In the summer of 1998, my friend Jim Greer and I hosted a week-long contest-oriented engineering and problem solving camp at our old junior high school. We modeled the contest after other engineering contest such as those held at MIT but scaled down the exercises to one or two hours and put a lot of emphasis on team work.
The most spectacular result was that everyone involved had a blast. We hoped that the students would go away with at least an improved vocabulary of engineering and team work skills, and I think that they did. We put a very big emphasis on vocabulary through out the week which I summarize below.
Our exercises ranged from outdoor rope-course-like elements to pen and paper exercises. We tried to relate all of the non-problem solving exercises to existing fields of engineering and introduce a few basic concepts and words. The following summarizes some, but not all, of the techniques we tried.
Pair the students into teams. One student describes a shape, the other one draws the shape based on the description without seeing it. The "director" must not show the figure to the "drawer" nor gesture with their hands. This is an excellent exercise for learning to communicate with clear and concise language.
People of all ages have an incredibly difficult time with this simple task. Students with geometric knowledge often do better as they will be familiar with radiuses, tangents, and other useful vocabulary. However, even geometric novices can become very efficient with a little practice. Accuracy will improve dramatically with just a few practices and a little help.
The most effective results are obtained by creating vocabulary. For example, an effective description is: "Let’s call the top of the page ‘north’. Starting from the dead center, imagine a point half way to the northern edge. Call this as point ‘A’. Now, imagine another point southeast of center halfway to the corner. Call this point ‘B’. Draw a thick link, about a pencil’s thickness, from point A to point B."
Ineffective descriptions are filled with vague language. For example, "Draw a kind of diagonal line from below the top center to the right." A look of confused pain and frustration in both students often ensues. Encourage them to agree on a common vocabulary. A contrived demonstration helps immensely.
A useful trick to this exercise is to use an overview description in conjunction with detailed instructions. For example: "We’re going to draw something that looks a bit like a smiley-face without the nose and missing one eye. We’re going to draw the mouth first which is a half-circle starting at…" This kind of "sanity checking" helps the drawer double check that the drafting instructions are logical.
This idea was inspired by similar exercises in [ROHNKE89]
This is an exercise similar to "Blind Shape Transcription" which teachwa the use of clear and concise language. The students are again paired into teams, one student the "director", the other the "builder". This exercise can be done with any standardize building system such as Lego, Tinkertoys, K*NEX, etc. (I prefer K*NEX). The director describes a pre-built shape and the builder recreates it while blindfolded using construction pieces which are randomly scattered between the pair. The director must not physically help the builder nor let the builder feel the original shape. The describer may verbally help locate pieces such as: "Move your hand to your right a little bit and you will find the medium-sized stick."
Like "Blind Shape Transcription", many people have a very difficult time with this exercise. Fortunately, there is a limited variety of construction pieces and therefore creating a vocabulary is not difficult. Encourage the students to agree on a vocabulary before they start such as: "short stick", "half-connector", "jointed half connector", etc.
Unlike "Blind Shape Transcription", this exercise requires that the students use a three-dimensional reference system. This is very difficult, and the students will get nowhere until they agree on what is "up", "right", etc. Encourage them to establish this before they begin.
A bad habit that can easily develop is for the director to "micro-manage" the builder. It is easy to forget that the builder is not a robot. For example, instructions like: "Move your hand towards me a little bit… a little bit more… stop! Now move your hand to your right a little bit… more… more… stop! Now pick up the piece directly below your hand" are too specific. More general instructions are more effective such as: "Find three half- connectors and three medium-sticks." Resort to help like "there is a medium stick on your right" only when the builder is stuck.
This idea was inspired by a electronic game of leading-the-blind at Entros Restaurant in Seattle Washington.
An egg is placed on a pedestal about three feet high. A rope circle is circumscribed around the pedestal with a radius of about 10 feet. The team must retrieve the unbroken egg without stepping inside of the rope circle by fashioning tools from a collection of household items. For supplies, I suggest a coffee can with no bottom, 12 inches of tape, 25 feet of string, a coat hanger, an egg carton, a 2-3 ft piece of PVC pipe, a file folder.
Most teams of four will solve this 10-30 minutes. There are many good solutions, and this fact creates a lot of conflict between the team-members as they argue about which approach to use. There are also a lot of bad solutions and teams will often become fixated on making a bad solution workable instead of abandoning it for a better alternative. There will frequently be a lot of "if we’d done it my way" and "I told you so’s" within the group which should suppressed by the instructor.
An array of cinder-blocks is placed in the arrangement illustrated in Figure 1 and the team is given four 4x4 wooden posts which are long enough to fit between any two blocks orthogonally, but not diagonally. The team is instructed to get all team members from one side to the other without stepping in the "swamp" between blocks.
There is a non-obvious optimal solution to this problem which is to place one of the posts between the blocks and then a second beam supported at the mid section of the first beam and a third block as illustrated in Figure 1. However, many teams do not find this elegant solution and thrash for a considerable time with team members stranded on blocks. Frequently, one team member, often a quiet one who stands back and considers the problem, will see the solution but will be unable to get anyone to listen. The instructor may be helpful by suggesting that everyone be quite for a moment and listen to everyone else’s suggestions.
A rope is often helpful, and team member should be encouraged to use it to lower the beams carefully on to the blocks because cinder-blocks will shatter if a beam is dropped directly on to them.
