved and now, with a higher bar, educators look like they are doing an even worse job and parents and students are not happy. So lets make the test easier. Here's one reason, of many, why education fails. Also take note the "...committee to study the results on the new exams to determine...whether the bar for passing...had been set too high". Given that officials are panicked about the results you have to wonder how independent the committee will be. If the level is determined to be set incorrectly will the company that designed the faulty test be held accountable? Will more money be required to create a test that gives the proper results? Stay tuned!
  • The DailyStatesman has a topic that I think is a winning idea, "The Hour of Code is a world-wide initiative during the Dec. 7-13 Computer Science Education Week, aimed at introducing millions of new learners to computer science....The Hour of Code involves the use of a self-guided tutorial which allows students to learn at their own pace and skill level. The tutorials expose the students to fundamental computing concepts on a level playing field and is intended to inspire today's youth to build technology..."They don't realize it, but when they're learning this and writing in functions, they're basically writing in x-y t-charts, applying algebra skills and again, applying critical thinking skills in the process."They're challenged in this process," Bolin says. "It's not for everyone, but you never know. You see kids with their interest peaked once they get into it."As evidence, Bolin says that a group of students he taught last year were so interested in advancing their coding skills, they continued the process at home. The group went on to compete at the National Jr. Beta competition and placed second in the nation."". Some schools are taking an interesting and innovative approach to education.
  • If you follow chess you know there is always a debate about whether the current chess players are better than great players from the past and, if so, by how much. The issue of chess ratings muddies the water because of chess ratings inflation. It makes some fans think the current crop of players is always best because their ratings are higher. But something unusual has happened:LiveChess12-5-15Notice that of the top 4 players in the world, three are in their forties. This really shouldn't be happening. Has something like this ever happened before?? I  think all of those players (Topolov, Kramnik, and Anand) would admit their "best chess days" (in terms of chess strength and not rating) are behind them. Is the current generation of 20 somethings really better than the last generation of players? It certainly doesn't show from the current rating list. And when you consider that much of the improvements in modern chess players are tied to them growing up with chess engines to spar with and help them get better, it's difficult to believe that the current generation is better. It seems clear that Topolov, Anand, and Kramnik would have been even more fearsome had they grown up  with the chess playing software that we now take for granted. So the question becomes, "Is this evidence that chess is dying as the current generation is not replacing the last one even on the basis of today's inflated ratings?". Chess rating inflation seems to be covering the decline in chess players. What do you think?

Problems: discrete math

I had to change the topic of my post this week once I read the article "Math is my religion" on the Portlandtribune.com website. The author, Brian Gentry, is a high school student and self described "math geek" who has been taking college level classes. He writes, "But my interest in math has allowed me to see the holes in our math curriculum. ... Rather than teaching kids integration, we should teach them the math that is most applicable to their life goals.". Two important courses that Mr Gentry thinks are particularly useful are geometry and discrete math. With respect to geometry, he writes "A fundamental piece of our geometry class is proofs, and the logic taught through proof-writing is used not only in math, but also in journalism, history and every other field that requires the construction of a logical argument.".  To which I say, "Amen"! With respect to discrete math, (singling out number theory) he writes "I was taught that I need to cite each theorem I use in my proofs and justify each application, just like a history major has to cite quotes and explain how each quote is relevant. I can say without a doubt that this class, if implemented in a high school curriculum, would be beneficial to everyone who took it. ". And that deserves a "Hallaleujah!". Brian goes on to quote a teacher, Barry Garelick, about the "...decreasing number of proofs in geometry textbooks over the decades. He contends that proofs are integral to geometry...In Garelick’s mind, proof-based courses teach students how to construct logical arguments, which I argue is not only central in mathematics but also in a variety of other fields.". To which I say, "Testify!".

As you can tell, I agree with Mr Gentry but, unfortunately, Brian knows more than the experts who are moving us in the wrong direction. It's not enough to have a good idea in the public school system, you've got to get some "experts" on board to change policy and then the devil is in the details of how they implement it mess it up. You see, Brian has the mathematical knowledge that so many " experts" are missing. He also has a sincere desire to improve the situation--but no real power to do anything. In our centrally planned model with high paid "experts" who don't seem to have either. It's no surprise education flounders decade after decade after decade. When you see well intentioned people get "Zuckered" out of 100 million dollars by experts and when you see in state after state that "experts" have set the bar for mathematical knowledge needed for a math teachers by a a multiple choice test which requires a calculator--at the same time they turn away people with STEM degrees-- you do tend to question motives. They build failure into the system and look for superficial ways to "improve" on some contrived school rating (such as paying for students to take AP exams).

