Geometry: back to work 


It’s been a good long while since this particular project occupied my attention and focus.  However, I’m currently motivated to finish it — or at least finish the nine pages that I already have outlined and planned.  There are six more pages that are unplanned except for the margins, which means that I have a total of fifteen pages left to write, and maybe a card or panel to put in the pocket of the book, an afterword of sorts to explain the project a little better than I did at the beginning.

What project am I talking about? This one, the geometry book that I began a long time ago practically in a galaxy far, far away.  In fact, from the earlier entries from 2013, I can tell that I was already about sixteen pages into it.  Now, I’m thirty-seven pages into it, and I have fifteen left.  I’m almost the opposite point in this project as I was four years ago.  Funny how these things circle around, right?

The current pages, #36-37

Of course today is the day that I made a mistake.  I drew out the process of comparing 1:√2, and didn’t discover my error (on the right-hand page) until I had already inked the diagram and written the explanatory text.  Always check your work in geometry before you render it in pen!

The next pages laid out (and upside down for some reason)

No matter.  I had the room to be able to describe the process incorrectly, add in A WARNING IN CAPITALS AND RED, and then offer the correction. Typical medieval manuscript at this point, really — sometimes errors creep in, and the lowly scribe has to figure out how to offer the correction clearly and legibly in less space.  I managed.

As I said, I have nine pages remaining in this project that are already laid out.  A lot of this project is me working through Andrew Sutton’s book, Ruler and Compass from Wooden Books.

Why did I return to it, though? Well, first, I’m trying to clear my desk of unfinished projects. This one has been a big one, and it’s been on my mind to complete for a while.  But for another, I recently took up the opportunities and challenges of tutoring again.  And I’m tutoring a few young people in geometry.  So this project is serving to lubricate and rub the rust off of my geometry skills. Even so, I’m finding that the knowledge of actual geometric proofs isn’t quite as useful as one might imagine.

A lot of the work that students do in geometry class these days appears to be algebra. There will be one diagram (with a note beside it to say, not to scale or not rendered accurately), and then a lot of algebraic notation, and the student is expected to work without a ruler and compassed just their brain power and maybe a calculator, to solve the problem.

Say what??

I don’t understand.

Are we teaching geometry, or geometric algebra?  It looks like the latter, rather than the former.  And I understand that teaching actual geometry is challenging, and that it involves looking at a lot of diagrams and working out a lot of constructions by hand… but heck, that’s what we do as human beings. Isn’t it?

I said to someone on Twitter today that

Screen Shot 2017-05-15 at 2.43.25 PM

pardon, I can’t figure out the ’embed tweet’ system for my server.

But that’s (more or less) true — we use our hands to instruct our brains, and vice-versa.  How do we actually learn geometry if we’re not using the tools that geometry has used for thousands of years (or reasonable electronic replacements, though I’d argue that such tools are not as good as actually using hands to manipulate a compass)?

In any case, here’s a place where abstraction often gets the best of us.  I think it’s time to bring back some actual geometry to the classroom, and not simply ask students to do it algebraically.  This is a set of skills that belongs in our students’ hands, and not just in their heads.

Tool racks

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My basement is damp.  Actually, when it rains these days (which is rarely, but the rains are usually strong and long), my basement floods. And sometimes it just floods even though it hasn’t rained.

It’s also hot.  After about 2:00pm, the basement workshop is too hot and humid to continue working.  It’s time to stop when you find that condensation is forming on you rather than on the pipes overhead.

It was the condensation on those overhead pipes which got me started on this project — to build a pair of walls of pegboard to hang my growing tool collection on.  You see, I have two small worktables in my basement, with one shelf out of the wet each — and not a lot of storage space above that. If you leave tools on the surface of these tables, or leave the power tools out of their plastic bag covers, they get dripped on.  And then they rust.  Rust and tools do not go well together.

So I built two peg boards.  It’s already clear that I am not going to stick around here for all that long, so I didn’t want to build hefty 2×4 construction designs for my tool racks.  I wanted something simple, lightweight, and — let’s be honest here, abandonable — that kept my tools out of the worst of the damp, off the floor and out of the drip lines of the pipes.

