Handouts: Integral Table


I've added a Table of Integrals, a PDF and the tex file that created it, to the Handouts page. This will let you customize the integrals to the ones most appropriate for your class.

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

  • Remember the big decline in SAT scores I posted not that long ago? The American Enterprise Institute has reported that a more comprehensive breakdown has been completed, "But the story was incomplete, because the College Board had embargoed the breakdown of scores by ethnicity until a few days ago. Now they can be published. Here are the 10-year changes in test scores by ethnicity:" Check out the chart of performance, in words, "The new text should point out that the white change was small, just an aggregate of 6 points. That black scores fell by an aggregate 14 points is troubling because their scores in 2006 were already lower than those of any other ethnic group. That the scores of Latinos and American Indians fell by 26 and 28 points is even more troubling. But how about those Asians! Their aggregate mean score rose by 54 points.". So it looks like the news isn't all bad. Whose the courageous soul who wants to explain the differences in perforamnace?
  • I mentioned here that one third of high school math teachers didn't have a degree in mathematics. That was based on 2007-2008 data. AllGov.com reports that with more updated data (2011-2012), "Almost half of high school students are learning history from a teacher without a degree in the subject.". A link on the page sends you to Humanities Indicators website which has data on other subjects, including math. There is a nice chart to help you make sense of the data. Math is roughly the same.
  • ScienceNews reports that Terry Tao has solved an old outstanding math problem that had a $500 bounty from the late Paul Erdos. The site only gives nonmembers the first few paragraphs of the article. Nature.com has the details and RJ Lipton's blog has more of the mathematics behind the story.
  • The Boston Globe reports "State education officials withheld MCAS math results from Boston’s English High School as they released statewide scores Thursday, citing irregularities that require examination....The score suppression came as a surprise to Boston school officials, who learned of it a short time before the state provided MCAS data to media outlets. Boston Superintendent Tommy Chang said the state did not tell him why the scores were withheld,...". Scores withheld for no reason? I hope that poor scores aren't the explanation.
  • The Daily Caller reports, "The state of New York looks to be the next state with plans to re-brand the Common Core by calling it something else but otherwise making virtually no substantive curriculum changes." I wonder how much tax money that will cost.
  • Business Insider does a follow up to the 100 million contribution to Newark schools made by Mark Zucherberg some 5 years ago, "One of the major miscommunications about how his money would be spent had to do with teacher contracts. Zuckerberg wanted to be able to create more flexibility in teacher contracts to reward high-performing teachers and be able to fire teachers with poor records of student achievement. But those types of protections are determined by New Jersey State law, and Zuckerberg couldn't simply come in and change the rules without going through the state legislature to make the changes......Zuckerberg envisioned the teacher contract reform to be a centerpiece of the reform and had intended for half of his $100 million donation to go to working on that cause.But instead, the opposite occurred. Chris Cerf, the New Jersey commissioner of education at the time, worked with the legislature and was able to negotiate some new accountability measures in teacher contracts. But the teachers' union only agreed upon those measures if the seniority protections remained intact.". I was recently pointed to a more thorough examination that I had missed by the NYTimes given here.  It's a veritable case study in how the layers of educational bureaucracy eat up most of the money--a fundamental reason (plus lack of accountability) that is the albatross around the neck of public education: "Their five-year plan gets off to a rocky start. Initial funds go to a bevy of consultants, most of them white, most of them well connected, some of whom are getting paid $1,000 a day...Moreover, it quickly becomes apparent that this is a top-down effort, with politicians and the well-to-do setting the agenda. When Booker sets up a local foundation to handle Zuckerberg’s gift, the seats on the board go only to donors of at least $5 million.....And Zuckerberg, a newcomer to philanthropy, seems frustrated by the inability to negotiate a union contract that would quickly raise the salaries of promising young teachers and pay substantial merit bonuses for high performers.....What ultimately derails this grand experiment is the unwillingness of the reformers to include parents and teachers in shaping the reforms.". Another piece from the NY Times says,"Almost half of Zuckerberg’s grant was spent (or committed) to help gain new labor contracts; out of the $200 million in his money and the matching grant, a full $21 million went to buying out unwanted teachers and other staff members, for instance. Yet Zuckerberg didn’t realize until too late that New Jersey state law — not teacher contracts — imposed the seniority system he was trying to get rid of....The district schools get $19,650 per pupil, but only $9,604 trickles down to the schools. Money that the charter school is spending on extra support is being soaked up by the bloated bureaucracy in the public school system. It is a devastating fact.".  Some excellent articles by the NY TImes. Mark Zuckerberg got an expensive lesson in how those managing the education of public school are enriching themselves first at the expense of the kids they oversee. It's difficult to reform public education  with such a huge structural obstacle to real change.
  • OregonLive informs us test scores are"Sky-high in writing, ultra low in math". And notice "Oregon and other states are mapping passing scores on their old exams to those new tests; Washington is the only other state that has completed the process.". That's a fancy way of saying that to compensate for more difficult tests, you lower passing scores--then schools can talk about tougher standards, even if they lower their performance. "Policymakers said they would determine which Smarter Balanced scores were equivalent to passing marks on the old state graduation exams and use those. Oregon's new graduation requirement in math is merely to score the lowest possible "Level 2" Smarter Balanced score, a basic skills level that is far from the "college-ready" performance standard agreed to by experts in 17 states, the state board decided.". The Bulletin explains, "What the board was doing was setting the closest match between Oregon’s old tests and the new exams. According to Oregon’s rules, the state can’t just bump up the standards for graduation without giving students some time to prepare. The rules say students have to be told by the end of eighth grade if they can expect to face tougher standards. That makes sense on some levels. But think about what it means. It means Oregon has not aimed at a high school diploma that means college ready in math or reading.". So when do newer standards come into effect?
  • The Seattle teachers' strike is over and NYC Educator is impressed by how well Seattle teachers gained.

