Now, if you’ve done any woodwork at all and set out to construct L-girders using drywall screws and pine 1x2 furring strips you would probably dismiss the idea of getting things perfectly straight and true. You’d probably just clip the boards together and start driving in screws at whatever spacing seemed reasonable. Some folks like to keep the resulting girder free of metal obstructions so they glue the joint and remove the screws once the glue cures, others skip the glue and leave the screws in. These 1x2 were so crazy that I thought it best to use glue and leave the screws in. I also decided that it would be a good exercise to drill pilot holes in the top flange piece.

I have one good quality cordless drill. Parceling out who gets to use it and for what is a sensitive process. As with the drill press, the experience of controlling a motorized device is quite stimulating (isn’t that one of the fundamental forces that makes model railroading so compelling?) And, once you’ve used an electric drill to drive a screw it seems absurd to do so by hand. So I bought a dozen $1 phillips head screwdrivers and established the principle that in general the cordless drill would be used for making pilot holes and screws would be driven by hand.

I divided the class into groups of four or five students and asked each group to lay out pencil marks for pilot holes on a length of 1x2, and referred them to the sketch I’d just projected:

In planning this session of the class I hadn’t considered how much learning was involved just to understand my sketch. I explained that the lines with alternating long and short segments were the symbol for a centerline, and sometimes they would see the word centerline represented with a symbol composed of superimposed “c” and “L” characters. Math is all about using symbols to represent ideas and giving meaning to the arrangement of those symbols. Since the centerline along the top flange in the sketch wasn’t the center of anything shown, I used a callout to describe what it was the centerline of.

Realizing that for many students, diagrams like this don’t have any three dimensional meaning and just look like a bunch of oddly angled lines, I called on students at random to have them describe what they thought was going on in the sketch. Some, but not all students understood that the goal was to drive the screws through the upper flange into the center of the bottom piece of wood.

I asked for an explanation of the detail on the right. Again some but not all students had figured it out. I apologized for not giving both details meaningful labels and emphasized that it’s important to provide labels whenever we’re using symbols to communicate.

The students were already familiar with the convention for showing a broken line that I used in a few places on the right of the sketch. They’ve been drawing a lot of coordinate graphs and know that whenever they zoom in on a remote portion of the data they indicate that with broken lines on the axes. They also know that I always demand labels on graphs, hence my apology for neglecting them in my sketch.

Finally they seemed to have a pretty clear picture of what they needed to do in order to mark the pilot holes so I told them to get to work. The learning energy of teams is dramatically more engaging than teacher-centered instruction and we were running short of time for the good stuff. Each team quickly identified that one important task was to determine what the offset was for drawing the centerline on the flange, and each team concluded that it must be ½”, half the width of a 1x2. I suggested that they use their tape measure to be sure.

Pandemonium. Once again we had to stop everything to discuss how it came to be that something called a “one by two” was actually “three-fourths by one-and-a-half.” As you know, whenever we encounter someone else’s meaningful convention for the first time it can be extremely annoying. Students experience that kind of annoyance on a daily basis and having to keep track of vast arrays of arbitrary knowledge, and it can be fatiguing.

Armed with the cautionary advice to measure things and take less for granted, the teams proceeded to divide ¾ in half and prepared to make their marks 3/8” from the edge. Someone from each team had already started measuring from the end of each flange piece, first 4”, then 8”, then 8” again. I showed them that although it wasn’t strictly necessary in this situation, they could improve the accuracy of their marks by pulling the tape all they way down the length of the piece first, then make their marks aligned with the static tape. I appreciated that they could describe back to me why this was better – errors didn’t accumulate.

This was also an opportunity to introduce the use of some other measurement and layout tools so after each team had used their tape measures to mark the 3/8” offset from the edge for the first few pilot holes I showed them how to use a speed square or combination square to make this process easier and more consistent.

Wow, class was almost over and we had barely finished marking the pilot holes, yet hadn’t really wasted a moment. My timetable for building a model railroad was getting revised, that’s for sure!

Jeff A.