Our Seventh Grade is heading to Cape Cod, so I thought it a good time to share the following excerpt from an article by Woodworking Teacher Gary Kessler, which appeared in the Summer 2014 issue of Saint David's Magazine:
For communities of students, I believe STEAM (Science, Technology, Engineering, Mathematics, and, at Saint David’s, the “A “signifies Aesthetics) has the potential to facilitate an approach to, and a meaningful engagement with, big ideas that are interesting and relevant. It is not a method, as such, so teachers looking toward STEAM need to help develop and understand guiding principles. The goal is to create curriculum-related experiences that are not just informative but intellectually and emotionally nourishing, involving the whole child...
In the evolution of the “Critters” project, I started out with no particular central question in mind. I did not even know very much about STEAM. I was doing work directed toward my personal interests as a woodturner. I have some background in geometry and wanted to see if I could develop a satisfactory method for constructing hollow wooden spheres (i.e., balls) from turned plate sections. I would cut carefully mitered pieces on the band saw, round them inside and out individually on the lathe, and later glue or otherwise fasten these “shells” together to complete a hollow sphere. I had in mind, however, that my students might use a much simpler method, with regular classroom materials and tools, to express essentially the same geometry. For me, this type of thing is both fun and a worthwhile challenge. However, I also had to consider how such a project would be appropriate for the boys, and whether they would find it enjoyable.
I think that familiarity with the geometry of the sphere and partitioning of 3-D space are going to be increasingly important in the future. Explorations into macro- and micro-worlds (where gravity is not the predominant force) are ongoing and becoming more common. To understand what conditions are like, it would be useful to be able to imagine a space where “up” has little or no meaning.
My spheres were also going to be partitioned into plates in a manner consistent with the Platonic
solids. The number of identical plate-shapes in a partitioned sphere must be one of the following: 4, 6, 8, 12, or 20. These are manageable numbers, and they conveniently correspond more or less to workgroup sizes into which a classroom of students could be organized.
So these two thoughts, future importance to society and convenient numbers (for teacher), encouraged me to keep thinking about a school use. But “fun and inviting” (to the boys) was the essential aspect that would need work.
I started at the end of school in June, and I was getting along pretty well with my wooden spheres, having soon determined all the necessary angles and made cardboard templates and such. In August, I attended a NYSAIS STEAM conference. It was great working with teachers of science, technology, engineering, art, and math, but those from other disciplines had equal input in discussions and team project-making.
Many of the teams employed 3-D printers, Arduino robotics, and other gizmos. In addition to wooden spheres to show colleagues, I had brought a few hand tools for making Platonic solid prototypes, and the STEAM committee provided supplementary materials. I latched onto some colored foam-core boards and some colored card stock and started slicing and splicing in my dorm room during breaks between meetings. I found that if I used circular disks rather than polygons as polyhedron faces, it radically reduced the amount of geometric construction and use of tape eliminated all gluing and clamping. Using bits of tape, the initially floppy structure would grow stronger as more disks were attached at their tangent points, and it became quite rigid as the last disc was attached in place— a nice “aha” moment. It left holes at the vertices of my colorful foam-core dodecahedron (a polyhedron normally with 12 pentagonal faces, 30 straight edges, and 20 pointy vertices), but this disc method yielded a sturdy structure that exhibited the Platonic geometry.
Soon after returning to school in September, I was looking for ways that the disc idea could be used in a curriculum project. Several possibilities arose, but the one that made the most sense was to incorporate it into the annual school trip to the Cape Cod Sea Camps with the Seventh Grade.
For this, I had to create something that didn’t clash with the rest of the program, and time was pretty short. I decided to simplify further and buy nine-inch plain paper picnic plates to use as discs and to use staple fasteners. I made, for each kind of polyhedron, templates to indicate where staple locations needed to be marked and coded instruction cards telling how many plates to join in a “ring” around each vertex. The “holes” at the vertices became design opportunities for adding on to the structures. I thought we could call them “plate-onic” solids. The boys could now make these things, but for what reason?
Within the scope of three days, the core activities in Cape Cod would mainly focus on the natural science of the ocean and seashore with the study of perspective drawing alongside.
Four program events, two of them outdoors “in the field” and one indoor presentation through Massachusetts Audubon, Wellfleet, coupled with a group of activities on one afternoon with Dr. Benway of Woods Hole Oceanographic Institution, would provide a wealth of information on sea life and ocean and seashore environments.
I decided that, for a change of pace and to help the boys digest some of that volume of information, they would design and make “creatures” adapted to an environment they would specify, either made up or one they learned about on the trip.
The creature would be imaginatively and playfully created out of a combination of new knowledge and fantasy, but its body would consist of a polyhedron with added attachments for limbs and other features. I went about constructing a prototype with a paper plate “cube” for a body, some rolled up newsprint for limbs, ears, and a tail, and a paper cup for a snout. Making up a species name, Pseudocanis hexahedris, I called it “Tripod” and wrote a short sample scenario for it.
