How high is 800 West Ferry?

How High is 800 West Ferry?

Spring has reached Buffalo. The seniors have gone (as a private school, we have figured out that the school runs better if the seniors are not in class after AP Exams and so we let them go). Students are tired of being cooped up in a classroom. How to justify going outside for class. Let's measure the height of a mountain.

O.K., Buffalo doesn't have mountains or even hills. But next to our school is a 170 foot tall building (800 West Ferry). That becomes our mountain. We are then going to calculate its height three different ways, with an equation, with a drawing, and with a computer model.

Some of my students have used an inclinometer (a protractor with a hanging weight) before in a geometry class, so making and using one is not completely unknown to all. However, I know that I will have to review. So we make the inclinometers in class and calculate the height of the ceiling using simple right-triangle geometry by measuring the angle of elevation and the distance to the wall from a starting point. Most teams get obviously wrong answers, so we spend some time to figure out why. We figure out that the angle shown on the inclinometer is the compliment of the angle of elevation. I then remind my guys that whenever you use a new measuring system, you always calibrate that system by measuring some objects whose measurements you know. That was a lesson mentioned way back in September, so most have forgotten it. At least a couple of my guys get a "Oh, now I see why this is important" moment. This activity takes most of a class period.



The next class is spent discussing the difficulties of measuring the height of a real mountain. We figure out that we can't get the measurements for a right-triangle. Some students then blurt out "law of sines" or "law of cosines". I then let them try it out. Some groups will figure out that they will have to use two triangles, but sometimes I have to lead them to that conclusion. If I had an infinite amount of time, I would let them figure out how to do things, but usually I have to give some strong hints so that we get the appropriate equation at the end of this class period.

The next day, we use less than half a class period to make the actual measurements. I have found that it is easiest to give each pair a 50' length of string to serve as their baseline. They then set their own. After each team get 3-5 sets of measurements, we return to the classroom to do the calculations.

I have my guys do each calculation three different ways. One way is to use the formula we developed in class the day before. Another way is to use graph paper onto where they find out that they will have to use an appropriate scale (most groups initially use a scale that is too big for the supplied graph). The third way is to use a computer model. I use Geogebra, but you could use any other system such as Geometers Sketchpad. Below is a picture of this model and then the actual model which you should be able to try.

If you are not seeing the interactive feature above, click on the "CanisusPhysics" link above (sometimes more than once).  The advanced feature of Geogebra is not quite stable yet for consistent results.
Or go to the site directly.

Recently (fall 2015), I have started to use the app Desmos (www.desmos.com) in class (see a previous post http://canisiusphysics.blogspot.com/2015/10/linearizing-data-on-ipad.html). I have translated the Geogebra app to the Desmos one which can be tried at https://www.desmos.com/calculator/x8k0s8r4cg.

The idea is that the height should be the same for each calculational method. Most teams will have vast discrepancies. Depending on the time available, I either have the teams redo the measurements and calculations the next day or have them do them on their own time until all calculations are within 10% of each other (it is amusing to see the teams take more time and care in making their measurements the second time around).


As a wrap-up, I like to show the graphic below to show all the work that was done to map the Indian sub-continent. I am still looking to find a PBS Nova program from several years ago that showed how that Great Trigonometric Survey of India lead to the first measurement of the height of Mount Everest. 

So, now I have a way of letting my guys go outside on a nice spring day while justifying this with myself, my principal, and concerned parents.

For AP students

When I do this with my AP students, usually early in the academic year, I have them measure distance with their walking stride. We spend some time gathering some distance vs number of steps on the nearby athletic field. They then do a linear regression analysis with their personal data, and use the resultant equation to measure a base-line.

More on using Geogebra in the Physics Classroom

There is a site with interactive physics apps you might like, and these apps work in an iPad as well as real computers.  The site is www.geogebratube.org.  Here is one example.

If you cannot see the interactive app above, go directly to the source here.


These apps are made with the FOSS program Geogebra which can be downloaded at www.geogebra.org.  Geogebra is not that hard to learn to use and the apps it makes can be used on any computer which has Java.  I have made a couple and placed them on my class webpage. You can even download source files from geogebratube and modify them if you want. 

