Unplugging Plug and Chug

Yo - Memorize This!In a disturbing coincidence, the stomach-turning "Plug and Chug" phrase cropped up in 2 situations this week.  In physics class on Wednesday, a student made a comment about "plugging and chugging" to get a solution. I stopped him at that point and did my typical rant against that type of approach to doing physics. (Note - he was NOT advocating it!)

In short, there's nothing more revolting to me as a physics teacher, and a physicist than the thought that somehow physics can be taught, and learned, by memorizing formulas and simply plugging in numbers and calculating.

How then to explain a quote by Erika Gebel in the Aug, 3, 2007 Philadelphia Inquirer? In an article titled "Masters of 'spring' theory: Physics Teachers embrace a new method", Gebel is describing exciting new changes to the way that physics is taught in high school. Citing the approach known as modeling physics , which had just been taught to local physics instructors in a faculty-development workshop in the Philadelphia area, Gebel reports that

Click to read more ...

A Myth of Gaussian Proportions

When I was a freshman in high school, my home room teacher gave us a very nasty assignment during an after-school detention session - to calculate 35 to the 35th power!

This assignment was particularly cruel and unusual punishment because there were no such things as calculators back in 1967.

What I really needed was something I didn't know about until college: a closed-form solution.

Finding closed form expressions for partial sums is a standard calculus exercise. The ur-example of this type of problem is the sum of the first n integers, which is easily shown to be n(n+1)/2.

This closed form expression collapses (n-1) operations into three. Because it yields an exact answer, it is not really a predictor, but, in a sense, it is a model of a process.

When this example is done in a calculus class, a typical accompanying story is how young Gauss solved this problem in record time, totally showing up the teacher who had given out the onerous task of adding the first 100 integers. (The version I always heard was that this was a punishment because the students had been particularly noisy that day. The sadistic mathematical punishments of my high school teacher certainly lends credence to this tale.)

Click to read more ...

In Praise of Friction The Media Slips Again

I recently posted a complaint about physics misconceptions promulgated by the media. To be fair, I need to report a good job describing the physics of a situation when it appears.

In an article posted on Dec. 27, 2006 by the op/ed staff of the North County Times (near San Diego), and titled A Physics Lesson, the authors do a very nice job of describing the role of friction in driving:

Your tires rely on friction to speed up, turn or stop. On a dry day, there's usually plenty of friction when the rubber hits the road. When it rains, the weight of your car must push water out of the way for the tires to reach the road.

The faster you drive, the greater amount of water your tires must push aside. If that water gets trapped between the asphalt and the tires, you'll lose control of your car -- you'll be hydroplaning. The lesson here is that when the roads are wet, you can't drive as fast as you would on a normal day. Even if the rain is light, slow down at least five to 10 mph.

When I teach a first-semester course in Physics, I typically begin the first day trying to get students to identify forces acting on them as they do basic things. My favorite example is on walking. I ask the following question: if you go from standing still to walking at a steady pace, you accelerated. According to Newton there must be an unbalanced force acting on you in the direction of your acceleration. What is this force?

Click to read more ...

A Jolting Message: Hemingway's Snow and Climate Change

Kilimanjaro, then and now. Click to enlarge.I have remarked before on the ever-increasing media coverage given to global warming. As more and more scientific evidence comes in about the effects of global warming (see my recent post On the Increase in Greenland Ice Loss), the facts, interpretations, scientific theories, and political reactions to climate change are incredibly varied in the face of almost overwhelming evidence. Making sense of what is really happening, and how we should react, calls for insightful commentary from expert sources.

One such source is an article by Doug Macdougall of the Scripps Institution of Oceanography titled Jolting Messages on Climate Change. (The Chronicle, April 2006). In addition to his clear enunciation of global climate change facts and a strong call for "jolting messages" that will move "politicians and the public into effective action," Macdougall reviews five books about climate change published in 2005 and 2006:

• Climate Crash: Abrupt Climate Change and What it Means for our Future, by John D. Cox
• Field Notes From a Catastrophe: Man, Nature, and Climate Change, by Elizabeth Kolbert
• Kicking the Carbon Habit: Global Warming and the Case for Renewable and Nuclear Energy by William Sweet
• The Weather Makers: The History and Future Impact of Climate Change, by Tim Flannery
• The Winds of Change: Climate, Weather, and the Destruction of Civilizations, by Eugene Linden

According to Macdougall, each of these books have strong points. I encourage you to read Macdougall's reviews, which are very even-handed. Some of the authors are more pessimistic than the others in terms of what can be done (via science, engineering, politics), but all agree on the scope of the problem. Most of the books do take on the sudden climate changes that were first observed in studies of the Greenland ice sheet.

