Saturday, January 25, 2014

Comets #hashtag

Comets are pretty amazing. On Friday in ED512, we had a brief review of the physics of motion while examining graphic organizers. The amount of kinetic energy in an object is one half the mass times the square of the velocity. While watching the Science Channel this afternoon, I learned that a comet can travel up to 1,000,000 miles per hour and be miles across. So, I picked a three mile diameter comet, converted into SI units and did the math (assumed that the comet has the density of water-ish). The kinetic energy of the quickly moving comet that I just described would have a kinetic energy of 5.89E24 joules. It's 5,890,000,000,000,000,000,000,000 joules. That is a lot. It's about 1,000 times the energy contain in all the natural gas in the world (not all the natural gas used this year, but all the natural gas reserves currently waiting to be extracted).

That got me thinking about the weird comparisons that we make. If something is long, we say that is the length of X football fields. If it's really long, we say it is the length of Y Empire State Buildings, laid on their side. When it's astronomically long, it could wrap around the Earth X times or to the Moon Y times. The volume of something large is measured in multiples of Olympic swimming pools (or fill up a bunch of football stadiums). We use strange units of measurement.

Wednesday, January 22, 2014

Baby, it's cold outside #hashtag

Students were complaining about how cold it was today. They were right. I checked the Weather Channel during break. It was twenty degrees colder in Walled Lake than in Siberia. Someone could get sent to the gulag and it would warm them up (both the slave labor and the outdoor temperature).

In case you are wondering, there is a 14 hour time difference between Michigan and Siberia. It was just after sunrise in Michigan, which according to the internet, is the coldest portion of the day. Meanwhile, it was well after dark in Siberia (the colder portion of the day, but not necessarily the coldest).

Monday, January 20, 2014

Tiering it up (ED510)

For our Geometry class, we implement a novel form of tiering most days of the week. Our Geometry class is a somewhat flipped classroom. Students watch videos introducing them to new material during the evening. They use a set of guided notes to help them keep track of the new material. On the day following in class, they begin with a diagnostic quiz. The quiz covered four or five problems from the previous section. Students have 15-20 minutes to work on the quiz.

When students are done working on the quiz, or after a given amount of time, we will go over the problems as a group. After going over the problems as a class, students give themselves a score for the test by totaling up the points from each problem that they correctly answered. The point totals correspond to three groups of problems that students work on in the classroom. Students who get none of the problems right would assign themselves to Group A; a student who got all the problems right would assign herself to Group C. Students are encouraged to evaluate their own level of understanding (ahem, metacognition). If a student if confident about his or her understanding of the material, the student is encouraged to ignore the numerical score on the diagnostic quiz and join the group that he or she thinks is most appropriate.

Here is one example selection of homework:Group A: Page 353-354 #16-17, 22-28, 29, 30-31Group B: Page 353-354 #22-27, 29, 31-35Group C: Page 353-354 #22-25, 29-31, 38-42, 51

While at first, it looks like a random sequence of numbers, there is a pattern. Students in Group A focus their attention on definitions and basic calculations.
Take a look at problems 16 and 17: 
There are still some problems that all students are expected to complete. Problem #29 requires students to evaluate two examples of student work. All students are expected to work on this problem; it shows up in each problem set.
Problem 51, on the other hand, only shows up in Group C’s problem set. It's a bit challenging.


How does tiering work in practice?

Creating the differentiated problem sets is relatively easy. There is a host of available resources that help select problems. The district has a unit planning guide which lays out the standards to be covered from each section of the textbook. The textbook maker provides sample problem sets depending on the desired difficulty. Designing the problem set is just a matter of aggregating information from three or four different resources. It takes time to look over the problems, but it’s doable. A satisfactory solution exists.

