The Very Spring and Root

An engineer's adventures in education (and other musings).

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November 2011

5 Minute Lesson: Kepler’s 2nd Law

Instructor: Mr. Nalin Ratnayake
Subject: Physics (algebra-based)
Target Grade Level: 11/12
Lesson Objective: Understand the major implication of Kepler’s 2nd Law.

Good morning class. Have you ever wondered about the motion of the planets? My name is Mr. Ratnayake (Mr. Rat will do). Today we will discuss Kepler’s 2nd Law of Planetary Motion, building on your previous knowledge of basic mechanics, algebra, and geometry.

In the early 1600’s, most astronomers believed that if the planets orbited around the sun, they must do so in circles. However, astronomical observations did not agree; planets seemed to move randomly in the sky. It was a mystery. A German mathematician named Johannes Kepler forever changed astronomy by demonstrating in his *first* law of planetary motion that by simply treating an orbit as an ellipse, instead of the previously-assumed circular shape, the simplicity and harmony of planetary motion became clear. He then went on to explain the consequences of elliptical motion in his *second* law, which states: A line connecting a planet to the sun sweeps out equal areas in equal times.

Refer to the diagram on your handout, or follow me on the board. Suppose I have here my orbital ellipse, and I consider the area swept out by the radius r in some interval of time. The planet has moved on an arc, by an angle θ as measured from the sun. Now we have set up our problem and will commence, like good scientists, to ask questions.

What basic geometric shape does this look like? (Triangle). Let me draw this triangle. Who knows how to find the area of a triangle? (one-half the base times the height). Ok. Do we have a variable on our diagram that looks like it would be the height of the triangle?  (the radius r).  And this arc forms the base. What is the length of an arc (You remember from geometry of course, it is the radius of the arc times the subtended angle.)  So the area (A) of this pie wedge is…. ½ (r θ) r , or ½ r2θ.

Let’s assume, as Kepler did, that this area must remain constant for the same time interval in an orbit. Consider our diagram. If our planet moved closer to the sun, say here, then the radius, our distance to the sun, is much smaller. To maintain the same area of triangle, what must happen to its base? (must get larger). Remember, this is the arc length we traveled in our orbit for a set time interval. We traveled farther in the same amount of time than we did out here! What can we deduce about our speed? (we went faster!). We move faster when we are near the sun on our orbit and slower when we are far from the sun on our orbit.

Was Kepler right? It turns out that his theory exactly matched observational data from astronomer Tycho Brahe; this explained previously erratic motions of the heavenly bodies with a simple concept. Today, Kepler’s Laws enable us to predict the motion of the planets, asteroids, comets, and satellites in space. NASA’s Mars Curiosity probe just launched this week. It will take 8 months to reach Mars. Thanks to Kepler’s Laws we know exactly where Mars will be and how fast it will be going in 8 months; and Curiosity will be in the right place at the right time.

Check for understanding, all together now, and I’m looking for every one of you to answer. As a planet gets closer to the sun, does it speed up or slow down? (Speeds up!) As a planet gets further away on its orbit, does it speed up or slow down? (Slows down!) Good. Any questions?

BTR Up for National Award

Aside  Comment

Just linked from Twitter to an article in Harvard Gazette mentioning Boston Teacher Residency as a finalist for the Innovation in American Government award.

“The importance of the Innovations in American Government Award has never been greater,” said Anthony Williams, acting chair of the National Selection Committee. “Government is facing unprecedented challenges, and I think all of us are sanguine to know that there are leaders and programs out there — including these government finalists — that are working to serve and engage our people better.”

Check out the full article for some background and how BTR fits into the metric.

Gary’s TFA – It May Already Be Out There

Gary Rubinstein has followed up his previous condemning critique of TFA with a plan for how he would fix it. He calls for greater rigor in new teacher preparation and an emphasis on long-term teaching.  Here is my response in the comment thread:

Thanks to your posts over the last few months, I have been also applying to alternatives to TFA, while continuing with the TFA application path as well.

