My confusion over the way to implement graphs in LaTeX prompted an earlier post where I started a Graph Theory, Sage, and LaTeX page. The first post suggested the Normal style for creating a basic graph: it's quick, clean and saves on printer ink. But using tkz-graph and tkz-berge you gives you a lot more control, if you need it. The two packages have enough differences in their approach that I thought a page of templates to serve as a starting point would be useful for me. Graph theory and discrete math, unfortunately, don't have much place in the educational curriculum so I've gone a little bit lighter on the details.
As you can see from the screenshot above we can change various aspects of the graph: the vertex color, the text color in the vertex, the color and thickness of the edges and even add labels. You can download the template and experiment with the code yourself.
Here are some stories that caught my eye over the last week:
- Start with the Detroit teacher strike. Detroit is a poster child for what's wrong with public education. EAGnews has the coverage, "Detroit Federation of Teachers members ditched their students to protest about pay today, despite data that shows they’ve been ineffective at improving the district’s worst-in-the-nation student academic performance....The combined results for students of all grades tested last spring shows a mere 2.9 percent met basic proficiency standards for science, 7.9 percent reached that threshold for math, 8.1 were proficient in Social Studies, and 14.6 met standards in English Language Arts." It's difficult to argue that teachers are professionals when their results are this bad.
- KOTAnews reports that Wyoming is dropping out of common core. Red Alert News claims that North Dakota is the 9th state to reject Common Core. The Salt Lake Tribune says "On Wednesday afternoon, Republican gubernatorial candidate Jonathan Johnson called for the end of SAGE testing in Utah schools.Not to be outdone, Gov. Gary Herbert issued his own call hours later, urging the state school board to abandon both SAGE and Utah's statewide education standards for math and English."Today I am asking the State Board of Education to consider implementing uniquely Utah standards," Herbert said in a letter to the board, "moving beyond the Common Core to a system that is tailored specifically to the needs of our state."".
- Be careful about doing math in a public place, especially if you seem like a foreigner. SOTT.net on "A woman sitting next to an Ivy League economist told flight crew she had security concerns about the man, after seeing him write in a foreign script. It turned out to be a differential equation.". How stupid have are we?!?
- The Washington Post has a fascinating article on "Education activists are increasingly becoming concerned about the computer grading of written portions of new Common Core tests....The standard PARCC contract indicates that this year, Pearson would score two-thirds of the students’ writing responses by computers, with only 10 percent of these rechecked by a human being. In 2017, the contract said, all of PARCC writing samples were to be scored by machine with only 10 percent rechecked by hand...This policy appears to contradict the assurances on the PARCC scoring FAQ page that says,“Writing responses and some mathematics answers that require students to explain their process or their reasoning will be scored by trained people in the first years.”...The Pearson and AIR contracts also promised studies showing the reliability of computer scoring. ...According to Les Perelman, retired director of a writing program at MIT and an expert on computer scoring, the PARCC/Pearson study is particularly suspect because its principal authors were the lead developers for the ETS and Pearson scoring programs. Perelman said: “It is a case of the foxes guarding the hen house. The people conducting the study have a powerful financial interest in showing that computers can grade papers.”....Indeed, research shows it is easy to game by writing nonsensical long essays with abstruse vocabulary......Unable to analyze meaning, narrative, or argument, computer scoring instead relies on length, grammar, and arcane vocabulary to do assess prose....On April 5, 2016, the same day we sent the letter, Rhode Island Education Commissioner Ken Wagner ...claimed that “the research indicates that the technology can score extended student responses with as much reliability- if not more reliability- than expert trained teacher scores …..”". In an educational system that creates a pathetically weak "standard" of teacher certification that has little to do with quality resulting in most students being unprepared for college even though graduation rates are rising, computer scoring makes perfect sense. Design an algorithm that can be programmed to deliver whatever percentage of good scores you want. It's not really about education, it's who gets the dollars and how to deliver product for as little money as possible.
- It's not really math, so perhaps we shouldn't be too surprised how badly statistics is doing in predicting the elections. ZeroHedge reports, "How poor have the election forecasters been this year? It is a topic many are discussing given the large number of upsets we've had during the Primaries. For example, statistician Nate Silver (who started the campaign season proclaiming Trump had <2% chance of being nominated) by March 1 predicted with 94% probability that Trump would win Alaska (he lost). Silver then predicted on March 8 with >99% probability that Clinton would win Michigan (she lost). Silver again predicted on May 3 with 90% probability that Clinton would win Indiana (she lost). But there is another issue besides being wrong, which is how much model flip-flopping is occurring just up to these elections. The most proximate example is Silver stating this past Sunday that Cruz had a 65% chance to win Indiana; the next day (Monday, the eve of the election) and with little new data, he "adjusts" that to Trump having a 69% chance to win! That's horrible! ". Low level math has you churn out answers supported by work for people to check. In statistics you show your data (which may have been massaged or manipulated) and argue your case. The essence of math is proof, and the nontheoretical statistics we encounter most every day has a high BS content. Statisticians like to claim how good it is "...if it's done right", meaning their way. But when the integrity of the data itself isn't open for inspection, statistics is open to widespread abuse in a way that math can't be.
- The Hechinger Report addresses the high math failure rates at universities. "A few years ago, administrators at San Diego State noticed high “D-F-W” (grades D and F, and withdraw) rates — 35 to 50 percent — for math courses, according to Michael O’Sullivan, chair of the math and statistics department. In 2014, the newly elected O’Sullivan, along with frustrated faculty, decided to overhaul the program. ....The changes at San Diego State and in other colleges’ math classes are similar to components of the Common Core Standards for Mathematical Practice...As of this year, San Diego State has implemented all seven pieces, said Michael O’Sullivan. It is too soon to know long-term results, of course, but for now the professors are happy that this semester’s Calculus II midterm grades increased by five to eight percent compared to previous years, according to Ricardo Carretero, professor of applied mathematics."
- Your funny money is no good here. ABC13 reports, "Now 14, Daneisha was hoping to eat that day's lunch of chicken tenders with her classmates using a $2 bill given to her by her grandmother when she was stopped by the long arm of the law. "I went to the lunch line and they said my $2 bill was fake," Danesiah told Ted Oberg Investigates. "They gave it to the police. Then they sent me to the police office. A police officer said I could be in big trouble."Not just big trouble. Third-degree felony trouble. And that's just one of eight counterfeiting charges investigated against high- and middle-school students at Fort Bend ISD since the 2013-2014 school year....Then the Fort Bend ISD police investigated the $2 bill with the vigor of an episode of Dragnet, even though at that school 82-percent of kids are poor enough to get free or reduced price lunch.The alleged theft of $2 worth of chicken tenders led a campus officer...to the convenience store that gave grandma the $2 bill...... The $2 bill wasn't a fake at all. It was real....The bill so old, dating back to 1953, the school's counterfeit pen didn't work on it...."He brought me my two dollar bill back," Joseph said. He didn't apologize. He should have and the school should have because they pulled Danesiah out of lunch and she didn't eat lunch that day because they took her money.""