Negative Times Negative is Positive

PropRealMost teachers I've talked to seem to hate having to talk about the Properties of Real Numbers. And while it's not the most interesting topic, it's a natural and I'd say essential time to expose your class to some simple proofs and learn something along the way. I think it's fair to say that most students (and even teachers) would have trouble explaining where "negative times negative is positive" comes from, so why not take the opportunity to give your class more exposure to proofs and take away one of those mysteries? I've put together a proof, shown above. You can find it on the Handouts page. EDIT (9/21/15): Fixed various typos and problems with the explanation. If you downloaded early, please make sure you've got the current version.

Here are some items that caught my eye last week:

  • Who hasn't heard about the 14 year old Texas high school student who got into trouble for building a clock that looked like a bomb? ZeroHedge, TruthDig, and The Intercept have their interpretation with Glen Greenwald delivering the most scathing indictment, "The behavior here is nothing short of demented. And it’s easy to mock, which in turn has the effect of belittling it and casting it as some sort of bizarre aberration. But it’s not that. It’s the opposite of aberrational. It’s the natural, inevitable byproduct of the culture of fear and demonization that has festered and been continuously inflamed for many years. The circumstances that led to this are systemic and cultural, not aberrational."
  • Reason.com reports on a high school student in Virginia suspended for one year for having a Japanese maple leaf and lighter, "Writes Dan Casey in the Roanoke (Va.) Times: An assistant principal finds a leaf and a lighter in the boy’s knapsack. The student is suspended for a year. A sheriff’s deputy files marijuana possession charges in juvenile court....There was only one problem: Months after the fact, the couple learned the substance wasn’t marijuana. A prosecutor dropped the juvenile court charge because the leaf had field-tested negative three times...."
  • Harvard University shows us that intelligent people can still make stupid policy. From RT.com, "The ubiquitous pronouns “he” and “she” are gaining some pals at Harvard University. During registration, students can now opt to be referred to by a whole host of gender-neutral pronouns, including “ze, hir, and hirs” or “they, them, theirs.” The Ivy League school in Cambridge, Massachusetts joins American University, the University of Vermont and the University of Wisconsin-Milwaukee in allowing students to select their own gender pronouns....The school is planning to train professors on how to look up students’ preferred pronouns. So far, 4,000 students have submitted pronouns, with just over 1 percent choosing something other than“he” or “she,” Burke told AP.". You can almost see this story developing in the future: Teacher fails to use the correct gender pronoun in addressing a student--said student feels embarrassment, shame, and emotional turmoil so teacher is disciplines/fired. Stay tuned!
  • John W. Whitehead of the Rutherford Institute has another collection of facts and stories to leave your head spinning. "By the time the average young person in America finishes their public school education, nearly one out of every three of them will have been arrested.More than 3 million students are suspended or expelled from schools every year, often for minor misbehavior, such as “disruptive behavior” or “insubordination.” Black students are three times more likely than white students to face suspension and expulsion."