The problem is getting students into the right group. Creating differentiated tasks is comparatively simple. While all students pick up the diagnostic quiz when they walk into the room, the actual engagement in the task varies from hour-to-hour and day-to-day. On some days, I would say only half the students attempt the problems before we start going over with as a class. After the quiz, I am not entirely sure that all students engage in a metacognitive conversation and evaluate their knowledge. I think that some of them just work with their group of friends (SHOCKING). Also, I know of at least one student who just counts up the number of problems, ignoring the potential differences in difficulty, and does the problem set with the fewer number of problems.

Another challenge to tiering is that tiering is not a word, at least according to the MS Word dictionary.

Sunday, January 19, 2014

Dalmatians #hashtag

This is the 101st blog post of mine. It has been a while since I posted anything related to puppies. Here are few other scattered thoughts...

From Star Trek:
Amanda: Spock, does the good of the many outweigh the good of the one? Spock: I would accept that as an axiom. Amanda: Then you stand here alive because of a mistake made by your flawed, feeling, human friends. They have sacrificed their futures because they believed that the good of the one - you - was more important to them. Spock: Humans make illogical decisions. Amanda: They do, indeed. 
Someday, I need to watch all of the Star Trek movies. With the exception of the latest movie ('Into Darkness"), I have seen pieces of all the movies. The line about the good of the many shows through the original series of movies. I wonder if, as movies get better special effects, if we settle for worse stories. That is not to say that the plots to the original Star Trek movies were solid. I am just not sure that the word "axiom" or discussion about the value of individuals would seep into most movies in the theatres nowadays. I wonder if my students have ever seen a movie that was thought provoking.

My freshman are learning about ATP in biology class. ATP is how the body stores energy in its cells. It consists of a molecule of adenine connected to a molecule of ribose with three phosphate molecules attached somewhere along the time. I was really proud of myself for remembering most of that from my high school biology class.

We learned about Doceri this week. For the first time in my life, I am seriously considering buying an iPad. The guy in Russia who regularly reads my website knows how much I love whiteboards. Doceri might actually be better than a whiteboard. There is not as much writing space as a wall full of whiteboards; I can only have so much information on the screen at one time. However, with the ability to zoom and record, there is an almost unlimited writing space in Doceri if students choose to review the material later on.

The more that I am in the classroom, the more I grow to hate the Doc-Cam/Projector combination. It's hard to keep track of what is actually showing up on the screen ("Can you zoom out?", "Can you move it over to the right?"). You can only fit about half a page on the screen. It's hard to get students to come up and use the doc-cam. I looked into getting a wireless Doc-Cam. However, for the price of a wireless document camera, I could buy an Ipad 2 and a nice laptop or PC (or almost a Mac Mini) and use Doceri and get a much better experience (along with all sorts of functionality when doing something aside from presentations).

Star Trek, ATP, Doceri. Oh yeah, and I wrote about puppies and used a properly placed semi-colon. That is pretty scattered. It's time to go do homework. G'night all. Happy MLK Day tomorrow.

Saturday, January 18, 2014

Why kids don't graduate college #hashtag

I read this article from the Fiscal Times. It's not the most credible source, but it was interesting to consider the reasons behind students failing to graduate from college.

One of the reasons that students fail to graduate from college, in four years, is that they start off behind. They spend their first year of college taking remedial classes which do not count towards graduation. This is something that I hope to prevent (that's my job from here on out).

Another reason that students do not graduate in four years is that they are balancing a work and school schedule. I am of two minds on this. On the one hand, working during college is great, it helps reduce the debt load carried by students. On the other hand, working during college probably isn't worthwhile. In the long run, it probably costs students money.

I did this calculation a few years back. For almost all students, it does not make sense to have a summer job. They would have saved money, just by looking at the tuition spent, by taking more classes at the community college instead of working for the summer (this is assuming students move 'home' for the summer). As an upperclassman, it makes sense to take summer classes, too. The average starting salary for a college graduate is around $44,000. So, graduating a year early has the potential to be worth $44,000 (at least). It's risky, but for most students, it would probably make sense to rack up a load of student loan debt (and maybe even credit card debt, crazy as that sounds) if it means graduating a year early.

