Geometry book: end of prep 

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I’ve been working on this hand-written book of geometry since at least 2013… maybe since 2011. There’s a total of fifty pages or leaves in it, although it’s an accordion-style Japanese album from Moleskine.  I recently started working on it again due to some recent geometry work in my life, and I’ve put in a few longish days.  The work itself is a manuscript to teach myself the material from Andrew Sutton’s book, Ruler and Compass, available from Wooden Books Press (a division of Bloomsbury).

Several years ago, it might have been early 2014, I laid out most of the remaining pages — the margins of each panel, the lines for the text, and the two or three geometry figures for each page.  For reasons passing understanding at this late juncture, I failed to lay out the last six pages of the book, or plan for the inside front cover.  The result was that I created a milestone, of sorts, in this project — the end of already-laid-out pages, six pages before the end, when I’d have to plan the remaining six pages and finish the inside front cover.

I’m now at that point.  My goal was to get here by Memorial Day weekend, and I’ve achieved that goal a bit earlier than expected.  I probably won’t be able to get back into this work until after the weekend, but I’ve made good progress.

Geometry Book

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Some of the geometry book I'm working on...

Eight pages of geometry

I forget which post Gordon said it in, but at one point he noted that nearly all books prior to the invention of printing were books of magic.  Sure, on the surface they might be called medical textbooks or scientific textbooks or books of geography or mythology or history. But at some level, all these books were books of magic — they were intended to change consciousness at some level.

Rufus Opus said something similar about making lamens. A lamen is usually a disk or a square that you wear on your chest during the conjuration of a spirit.  The act of writing one, of punching a hole in the parchment, and putting it on a string or a chain or a lanyard, is a creative act.  If the emblem you write on the lamen is the signature or symbol of a spirit, your hand is going through a kinesthetic meditation on the nature of the relationship between the conjurer and the spirit.

Something similar is happening as I create this book.  It’s a Moleskine Japanese Album, the larger size, so the pages fold out into this lengthy ‘wall’ or ‘screen’ of emblems — about 5 1/4″ x 8 1/4″ inches per panel, but about 115 1/2″ long — call it about 9′ 7 1/2″.

I think about this project from time to time — more lately, since I’ve been working on it the last few days — and every time I do, I’m somewhat more dismayed at the current state of geometry teaching in the United States.  By all the accounts I’ve found, and by the anecdotal evidence I’ve collected on my own, we’ve stopped teaching students to use rulers and compasses in the study of geometry.  It’s too hard to remember procedures, or students don’t know how to use those flimsy plastic compasses well and the good ones are too expensive, or Euclid isn’t widely available, or … or… or…

The excuses multiply like dandelions after a rainstorm.

I don’t know that this book “will become an heirloom of my house forever,” as one of the somewhat-more-fictional sagas would have it. But I do know that I learned more geometry from the construction of the book than I ever learned in a class.  And I wonder if there’s not a better way to teach geometry embedded in that discovery?

  • Each student gets a good compass, a good ruler, colored pens or pencils, and a blank notebook.
  • Each student learns the construction for a harmonious page layout
  • Each student learns a set of procedures for:
    • Perpendicular bisectors
    • duplication of angles
    • construction of parallel lines
    • construction of similar triangles
    • construction of polygons from given sides
    • construction of polygons within circles
    • transference of a given length or distance to another angle
    • construction of nets for 3-dimensional solids
    • construction of the root-2, root-3, root-4, and root-5 (phi/Φ) proportions
    • division of lines into thirds, fourths, fifths, eighths, ninths, and sixteenths
    • construction of grid and tile patterns
    • construction of simple polygonal combinations to find the sides of super-polygons.

This benefits future craftspeople, because they’re receiving an education in proportions and common mathematical relationships, and it’s not all algebraic notation.  It brings back the beauty of geometry to the mathematics classroom.  It gives all of society a common language for seeing mathematics in the natural world.  It trains future architects and engineers in precision diagramming, and gives future laypeople practice in reading such diagrams.

And it creates hundreds of unique copies of books of practical geometry that are themselves handbooks to a forgotten magic — a magic of beauty, of proportion, of color, of relationship, of graphic design. Students would get to learn ALL of that in the process of producing their own books over the course of a semester or a year. The quality of their book would gradually improve, as their understanding of the geometry improved, and as their love and care of the book improved. Think of all the other studies that could be folded into the creation of the book, too: handwriting, color theory, graphic design, book design, clear writing about mathematics, methodology.  The book is a grade — and students who kept their book up to date would find it useful while taking tests to remember what they had created in their own handwriting. The book itself would be a palace of memory for all the geometry they had learned, just as mine is.

All of the actual constructions are covered in Andrew Sutton’s book Ruler and Compass.  But actually implementing it is on the individual teacher.  And it’s likely the case that the teacher will need some substantial support from an administration that sees and cares about quality instruction.

But it can be done.

Geometry: back to work 

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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.

Fidgeting and Hand Skill

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There’s a lot of outrage about fidget spinners right now. Some teachers are saying ban them! Other teachers are saying, Let students have them.

It’s a stupid argument.

Remember yo-yo’s? Finger skateboards? gear-powered spinning tops? String powered spinning tops? How about Rubik’s Cubes which made a comeback a couple of years back? Wind-up cars that did tricks?