Click to read more ...

Frisbees in Space: Gettin' Funky With Gravity

This is a cautionary tale of frisbees in space, and those in the media who report about them...

Probably the main issue in all of physics education is how to help students learn in the face of their often serious misconceptions about the nature of forces in the world. Most carry with them an Aristotelian view of physics, in which forces are needed for motion. This view is in direct contrast with Newton's Laws (specifically the First Law). According to Newton, forces are needed to change motion, i.e. accelerate an object.

The Aristotelian view leads to totally incorrect views of everyday situations, views that are repeated continually because they have become so ingrained in our thinking and reactions. For example,when a driver moves to the left when making a sharp-right-hand turn, the common statement is that there is a "centrifugal force" pushing leftward. There is no such force: the driver is moving straight while the car moves to the right. The driver then feels the door on the left - the inclination is then to assume that a force "pushed" the driver into the door. There are many other situations where we instinctively believe that a force is acting when in fact it isn't. (See Aristotelian Physics and Why We Hate It by R.G. Brown of Duke U.)

Click to read more ...

The Evolution of the 40 - 40 Club

This just in from the Nov. 28, 2006 Onion -  Kansas Outlaws Practice Of Evolution:

TOPEKA, KS - Any living being that undergoes genetic modification favoring survival could face jail time under the new law.

A really clever piece on our favorite state, I enjoyed reading it today probably a whole lot more than if I had seen it yesterday - a day of unfortunate and fortunate events.

I was at Penn State attending a meeting of the Scientific Benchmark subcommittee of the PA Governor's Commission on College and Career Success.  The subcommittee's charge includes proposing revisions to the current PA state teaching standards.  This was my first meeting, and I was amazed to meet such an energetic and dedicated group of secondary and higher-ed faculty working on this important project.  Everyone in the room has one overarching goal - to ensure that ALL students learn essential mathematics and science concepts  and skills - necessary for success in today's, and especially tomorrow's world.

This was the fortunate event.

The unfortunate events were my reading two disturbing articles earlier in the day.  In one, I read a report of the August survey done by Jon Miller of Michigan State University. The results of the poll suggest that only 40% of the U.S. believe in evolution (BTW, the only country with a smaller percentage is Turkey, while countries such as Sweden and Denmark have an 80% belief rate)  Miller's study attributes this disturbing dichotomy as a perfect-storm effect of religion, politics, and LACK of GENERAL SCIENTIFIC KNOWLEDGE of core biological ideas.  (Check out the National Geographic report on the poll.) 

The other article was even more depressing:  The Chronicle of Higher Ed reported that in a survey by the American Council on Education, 46% of those polled said that colleges and universities should not require students to take more courses in math and science, while 46 percent said students should be required to do so. This deep division is evidence that all of the messages and news about American students falling farther and farther behind in terms of essential skills for the 21st Century are not being heard.  (Click here to read the original study - "Math and Science Education and United States Competitiveness: Does the Public Care?")

Where is the Math/Science PR?  With the constant stream of news stories about American students falling further and further behind the rest of the world's students, it seems to be everywhere, but no one (or at least 40% aren't listening.

Luckily for me, but really luckily for our students and our country, the fortunate event outweighed the unfortunate events.  The effort to make science standards the best they can be as a preparation for our students' future success will also produce a perfect PR machine, as students who are successful realize that it was the mathematics and science that formed the foundation of their success.   And the students who follow them will generate the demand that will lead to more math and science at all education levels.

Then we won't be in the 40-40 club anymore, which will be quite an evolution!

The Gateway to Educational Materials

A Cantor Set on an Egyptian column. Click to enlarge.An excellent resource for any teaching, but especially K-12, can be found at the Gateway, a site run by the U.S. Department of Education and Syracuse University.  The site is  the project of  a consortium whose member institutions join what is known as GEM, the Gateway to Educational Materials.