I’ve found some incredible programs, many of which are doing what you think needs to be done, though on a smaller scale than TFA (and hence without the massive PR, so its harder to hear about them). But if you look, you will find…

Top of my list is the Boston Teacher Residency ( A one-year immersive masters in education program is followed by a three-year commitment to Boston Public Schools. The masters program includes four days a week of student teacher during the school year, and two summers on either end of full-time coursework at UMass. If I get accepted to this, I will definitely go over TFA.

There’s an alliance of such programs at I’ve found most of the others fall somewhere in between TFA and BTR on the preparatory rigor scale, but there are so many alternative options. If you are interested in TFA for the right reasons, as I think I am, then take a look at these other programs too… maybe TFA will be right for you, maybe not. But its not the only structured alternative cert pathway out there, especially for career-changing professionals. As these residency models gain more exposure, TFA will have competition for the national stage in education reform teaching entry programs, and that may be all that is required to prompt change.

on November 23, 2011 at 4:57 pm

I think Gary is right on to be concerned about these issues, and so should anyone not solely interested in short-term, band-aid solutions. The problem cannot be improved by throwing untrained idealists into classrooms who put in a couple of years to say they did their time in the trenches, and then wash their hands of it.


Dear Nalin,

Congratulations! I am pleased to invite you to Teach For America’s final interview day. We enjoyed learning more about you during your recent phone interview and would appreciate the opportunity to meet you in person.

As you plan for the next steps of our application, log on to the Applicant Center now to complete the required actions and forms by the specified deadlines:

    • Sign up for your interview date and location by 11:59 p.m. ET tomorrow, November 17. Dates and locations are available on a first-come, first-served basis and go quickly, so we strongly encourage you to schedule your interview now!
    • Request an official transcript from your registrar as soon as possible so you can upload it by 11:59 p.m. ET on November 25. For more information about our transcript upload process, check out our blog.
    • Mark your calendar with the required forms and documents deadlines found on your Status page.

We are excited to learn more about you and your interest in joining our corps. If you have any questions, please contact us at


Sean Waldheim
Vice President, Admissions

Warm Regards

Dear Nalin,

Congratulations! We have received your online application and supplemental materials. Your application is now complete and under review.

Your application will be reviewed by the Admissions Committee and email notifications will be sent to all candidates regarding invitations to attend Selection Day.

By tomorrow afternoon you will receive a follow-up e-mail with additional information about the timeline for the next steps in our Early Admissions Process.

Thank you for applying to the 2012-13 Boston Teacher Residency program. We will be in touch soon.

Warm regards,

BTR Admissions Team

The TFA Conundrum

Well, I had my TFA phone interview on Saturday morning, and I thought it went very well indeed. The interviewer, herself a TFA teacher in New Orleans, seemed friendly, engaged, and very interested in me. I had ready responses with detailed examples to all questions, and the feeling was very much relaxed and conversational.

To be honest, I’m second-guessing TFA quite a bit. On the one hand, there is a lot of great press and commentary out there on the organization. On the other… some fairly virulent criticism. The TeachForUs independent blogging network has provided both types of accounts; on the whole it is a confusing blend of the inspirational and insidious.

As I indicated in an earlier post, I do not harbor much concern for the anti-TFA sentiments that are really directed at individual motives and behaviors of TFA corps members themselves. For example, deciding to stay in teaching as a “service project” for only two years before leaving, or declining to pursue further training and education. These are decisions that anyone entering teaching could make, TFA or not. In fact, from what I read anyway , the retention rate for any teacher in an urban or low-SES school is pretty atrocious, TFA or no. Does TFA encourage a revolving door by only putting a 2-year minimum on recruits? Maybe. But I bet that a lot of people end up staying in teaching that never would have considered it as a career otherwise too. How long I stay in teaching and what my motives are for entering it are up to me, not TFA, so I find that criticism personally irrelevant.