  • Reason.com with a story on the Obama administrations failed plan to rank colleges. "A big part of the plan—the biggest, really, and possibly the most interesting and certainly the most contentious—was Obama's promise to rank schools into various categories based on whether or not they deliver to students....So the site is finally up and...doesn't have the rankings....Critics, including many of the presidents at elite private colleges, lobbied furiously against the idea of a government rating system, saying it could force schools to prioritize money-making majors like accounting over those like English, history or philosophy."
  • LewRockwell.com looks the "Attack on Teachers". Walter E. Williams writes, "Nationally, an average of 1,175 teachers and staff were physically attacked each day of the 2011-12 school year." Check out the video of the horrifying, "325-pound high-school student in Houston [who] knocked out his 66-year-old female teacher".
  • Common Core test results have been coming in, and they don't look good. WBEZ in Illinois reports, "In high school, just 31 percent of students met or exceeded expectations in English. For math, the percentage meeting expectations was 17 percent, with zero percent exceeding those standards." while Oregonlive.com says, "....at best, two-thirds of Oregon students read and write well enough to be on track for college or a good job and just 40 percent cut it in math." and NPQ says, about California results, "Taken on their face, the results are disturbing. Looked at more closely, they challenge the prevailing wisdom about how to improve our public educational systems." and then quotes the San Jose Mercury News: "In math, scores were lower and the gaps wider: 69 percent of Asians, 49 percent of whites, 21 percent of Latinos and 16 percent of African-Americans met or exceeded standards. Among students from low-income families, scores also lagged. Only 31 percent met or exceeded standards in English, and 21 percent did so in math." and state education officials suggested we wait several years to draw conclusions (do you think they would have if the results were good?).
  • CNN Style has an article "Next da Vinci? Math genius using formulas to create fantastical works of art"
  • Newson6.com, an Oklahoma news channel, reports "For the third year in a row, Oklahoma will not give a standardized writing test next spring that counts toward a student’s score or a school’s letter grade. That means the state is paying a vendor at least tens of thousands of dollars for a test that yields no results....The state also could forego an official writing test in spring 2017 because the spring 2016 field test will be based on current academic standards due to be replaced. Another field test based on new standards may need to be done in 2017 before offering a valid writing test in 2018. The repeated suspensions of a gradable writing test have raised questions among some lawmakers about whether the Education Department is violating state law.". Beyond the waste of money and lack of accountability notice the reference to the replacement of academic standards. That's a common theme to the education dance over time: call attention to the poor state of education, spend years of planning and lots of dollars on education professionals to improve it. Botch the implementation, see no meaningful results, and then look for the next replacement. It's (roughly) a 5 year cycle. The article blames the rubric for much of the problems, "The rubric also failed to properly guide evaluation of the original content written by students. After invalidating the 2014 scores, Barresi said she directed staff to make a new rubric for 2015. The person tasked with creating that rubric was fired by Hofmeister when her administration took over in January 2015, and the new rubric was never finished. Fitzgerald, who worked under both Hofmeister and Barresi, said she was unaware of plans to create a new rubric.". Read the full article to get a better idea of the broken public education system in Oklahoma.


Indefinite Integrals 7


I've added another problem to the Sagetex Integrals page. The new problem has the student evaluate an integral by rewriting it using partial fractions.