The fact is I've never talked to anyone with a graduate degree in math who thinks ripping proofs out of the curriculum is a good idea but that's where the current mathematical curriculum has taken us. The proofs that "us old folks" associate with geometry are gone and/or watered down. Is that because proofs don't prepare students for higher level math?  Of course not---but if students can't master proofs and much of the proof content is replaced and what remains is watered down test scores might rise.

There is no reason, based on math, to remove proofs--proofs are the essence of mathematics--and getting students some foundation in proofs would help better prepare them for college. So today's curriculum prepares a student for math less than before in that key area. Clearly the educational central planners have no clue when it comes to math. But even if they did many teachers have no idea what that discrete math means and that presents a huge obstacle to implementing Mr Gentry's excellent idea: remember one third of the high school math teachers don't have a degree in mathematics so there's going to be far less who have taken and are qualified to teach discrete mathematics. And finding these people is at odds with the various Bull**** certification requirements that create an artificial teacher shortage in various states.  Take a look at the story below on California and Common Core to see the complete lack of planning and the resulting fiasco. Whose accountable for the mess? Nobody. Who pays the price? The kids. It's difficult for me to imagine anything more than centrally planned failure of implementation.

With that in mind I've posted an example of a discrete math problem which is more understandable/natural than "Two parallel lines are cut by a transversal...". The problem is posted on the Problems page. There are $latex n \geq 2$ people are at a party. Prove that there are two people who know the same number of people." Of course, there's a little explanation needed: Two people either both know each other or they don't. That is, it's impossible for A to know B but for B not to know A. Also assume that a people don't "know themselves". A very surprising result that can be proven using mathematical thinking/logic. It uses the Pigeonhole Principle and of course, you can relate it to graph theory, too.