The construction activity was organized into three phases, to be followed by a presentation session. The first phase, involved communal construction of ten each—tetrahedron, hexahedron, octahedron, and dodecahedron. (We deliberately dropped the icosahedron, for simplicity). That would be enough for the 40 boys on the trip to each make one. At each of eight tables there were paper plate discs, staplers, instruction cards, and templates with pencils for marking the spots for stapling.
After brief instruction on how to use the templates and how to read the symbolic pattern on the card, construction proceeded. There was a small bit of confusion at first and energetic discussion at the tables. Teachers helped a bit getting the ball rolling, but then there was quite a bit of self-organizing among the five students at each table as they zoomed forward in their constructions, and they were soon finished. There arose one or two small “errors” among the more complicated structures that led to a short but significant impromptu discussion of the value of “variation” in nature. I planned for a 50 or 60 percent success rate, but 40 viable structures were successfully completed, for 100 percent.
Teachers were amazed and impressed. Pinching myself, I congratulated the students and announced, “The individual ‘plate-onic’ solid you made belongs not to you, but all belong to the community for critter construction.”
Next, randomly teamed by teachers, 20 pairs of boys adjourned to the other side of the partitioned dining hall to create an imaginary setting and write a short script focusing on five things: creature’s name, where it lives, what nourishes it, one adaptation to its environment that the team incorporated, and the shape chosen for the body.
Once their script was finished, each team in turn picked out one of the 40 structures, materials for attachments, markers, etc. and began creature construction. Some teams chose to use two or more polyhedra for their “critter.” Every team that evening lost track of time, thoroughly engaged in this activity, and we teachers allowed them to go quite a bit beyond normal curfew.
The next day after dinner came the final part: team presentations. Each team was recorded delivering a one-minute presentation of its “critter,” addressing each of the five things in the script. The teams were quite comfortable being recorded in front of their peers, and each boy in his own way revealed something memorable about his personality and engagement with his project.
The amount of time spent developing this project was considerable, but the rewards made it well worth it. I do not remember ever being discouraged or weary during the process. It may seem odd, but I now feel a kind of gratitude toward platonic solids that was not present before. It’s as if they, or rather the iterations of them by the 40 students engaged in this exercise responded to questions that were implied all along.
I put it to the boys this way: “It’s well and good that Nature is able to take a shape and endlessly repeat it, as we see. But Nature does not read math textbooks, so how does it do this?” I figured this little exercise might indicate for them how repeating coded patterns might have something to do with it, each pattern making a different form out of similar component materials, and I think it was successful. But I did not anticipate the bit about variants. This points to deeper questions about how Nature could contain such a variety of forms, why some traits are heritable, valuing and tolerating difference, and more.
I am grateful for the support I received from Headmaster O’Halloran and Upper School Head Sara Peavy, the generous help and support from my teacher colleagues on the Cape Cod trip, the expert input of the naturalist presenters from Mass Audubon (Wellfleet), and the cheerful beneficence of Dr. Benway of the Woods Hole Oceanographic Institution. The unfailing cooperation of the staff at Cape Cod Sea Camps, Brewster, Massachusetts, in helping us make use of their amazing grounds and other facilities really smoothed the way, and it was greatly appreciated, as always. Finally, thanks go to the boys of Saint David’s class of ’15. Their openness to giving of themselves in this activity is encouraging to me beyond words. I will remember that with gratitude for a long time.
For communities of students, I believe STEAM (Science, Technology, Engineering, Mathematics, and, at Saint David’s, the “A “signifies Aesthetics) has the potential to facilitate an approach to, and a meaningful engagement with, big ideas that are interesting and relevant. It is not a method, as such, so teachers looking toward STEAM need to help develop and understand guiding principles. The goal is to create curriculum-related experiences that are not just informative but intellectually and emotionally nourishing, involving the whole child...
The “Critters” Activities
In the evolution of the “Critters” project, I started out with no particular central question in mind. I did not even know very much about STEAM. I was doing work directed toward my personal interests as a woodturner. I have some background in geometry and wanted to see if I could develop a satisfactory method for constructing hollow wooden spheres (i.e., balls) from turned plate sections. I would cut carefully mitered pieces on the band saw, round them inside and out individually on the lathe, and later glue or otherwise fasten these “shells” together to complete a hollow sphere. I had in mind, however, that my students might use a much simpler method, with regular classroom materials and tools, to express essentially the same geometry. For me, this type of thing is both fun and a worthwhile challenge. However, I also had to consider how such a project would be appropriate for the boys, and whether they would find it enjoyable.
I think that familiarity with the geometry of the sphere and partitioning of 3-D space are going to be increasingly important in the future. Explorations into macro- and micro-worlds (where gravity is not the predominant force) are ongoing and becoming more common. To understand what conditions are like, it would be useful to be able to imagine a space where “up” has little or no meaning.