These two panels don’t hold all my tools.  But they hold enough of my tools that I no longer need to pile things on top of one another.  And they’ve freed up space in my Japanese Toolbox for the things that are particularly dust and damp sensitive.  Progress is being made.

Making a Clamp

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IMG_1189.jpgToday was the day I planned to start cutting boards to build a woodworker’s tool chest a la Chris Schwarz.  I chickened out and built a clamp instead.
Whenever I see some photos of someone assembling boards into a panel, though, clamps rather like these appear to be in use.  Essentially, each clamp is a pair of boards with a series of holes down the length of the board, and a pair of pegs. The pegs are matched through the two boards, and a wedge is used to drive the assembly tight, and hold the boards together during a glueing operation.

I’m going to need three or four of these clamps, I think.IMG_1188.jpg

I wound up designing a couple of flying jigs as I built these clamps.  First, I built a small template for marking out where the holes go, and how long to build the clamp.  Then, I clamped the two boards together to drill the wood on my drill press, so I got precise matches between one board and the next.  Then, I attached a piece of wood to the build plate of my drill press, and used that to press the future-clamp boards against, so that I maintained the point of the drill in a firm line down the board.

Then I got really creative.  I marked the center of each hole on the side of the future clamp-boards, and put a line on the jig clamped to the drill press, and used the matched lines to decide when to lower the drill press bit into the wood.  You can see that complete system at work here in the third picture:

IMG_1148.jpgWhen you look closely, you can just see the clamp holding the two future-clamp-boards together on the right.  And then in the middle, you can see two clamps, a spring clamp and an adjustable bar clamp, holding the straight-edge in place while I drill the holes.  Being left-handed while trying to manage a right-handed drill press isn’t the easiest.  Adding a camera makes the whole thing look impossible.

The next stage of development would be to build a ‘sled’ which supported both ends of the wooden bars for the bar-clamp, while allowing me to center both boards easily at the next drill point. (It occurs to me that it’s very hard to write about making tools with jigs and templates, because I’m writing about clamping things to make a clamp, but I actually have several types of clamp holding down several different pieces of wood doing different things… and all these different bits and bobs and thingamajigs have actual names, but I don’t know them.)

Midway through the whole operation, there needed to be an adjustment of clamps — on the jigs, on the project — so that the holes could be drilled at the ends.  And then there was further adjustment so that I could finish drilling the holes all the way through the lower board.  And… and…

Did it save me any time?  No? Yes? I’m not sure.  But I note that I have a new tool in my workshop that I didn’t have before.  In any sort of design work, in any sort of maker work, it’s important to remember that Tools Make Tools Make Things. 

So if you can’t or won’t make the thing itself, make a tool that makes it easier to make the thing when you’re ready to.  I’m more ready to make the tool chest tomorrow, because more of the tools I need are ready as a result of the work I did today.

I also discovered what feels like an important principle of my work in wood:  Use power tools to make tools and jigs and templates.  But the project is why I have hand tools, and so that’s where I use them.


Magic: Druidic Tools


Druidic toolsStrictly speaking, this isn’t an Autumnal Maker School post.  One, I finished making ten things already, and two, I don’t know that things that I’m making specifically for magical purposes should get counted as part of the total anyway.

John Michael Greer, the head of the Druidical Order of the Golden Dawn ( has recently made available to members the results of some of his research — a secret/sacred alphabet for druidic work, designed to be used for divination and for ceremonial work of various sorts.  It’s difficult, I think, to work with a material like this magically, before one has worked with it physically.

That is to say, if you can’t work with the magical teaching material in all four realms of being, chances are pretty good that you can’t work with it at all.

Now, there are four realms of being.  Actually, there’s probably considerably more than four, but druidry teaches that there are at least four distinct realms or worlds, and that these can be associated with the four elements of Earth, Water, Air and Fire (and maybe Spirit); and that these worlds correspond roughly or distinctly to physical matter, emotion and thought, intellectual ideas, and ‘energy’ or soul.  This is a simplified teaching — chances are you have your own version of this.