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

  • One of my favorite nontechnical math books is  "The Man Who Knew Infinity". A movie based on the book is finally out. IFLScience talks about Ramanujan and has a clip from the upcoming movie.
  • The TCEC Season 8 Superinal is about 60% done and Komodo leads Stockfish with 4 wins, 1 loss, and 65 draws. With so many games to play Stockfish has a mathematical chance to win but given the consistent nature of computer play; i.e., computers don't blunder or get tired/overconfident, this match is essentially over. Nevertheless, you can keep following the match here.
  • Kevin Knudson with an excellent article on Forbes: "I then casually mentioned that if you take the harmonic series and throw out the terms whose denominators contain a 9 then the resulting series converges...And, there’s nothing special about 9; you can toss out terms containing any particular digit. In fact, you can pick any finite string of digits, toss out the terms containing those, and the result converges. With that set-up, let’s talk about what all this means and how we can prove it..". Read the article to find out the details. If you teach AP Calculus, you really should take a look.
  • Student protests are happening at college campuses all over the country. The Chronicle of Higher Education mentions a bunch here. The Washington Post has an in depth piece on Yale and the student demands, "The students also are asking Salovey to remove Nicholas and Erika Christakis from their positions at the helm of Silliman College, one of Yale’s 12 undergraduate residential communities. The pair became the subject of students’ ire when Erika Christakis, the associate master and an early childhood educator, sent an e-mail to students encouraging them to view offensive Halloween costumes as a matter of free speech and free expression."
  • ZeroHedge looks into the demands from students at the Amherst College. There is a long list of demands but take a look at demand number five: " President Martin must issue a statement to the Amherst College community at large that states we do not tolerate the actions of student(s) who posted the “All Lives Matter” posters, and the “Free Speech” posters that stated that “in memoriam of the true victim of the Missouri Protests: Free Speech.” Also let the student body know that it was racially insensitive to the students of color on our college campus and beyond who are victim to racial harassment and death threats; alert them that Student Affairs may require them to go through the Disciplinary Process if a formal complaint is filed, and that they will be required to attend extensive training for racial and cultural competency." Did you get that? People who posted a flyer on how free speech is dead (picture posted) need to be disciplined and re-educated --- along with those who post "All Lives Matter"---if these intolerant zealots get their way.
  • NYDailyNews posts a disturbing and "chilling" video in the case of the student on trial for killing his math teacher.
  • Edsource.org has an all too typical  story of Common Core implementation problems. "During the five years since California adopted the Common Core State Standards for mathematics and English language arts, the search for high-quality textbooks and curriculum materials has been a sticking point, in some cases a major one, in effectively and speedily implementing the new standards....The root of the problem, argued Phil Daro, a principal author of the Common Core math standards, is that “districts tried to switch to the Common Core before there were any books aligned with them.”That, however, was not the fault of districts. The state adopted the Common Core in 2010, but the State Board of Education only  approved a recommended list of K-8 math textbooks and materials in January 2014 – and only did so two weeks ago for K-8 materials in English language arts. But focus on the fact that even though Common Core was known to be coming years in advance and that it is 5 years after it is adopted and they still don't have quality curriculum materials. How bad is the state DOE when teachers still don't have "the basics" under control after 5 years, especially when they had years of planning before Common Core was implemented? California's plight is going on in many states and it's a big reason why the educational system doesn't improve much. But with a new election around the corner don't be surprised if another educational model takes its place. Then more years to transition to implement another bad system. More money to spend designing tests,etc. Wash, rinse, repeat.
  • LewRockwell.com has a Walter E. Williams piece "Education Disaster" which looks at the latest Nation's Report Card, "When it comes to reading and math skills, just 34 percent and 33 percent, respectively, of U.S. eighth-grade students tested proficient or above — that is, performed at grade level or above. Recent test scores show poor achievement levels in other academic areas. Only 18 percent of eighth-graders are proficient in U.S. history. It’s 27 percent in geography and 23 percent in civics. The story is not much better when it comes to high schoolers. According to 2010 and 2013 NAEP test scores, only 38 percent of 12th-graders were proficient in reading. It was 26 percent in math, 12 percent in history, 20 percent in geography and 24 percent in civics." So failure is the norm. Moreover, Williams writes "Richard Vedder, emeritus professor of economics at Ohio University, argues that there has been a shocking decline in college academic standards. Grade inflation is rampant. A seminal study, “Academically Adrift,” by Richard Arum and Josipa Roksa, argues that very little improvement in critical reasoning skills occurs in college. Adult literacy is falling among college graduates. Large proportions of college graduates do not know simple facts, such as the half-century in which the Civil War occurred. Vedder says that at the college level, ideological conformity is increasingly valued over free expression and empirical inquiry."
  • EAGNews on the teacher arrested for running his own brothel, "McCrimmon was arrested when authorities shut down his Memphis nightclub, Walt’s Place, over the weekend. Undercover officers allegedly made eight separate prostitution transactions there, including deals organized by McCrimmon himself, before they raided the Parkway Village establishment Saturday, according to The Commercial Appeal. Police allege the club charged patrons a $20 “membership fee” for events that featured strippers and other activities, but did not have a compensated dance permit. Walt’s Place also served booze without a liquor license and provided a VIP room for $50 sex sessions, police said....McCrimmon has since resigned from his teaching position, My Fox Memphis reports.". Perhaps he'll be moving to another state? Be on the lookout...
  • I was shocked to see someone claimed to have solved the Riemann Zeta Hypothesis. Whose that? From where? What the? A quick search made it clear someone was full of BS. With no "reputable" site proclaiming the amazing story I had to wait to see how it played out. Now Quartz has an article explaining how he "fooled" the British media:  "Leading British media, including the BBC and the Daily Telegraph, ran the story of Enoch winning the award, but a little digging suggests they might have jumped the gun.". Very little digging, in fact. The article continues, "Enoch has an academia.edu page where the “proof” of the solution to the Riemann Hypothesis has been uploaded—but that has also come in for criticism, as the proof is believed to have been plagiarized.". So bottom line is it doesn't take much to fool the press---and the Riemann Zeta Hypothesis is still open. The Aperiodical gets more in depth on the deception of what did and did not happen. Hey, at least he's not running a brothel.
  • EAGNews with reporting the lengthy and somewhat outrageous demands, including "A mandatory class for everyone, including staff and administrators, about the “historical racial violence of this University and town …”...Housing and bathrooms that are not segregated by gender.". LewRockwell hosts a smackdown piece by Fred Reed directed at bad universities like what we see at UNC: "In all likelihood you will waste these four years of your time and mine in this institution...during which you will take absurd courses of your own devising, courses having nothing to do with the purposes of education, of which you know nothing....When you graduate, a terrible shock awaits you. You will find that employers have no interest in your wearisome righteousness. They will not pay you for Victims’ Studies or  contemplation of grievances. They will not care about the high GPAs you got through grade inflation or sleeping with the professor. They will expect you to do your job, if there is a job for you to do."
  • With intolerance and free speech under assault at the universities, Reaon.com has a video clip from the documentary "Can We Take a Joke". I haven't seen the movie, but I'm guessing the answer is no."

