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High School Tutoring
For about ten years starting in 1997, I had been a volunteer tutor in math and physics at Cambridge Rindge & Latin High School with Cambridge School Volunteers , and for nine years, also an advisor to the Science Olympiad team.
The tutoring consist of an hour twice a week after school, at the high school Tutoring Center superbly managed by Rene Meshon. The students have to decide for themselves that want some help, rather than being placed there unwillingly by parents or teachers. This means that they've already crossed that first level of motivation in signing up. They are then matched to a tutor for regularly-scheduled sessions, usually twice a week.
That's not to say that all are equally conscientious. No-shows are a common complaint among the tutors. But the rewards far exceed the annoyance of occasional no-shows. And if an assigned student doesn't come, there's often the chance to work with a walk-in instead.
The main virtues in tutoring are not only knowledge of the material, but also high degrees of flexibility and patience. The tutor must be able to sense when a particular approach in solving a problem isn't working, and has to be able to quickly try other ones. It's also important to have the student do as much of the work as possible, with guidance, rather than doing problems for him or her.
Student abilities and background will vary greatly. Some are recent immigrants who might not understand the wording of certain problems rather than the concepts. Preparation is sometimes poor - I've had students in algebra that didn't know what 6 time 6 was without a calculator. They will often try to work too fast or will guess at answers; the rising inflection at the end of their response usually prompts a "are you asking or telling?" from me. My objective will always be understanding and reasoning, assuming or hoping that some will sink in, even by a kind of osmosis.
When possible, I will also tell them why the problems and concepts on which they're working are important, and how they apply to real life. On the other hand, there are times that I'll admit to them that they'll never see a particular kind of problem again (such as, say, synthetic division).
The reward comes in trying one's best to help, and in seeing a student be able do do or understand something that he or she did not before. There's also appreciative feedback from the dedicated staff that runs the Tutoring Center. Then, to my great surprise, on May 7, 2003, I became a recipient of a Mack I. Davis II award for "extraordinary service to the Cambridge Public Schools" (more at the Harvard Gazette site). Having attended previous receptions where this award was presented, this was a great honor, and so I am very proud of it.
About the only negative in the whole experience is the parking situation around the school. The People's Republic of Cambridge has lots of "Resident Parking Only" and only a limited amount of metered parking, of which only a fraction has 2-hour instead of 1-hour meters. Because the tutoring session is one hour long, I have to search out one of the 2-hour spaces. My entreaties that tutors get some help with the parking situation have drawn sympathetic ears, but no action.
The incarnations of "lovely Rita" in Cambridge are also very agressive ticketers. Once I stayed longer than the tutoring hour with students that were making some progress, only to find that by returning to the car two minutes too late I already had a ticket. An appeal to the Parking Clerk citing extenuating circumstances was rejected, and a letter to the mayor did not yield any response.
Advisor to the Science Olympiad team
The Science Olympiad is a one-day competition where teams from various high schools compete in many events. The events are known beforehand, and there are about ten weeks of preparation.
The year 2007 was my ninth as an advisor, one of a number volunteers, on the Cambridge Rindge and Latin Team, specializing in construction events where the objective is to build as light a structure as possible that will hold a certain weight. The events in which I've advised are listed on the right.
Update: In 2008 I decided to suspend my advising of the CRLHS Olympiad team, feeling that it had lost its focus on enjoyment and interest in science. My last advising experience was one of herding cats, badgering the construction team to get to work on the project and to learn from what I was trying to help them with. As one of the other advisors commented, it seemed more like a social club now. There was also a deterioration in performance: before 2006 the team placed consistently in the top seven during the competition, from 2006 to 2008 it has placed in the mid-twenties.
Construction Events:
Boomilever (2001-2003)
Tower (1999-2000, 2004-2006)
Storm the Castle (2004-2005)
Other Events:
Sounds of Music (2002)
Experimental Design (2003)
There is an official Massachusetts Science Olympiad site, with lots of information about the various events, and also scoring results of the competitions. High school is Level C. Cambridge Rindge and Latin generally placed quite high among the approximately 30 teams, until 2006:
twenty-sixth place in 2008,
twenty-third place in 2007,
twenty-third place in 2006 (what seemed like an off-year turned into a trend),
seventh place in 2005,
tied for fourth place (and fifth) in 2004,
fourth place in 2003,
sixth place in 2002,
fourth place in 2001,
third place in 2000,
first place in 1999.