My goal was to walk into the Design Lab, find parts or materials that had already been ‘used’ or ‘damaged’ in some fashion, and turn them into something that could be my physical representation of this alphabet in the lowest realm of Earth.

The representation had to be:

  • made of already-used or abandoned materials
  • assembled during a class period or two today
  • be useable for divination
  • indicate (to me, anyway) its magical purpose
  • be the tool(s) and hold them in some fashion.


This amounted to twenty-eight disks of wood that I scavenged from a game design project that a kid had been working on, and that had gone awry.  I thought that I could pyrograph/write the characters on one side (and their Roman/English names on the other; and then four special disks for four additional signs I intend to include).  I found two pieces of felt, one black and one white, to turn into the bag; the black felt was slightly larger, so it became the part with the ‘flap’ for the bag.  I found a button on the floor, and that would be my closure.  I also found a length of yarn, to turn into braid for the edges/seams of the bag.  I gave myself some leeway, and used a new piece of string for binding the bag together.


I pyrographed the twenty-eight characters (and their reverses) first, and that took about 50 minutes.  In double-checking them now, I discover that there are two which I haven’t pyrographed the backs, yet, and I’m going to have to do those on another day sometime soon.   The pyrograph tool had been left plugged in by a student, and I was going to have to unplug it soon anyway; I simply put it to another purpose first.

I hand-stitched the bag with a spare needle and some new thread.  I attached the button. The button is wood, and has only two holes, so I had to modify my process for sewing on buttons to account for this.

I then began making the braid.  As you can see from the photograph, I’m not yet done making the braid.  However, the braid will provide both a decorative pattern on the front of the bag ( I think I have enough yarn for that), and provide some edging along the sides of the bag and around the edges of the flap.  The braiding is taking the longest time; and in fact at this point it’s the nicest element of the whole design; part of me wants to save it for a project made of better materials than a bag made out of craft felt. However, a deal’s a deal.  By the time I’ve made all the yarn into braid, and attached the braid to the bag, I imagine it will look pretty nice.

Last night, as well, I took a notebook I’m already using, and wrote out the 24 characters of the alphabet, and their meanings, and their correspondences both to the (druidic) tree of life, and to the cards of the Major Arcana (some of them, anyway) in the Tarot deck.  That completes the work I’ve done for the emblems.


What did this give me, besides a whole lot of work on something that some of my readers may regard as useless?  Well, for one, I realized that I’m able to work across a multitude of craft disciplines: in string, in sewing, in scavenging, in repair, in wood, in measurement, in conceiving a project and seeing it to conclusion in a short while.  This is no bad thing, in my line of work.

From a magical perspective, I took the first few steps in learning a new element of this particular tradition: I began learning the alphabet of the tradition, and how to read its lore.  I demonstrated reverence for the teaching by copying it out by hand, and I demonstrated reverence for the teaching itself by trying to emulate its practice in the creation of an object to house this element of the tradition (this, by the by, isn’t actually part of the official lore — to make a bag and braid-decorate it out of used materials — just how I’ve chosen to do it).   And I’ve made the thing, knowing that I’m likely going to have to make it again, anew, once I’ve really studied and understood this material.  Hmph.

From a teaching perspective, though, I have understood finally just what it is that I’ve spent the last five years learning, and what I’m likely going to have to take five years to teach to my students in the youngest grades — how to move between disciplines, and materials, and mindsets, with relative ease.  I learned how to do that from choosing to be a magician and a druid and a Maker.  I wonder how I’ll go about teaching them how to do what I do, without necessarily teaching them the magic.

I don’t imagine it will be easy.  Hmmm.

Autumn Maker School: Braiding Disk


I’m running this program called Autumn Maker School. The requirement is that you make ten things. Ideally they should be useful.  So far I’ve made a few things: a first-draft volvelle, and a computer program that calculates the area and perimeter of a hexagon or other polygons, and a little graphic design puzzle based on Khonsu the Egyptian god of the moon.  

Design lab// I made a braiding disk.  I made a 12-notch variant of this one, because third-graders learn about calculating time, and this way you can teach kids time movement at the same time that you teach them braiding.  It’s not a particularly complicated device.

