On the Path of the Elders
Wednesday, March 24, 2010
Saturday, March 20, 2010
SPECIAL TO THE WASHINGTON POST
(Mar 20, 2010)
March Madness, the annual NCAA basketball playoff spectacle in which millions of us, firmly docked in front of the TV screen, consume 1,000 calories an hour while watching young athletes burn 12 calories a minute, began this week.
If you're planning to participate in this national sit-in, you can drastically enhance the viewing experience by pondering the parabola.
It's the elegant arched trajectory naturally formed by any projectile, from an artillery round to a tomato, moving in a gravitational field. Parabolas have been extensively studied since people started throwing stuff at each other, and they shape the outcome of many ballistic sports, such as baseball, golf, football, shot put and more. But they reach their apex in basketball, where field goals and free throws demand precision control of parabolas.
But not just any parabola. Success favours a fairly high arch. The ball must pass through the hoop with a little room to spare, and that limits the possibilities. The hoop is roughly 48 centimetres in diameter, and the men's ball is about 24 centimetres wide (women's about 23.5). So if the men's ball were thrown straight down from above that is, at an angle of 90 degrees to the horizontal hoop rim, as in the classic Michael Jordan airborne dunk, there would be just under 11 centimetres of free space all around, a comfy margin.
But as the angle decreases and approaches the horizontal, the free space for a "nothing but net" shot gets much smaller. At 55 degrees, it's about 6.4 centimetres. At 45 degrees, it's down to 3.8 centimetres. And at 30 degrees, it's basically impossible to get the ball straight into the basket, even with a full scholarship and more tattoos than a Hell's Angels convention.
Not surprisingly, increasing the height at which the player launches the ball not only reduces the distance to the basket, but raises the entry angle of the ball's parabolic arch, allowing more free space.
In a 1980s study, Peter Brancazio, a Brooklyn College physics professor, determined that adding two feet to the height at which a shot leaves the player's fingers increases success by a whopping 17 per cent. No wonder you see so many jump shots.
But is there a launch angle that gives the maximum probability of a perfect telegenic swish? Well, there are many different parabolas that will do the job, and the choice varies according to player height, personal preference and court position.
But one way to decide, Brancazio wrote 25 years ago in Sport Science: Physical Laws and Optimum Performance, is to "consider the amount of force needed to launch the shot.
"It is to the shooter's advantage to use as little force as possible," he reasoned, because the less the force, "the more quickly and effortlessly (the ball) can be released."
Okay, fine, but how do we know what takes the least force?
Here, physics comes literally into play.
We know from theory and experiment that you get the most distance with the least effort by firing a projectile at 45 degrees, exactly midway between vertical and horizontal. And we can assume that least-effort shooting is really important for a player taking a jump shot, because he or she can't push against the floor for power, especially in heavy defensive traffic. So the fastest and easiest angle would seem to be 45 degrees.
Except when it isn't, which is a lot of the time. The reason is that 45 degrees is the ideal least-effort angle only if the ball is shot from the same height as the basket, which is 10 feet above the floor. So it's perfect for a 7-foot player whose arms reach two feet over his or her head, and who jumps a foot off the floor to shoot.
The rest of us will be launching the ball "uphill" (that is, as if we were firing a cannon at a target on a higher elevation). So we'll need larger angles.
How much larger? Again, science comes to the rescue. Brancazio explains that you need 45 degrees, plus half the angle formed by a straight line between the position of the ball at launch and the basket. Depending on your height and where you are on the court, that typically ranges from 7 to 14 degrees.
Thus, for a shot leaving your hands at eight feet above the floor from 18 feet out, you'll want to launch the ball at a bit more than 48 degrees. For most players at a distance of 10 to 25 feet, the least-effort angle ranges between 47 and 52 degrees.
Using that system, you can calculate the ideal free-throw angle. It's 13.75 feet from the free-throw line to the centre of the basket, and a 6-foot player launches the ball from about seven feet above the hardwood. That works out to a shooting angle of 51 degrees.
Of course, Brancazio did his calculations long before the advent of the modern computer. But a new state-of-the-art study gives basically the same result. Last November, engineers at North Carolina State University published an analysis of hundreds of thousands of 3-D computer simulations of free throws. Their optimal angle: 52 degrees. (Check it out during the playoffs. Seen from the side, a 52-degree free-throw parabola has its highest point just about even with the top of the backboard.)
Free-throw success is also improved by adding a little backspin, which pushes the ball downward if it hits the back of the rim.
The North Carolina State engineers calculated the ideal rate of free-throw backspin at three cycles per second. That is, a shot that takes one second to reach the basket will make three full revolutions counterclockwise as seen from the stands on the player's right side.
While you're at it, stop to remember Menaechmus, the geometer who first described the parabola in the 4th century B.C. He never made a layup, but he had game.