2005 Science Olympiad team
(Laura Margosian photo)
Tower
Just like Boomilever (see below), a construction event in which the objective is to build a structure with minimum mass that will support a 15 kg weight. Tower is easier than Boomilever in the sense that it's inherently a more stable structure than a cantilever. However, this puts a premium on low mass.
2004: As usual, the only materials that can be used is wood with a cross-section of 1/4" x 1/4" or smaller, and glue. For the 2004 competition, the structure had to be at least 500 mm tall, and the upper 200 mm had to fit inside an 80 mm diameter cylinder. The base has to straddle a 200 mm x 200 mm hole.
The 2004 Tower team took a somewhat conservative approach with a structure weighing 25.7 grams that held the full 15 kg mass easily during testing; they placed fifth overall in the competition.
2005: The rules changed a little for 2005 - now the tower was required to be at least 600 mm tall, with the upper 300 mm fitting inside an 80 mm diameter cylinder. The team changed the design of the top section so that it consisted of triangles rather than vertical members, and used 1/8" x 1/8" balsa. The bottom part was made lighter by eliminating some bracing and going to 3/16" x 3/16" legs. Best of all, the team performed a number of separate tests of the bottom and top parts to gather information on stability. As a consequence, the final model for the competition had a mass of only 19.19 grams and held the full 15 kg weight, quite a feat since its mass was only 75% of last years although 20% taller! This achievement was rewarded by placing 2nd in the competition.
Paul, Matt and myself
(Laura Margosian photo)
Applying the load
Afterward: it held!
2006: The rules changed again, as they usually do from year to year. The height of the lower part was a maximum of 150 mm, with the top part being 350 mm high. With the team consisting of one member for almost all of the project, we decided on a top section that would be easier to construct than last year's. With time to build only one model, we decided not to test it to avoid the risk of breaking it. At the competition, it held more than the full weight of 15 kg, while weighing in at 21 grams. The rules this year, however, did not place the models that held full weight above the ones that didn't; the efficiency score of load held divided by mass of tower was used to rank all models, even the ones that broke. With that criterion, the CRLHS tower placed eight, the second-best showing by the team in an off-year.
Storm the Castle
The objective in "Storm the Castle" is to construct a throwing machine, or catapult, that will throw a projectile over a large distance with great accuracy. It turns out that there's a great interest in and lots of information available on these devices, or trebuchets:
The 2004 project team consisted of two the best people in the CRLHS Science Olympiad group, and so put together a very robust and effective device; they placed second in the competition.
The 2005 rules required the device to be less wide. The team, after modifying the 2004 structure, struggled with it and unfortunately was unable to achieve consistent results.
Boomilever
The challenge in this event is to build a cantilever structure able to hold 15 kg (about 33 pounds!) at a point 50 centimeters (about 20 inches!) from the wall on which the structure is mounted. One constraint is that no part of the structure may touch the wall more than 15 cm below the point where it is mounted - basically, one is trying to hold a weight applied with a lever arm of 50 cm with a lever arm of 15 cm. Only wood with a maximum cross-section of 1/4" x 1/4" may be used, except for the attachment base(s); i.e., where the structure is held to the test wall by one or two 1/4" bolts. Two 1/4" holes spaced by 20 cm are provided for mounting.
The loading of the structure is applied through a 50 mm x 50 mm block that sits on it. A hook is attached to the block, to which hook a bucket is attached - the bucket is then filled gradually with sand or water until the full 15 kg load is reached.
In our third year in this event, our learnings from the previous two years were rewarded with a structure that held the required 15 kg, and placed second in the competition. To show how difficult it is to build this structure, out of about 25 schools that competed, only 7 had Boomilevers that held the full weight. Sometimes there's heartbreak - one school's Boomilever broke at a weight of 14.4 kg, only 0.6 kg from achieving the objective.
We had a similar experience last year. As the last school to test its Boomilever, we knew that if it held the full weight then it would take first place. The bucket was filled with more and more sand, yet the structure held rock-solid, without even any bending. The suspense was breath-taking, but then at about 12 kg the structure gave way - one of the attachment bases had failed.