The Gateway is an essential site, both for educators, and for anyone interested in anyone learning any topic on-line.

You will use the Gateway primarily for its very sophisticated search engine, specifically designed to search for  educational materials.  When you search for a particular topic, e.g. "fractals", you will get a nice listing of hits that describe not only online educational fractal resources, but also a categorization scheme linked to the appropriate educational setting.  This is implemented on-screen by a category list that appears in a right-hand pane following a search.  Similar to clusty, the categories allow you to instantly narrow your search into one of the categories.  The categorization is an incredibly helpful way of finding the right resource for you class.  For example, back to the fractal search:  categories include areas such as curriculum support, lesson plans, and individual categories for grades 1 through 12.

The real benefit of the categorization scheme, however,  are the categories that you probably aren't aware exist - these are the ones that allow the cross-connections across all disciplines to become evident.  One of the categories that appear when searching for "fractals" is Cultural Perspectives on Mathematics.  A click here yields 5 hits, one of which is  African fractals: modern computing and indigenous design, an article on a fractal geometric view of the " self-organized location of huts in Tanzania, art design among the Mangbetu in central Africa, and Mali windscreens."

So plan to spend plenty of time on the Gateway - learning, teaching, and marveling at the sophistication and power of a search engines designed specifically for the educational community.

Information Science Blogging

I've read the articles of Joyce Kasman Valenza for years in the Philadelphia Inquirer, where she is a columnist in the tech.life@inquirer section, but I've just now come across her blog, and her library page for Springfield Township High School.

Joyce  is pursuing a Ph.D. in the Interdisciplinary Doctoral Program at UNT’s School of Library and Information Science.  Her blog,  Joyce Valenza's Neverending Search, is an incredible resource or all things info-and ecucational-technology-related.  She is also an EduBlog 2005 winner. 

A nice feature of her site is a blogroll that consists of many dozens of information-science blogs.

So look into Joyce's work, and sites - they are invaluable for any type of information literacy course.  You will also e able to find many posts on the efficacy of blogging and wikiing in the classroom.

Science by Blogging

Particle Physics Tracks in a Bubble Chamber. Click to enlarge.Blogs are normally thought of as more personal diary/opinion vehicles, but  I have believed in the potential for blogs as an exciting teaching tool ever since my small success with blogging in the Fall 2005 Chaos and Fractals course. 

This potential is taken to the nth degree in a very informative article by  Sean Carroll in APS News (May 2006).   There Carroll describes his own view of blogging as "a great opportunity for physicists to exchange ideas more readily with each other, and to let the rest of the world share the thrill of the process by which science truly progresses." 

Carroll, is a a member of the Cosmic Variance group blog whose physicist/astrophysicist contributors write about "science, art, politics, culture, technology, academia"  (the similarity to FractaLog is not intentional - but I am heartened to see all of these scientists out there willing to place their science in the context of life itself.)

Read Carroll's article for ideas of how blogging helps him, and how it might help you - in teaching, research, and, everything else.

Carroll describes a number of interesting blogs.  I list them here as a resource.

Click to read more ...

The Chaos Game: 3rd Grade vs. University Faculty

I just finished two separate presentations of the Chaos Game exercise that I typically use to start the Honors class to students at Arcdia University. Most of the students were education majors - and most of them were elementary ed majors. I am always pleased at the reactions to the game - especially from students who believe, or claim to believe, that they are not good at mathematics. The Chaos Game is such a rich exercise, especially given the approach of Understanding vs. Prediction, that most get caught up in the inadequacies of prediction, and the frustration of not being able to get a real comprehension of how the patterns (and colors) arise.

But the best part of the exercise, for me, is the ability to run it in almost any setting - from a 3rd grade classroom to a university mathematics department. Each group will get something different from the exercise. Personally, I prefer the response of the 3rd-graders, who , unlike mathematics faculty, don't try to understand what is happening at a deep mathematical level. Instead, they react purely to the shapes and colors, and their inquisitiveness makes for a wonderful teaching moment.

Education majors, and especially elementary education majors, are also a terrific audience for the Game as we play it. I believe that most of them could see how the exercise, or something similar, can be transported to their own future classrooms!