While the following apps are not directly on Geogebratube, I recommend that you check out the ones made by Daniel Mentrard at http://dmentrard.free.fr/GEOGEBRA/index.htm.  He has a large collection covering all areas of what we teach.  Check out this from his site.


 I have found that if you erase htm (or html) in the address bar of your browser and replace it with ggb, you can usually download the source file so that you can replace any French text with English before using it in class or you modify it in any other way.

Currently the only way that a student can interact with these apps on an iPad is through the Geogebratube site, but there are indications that future developments in the Geogebra program will allow you to embed these apps into an ebook that can be read on an iPad directly without going through a web-browser.

While most of the apps you find at Geogebratube are not as refined or sophisticated as ones that you may already be using from PhET (phet.colorado.org) or Open Source Physics (www.opensourcephysics.org), you can make these apps without paying for program to make Flash apps and your students using iPads will not be left out.  Since my school is going to be an "iPad school", this tool looks like it will be a major one used in my classes in the future.

Special Relativity without Algebra

 What's so Special about Relativity?

Special relativity is one of those fun topics I like to do when possible.  While I usually cover it the last week of school, this year I have decided to do it the week between the Easter break and the start of the student projects on modern physics.

I start in the usual way, by motivating the scientific conclusion that everybody measures the speed of light to be the same, no matter how they are moving.  This then leads to using the animation that shows that a moving clock ticks slow.  But rather than use the geometry of this situation to derive the time-dilation equation (a MEGO exercise most times), I use the interpretation of SR that everybody is moving through space-time at the speed of light.  If you are at zero speed in space, you are moving through time at the normal rate.  If you are moving through space at a non-zero speed, you are moving through time at a slower than normal rate.

This interpretation then leads to using this model.

This is a picture of a Geogebra dynamic model that I display to the class (available here) and that they can use on their iPads.  Students are given a worksheet which they use to calculate the time dilation for various speeds and also the speeds needed for various time dilations.  The next day comes time travel!

By not using the algebraic equations too soon, I have found more students engaged and  understanding SR. We then spend a couple of days discussing the possibility and feasibility of time travel.

P.S.  If you have not checked the program Geogebra, I suggest you do.  Learning how to use it is not too hard, and there are some examples (and more) you can use in your class.  Since it is FOSS, you share it with your students, embed things in webpages, and otherwise make static situations dynamic.  Below is the model embedded in this page (if you don't see the app, come back later.  I am having problems getting it to work on this page.  Go to this page to see it in action.).

Modern Physics, for and by students

One advantage to teaching at a private school is that I am not held hostage to the year-end New York State Regents test.  So, when it comes time for atomic and nuclear physics, I can de-emphasize the mathematics and emphasize the history and timeline of discovery.  Which also means that I can hand over the day-to-day work to the students.

This started a few years ago when I was thinking of ways to combat the final few weeks of senioritis.  It was also at a time when the Principal wanted us to move away from final exams for the seniors and toward using "alternate assessments".  So, I decided to have the students teach the other students the units on Modern Physics.  Even if the seniors tune out the rest of the time, they will at least know something about one part of atomic-nuclear physics.

May starts in January

Every year I tweak things a little, but I have the basic framework in place.  Shortly after the January Exams, I show my guys the topics to be covered and the grading rubric which are then posted both in the classroom and on the class website.  About a week later, I publish a schedule for those presentations.  They then have about a week to chose a partner and decide on topics of interest.  The first couple of years, I would have the teams give me a list of desired topics (in order of preference) and days on which they would be taking AP exams.  I would then spend many hours trying to make everybody happy (you know how that ends up).  I now make it easy on myself.  

No Blood Please

On decision day, I have my guys work things out themselves.  I gather the seniors in the back of the room, put down a copy of the schedule, and tell them "I don't care how you decide, as long there is no blood.  I just want you guys to agree as a group on what teams will do what topic."  To cover my butt, I do remind them what it means to be a Jesuit-educated gentleman, and that I reserve the right to make the assignments if I think that things are not working out, but I have not had to do that yet.  The guys generally do spend some time making sure that most teams are satisfied with the assignments.  After the seniors have made their decisions, the juniors have their turn.

