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Concrete Action in a Non-Square World

Two of Robby's current interests have come together in a productive way. Following my buying him a new tool box, he elected to take up wood working in an after school program. His delight in building ship models led him to declare he was going to build a 9 foot long wooden aircraft carrier. I voiced absolute objection but, content to let the fantasy grow, said he could plan the ship and scale down the model later to some reasonable size. Later he asked advice:
Robby: Dad, how much is 9 feet take away four ?
Bob: 5 feet.
Robby: No, I mean take away 4 inches.
Bob: Come here and I'll show you.
Robby came to my desk and worked out this exercise:

    9'   -->    8' 12"
   -4"   -->   -0'  4"
  ----        --------
    ??   -->    8'  8"
This dimension, 8' 8", is for the sub-structure of the carrier. The 9' flight deck will overhang 2 inches at each end. In response to this and other expressions of the need to draw plans, I introduced Robby to orthographic projection (front, side, and top views).

Thus when last week I entrained him in my task of building a run for our dog (of 2 x 3's and hardware cloth), it seemed appropriate to ask him to draw plans. This was even more the case because I had formerly asked Robby to compute dimensions on the sizing drawing to determine how long should be the 2 by 3's we needed to make the frame. We were to enclose the two ends of an area 11' 3" wide. Because I knew the available lengths of 2 X 3's are 12', 14', and 16', I set up the three sums underneath the drawing and had Robby compute the board residues we would have after cutting out our lengths. We selected the 14' length as what we wanted because each board would yield a length and an end piece (we did not expect to need a 5' high fence for our Scotch terrier).

In the process of explaining that sizing drawing and my objective for the project to Robby, I drew on the reverse of the 3 x 5 card with drawing A, the drawing B (see Figure: Four Drawings). The purpose was to locate our additional fence in a picture Robby would recognize (the fence behind the back of the house we lived in). As I gathered my tools and set up saw horses for working on, Robby drew his 'plan', drawing C. Contrasting drawing C with drawing B, you will notice it has vertical lacing similar to my earlier drawing (the hardware cloth, with its square mesh, was rolled up beside where Robby was sat drawing his plan), and his drawing is more detailed in showing the diagonal mesh of the chain link fence. Robby's drawing placed our planned construct in its setting, its context, but was useless for keeping track of the various dimensions one might want to use in calculations. I showed Robby, in drawing D, the kind of plan I had in mind and tried to indicate its purpose. I was surprised that his new idea of a planning drawing leaned so to verisimilitude.

Figure: Four Drawings
Since Robby did not seem interested in my abstract drawing, we proceeded to the morning's rough carpentry. If you can't compute precisely the sizes of the parts you need, you can fall back on the handy-man's technique of transferring dimensions, i.e. you lay a board next to the place it is to go and mark off the size it need be to fit. We proceeded in this simple, traditional way.

Transferring dimensions is frequently the procedure of choice in the repertoire of both the craftsman and the handy-man; one reason is that the rustic carpenter is thus less vulnerable to the failings of his calculation skills; a second is that few things in this world, either natural or manufactured, are square; a third reason, decidedly relevant in this case of force fitting a wooden frame between a chain link fence and a masonry wall, is that you must sometimes worry about how your new manufacture relates to other things it is used with. Thus one lesson Robby could find in this project is that if you can't make an abstract plan, the concrete constraints may be enough, may even be your best bet, to finish the work at hand. Similarly in calculations, if you don't remember or can't understand some perfect algorithm, your commonsense knowledge helps you muddle through and may even be adequate to your needs. Though on the surface this may seem a negative lesson, it may be among the most important notions he can come to appreciate. Indeed, if particular solutions to problems are messy and inelegant, general solutions to really hard problems are usually impossible. As the characterization of his learning shows, such a conclusion is quite congenial to Robby's own problem solving practice.

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