The exact rules must be made very clear and enforced by the instructor because there are a variety of ways to "cheat." Some possible rules are:
This idea was taken directly from [ROHNKE89]
Two lines are demarcated equidistant on either side of a horizontal tree limb such that two 4"x4"x8’ wooden posts can reach from one side to the other (with a little slop) when laid end-to-end. All team members start on one side and must get everyone to the other side. A collection of tools is supplied. I suggest: 20’ of string, 20’ of strong rope, a coat-hander, a 2-3’ PVC pipe.
This is a hard problem. The first problem to be solved is suspending a rope from the tree branch which is too high to reach. Attempts will be made to throw the large rope over but if properly designed, these attempts should fail. Instead, the sting should be thrown over and then used to haul the larger rope over.
There are only a few solutions to this problem and all involve suspending one end of a board with the rope hanging from the tree and then hauling the other board out and suspending it on top of the other board as demonstrated in Figure 2.
While it is technically possible to solve this with only one person, the most common solutions involve one team-member holding one end of a board while the other team members jump to the other side. Unfortunately, this strands the last person (the one holding the board) and the rules say that everyone must cross.
Young teams may need up to an hour to solve this (some may never solve it). Older teams will typically solve it more quickly as they typically intuit some of the logistical problems such as using the string to pull the rope over the tree.
See the anecdotes about a typical male vs. female approach to this problem.
Teams are given equal quantities of drinking straws, paper-clips, string, and tape with which to build the tallest possible structure. The simple rules elegantly reveal the subtleties of structural engineering.
In this exercise, optimal results are obtained through very careful design and fabrication. Most students will, however, attempt to build a structure ad-hoc which will be surprisingly unstable to them. The most common problems result from using four-sided geometrical units instead of triangles which results in unstable joints. Another common problem is weak joints caused by sloppy assembly. The students should be encouraged to be precise and methodical; to measure twice and cut once.
This exercise is greatly improved if the students are given time to play with the tools free-form before building the tower and engaged in a conversation about their discoveries. The teacher may encourage them to analyze existing tall structures such as radio antennas, the Eiffel tower, etc. A discussion of triangular stability, tensile and compressive forces are all helpful.
The instructor should be particularly careful about the analysis of common structures such as buildings. Structures such as homes or sky scrappers appear to use exclusively rectangular primitives (walls, floors, ceilings, etc.) and this fact leads most students, quite logically, into building their structures with similar rectangular form. An elegant demonstration will explain this anomaly. Cut a sheet of thin plywood or plexi-glass into a square. Devise a way to stress this sheet on one end such as hanging weights from it or compressing it with bar clamps while supporting the sides so that it can not bend. Begin to cut material away as shown in Figure 3. Repeat this by removing more and more material until a triangular cross member is formed. This demonstrates that a sheet actually serves as a triangular support. Thus, the sides of houses and buildings often rely on the sheeting to supply diagonal support, not just to cover the walls.
Student teams must build a contraption out of a standard construction set such as Legos, Tinkertoys, or K*nex (I prefer K*nex) which must launch a ball as far as possible. Human force must not be used to propel the ball, only to initiate the machine. For example, someone may pull on a string which releases a latch and allows a ball to roll down a ramp, but they may not build a sling to launch the ball.
There are three general solutions to this problem: ramps, catapults, and trebuchets (levers). Trebuchets are by far the best solution because they are actually using human power to launch the ball albeit in an indirect fashion. Unfortunately, this violates the rules and is likely to cause an argument from the losing teams, so the instructor should be prepared with a decision about this.
This exercise is simple and takes only about 30 minutes to prepare. During construction, teams will practice with their machine and this causes problems if the teams can see each other when one team "steals" another’s ideas. This also causes problems when one team realizes that their solution is inadequate and become sore losers before the contest is even started. Boys, in particular, tend to become very destructive when they realize they are going to lose and find ways to "accidentally" break other teams contraptions.
Paired teams devise a non-verbal code to communicate across a long distance. Each team is given an identical text-only message which
The best thing about this exercise is that one of the rules is "no talking." The accompanying silence is a great joy to the instructors after days of yelling over the din of students.
Without guidance, students are typically at a loss to create a code from scratch. Unfortunately, when the instructor demonstrates a code such as a numbering system, the students will take this very literally and will only devise numbering systems. The instructor may want to help students in teams only so as to ensure there is more than just one variety of solution.
Students are also unlikely to create a compression scheme such as omitting vowels unless this idea is suggested to them. Similarly, students are unlikely to devise flow-control semaphores such as "wait, I didn’t understand the last message" and "repeat last word" unless they are prompted to do so.
The students are split into two large teams, one on each side of the gym. Each team is given an identical collection of miscellaneous items such as hula hoops, jump ropes, wheeled platforms, and balls. The teams must get everyone across the gym without touching the floor.
This simple game can be used anytime and is especially good at the end of the day when there isn’t enough time for another fully planned activity. Very surprising uses for the tools will frequently be devised. Be warned, this will become an extremely noisy activity as the students yell back and forth to each other.
This idea was created by Roberta Lintz, St. Andrew’s Episcopal School, Austin, TX
[ROHNKE89] Cowstails and Cobras II; Rohnke, Karl; Project Adventure, July 1989; ISBN: 0840354347