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

  • ZeroHedge reports on the dire condition of Chicago schools. "The fallout from the budget crisis is far-reaching in the state with the latest example being Chicago’s public school system (the third-largest in the country), which opened this week with a budget shortfall of nearly a half billion dollars...The school board warns of deep cuts later this year if Illinois, which faces its own fiscal crisis, doesn’t deliver an additional $480 million in the coming months, representing roughly 8% of annual district spending...Which means asking the ineffectual state legislature for $480 million, but thanks to gridlock in Springfield, there are no assurances that aid is forthcoming and that, in turn, means that once it's all said and done, the third largest school system in the country will be forced to layoff thousands and implement what amounts to a partial shutdown. "
  • Texample.net has posted an additional 12 problems to its site.
  • Slate.com with some interesting teacher interviews on how Common Core changed their jobs.
  • TheStranger.com couldn't have a stranger post. Parent sacrifices to send their child to private school to get a better education, gets the education that they couldn't have in a public school and then concludes that private schools are not the answer. Here's the beginning, "Some years ago, I learned that my son, 13 at the time, didn't know basic algebra. He was attending a public school in North Seattle. He is black, his classroom was stuffed with students, and his teacher had a vague idea of who he was. His parents decided to send him to a private school. In a year, his grasp of mathematics was normalized. And five years later, he was able to master Mathematical Applications for the Management, Life, and Social Sciences. And I'm certain if he had remained in the public school system, this meaty book would have been Greek to him. But despite the sacrifice my family made (we are not rich), I still think it's wrong to send children to private schools. It's a very desperate solution that, as a whole, worsens a very bad situation.". HUH?
  • ABC7news reports, "Less than half of all California students passed new math and English tests aligned with the Common Core standards...Forty-four percent of students in third through eighth and 11th grades met or exceeded the new language-arts assessment, while 34 percent passed the math test."
  • The Daily Signal has the story of the week. There's a teacher strike in Seattle, WA and we're told, "53,000: Number of students in Seattle who did not go back to school on Wednesday as public school teachers voted to strike. This comes after failed negotiations between the Seattle Educators Association and the Seattle School Board...Teachers have a variety of demands, including, among other things, “professional” pay and “educator work relief.” Seattle teachers’ median pay is $60,400, not including benefits, exceeding Seattle’s median income of $43,200..The union wants a nearly 17-percent pay increase for teachers, to compensate for the district’s proposal to add 30 minutes to the school day.Remember that median pay, which is close to 50% more than the parents they work for is earned over the school year. I wonder how the parents feel about teachers needing more money and "educator work relief".  Later in the same article you've got another little known statistic: "90 Percent: The percent of college freshman who do not pay full price for tuition... Which raises the question: if students aren’t paying for tuition, who is? The Obama administration’s continual efforts to make student loan forgiveness more generous leaves taxpayers on the hook for a significant slice of outstanding student loan debt—estimated at around $1.12 trillion. The massive amount of student loan subsidies in today’s economy has undoubtedly distorted the market, and high debt levels have kept many of today’s young people from achieving the American dream." ZeroHedge readers know this is a big problem going forward; see, for example, here or here.
  • Remember that Common Core was supposed to raise the bar on performance? And remember that "...standards and the standardized testing that goes along with them are more difficult than students in most states have confronted."? At least that was the claim before Common Core became a 4 letter word and supporters dialed it back by claiming that Common Core was only a set of guidelines-and it makes no sense to criticize standarts. As the article link above mentions, NY test scores plummeted 30 percent and Arne Duncan made his famous comments about "soccer moms". So I was a little surprised to see the NY Post with "While Mayor de Blasio trumpeted increases in this year’s Common Core test scores, state officials did not reveal that they lowered the number of right answers needed to pass almost half of the exams.In the third year of the tough exams, the state Education Department again tweaked the “cut scores.”"...The mayor held a press conference last month to hail the scores. Overall, 30.4 percent of kids passed English, up from 28.4 percent last year. Those rated proficient in math rose to 35.2 percent, up from 34.2 percent last year...But the manipulations make the results murky.“It makes me question the reliability and validity of the results,” said Fred Smith, a former testing analyst for city schools....State education officials did not answer questions raised by The Post, but last year admitted cut scores were lowered on six of the 12 exams....The state has a history of inflating scores. Between 2006 and 2009, officials reduced the number of raw points students needed to pass exams.Former Mayor Mike Bloomberg also cited the rising scores as proof of great progress. When the tinkering was exposed, the state insisted the cut scores had to be lowered because the questions had gotten harder, but a commissioned study later found them easier." .  When education is public, there is a vested interest for government officials to fiddle with the results. That prevents problems from being addressed and people being held accountable for the results--in fact, in this case, they're trying to get praise for poor results. It's not surprising that results have been miserable for decades and won't get better. Make education private and school officials don't have the power to fiddle with the numbers.

