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
- 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.