Basics: Simplify Like Terms

SimplifyLikeTermsI've added another worksheet to The Basics page; this one is on "Simplfying Like Terms". In this process of trying to solve a problem in the last worksheet (where Sage turn multiplication into *) I did a search on how to fix the problem and found the answer on this website: latex() the expression. So with that problem solved, I've revised the previous Worksheet on evaluating expressions so that it prints without * for multiplication. If you had downloaded the earlier version you should get the updated version to replace it.

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

  • Okay, I HAVE to start with a real honest to goodness mathematical breakthrough. László Babai, a mathematician and computer scientist at the University of Chicago  appears to have proven a very important result. Sciencemag.com has the details, "In the "graph isomorphism problem," the challenge is to determine whether two graphs are really the same or not. Babai has found a new algorithm to solve that problem, as he announced today....For the previous best method, invented in 1983 by Eugene Luks, a mathematician and computer scientist at the University of Oregon in Eugene, the number of steps grows almost exponentially with the number of nodes in the networks to be compared. In Babai's algorithm, the number of steps grows only slightly faster than polynomial time.... If it holds up, the new algorithm simply proves that the tough cases that stymie the current algorithms can also be solved efficiently, "
  • A MUST READ article. In an earlier post I mentioned the problems Kentucky was having with Common Core. The Federalist looks into the details. Some key passages, "In connection with federal Race to the Top grant applications in 2010 and No Child Left Behind waivers in 2011, states had to demonstrate that their institutions of higher education (IHEs) would “exempt from remedial courses and place into credit-bearing college courses” students who attained a certain score on Common Core-aligned assessments.". So the "Common Core is just a bunch of standards" trope that has become the first line of defense is shown to be false again. Back to the article, "So what happens when those unprepared students matriculate at a college that has already agreed to place them in courses that count towards graduation, without remediation? Exactly what is now happening in Kentucky... students who formerly would have gone through remediation are now to be thrown into credit-bearing courses. But since such students obviously won’t be ready for real college work, the courses will be designated “co-requisite”—meaning lagging students will receive extra help of some sort so they can catch up...By and large, professors weren’t consulted before their colleges and universities signed onto the Common Core scheme. They are only now beginning to understand that Common Core will result in hordes of unprepared students showing up in their freshman classes, and that the professors will be expected to relax or suspend course quality to hide the problem...Common Core’s promise of “college readiness” means nothing if the definition is set not by colleges themselves but rather by the standards-writers.".
  • The TCEC Superfinal is nearing the halfway mark. It's 3 wins for Komodo versus 1 win for Stockfish. There are 36 drawn games. You can follow the matches here.
  • A connection between quantum physics and $latex \pi$ isn't as irrational as it sounds. Phys.org has the incredible details, "In 1655 the English mathematician John Wallis published a book in which he derived a formula for pi as the product of an infinite series of ratios. Now researchers from the University of Rochester, in a surprise discovery, have found the same formula in quantum mechanical calculations of the energy levels of a hydrogen atom.". Continue with Science20: "Friedmann did not set out to look for $latex \pi$ nor for the Wallis formula. The discovery began in a quantum mechanics course taught by Carl Hagen, a professor of physics at the University of Rochester and one of the six physicists who predicted the existence of the Higgs boson. While the quantum calculations developed by Danish physicist Niels Bohr in the early 20th century give accurate values for the energy states of hydrogen, Hagen wanted his students to use an alternate method--called the variational principle--to approximate the value for the ground state of the hydrogen atom...Addressing the centuries-long gap between the 17th century Wallis formula, the 20th century quantum theory, and the decades that passed from that time to now, Doug Ravenel, a professor of mathematics at the University of Rochester, points out that Friedmann and Hagen used long-established concepts of their fields to arrive at their result, so even mathematicians and physicists who lived many decades ago would have been able to appreciate it."This is a beautiful connection between pi and quantum mechanics that could have been found 80 years ago, but was not discovered until now," said Ravenel, congratulating the two authors."
  • Inside Sources has the article I want to quote in one place, "Two multistate testing groups — the Smarter Balanced Assessment Consortium (SBAC) and the Partnership for Assessment of Readiness for College and Careers (PARCC) — received $360 million in taxpayer funds to create Common Core-compliant tests. But there are growing concerns over the program, such as the cost and classroom time consumed by state tests.". It's difficult to imagine that a committee couldn't come up with appropriate test questions in the years that led up to Common Core being implemented without spending one tenth the amount. Open source the problems, cut the costs, and spend the money on the kids, not on the corporations.
  • That hysterical, profanity laden tirade by the Yale student in my last post is just one example of the nonsense going on in public and private education. ZeroHedge has a response by a UNC-Wilmington law professor that's gone viral. Here are some excerpts, "Let’s get something straight right now. You have no right to be unoffended. You have a right to be offended with regularity. It is the price you pay for living in a free society. If you don’t understand that you are confused and dangerously so. In part, I blame your high school teachers for failing to teach you basic civics before you got your diploma. Most of you went to the public high schools, which are a disaster. Don’t tell me that offended you. I went to a public high school....Unbelievably, a student once complained to the Department chairwoman that my mention of God and a Creator was a violation of Separation of Church and State. Let me be as clear as I possibly can: If any of you actually think that my decision to paraphrase the Declaration of Independence in the course syllabus is unconstitutional then you suffer from severe intellectual hernia. Indeed, it takes hard work to become stupid enough to think the Declaration of Independence is unconstitutional. If you agree with the student who made that complaint then you are probably just an anti-religious zealot...".