Monday, March 15, 2010
Creative Puns for Educated Minds
1. The roundest knight at King Arthur's round table was Sir Cumference. He acquired his size from too much pi.
2. I thought I saw an eye doctor on an Alaskan island, but it turned out to be an optical Aleutian
3. She was only a whiskey maker, but he loved her still.
4. A rubber band pistol was confiscated from algebra class because it was a weapon of math disruption.
5. The butcher backed into the meat grinder and got a little behind in his work.
6. No matter how much you push the envelope, it'll still be stationery.
7. A dog gave birth to puppies near the road and was cited for littering.
8. A grenade thrown into a kitchen in France would result in Linoleum Blownapart.
9. Two silk worms had a race. They ended up in a tie.
10. Time flies like an arrow. Fruit flies like a banana.
11. A hole has been found in the nudist camp wall. The police are looking into it.
12. Atheism is a non-prophet organization
13. Two hats were hanging on a hat rack in the hallway. One hat said to the other, "You stay here; I'll go on a head."
14. I wondered why the baseball kept getting bigger. Then it hit me.
15. A sign on the lawn at a drug rehab center said: "Keep off the Grass."
16. A small boy swallowed some coins and was taken to a hospital. When his grandmother telephoned to ask how he was, a nurse said, "No change yet."
17. A chicken crossing the road is poultry in motion.
19. The short fortune-teller who escaped from prison was a small medium at large.
20. The man who survived mustard gas and pepper spray is now a seasoned veteran.
21. A backward poet writes inverse.
22. In democracy it's your vote that counts. In feudalism it's your count that votes.
23. When cannibals ate a missionary, they got a taste of religion.
24. Don't join dangerous cults: Practice safe sects!
Friday, March 12, 2010
Canadian schools got results with more teachers
Thursday, March 11, 2010
Six Nations District Numeracy Committee Meeting Minutes
Thursday, January 21st, 2010
JC Hill (2:30 – 4:00)
Present: Alice Anderson, Carrie Froman, Janis Thomas, Judy McNaughton, Joe Restoule General
Absent: Sandy Hill
Review minutes from last meeting
In order to accommodate time for the guest speaker, minutes were e-mailed out for approval in advance of the meeting. No amendments were requested so minutes are considered approved.
Special Guest Presentation by Understanding Math personnel
Cynthia Rutledge from Neufeld Math presented on the Understanding Numeration (K-3) and Understanding Math (4-10) software. Approximately 10 other Six Nations staff members were also able to attend. Cynthia spoke at length about the program and demonstrated several lessons across different strands/grades.
The following are a few pieces of information she shared:
-training is sold along with the software, and is a key element to its success
-the software includes over 3000 lessons
-there is the ability to track progress of students
-it does not need to be used on SMARTboard (though this enhances it); a data projector is sufficient for classroom instruction use
-the software includes word banks for student/teacher use, as well as a search engine
-many lessons explore different approaches to a mathematical concept (for example, five different ways to approach multiplication)
-the entire Thames Valley District School Board has a license
-Neufeld math prefers to sell licenses at a district level (it works out to roughly $25 per student)
-licenses are lifetime, with upgrading included when available
-students are recommended to work in triads, using the “flight plan” method of 1 driver, 1 recorder, and 1 task manager (pilot, navigator, co-pilot); also a student driver at the front of the room to allow teacher to circulate amongst students
-Neufeld is working on other strands besides Numeration for grades K-3
Math Assessment Tools
Due to the length of the Understanding Math presentation, all other agenda items were moved forward to the next Numeracy Committee meeting. Members did stay after the presentation to discuss a few items, as reported below.
PD planning for Numeracy Nets: Webinar is scheduled for Feb. 25th or March 11th, as Pearson will not be supporting Numeracy Nets with in-person PD, only webinars.
Ideas for ONAP implementation:
Follow up on participation:
Math contest (Caribou)
Upcoming dates/Classes involved:
Yesterday’s results: Teachers were given copies of their school’s Caribou results, as well as certificates to share with the students who participated in the contest.
ILT Literacy/Math Night on November 26th
Report on how it went:
ECG Math Night
There was no information to share about this.
Explore Learning Teacher Passwords
PD opportunity update: Explore Learning has been contacted and are available for a half day or after school PD session.
Math Trek 4,5,6
Mr. Hickey handed out copies of this software for each school to have.
Wednesday, March 10, 2010
Monday, March 8, 2010
Friday, March 5, 2010
Check out the 5 "A"s, the 4 "D"s, and all the fluencies required of the digital citizen at the 21st Century Fluency Project. Then think about the skills we hope to develop in our students.
Thursday, March 4, 2010
You may have noticed that i've installed a Roll Up the Rim to Win tally on the sidebar. This is NOT to demonstrate how sleep deprived i am or how proficient i am with my coffee waltzing. It is to show how real life probability examples are everywhere for your students to track and talk about.
Wednesday, March 3, 2010
This January 28th article from E School News stresses the importance of visual stimulation for helping our students learn more effectively, and the new ideas companies are coming up with that are geared toward this strategy.
posted by Lee Crockett
Visual Learning a Key Strategy for Helping Students Succeed
Software that takes a visual approach to teaching math has led to double-digit gains in the test scores of Orange County, Calif., students—and the software’s maker was one of several ed-tech companies demonstrating new visual learning products at the 2010 Florida Education Technology Conference (FETC) in Orlando.