But it meets one of my key criteria for success in the design lab: using our tools to make a tool that makes a thing.  I love it when a kid uses our carpentry tools to make a tool that makes something else — and the idea of using a tool-set to make a braiding tool which then allows kids to make friendship bracelets for one another, and maybe cord which can be attached to their clothing, and so on… that pleases me.

The third grade teacher seemed pleased too.  My tentative plan calls for making another twenty-five braiding disks over the next few weeks, so that then we can teach the third graders how to braid.  Those kids will then (hopefully) be more interested in working with cord, braid and similar materials in the future, and the weaving and dyeing and sewing programs I’ve worked on developing will make more sense.  It should be good.

The disc itself is not particularly complicated.  It’s simply a piece of poplar, cut in a circle, and then notched twelve times around the edges. The center hole is an artifact or side effect of the circular saw cutting through the wood.  The numbers are currently put in place with pencil; a final version would have wood-burned numbers, probably on both sides.  I think I’ll have to make a little guide with seven or eight patterns in it, as well, a booklet that kids can assemble — some with three strands (hour, minute, and second hands? Hah I’m on to something here!), some with four strands, some with five, six, seven, eight and maybe even eleven.

Thirty Days of Making: Tracing Board


I’m in Day 18 of a short series: Thirty Days of Making. Every day for the next thirty days, I intend to make something, anything, that is in some way connected to school. There won’t always be pictures, and I reserve the right to credit myself for things that I help my kids make. But I’ve decided that I need thirty days of maker success and maker failure under my belt to be a better designer.

I’ve decided that artwork counts, but not writing (unless it’s part of the art, like calligraphy). Digital work counts, but it has to be useful or publishable.

Some days there will be pictures, some days there won’t be. Each blog entry will contain a list of some of the materials and tools, a quick review of the success or failure of the Making, and a reflection on what I think I learned from the endeavor.  (My friend Alicia is beginning a new series along these lines, 12 weeks of the Artist’s Way — I wish her well in her process, go check her out!).

 Reason for the Project:

Last year, I talked with a group of students about some of the ways that Freemasonry had an influence on early American history. But I’m a Freemason, so there are significant limits on what I could say to them about what membership entails. And so, I developed a little ‘lodge group’ on the fly, called the Society of Successful Students, to explain how a semi-secretive group uses the ordinary working tools of daily life to transmit special messages to its members.  As in the freemasons, these tools were arranged on a ‘tracing board’ to help explain the concepts to new members of the group.

Thirty Days of making: Tracing board

A tableau of tools

The Society of Successful Students (not my best alliteration, I admit) used a tracing board which was a great example of ad-hocracy on my part. Now, a year and more later, I was trying to reconstruct the tracing board for a new group of students, to explain how a system could work. And now I share it with you.
Process and Results:

I knew what materials I wanted to include in the tracing board for the Society of Successful Students, so the first part of my process was finding all of the materials from various places around the school.  Virtually nothing in the assemblage here is mine; they’re borrowed from students and teachers.  I thought about covering all of the brand names and suchlike but that was too complicated.  I wanted to line the edges of the tracing board with colored pencils, but I couldn’t find the right number (although now I know what to look for the next time I want to lay this out… heh heh heh).

The results, I think, are fine though, as they are.   Pretend that you’ve just been initiated as a Successful Student, and listen in as the Master of the Class explains matters to you.  A Successful Student knows that:

  • the three kinds of paper – plain, ruled, and graph – represent our creative, narrative, and analytical selves.
  • the calendar or plan-book represents our intention to begin our studies with the end in mind, and plan our time wisely.
  • the index cards remind us to repeat the knowledge of our studies until it becomes secure in our memories
  • the scissors and tape remind us to cut and shape and assemble our work to suit our plan.
  • the paper clip and the binder clip remind us to organize and sort our work to suit our studies, and to reorganize often.
  • the eraser reminds us to scrub out our mistakes in casual work, while reminding us that every mistake leaves a mark.
  • The three pencils – new, dull, and sharpened – remind us to prepare ourselves and our tools to match the projects we do.
  • the sharpies remind us to broaden our mark on the world when the work will be seen by many
  • The compass, by its quality, reminds us to choose the best possible tools for our work, and to work with precision.
  • By its position on the ruler below it, the compass reminds us to do homework efficiently, in no more than two hours, with breaks every half-hour.
  • The ruler reminds us that, as younger students, we can only devote twelve hours to study
  • but the blue and black pens remind us that our best work should be done mainly during daylight hours, from 7:30 to 3:30.
  • The calculator reminds us to do complex calculations with machine backup; but it’s off to remind us of the importance of doing basic mathematical thinking with our minds.
  • The highlighters, by their presence, remind us to take notes and draw in important concepts; and by their color, to learn to prioritize between the greater, the lesser, and the unimportant.
  • The colored pencils remind us to work with more hues and awareness of color and design than ordinary school work requires — that excellence comes from paying attention to details.

Reflection on My Learning

I’ve built this particular assemblage before.  I’m not sure that I learned very much from it, except that the tools that I expect students to use (and which they do use), have the potential to carry meanings deeper than the simple meanings we assign to them. This is really the basis of symbolic language, and symbolism in general, that I’m showing off to the world.

But maybe, by presenting you my readers with a version of this tableau and the esoteric meanings underlying the items within it, you too can become Successful Students. In a sense, by knowing these deeper meanings, you already have become such.

I also wish that I had thought to glue down the objects that I assembled (or that some of them were not so high-quality, so that I COULD glue them down).  I think it’s an artistic form that warrants further attention, especially since it’s a form that I groove on — the tableau of ordinary objects possessed of deeper meaning than usual.

Reflection on General Learning

There’s a series of videos called “Working To Code” by Tom Sachs that is sort of related to this. I’m thinking of knolling, which appears in the film called “Ten Bullets”:

Part of me wonders if “knolling” is supposed to be a joke I haven’t gotten yet, but I teach kids to do this in the Design Lab.  They don’t, but I teach it.  First, it sets a specific place or space up as a given working environment for a given student.  It says to other students, “I’m working here, leave my stuff alone, and I’ll be back.”  But I think it also helps clue the student into the core concepts of what they were working on, and what they should be doing when they come back to work.  And I think it’s beautiful.  Laying out a tableau or a tracing board is kind of like knolling — it’s a way of adding a spiritual or a emotional level to one’s working tools.


Four of five stars.  I could lay this out again, especially with a photograph, and explain the meanings of the tools. A few students saw what I was doing, and remembered some of the items from last year.  If these objects were glued to a board, or even drawn in place, they’d serve as well as a freemasonic tracing board.  There’s some value in this technology. Overall, though, this is mostly an art project rather than a design project, and it was temporary rather than permanent.  Wanting to make it permanent as a physical object, though, is maybe an unnecessary level of detail.

Tool Time


I keep saying that you can’t think with tools you don’t have. I mean this metaphorically, in part: if no one has taught you how to break your writing into paragraphs, you don’t. That’s a tool. Another kind of tool is more literal: a pair of tin snips. Until you’ve had the pleasure of cutting metal, it’s hard to believe how easy it is, or how hard it is to do well.

It’s hard, as well, to use power tools of a given kind before you’ve used the hand version. At yesterday’s fair I bypassed all kinds of electric sanders and saws in favor of two working hand drills and a pair of tin snips. I almost bought a book press too, to turn into a mini printing press, but it was $100 and I didn’t have that cash with me.

The guy also had inside-calipers and outside-calipers for precise measurement that may have been a century old, but they cost more than I could have afforded. And yet the result of my not buying them is that we won’t be able to think about those measurements in the design lab. At least, not yet. And this is sort of the point: until you can drill holes easily and precisely, you don’t think about holes as contributing to a solution to a problem. Once holes are part of your repertoire of solutions, because you know how to use a drill, you think about them as part of your mental process.

And so I wonder what set of tools to make available to kids in the design lab. Because whatever tools we give them to use become part of their mental repertoire as well as their physical one.

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