  • Alternet.org with an article that says "According to statistics released by the U.S. Department of Education and published by NBC News, in the 2011-2012 school year, teachers called the cops on students a total of 31,961 times in the state of California alone, leading to 6,341 arrests. With 175 8-hour school days, that means a cop is called every 2.6 minutes. At one California school district, in particular, East Side Union High School District in San Jose, police were called on students 1,745 times during the 2011-2012 school year. This one school called the police on students more than 10 times a day."
  • The University of Kansas gives in to the PC extremists. Infowars notes "
    A governing body made up of students at the University of Kansas has voted to eliminate their use of gender specific pronouns, stating the terms pose “microaggressions” towards people who don’t fit traditional gender roles....The student government’s move to eliminate gender nouns comes after the National Science Foundation spent $125,000 at KU last year studying how adjectives could be perceived as racist or sexist."
  • The University of Missouri has had the spotlight turn on it. ZeroHedge has a piece that says, "For months, black student groups have complained of racial slurs and other slights on the overwhelmingly white (79% white and 8% black) flagship campus of the Missouri's four-college system. Today, amid a campus in open revolt and at least 30 black football players announcing that they would not play until the president was gone, AP reports that Mizzou President Tim Wolfe has resigned effective immediately urging students and faculty "to heal and start talking again to make the changes necessary." Protestors demanded that Wolfe "acknowledge his white male privilege," that he is immediately removed, and that the school adopt a mandatory racial-awareness program and hire more black faculty and staff.". So much is going on there that I have no idea about, but what has gotten my attention is the behavior of faculty in student demonstrations. The Daily Mail has captured a lot of the stupidity. "The civil rights protests at the University of Missouri took an unexpected turn on Monday, when a media teacher was caught on camera harassing journalists trying to cover the national story....Melissa Click, an assistant media professor at the university, is seen coming up to Mark Schierbecker, another photographer recording the exchange, to cover his camera and demand that he leave....She then comes back to the photographer and starts yelling in his face: 'You need to get out. You need to get out'. When he explains that 'this is public property' and he can stay there because 'it's owned by the university' Click takes on a mocking tone.'That's a really good one. I'm with the communications faculty and I really get that argument - but you need to go. You need to go!' Click says.'Who wants to help me get this reporter out of here?' she yells out. 'I need some muscle over here.'...Her aggression towards journalists is perhaps strange since just two days earlier she publicly reached out to the media on Facebook to cover the story." The AL.com website indicates she wasn't the only faculty involved: "Janna Basler, Mizzou's director of Greek life and leadership, tells Tai that he needs to "back off" and "go." She brushes against him, and Tai asks if she's employed by the Office of Greek Life. Basler responds, "My name is 1950." She also tells Tai that he is "impinging on what [its members] need right now, which is to be alone," that report states."As the students behind Basler begin to push forward, she makes physical contact with Tai, prompting him to object, to which she responds, "I don't have a choice." The students seem to decide that since he's not going to move, they're going to move forward as a human chain, physically pushing him back with their bodies. A student adds, "It's our right to walk forward."". But there is a consequence for adults who act like kids: TheManeater reports, "Multiple petitions have been created calling for the removal of two MU employees after a video surfaced documenting an incident on Monday, Nov. 9 in which they demanded that journalists leave the Concerned Student 1950 campsite. Assistant Director of Greek Life and Leadership Janna Basler and Assistant Professor of Mass Media Melissa Click can be seen in the video shouting at MU student and former Maneater staffer Tim Tai and other journalists."
  • New York Magazine looks at the Missouri situation from the PC angle: "The student protest at the University of Missouri began as a response to a serious problem — outbursts of vile racism on campus — and quickly devolved into an expression of a renewed left-wing hostility to freedom of expression...It is also undeniably true that outbursts of political correctness disproportionately take place in campus settings. In recent weeks, UCLA, Wesleyan, and Yale have seen left-wing student activism aimed at shutting down the expression of contrary viewpoints....As far as the students are concerned, they represent the cause of anti-racism, a fact that renders the need for debate irrelevant....People on the left need to stop evading the question of political correctness — by laughing it off as college goofs, or interrogating the motives of p.c. critics, or ignoring it — and make a decision on whether they agree with it.". Well said. Forbes has noted "Melissa Click has become of symbol of what many parents dread when they send their children off to college. From her bullying of students to her doctoral thesis on the whiteness of Martha Stewart and her classes in “visual literacy,” she crystallizes the view that tuition dollars are spent on nonsense, and sometimes worse....That an assistant professor of “mass media” in the department of communication was unaware of the instantaneous power of YouTube and social media is another reason for parents to wonder about the wisdom of spending their money on Click.". ZeroHedge posts when Melissa Click resigned.  Huffington Post looks at her apology, line by line, and calls it Bull****. Fox2Now reports that "...Janna Basler has been relieved from her duties as director of Greek Life & Leadership, pending a university investigation into her actions."
  • EAGNews on how "...the Buffalo school district spent $5,045,586 on the union’s insurance “cosmetic surgery rider” from July 2014 to June 2015....Just look at what the district has spent over the past four years on cosmetic procedures for teacher union members:* July 2014-June 2015: $5,045,586
    * July 2013-June 2014: $5,439,218
    * July 2012-June 2013: $5,221,293
    * July 2011-June 2012: $4,966,179That’s $20,672,276 that has been diverted out of the classroom for expenditures that have nothing to do with educating children."
  •  BoingBoing ask "What would happen if you mixed a math education tutoring site with a late night 900 number?". Click on the link do the reading and watch the video to find out. You'd be very naughty to watch the video at school; wait until you get home. But if you click on the link at the bottom you'll get to BostInno which says "Joking aside, Solve X 4 U is a legitimate homework help business. According to the startup’s website, they can help with problems pertaining to a wide range of difficult STEM subject areas, including statistics, accounting, economics and chemistry. Depending on how many customers they’re servicing, Solve X 4 U will come to your aid within about 24 hours, so plan your homework assignments accordingly."