The results for the 7 this year that held full weight were
The Score is a measure of structural efficiency, or weight (really mass) held divided by the mass of the structure.
Click on the thumbnails below for an expanded image of some of the structures that held the full weight:
Caption: From left to right:
Belmont,Newton North,
Stoughton,Cambridge R&L
Note: In the images above, the Boomilevers are sitting on their attachment bases; under test conditions, they would be mounted on a vertical wall as a long cantilever, as in the image on the left below.
Our Boomilever (thumbnail to the left - click on it for a larger image) evolved over the last several years, as various weak points were discovered in structures that broke before they were able to hold the full weight.
Caption: Boomilever mounted on a home-made test wall, with the test wall legs on two tables separated by a gap. The load is applied with the block at the right - the hook on the block holds the chain to which the bucket (not shown) is attached. The structure is attached to the wall by two 1/4" bolts, separated by 20 cm, holding the two attachment bases. The bottom legs at the wall are just above a line drawn on the wall that is 15 cm below the attachment holes. This structure held the required 15 kg, while weighing only 66 grams.
Throughout, the design sought to be tolerant of construction imprecision.
Some of the design considerations that evolved over time are:
The long structural members at the top are in tension, while the ones at the bottom are in compression. Tension tends to straighten the top members, so they will not need much bracing. On the other hand, compression tends to make the bottom members bow outward, so substantial bracing is needed to prevent failure through bending. A brief moment analysis showed that the force in a long member is at a minimum, though considerable, when it is horizontal. It was therefore decided to make the compression members horizontal, to reduce the bending, and so to have the tension members angled.
We decided early on that surface-to-surface contact between wood pieces would give us the strongest glue joint. The alternative butt joints, where ends of pieces are glued to other pieces, seemed hard to build reliably and likely to fail in tension. This meant using small spacer blocks of wood so that braces could be glued so that joints at both ends would be in the same plane.
Our choices for wood were balsa and basswood, the latter being stronger but also denser. We restricted the use of basswood to the tension and compression members, and to the attachment bases. That gave us the strength we felt we needed for the compression members. We had initially used balsa for the tension members, but first found that we needed to reinforce them; later, we experienced failure at an attachment base because the wood fibers separated in tension, although the glue joint held.
The 50mm x 50mm load block sits on two short horizontal pieces separated by 40 mm; these short pieces also join the compression members at the front end. A critical piece of vertical bracing on each side runs from the inward short piece on the compression member to the tension member just above it. We discovered that without this bracing, about half of the load acted on the inward short piece and produced spectacular downward bending of the compression member.
Sounds of Music
In this event, the two team members are asked to construct two musical instruments which are capable of playing all the notes of a chromatic scale with equal temperament over an octave from C5 to C6. They need to be able to play two tunes as a duet, one supplied with the event description, and another of their own choosing. With Concert A4 = 440 Hz, the range C5 to C6 consists of 13 notes from 543.25 to 1046.50 Hz, with adjacent semitones in the ratio of the twelfth root of two, or 1.0595 .
Last year's (2002) team chose to construct musical chimes and a plucked string instrument. Chimes can be made fairly simply by cutting aluminum tubes or rods to the proper length and then hanging them from a frame, to be played by striking them with a wooden stick. The detailed theory of musical chimes is fascinatingly complex - they are one of rare instruments that have non-harmonic overtones; i.e., they are not integer multiples of the fundamental. I've described the theory in a note on Musical Chimes, a note which gave me a fix of some higher-level math.
The stringed instrument had its own challenges. With the required frequency range of C5 to C6, it's possible to build instruments where the length of string requires a tension that exceeds the yield point of steel. My advice to the team was to "think ukelele".
Experimental Design
At the Science Olympiad event, the team is given some materials (which they haben't seen before) and asked to design an experiment. perform it, take data, and write it up as a report, all in 50 minutes! They are allowed to use a calculator, meter stick and watch. As one can imagine, there's a premium of breadth of knowledge, quick-wittedness and good teamwork.
Some material kits which I assembled for the team
Several different kinds of balls - tennis, lacrosse, golf.
A bucket, a graduated beaker, and a rubber hose.
A set of five dice.
A large flat board, two wood blocks, several sheets of sandpaper with different grit, a sheet of glass.
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