Lucas Chess


Recently, I found myself in need of software to modify PDFs. Luckily, I remembered that Portable Apps had a program that worked, thanks to WINE, and after solving my problem I spent some time looking at the newer software. Lucas Chess caught my eye, and I gave it a try: it's a great tool for those learning chess--better, I would say, than Fritz and free. Some of the tools are explained on the website:

  • Training positions
  • Play like a grandmaster
  • Find best move
  • Learn openings by repetition
  • Training with a book
  • Your daily test
  • Resistance Test
  • Determine your calculating power

And more! But before you get started, you need a board you're comfortable with. Lucas Chess offers a lot of possible settings:


The ability to control the colors of the board, borders, and arrows is comprehensive. And you have a lot of choices for pieces, too. Heck, you even get a lot of choices for chess engines--take a look.


But wait! There's more. You get control over the depth of search, so you can dumb the engine down to your level as needed and get a speedy computer reply. The chess tutor watching your play gives frequent input, especially when your move isn't quite good enough and then you're given several possible continuations (in one case I had 11 alternate moves suggested) that you can accept or reject-that's shown in the first picture of the post. When you're done, you can get the computer to analyze your game and create some graphics and stats to describe the game. Here's the computer analyzing a game; note the bar in the upper right hand corner.


Of course, no trainer would be complete without some "Mate in ---" puzzles. Here's an easy "MATE IN 4" problem I'll leave you with. The answer to the problem is at the bottom of the post.



I tested Lucas Chess Portable from Portable Apps; my only complaint would be the default fonts were not particularly clear.

Here are some stories that caught my eye this week.

  • Reason.com posts on the underhanded tactics by Michigan teachers' union to keep teachers in the union. "Are you a Michigan public teacher who wants to leave your union? Sorry, you’re too late. Michigan is a Right-to-Work state, and teachers have the right to opt-out of their union—but only if they do so during the month of August, and only if they manage to find the top secret post office box that accepts union resignations, according to the Michigan Education Association."
  • Michael Krieger's"Liberty Blitzkrieg" has a piece "South Dakota Makes Teaching Early American History Optional for High School Students". Which educational expert person decided on this?
  • The big news for the week is the decline in SAT scores.  IJReview has a report and video on the 5 year decline in SAT scores: "Without knowing for sure what’s at the root of the decline, it’s difficult to know how to change the results.". I had to follow the link to TIME magazine to read the expert quote, "“I worry when I see headlines about score declines, when you could just as easily say it shows increases in SAT and ACT participation, and that is good news,” said Andrew Ho, a professor at Harvard’s Graduate School of Education, who is an expert on testing and accountability in education.". "Could" is such a nice weasel word that "experts" like to use. I "could" become the next MMA sensation but don't count on that ever coming true. It's not clear from his quote whether he thinks what "could" be true is likely. So rising and declining test scores get spun as good news by experts. Bloomberg News has a more realistic assessment even if they aren't "experts"--and they have some charts to illustrate it. From the article, "The mean score on the math portion of the SAT, 511, is the lowest since 1999. The highest possible score on each section is 800. The reading score of 495 is the worst since 1972, according to data provided by the College Board. The test administrator reported the lowest score for the SAT's writing section since it began in 2005...ACT Inc. also delivered gloomy news about the preparedness of the next generation of college students. The company measured how many students were ready for college based on their scores on the ACT this year......More than 30 percent of this year's graduating test takers scored below that threshold in the math, science, reading, and English sections of the ACT, suggesting that they would have a tough time excelling in a wide range of college classes.". A good time to remember this post where Michael Snyder has some sobering statistics. It doesn't seem like that Harvard "expert" on testing and accountability even sees a  problem.
  • US News has the run-down on problems with incomplete data from Common Core testing.
  • Washington Post with a look at theory and practice for Common Core. "Teachers are often assigning work that asks far less of students than the Common Core standards require, according to the organization. Children are rarely asked to write more than a few sentences at a time, for example, and are seldom asked to grapple with complex ideas and arguments.Those conclusions are based upon an analysis of more than 1,500 language arts, humanities and social studies assignments that teachers gave middle-school students in two unnamed urban school districts during a two-week period last school year."
  • The Tifton Gazette reports that Georgia has a Common Core proficiency rate of under 40%.


ANSWER: 1. Qxf6+ Rg7 (Qg7 2. Qh4#) 2. e7 Qxe7 3. Rxe7 with mate by Qxg7 or Qh4.