The Basics: Evaluating Expressions


I've added a worksheet to The Basics page. This is programmed using $latex \LaTeX$ and the sagetex package so that every time you run $latex \LaTeX$ on the file it creates another randomized worksheet. You should get a free Sagemath Cloud account to run it (that link is on the sidebar as well). I used a "quick and dirty" approach by generating the same type of problem over and over using a for loop. The problems were built into the Sagetex Test Template created some time back and posted on the Handouts page and you'll need to change the teacher name to avoid any questions about who "Ima Putz" is. The extra wrinkle in the worksheet is the creation of answers. It's done on the fly as the problem is being created. The string outputP holds the typesetting of the Problems and the string outputA holds the typesetting of the Answers. Each time a problem is created, outputP is modified and then outputA has the answer appended to it. In this way you've got an answer key which should be correct if I didn't make any mistakes.

Here are some stories which caught my eye over the past week.

  • Who hasn't seen the video of the school officer "choking and slamming" a student who wouldn't hand in her cell phone after she was caught using it in class? Sputnik News has the original report here, followed by a report here on how the officer has a history of problems. The officer was fired, according to the latest report.
  • An article you have to read to believe. What happens if a private school does a terrible job educating students? They have to fix the problem or go out of business. After all, who will pay to get a miserable education? It has to be better or students will go to the "free" public school. The public school system is different--it lacks that accountability. The teachers aren't going to lose their jobs for poor performance and the students are stuck in the local public school. A typical public school will focus on getting all students to meet minimum standards. In an attempt to get some of the poorer students more proficient (it helps the school's score) material gets dumbed down. But in many cases the worst students are not interested in making an effort to improve and performance at all levels suffers. The lower bar means students need to do less to pass and so many do less--a negative cycle that's hard to break. If administration is poor then you've got the next story. Daily Caller reports, "Officials in at public school district about 50 miles north of San Francisco have found a new and exciting way to coddle kids. Under a new policy, students will be able to earn passing grades with scores of just 20 percent...Also, a school district-wide rule forces teachers to give every student a score of 50 percent even if they don’t complete a scintilla of homework or make an effort to mark down an answer on a test or quiz." While the article quotes some teachers who hate the system, there are education professionals some people who disagree, "Excited school district officials have also praised the generous grading system. The officials say students who are academically terrible won’t become demoralized as long as teachers are forced to hand out passing grades. And students who somehow manage a 19 percent or lower will remain encouraged.". From my own experience, students who "manage" a 19 percent do it effortlessly. That is, they put no effort into the course and their parents aren't there to keep them on track. They aren't demoralized; they just don't care. I think vocational educational is the only possible way of getting those students on track. Lowering the bar is a recipe for failure. Why do education professionals some people try to implement such an obviously stupid idea? It seems more about making the admin look good than about improving student performance. Yet in a public school this type of incompetence doesn't get fixed.
  • US News and World Report has a report on all the testing. "The drop in proficiency, which is a first-time occurrence in math since the test was first administered in 1990, comes after a series of years in which the country experienced gains in math and reading on NAEP. "
  • Sott.net with a piece on Dr. Wendy Bradshaw. Although she "...is far from retirement age and she has PhD in education, she's leaving her profession because of standardized testing, which she explained in a Facebook post which has been shared more than 44,000 times since it was posted on Oct. 23.". The letter is an indictment of the current system and although she never mentions Common Core by name, it sounds like she doesn't like it. You decide, "Like many other teachers across the nation, I have become more and more disturbed by the misguided reforms taking place which are robbing my students of a developmentally appropriate education. Developmentally appropriate practice is the bedrock upon which early childhood education best practices are based, and has decades of empirical support behind it. However, the new reforms not only disregard this research, they are actively forcing teachers to engage in practices which are not only ineffective but actively harmful to child development and the learning process. I am absolutely willing to back up these statements with literature from the research base, but I doubt it will be asked for."