At FETC, the nonprofit MIND Research Institute discussed findings of a 2009 study suggesting that students using the group’s ST Math software experienced dramatic learning gains.
ST Math is a supplemental program for students in grades K-5 that is based on decades of neuroscience research at the University of California, Irvine. The software taps into the brain’s innate “spatial temporal” reasoning ability to visualize and solve math concepts and problems, its makers say.
Students solve math problems presented as visual puzzles, before they are ever introduced to abstract math language and symbols. Through a carefully engineered sequence of fun-to-play software “games,” students work at their own pace to solve increasingly difficult problems that eventually require them to think multiple steps ahead in space and time—and they receive instant feedback about why a solution works or doesn’t.
More than 15,000 students enrolled in 64 elementary schools are taking part in the Orange County Math Initiative, a five-year community partnership involving Orange County schools, leaders in the business community, UC Irvine, and MIND. The 64 participating schools are in the lowest-performing 30 percent of California elementary schools; 80 percent of their students qualify for free or reduced-price lunches, and 60 percent are English-language learners.
Yet the percentage of these students who tested at the Proficient or Advanced level on California’s most recent state exam increased by more than 12 percentage points, MIND said, compared with the state average of 4.5 points.
“We’ve seen what can be done with the benefit of a tool like this,” said Andrew R. Coulson, president of MIND’s education division. Now, Coulson said, his organization is trying to make the software even better.
At FETC, the institute previewed its fourth generation of ST Math. Earlier versions of the software used a one-size-fits-all pacing, Coulson said; version 4 changes that, allowing educators to customize the pace and sequencing of lessons to better align them with whatever core curriculum their school is using.
Users can edit the software’s sequencing calendar with a drag-and-drop feature, and the new version includes pre- and post-tests to check students’ progress.
Tuesday, March 2, 2010
Monday, March 1, 2010
This year's conference hosted a special Friday afternoon general session for Bill Daggett, noted author and president of the International Center for Leadership in Education. Daggett is the creator of two widely used educational frameworks, the "Application Model" and the "Rigor/Relevance Framework." The latter is a practical planning and instructional tool for determining the relevance of curriculum and assessment to real-world situations.
Daggett's message to his listeners was that career and technical education (CTE) is needed as never before, yet we must get beyond the old voc-ed model of the 1980s and 1990s. We must find ways to integrate CTE with academics as well as art, music, and physical education. If we can do that, he said, these will be "the best of times." If we hang on to an obsolete model, they will be "the worst of times."
Daggett pointed out that today's highest-performing schools are the ones that have been willing to change. They do things differently. "They explore why we should change," he said, "not because we're uncomfortable with the past, but because the world is changing."
Daggett's Application Model outlines five stages in the application of knowledge: (1) knowledge in one discipline, (2) application within disciplines, (3) applications across disciplines, (4) application to real-world predictable situations, and (5) application to real-world unpredictable situations. As educators, we want our students to be independent thinkers who are comfortable in stages 4 and 5, but standardized testing (and hence most teaching) focuses on stages 1 and 2. CTE is the only way to get students to stages 4 and 5, but, unfortunately, most people don't recognize that fact. CTE is still held back by a negative image. Most people still think of CTE as "shop class."
Daggett's Rigor/Relevance Framework is a Cartesian grid representing the intersections of the five stages of his Application Model (horizontal axis) with the six stages of Bloom's Taxonomy of Learning Domains (vertical axis): (1) knowledge (or awareness), (2) comprehension, (3) application, (4) analysis, (5) synthesis, and (6) evaluation. (For a graphic of the framework, visit http://www.leadered.com/rrr.html.) Educators should strive to enable their students to function at the intersection of high levels of knowledge and application, but this cannot be accomplished through conventional approaches. We can't get there one discipline at a time, Daggett said. We must integrate disciplines in ways that promote rigor and make learning relevant to an increasingly diverse student population.
Daggett stressed the seriousness of the challenges we face. Our young people live in a technology-driven world that many adults only vaguely understand. To make his point, Daggett showed a video of "siftable chips," inexpensive digital building blocks that interact with the user and with one another. In today's world, computers will fit in wrist watches, buttons, and eyeglasses. Separate computer keyboards and monitors will soon be a thing of the past. The American educational process must adapt to these and many other technological developments. Otherwise, it too will soon be stuck in the past.
According to Daggett, the need for dramatic change in education is also driven by economic factors. Three decades ago the United States was the dominant economic power in the world, but that is changing. China has become the world's manufacturer and has a vast population—over 100 cities with more than a million people, compared to ten in the United States. India is even more populous, and is making rapid advancements in technology. Today the world's fastest-growing economies are found in countries that, historically, have lagged far behind the United States: Vietnam, Argentina, Brazil, Indonesia, and Panama.
In Daggett's view, the major challenge facing American education today is finding a way to keep pace with an ever-changing global business environment—all the while making the most of diminishing resources. It's doable, though, he explained, if we are more dedicated to improving the lives of our students than we are to preserving the status quo.