Another unexpected reason that students don't graduate "on time" is that they end up with extra credits. The average college graduate ends up with sixteen extra credits (four or five superfluous classes). This was something that was partially true for me. I graduated with an extra six credits. Another issue for students is scheduling for classes. This has been something that has been true for me as a graduate student. I would have loved to have picked up a political science endorsement, but the two classes that I needed to take were only offered once a year during the morning. So, while it won't affect my graduation, I can imagine the issues surrounding finishing off those rarely offered graduation requirements.

I'll close with a fun fact: Only 1.5% of students graduate college in three years or so. Who are these freaks?

Saturday, January 11, 2014

New Menus #hashtag

I saw this menu item at a local dining establishment. I wonder if Doug Nussmeier likes meatball subs.

Mpemba Effect #hashtag

Erasto Mpemba was a high school student in Tanzania who noticed, during a project to make ice cream, that heated milk froze more quickly than the cool milk when placed in the freezer. When he asked his science teacher about his observation, his science teacher told him he was wrong. He persisted. Eventually, he came across a college professor (Dr Denis Osborne) who would repeat his experiment. The professor ended up coming to the same results. Under some circumstances, hot water will freeze more quickly than cooler water (under some circumstances, cool water freezers more quickly than warmer water, too).

So, there are two interesting things about this story. First off, this observation was made forty years ago and we still do not understand the effect. Almost every house in America has an ice tray. We know water freezes. However, we cannot be entirely sure how long it will take for water to freeze. There is still a mystery about something as elementary as ice cubes. Secondly, this initial observation was not made by physicists or chemists at the leading research universities, but by a high school student in a developing country.

Youtube: Freezing Water:
How long does it take for water to freeze? A really long time. Check out the six and a half hour long time-lapse video (Cut down to just over seven minutes). The outdoor temperatures varied between -10 and +2 degrees Fahrenheit.

Physics Q & A by the nice folks at the University of Illinois
More about the Mpemba Effect

A somewhat related phenomenon is the Leidenfrost effect. It has to do with the boiling of water.

Thursday, January 9, 2014

Weight Loss made easy #hashtag

The easiest way to lose weight is to climb a mountain. Now, it is not just the sweat lost or the fat burned that helps mountain climbers lose weight. One could be carried to the top of a mountain and still lose weight. You see, weight on Earth is the measure of the force of gravity between an object and the planet. The further the object gets away from the Earth, the less it will weight. At sea level, I weight a bulky 183 lbs. If I were in the International Space Station orbiting the Earth, I would weigh almost nothing. There is a continuous line. If I could climb a ladder from the Earth to the Space Station, assuming that I didn't get tired along the way, I would notice that it took less and less effort to climb each rung as I got farther and farther from the Earth.

So, how much less would I weigh on the top of the mountain? If I were on top of Mount Everest, I would lose about two-thirds of a pound of weight from what I weighed laying out on the beach. My clothes would still fit me just as well. I'd be the same size, I would just weigh less. Not only would I weigh less, but everything with me would weigh less. So, if I happen to bring some free weights or some dumbbells with me, and assuming I could cope with the freezing temperatures and the thin atmosphere, I would notice lift a slightly heavier weight. It would not be that I had gotten strong, it would be the the numbers labeling the weights were no longer accurate. That weight that was labeled 20 lbs down at sea level would actually only weigh 19.93 lbs on the peak.

Does it get any better than this? Mount Everest is the highest mountain on the Earth, so it is the farthest I could get away from the center of the Earth, right? Actually, there might be a better place. In elementary school, we all learned that Christopher Columbus proved that the world was round (No part of that statement is true). You see, the Earth is not a sphere or ball. It is round-ish. The distance around the earth at Equator is more than the distance around the earth going through the poles. The Earth is like a sphere that got a little squished. So, if there was a really tall mountain near the Equator, then it might be farther from the center of the earth than the top of Mount Everest. Such a place exists! It is the volcano Chimborazo in Ecuador. It is more than two kilometers (more than a mile) farther from the center of the earth than Mount Everest. So, all things being equal, I would weigh three-quarters of a pound less on top of Chimborazo than I would sitting on my couch at home.