  • Science Daily with some educational research from Sweden, ""Most digital learning tools used in schools are unsatisfactory and only test the knowledge the pupils already have"..."However, digital learning tools can provide great educational benefits, as long as they do not become books on a screen, but use their digital advantages. This involves providing good feedback, showing that there are different ways of thinking to reach a goal, and presenting consequences that that cannot be demonstrated in a book," says Björn Sjödén."
  • A nice article in Quartz on Singapore teaching "productive failure" in math: "Students who are presented with unfamiliar concepts, asked to work through them, and then taught the solution significantly outperform those who are taught through formal instruction and problem-solving. The approach is both utterly intuitive—we learn from mistakes—and completely counter-intuitive: letting kids flail around with unfamiliar math concepts seems both inefficient and potentially damaging to their confidence..On procedural knowledge, or applying the formula, there was no difference between productive failure and direct instruction. But on conceptual understanding—understanding what it means and possessing the ability to adapt the information—the productive failure students dramatically outperform their direct instruction peers.."
  • The Baltimore Sun on Maryland's PARCC performance, "The first results of testing on the Partnership for Assessment of Readiness for College and Careers tests — introduced as part of sweeping educational changes begun several years ago — showed only 31 percent of students met the standard for Algebra I and 40 percent of students met the standard for 10th-grade English....Only a quarter of African-Americans, 7 percent of special education students and 23 percent of students who qualify for subsidized lunches met the benchmark in English. The worst performance was by students learning to speak English, many of them immigrants. Only 2.3 percent of those students were proficient."
  • The Atlantic with a nice article on the new changes to the SAT: "The college-admissions test is being restructured as an extension of the controversial public-school reading and writing standards.". With respect to the math section "The math test will consist of nearly 60 questions split between two sections, one that allows a calculator and one that doesn’t." but this passage sounds bad "“The current SAT asks questions where the material is remarkably simple, but students have to figure out what exactly they are asking for,”". What's wrong with harder math and more straightforward question?
  • NJ PARCC results were mentioned last post. But Newsworks reports there is a twist: "The proficiency rate for PARCC’s geometry test was only 24 percent. In Algebra II, the proficiency rate was 23 percent.....Under state law, students must pass the state’s exit exam to graduate. But under an improvised system put together by the administration for the first three years of the new testing, 12th-graders will have other options....When asked whether the state even has the capacity to handle an appeals process that may include tens of thousands of students, state Education Commissioner David Hespe said the necessary resources will be found: “We’re a big department; we’ll deploy whatever we need.”". Sounds like a big mess.
  • The Obama administration has changed its stance on testing in schools. Vox has this story "After seven years of trying to hold schools and teachers to higher standards — and testing to make sure they meet them — Obama said he's taken it too far. "When I look back on the great teachers who shaped my life, what I remember isn't the way they prepared me to take a standardized test," Obama said, saying he's concerned about "too much testing, and from teachers who feel so much pressure to teach to a test that it takes the joy out of teaching and learning."Beginning immediately, the Education Department is going to start directing states and districts to spend less time testing and to give fewer tests.". More details here, "They've promised to give grants to states to review the tests they're giving and determine which ones to cut. They plan to provide specific instructions on how states can use other federal money to study and cut tests..Most importantly, they're also backing down, at least slightly, on linking test scores to teachers' evaluations. ."