E-books are real books

Our students live on-line. So that my guys at least know a lot of good information can be found in books and not just on websites (and that Wikipedia is not the end-all-and-be-all), this year (2013) I spent time showing my classes how to find and download ebooks from our local library system.  Since we live in New York State, we are also eligible to get a card from the New York Public Library. I showed them how to apply (with the warning that there is a 2-3 week turnaround time). The reason I like the NYPL site is that there are a lot more physics-oriented books there. Also, since some of my seniors will be going to college out of state, I let them know that the NYPL will not know that they have moved. They will have one more resource available to them to help make their college career successful.    

Drinking from a firehose?

Am I  showing my guys too many books? It is well-known that when presented with a plethora of choices, many people give up and just make random choices. I sense that that is what is going on with some of my guys. I am tempted to make a list of appropriate books for each of the topics, but I don't want to spoon-feed my guys. Please give your opinion in the comment section below.  
 

An Outline can't be Copied and Pasted

The teams then have 2-3 weeks to write an outline for their projects (timed so that they have the Feb break to work on this if they want).  I then review those outlines for the basic material I want covered and make some "comments for improvement".  The teams then have 2-3 weeks to work on the drafts.

Not a First Draft

Notice that I do not use the term "first draft".  To most high school students, "first draft" means "I can just throw some stuff together at the last minute to pass in, but I will wait to do the real work the night before our team is up to present."   I tell my classes at least three times that I am using the academic and bureaucratic definition which means the draft is the proposed final version; it is being reviewed only for minor revisions.  I know that most teams will still need major revisions, but I want them to do some work at this time.  

I then review the drafts and "make comments for improvement".  I try to time this so the the teams have the Easter break to work on their final presentation (although the solar-lunar cycles don't make this possible some years).  I have learned to tell my guys that I am reviewing only for content, not for veracity.  One year, a team made a glaring mis-statement during their presentation.  When I called them on it, they pleaded that when I gave the comment "Looks good" on their draft, it meant that to them that all aspects were good.  

The presentations are scheduled for the two weeks of the AP exams and the two weeks after.  I sit in the back, marking the rubric.  At the end of the presentation, the students ask questions, then I have my turn.  If there is time, I will use the end of the class to "amplify" on some things that I think need be discussed.

While still a work in progress, I have found this approach to atomic and nuclear physics a decent one for high school students.                 

Drinking the Kool-aid

Hats off to the marketing people at Apple.  They have convinced many people that the future of education lies within the slender confines of the iPad.  The past is just that, the past.  Clinging to such archaic remnants is almost anti-American.  However, I see and value the past that Apple thinks is useless.

My school is becoming an iPad school next year.  While I look forward to the common platform that students will have, I lament the things that I cannot do with them in my classroom.  Sites such at PhET and Open Source Physics which use Flash and Java do not work on the iPad.  The educational value of these sites is without parallel online.  I had hoped to incorporate some of these applets into the electronic textbook I wanted to modify for use in my classroom.  I am unimpressed with the physics textbook that they offer up as an epitome of an iBook. 

So, one of my summer projects will be to learn JavaScript and figure out how to add such applets to my ebook.  The last full-scale language I have programmed in is Pascal.  While I have recently written some basic shell scripts for my Linux computers, big programming is another thing.  So, thank you Apple for making me learn new things.

Realizing that I have to change

Good teachers find what works in the classroom and stay with that.  Great teachers know that what works one year may not work in future years.  This year, I realized that I have been merely a good teacher.  I want to become a better one.  This blog will chronicle that journey. 

 I must acknowledge my debt to other teachers who have inspired me to use different means to reach my students.  The high school teachers  Frank Noschese , Rebecca Howell, and Brendan Noon have given me good examples of using web-based tools to good advantage.  The university professor Rhett Allain has given me many good examples of using the video analysis software package Tracker (though I have not forgiven him for beating me to writing about the physics of Angry Birds).  I hope I can equal their contributions to physics education.