My spheres were also going to be partitioned into plates in a manner consistent with the Platonic
solids. The number of identical plate-shapes in a partitioned sphere must be one of the following: 4, 6, 8, 12, or 20. These are manageable numbers, and they conveniently correspond more or less to workgroup sizes into which a classroom of students could be organized.
So these two thoughts, future importance to society and convenient numbers (for teacher), encouraged me to keep thinking about a school use. But “fun and inviting” (to the boys) was the essential aspect that would need work.
I started at the end of school in June, and I was getting along pretty well with my wooden spheres, having soon determined all the necessary angles and made cardboard templates and such. In August, I attended a NYSAIS STEAM conference. It was great working with teachers of science, technology, engineering, art, and math, but those from other disciplines had equal input in discussions and team project-making.
Soon after returning to school in September, I was looking for ways that the disc idea could be used in a curriculum project. Several possibilities arose, but the one that made the most sense was to incorporate it into the annual school trip to the Cape Cod Sea Camps with the Seventh Grade.
Within the scope of three days, the core activities in Cape Cod would mainly focus on the natural science of the ocean and seashore with the study of perspective drawing alongside.
Four program events, two of them outdoors “in the field” and one indoor presentation through Massachusetts Audubon, Wellfleet, coupled with a group of activities on one afternoon with Dr. Benway of Woods Hole Oceanographic Institution, would provide a wealth of information on sea life and ocean and seashore environments.
I decided that, for a change of pace and to help the boys digest some of that volume of information, they would design and make “creatures” adapted to an environment they would specify, either made up or one they learned about on the trip.
The creature would be imaginatively and playfully created out of a combination of new knowledge and fantasy, but its body would consist of a polyhedron with added attachments for limbs and other features. I went about constructing a prototype with a paper plate “cube” for a body, some rolled up newsprint for limbs, ears, and a tail, and a paper cup for a snout. Making up a species name, Pseudocanis hexahedris, I called it “Tripod” and wrote a short sample scenario for it.
The construction activity was organized into three phases, to be followed by a presentation session. The first phase, involved communal construction of ten each—tetrahedron, hexahedron, octahedron, and dodecahedron. (We deliberately dropped the icosahedron, for simplicity). That would be enough for the 40 boys on the trip to each make one. At each of eight tables there were paper plate discs, staplers, instruction cards, and templates with pencils for marking the spots for stapling.
After brief instruction on how to use the templates and how to read the symbolic pattern on the card, construction proceeded. There was a small bit of confusion at first and energetic discussion at the tables. Teachers helped a bit getting the ball rolling, but then there was quite a bit of self-organizing among the five students at each table as they zoomed forward in their constructions, and they were soon finished. There arose one or two small “errors” among the more complicated structures that led to a short but significant impromptu discussion of the value of “variation” in nature. I planned for a 50 or 60 percent success rate, but 40 viable structures were successfully completed, for 100 percent.
Teachers were amazed and impressed. Pinching myself, I congratulated the students and announced, “The individual ‘plate-onic’ solid you made belongs not to you, but all belong to the community for critter construction.”
Next, randomly teamed by teachers, 20 pairs of boys adjourned to the other side of the partitioned dining hall to create an imaginary setting and write a short script focusing on five things: creature’s name, where it lives, what nourishes it, one adaptation to its environment that the team incorporated, and the shape chosen for the body.
Once their script was finished, each team in turn picked out one of the 40 structures, materials for attachments, markers, etc. and began creature construction. Some teams chose to use two or more polyhedra for their “critter.” Every team that evening lost track of time, thoroughly engaged in this activity, and we teachers allowed them to go quite a bit beyond normal curfew.
The amount of time spent developing this project was considerable, but the rewards made it well worth it. I do not remember ever being discouraged or weary during the process. It may seem odd, but I now feel a kind of gratitude toward platonic solids that was not present before. It’s as if they, or rather the iterations of them by the 40 students engaged in this exercise responded to questions that were implied all along.
I put it to the boys this way: “It’s well and good that Nature is able to take a shape and endlessly repeat it, as we see. But Nature does not read math textbooks, so how does it do this?” I figured this little exercise might indicate for them how repeating coded patterns might have something to do with it, each pattern making a different form out of similar component materials, and I think it was successful. But I did not anticipate the bit about variants. This points to deeper questions about how Nature could contain such a variety of forms, why some traits are heritable, valuing and tolerating difference, and more.
I am grateful for the support I received from Headmaster O’Halloran and Upper School Head Sara Peavy, the generous help and support from my teacher colleagues on the Cape Cod trip, the expert input of the naturalist presenters from Mass Audubon (Wellfleet), and the cheerful beneficence of Dr. Benway of the Woods Hole Oceanographic Institution. The unfailing cooperation of the staff at Cape Cod Sea Camps, Brewster, Massachusetts, in helping us make use of their amazing grounds and other facilities really smoothed the way, and it was greatly appreciated, as always. Finally, thanks go to the boys of Saint David’s class of ’15. Their openness to giving of themselves in this activity is encouraging to me beyond words. I will remember that with gratitude for a long time.
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