PEMDAS: notes


As I mentioned last post, I've been interacting with some middle school students. PEMDAS has been an important topic. I've put together some brief notes, shown above, that could form the basis of a lesson: warm up problems (which could then be the basis of discussion), teaching points, and then some more difficult problems involving PEMDAS, The solutions are at the end. The level of difficulty is more towards high school school students or an "honors" course at the middle school level. I've created a new  page called The Basics where you can download the PDF. I will post other introductory material there as needed. The Basics link is located on the sidebar, too.

Here are some stories that caught my eye this week:

  • Zero Hedge has commentary on a provocative piece in the The Economist magazine: "MICHAEL WANG, a young Californian, came second in his class of 1,002 students; his ACT score was 36, the maximum possible; he sang at Barack Obama’s inauguration; he got third place in a national piano contest; he was in the top 150 of a national maths competition; he was in several national debating-competition finals. But when it came to his university application he faced a serious disappointment for the first time in his glittering career. He was rejected by six of the seven Ivy League colleges to which he applied.". The article has the nice quote from, "...Supreme Court Chief Justice Roberts on this subject: “The way to stop discrimination on the basis of race is to stop discrimination on the basis of race.”". So true; but as private institutions they can do what they want. They are, however, undermining the prestige of their school. The loss of confidence in quality, combined with the cost of a US college education doesn't bode well for the future of US college education.
  • Payson Roundup wants to know why math scores of Arizona students have "plunged". According to the article, "Arizona students are worse in math than students in 33 other states according to data provided by the Nations Report Card. Arizona is not the only state that is struggling with proficiency in mathematics; the entire United States has poor mathematic proficiency scores. The National Assessment of Educational Process found that 7 out of 10 students in the U.S. scored at or above basic level in mathematics in 2013."
  • Huffington Post's Peter Greene delivers a verbal smack-down to a nonsensical Politico article. Nice job Mr. Greene!
  • The Atlantic has a piece on "The Anti-Free Speech Movement at UCLA". From the beginning of the article, "A half-century ago, student activists at the University of California clashed with administrators during the Berkeley Free Speech Movement, a series of events that would greatly expand free-speech rights of people at public colleges and universities.Today, activists at UCLA are demanding that administrators punish some of their fellow students for expressive behavior that is clearly protected by the First Amendment.". The article dishes out some blame, too: " The San Francisco Chronicle put it this way: “Regent Dick Blum said his wife, U.S. Sen. Dianne Feinstein, D-Calif., ‘is prepared to be critical of this university’ unless UC not only tackles anti-Jewish bigotry but also makes clear that perpetrators will be punished.” The lawyer Ken White wrote that “Blum threatened that his wife … would interfere and make trouble if the Regents didn’t commit to punish people for prohibited speech.”"
  • Listverse has "10 Things You Probably Didn't Know about Albert Einstein". What do you know about the Einstein refrigerator?
  • California has banned schools from using "Redskins" as a team name or mascot beginning Jan 1, 2017. "The new law will affect four California high schools in Merced, Calaveras, Tulare and Madera counties.". Does this mean they condone the "fighting Irish"? Perhaps that's the next lawsuit. Curiously enough, Governor Jerry Brown "...vetoed a separate measure that would have barred public properties from being named after individuals associated with the Confederacy."
  • Edsource has an article on poor California test scores, "In fact, only one-third of California students in grades 3-8 and grade 11 met the math standard – compared to 44 percent of students who met the standard in English language arts.". Did you get that? Failure is "the norm". Always remember that the test scores would be lower if it weren't for the many students who get a tutor to help them learn. And take a look at all the it's-no-big-deal talk and Common Core challenges talk. With respect to Common Core: "“Los Angeles started implementing Common Core three years ago,” Dorado said. “It takes time and a tremendous amount of work. In LAUSD, we’re talking 500 elementary schools alone.”Another challenge has been the shortage and quality of curriculum materials aligned with the standards. “Many teachers are in the implementation phase,” said the California Mathematics Council’s Vierra. “Many districts are still getting around to buying the curriculum (materials they need).”“A lot of teachers are cobbling together old materials with lessons they find online and material the district is providing,” she said. “Much of the math curriculum is still very fragmented.”". That's similar to my experience--despite knowing years in advance what was coming the school systems are still behind the curve years after Common Core was "implemented".