What *is* concerning for me, however, is that I might end up being associated with an organization that is tied to much less substantiated, but far more worrisome, tactics. Gary Rubenstein, the (in)famous ex-TFA TFA critic, has written extensively on his blog about such tactics, and lately posted his most scathing yet . For example, expanding into districts that are laying off teachers? If TFA purports to send teachers with only five weeks of training into schools, they had better be filling slots that could not otherwise be filled by any qualified candidate. Are districts, under ever-tighter budgetary and political pressure, laying off experienced, unionized teachers in favor of politically backed, inexperienced, cheap fresh-outs? For the specific case of STEM subjects, I really doubt this is the case, so perhaps this doesn’t really apply to me either. But again, do I want to be associated with an organization that might/would do that?

Another big picture concern: the “Education Reform” movement. I am vehemently opposed to privitization of the public school system, just as vehemently as I have been opposed to the contracting out of RDT&E (Research, Development, Test, and Evaluation) at NASA. Without tangenting too far into all the ways that private money has our federal and state governments by the cojones, I will simply say that TFA appears to be firmly on the side of those who would use wildly inaccurate quantitative metrics to force in private charter control (or vouchers or what have you) of a public system, shortchanging students and laying off those damn lazy unionized teachers along the way. Not sure I like that either… While I’ve definitely had some lazy and/or ineffective teachers, blaming an already strained profession for systemic racial and socio-economic divides is scapegoating at best, and harmful at a long-term genocidal level at worst .

I guess what it comes down to is the basic question: Is it ok to use a possibly less-than-ethical organization as a means to an end of doing greater good individually? Or does any association with an ethically questionable (not conclusively bad, just questionable) organization negate/taint any good that may come of it?

These questions and others led me to diversify my options. I am proceeding with the TFA application – I should hear in a week if I advanced to the final day-long interview session that takes place at the end of the month. I will be notified of the final admissions decision and placement school/subject on January 17th.

However, in addition, I am also applying to the early admissions track for the Boston Teacher Residency . BTR places admitted members into a year-long, intensive Masters program at UMass Boston, combining urban teacher preparation with four days a week of student teaching. Upon completion of the Masters, residents are placed in the Boston Public Schools, and receive a full waiver of the tuition of their training upon completion of three years of service.  BTR is also clearly committed to community development and long-term teacher retention for what seems like truely transformative change. Making the November 15th deadline means a possible Selection Day interview invite in mid December, an interview in early January, and a final notification of acceptance on January 20th.

I guess I’ll have to figure this out by then. I have a feeling though, that like other significant forks in the road in my past, one path is just going to seem intuitively right, and I’m going to just take it and be too busy kicking ass at whatever challenges lie around the corner to ever look back. I just don’t know which it will be yet.

Expanding the Options

Whew, ok TFA application was submitted successfully on the 26th… I should find out on the 3rd (day after tomorrow) if I advanced to the phone interview phase. No time for details at the moment, since I’m in the middle of tech week for a play that is opening this Friday (yeah I know, busy enough?)… but due to ever-growing philosophical differences with TFA, I’ve decided to pursue other routes into teaching as well, at least so that I have a few options to consider.

I have started an application to the Boston Teacher Residency program, which looks amazing. The early application deadline (just two weeks away… eeep) results in an admissions notification at about the same time as TFA (third week of January), so I will be able to compare the opportunities if I happen to get both. I’ve filled out the basic app, ordered transcripts, and uploaded my C.V. and relevant course listing. Remaining: see if my two TFA recommenders will also be willing to fill out the online forms for this one too, and also to add at least one more. Also, the essays… should be similar to my TFA ones, but I want to tailor them specifically for this program.

Also in work, but with much less progress (and less clear deadlines): the Chicago Teaching Fellows. More later.