*Assumptions used to make these calculations. The mass of the Earth is 5.9 x 10^24 kg, the radius of the earth is 6,371 km. The distance from the top of Everest to the center of the Earth is 6382.3 km and the distance from the top of Chimborazo to the center of the Earth is 6384.4 km. Also, I used 6.67 x 10^-11 as the gravitational constant. Also, in real life, the mass of the mountain likely effect the calculations. It would be interesting to know if anyone has brought a very accurate scale up Everest.

Tuesday, January 7, 2014

Sharp Criticism #hashtag

Normally, I don't care for anything Drew Sharp has to say. However, I read this article.
Ohio State didn't help the conference, proving that its No. 2 national ranking prior to the Big Ten championship game was more a product of hype than an honest assessment of its quality. The Buckeyes hadn’t played anybody ranked in the top 15 during their 24-game winning streak. And it showed.
When the Buckeyes finally played two good teams, they lost both — losing to the Spartans in Indianapolis and getting schooled by 12th-ranked Clemson in the Orange Bowl.
I'll have to read more of what Drew Sharp has to say in the future.

Monday, January 6, 2014

Polar Vortex #hashtag

FREEP: The Polar Vortex

I'll admit it. I was excited about the possibility of having a snow day today. When I read on the internet that school had been cancel, I felt relieved. I get one more day to work on readjusting my sleep schedule. I get one more day to get ahead in the readings. Then, when I found out that tomorrow was going to be a snow day, I was disappointed. I like going to school. Stupid polar vortex.

Sunday, January 5, 2014

The end of give a penny take a penny #hashtag

Let's say that you own a store in Michigan you don't like pennies. You want to price the items in your store so that no matter what people buy, the total price will not require the use of pennies. One idea might be take one cent off for every dollar. So, if an item was priced at $0.99, the total after tax would be $1.05. An item priced at $1.98 would give a total of $2.10 after tax. It’s really easy to do this for any single item. By adding or subtracting a few pennies, it’s easy to get an after-tax total that would not require the use of pennies.

The problem is with combinations and rounding. Following this pattern, consider two items priced at $4.95. Buying the individual items would result in a purchase price of $5.247 which rounds to a nice $5.25. The use of pennies has been avoided. However, if someone put two of these items on the same bill, the price would double and one would end up with a total of $10.494 which rounds down to $10.49. The plan has been foiled.

So, our first plan has failed. Rather than guess and check, let’s look at the algebra. Let P be the price in pennies in the pre-tax price and N to be the number of nickels after tax. What we are looking for is a P and N that are whole numbers and satisfy the equation.
Having reduced the fraction, the only way that N can be a whole number is if P is a multiple of 250 (otherwise, the fraction on the right hand side of the equation will not simplify to a whole number). So, there is a way to avoid the use of pennies. If every item in the store is priced at $2.50 or whole number multiple of $2.50, then post-tax total will always work out to a number that does not require the use of pennies. So, there you go, problem solved. 

* What is wrong with pennies? For one reason, they are economically inefficient. You can read about it here or just search for one of the posts from my friend Mankiw. Another reason might be historic. Consider South Carolina (which has a similar six percent sales taxes to Michigan) or Georgia (the math would be similar with their four percent sales tax). There are probably some folks out there still bitter about the "War of Northern Aggression."

One might argue that getting rid of the penny would make more copper available; copper is an important item in all sorts of electronics. This isn't a very good argument. While modern pennies look like they are made out of copper, there is only the tiniest layer of copper covering a zinc disc. Only 2.5% of a freshly-minted penny is actually copper. On the other hand, nickels, dimes and quarters are at least 75% copper. So, as the old adage goes, you cannot judge a coin by the plating that covers it. Also, all that shimmers is not necessarily copper.