Fidget Spinners have a place and a time in children’s hands.  And as some of you know, one of my mantras or principles is that What the Hands Do, the Mind Knows.  But here’s the thing.  If you don’t want the latest finger-toy-de-jour in your classroom, then you have to find other ways to put those hands to work, learning actual hand skills:

  • teach calligraphy
  • teach knitting
  • teach drawing
  • teach geometry with an actual ruler and compass
  • teach the use of a slide rule or abacus
  • teach the building of automata (cogs and gears)
  • teach carpentry and build yo-yos, finger skateboards, spinning tops, and fidget spinners.
  • teach contact juggling
  • teach juggling
  • teach beading
  • teach woodcarving
  • teach origami
  • teach flint-knapping
  • teach ceramics throwing on a wheel
  • teach students 3D geometry through the assembly of nets of the Platonic solids.
  • teach color theory and coloring at a more advanced level through color pencils.

The fidget spinner is an outward and visible sign of an inward need — a need for the hands to learn something.  Kids’ hands fidget because they’re of an age to want to do something, not just sit still.

(And I KNOW that we’re not making them sit still in schools — that they’re doing personal practice as well as listening, reading, writing, reflecting on their work and all that sort of stuff. That’s not what this is about).

Human beings need to use their hands. We learn things through manual dexterity, through touch, through manipulation of objects.  Our constant rejection of the toys-de-jour, be they yo-yos or balsa wood flyers or paper airplanes or fidget toys is part of the reason kids don’t learn as much in school as they could.

So if you want to fidget-spinner proof your classroom… figure out WHAT tool or hand-skill you want your students to have, learn HOW to teach it, and then TEACH THAT.

#edcampswct follow-up

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During the last session of yesteday’s #Edcampswct (see edcamp.org about what an Edcamp is), I led a discussion on MakerSpaces and Maker Programs.  I want to summarize what points I made there, and provide links to deeper insights on those subjects; and make a few further points that I don’t think I made in the time allowed, but were on my mind.

Here are the key points, which are further summarized below (@MrPerraultGES took a photo of my notes):

  1. Visual Thinking
  2. 2D makes 3D
  3. Tools Make Tools Make Things
  4. What Hands Make, Mind Knows
  5. Recycle and D.I.Y.
  6. Space Requirements
    1. Tool Storage
    2. Materials Storage
    3. Project Storage
    4. Workspace
    5. Input/Receiving
    6. Archive Process
    7. How-To Library
    8. Repair (and Sharpening)
    9. First Aid
  7. Best Practice vs. Liability
  8. (And to these 7 steps  I’m adding—
    1. Games and Game Playing
    2. Past vs. Future Orientation )

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Book: Your Starter Guide to MakerSpaces

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This is a book review. It’s part of a new series on this blog that began last week.  I hope you find it useful.

Your Starter Guide to Makerspaces
by Nicholas Provenzano (@TheNerdyTeacher)
Blend, published 2016
ISBN-13: 978-0692786123 (Paperback) N.B. I read the Kindle edition.

✦ ✦ ✦ ✦ ✦ ✧ ✧

I’m deeply interested in MakerSpaces, of course, and I make quite a lot of things myself.  This is a fairly short book, as well, and more of a workbook than a true book.  As the author titles it, it’s a Starter Guide, not an exhaustive examination of the topic.

Yet given how many times I say, “I teach about and in makerspaces,” that the response is “What’s a MakerSpace?” both Nick and I have a good deal more work to do (fair warning, Nicolas Provenzano and I follow one another on Twitter) in bringing this idea to the masses.  It’s not part of the common lingua franca yet, and it could be and should be.  But that means that we have to do the job of educating the public, and stakeholders in schools and libraries and other institutions that could have MakerSpaces successfully.

The book contains eight short chapters:

  1. What is Making?
  2. I know what Making is; why should I care?
  3. Where does a MakerSpace go in a school?
  4. Making allies
  5. What goes in a MakerSpace?
  6. MakerSpaces and Project-Based Learning
  7. Failure and MakerSpaces
  8. Final Thoughts

He also concludes with information about his own identity as a Maker and teacher, and how to reach out to him and use his skills as a teacher-educator in your own institution. Which is awesome.

One of the things that I didn’t benefit from, that readers of the paperback edition may enjoy, is that this is a workbook.  As any good Maker will tell you, the interaction process between the thing that you make, and the audience you make it for, matters.  That’s certainly true here. Even in the Kindle edition, the illustrations and workbook pages give you the opportunity to engage with the book by writing your own (offline) lists and make your own mind-maps of the things that the book inspires in you.

The book’s primary audience is a teacher, particularly one who is already invested in the idea of project-based learning (PBL), or who has support within her institution for a change to a more hands-on program that involves building and creating within STEM (Science, Technology, Engineering, Mathematics) fields.  I’ve argued elsewhere that it should be STEAMED (adding Arts, Entertainment, Design) but very sensible commentators have responded to that.

Provenzano admits that this is not a book for an advanced practitioner, but a starter guide.  It’s not systematic, but rather it’s a combination of encouragement, first-hand accounts from a MakerSpace-as-classroom that he himself ran, and top-level considerations of equipment, toolkit, and mental attitude that help MakerSpaces get launched and succeed.  This kind of teaching and learning is valuable and important, though I wish he’d included more discussion about budgeting and financial planning for MakerSpaces, because money (where it comes from and how to get supplies, tools and equipment with it?) and time (how does the MakerSpace avoid burning out the teacher[s] who run them?) are rarely addressed in MakerSpace books and articles to nearly the extent they need to be.

That said, Provenzano does address a number of important points, like the scale or size of a MakerSpace, what equipment and tools it needs to have, and how much access a school should/could provide to its student body to use the space.  He addresses the process of finding allies for a MakerSpace program, in the student body and administration, in the parent and alumni community,  and in the local business climate.  The book concentrates to a high degree on what is wrong with schools, and shows some cheeky rebelliousness — but this is often the only posture a would-be change agent can take in the modern American school climate: if schools weren’t doing anything wrong, there wouldn’t be a need for MakerSpaces, would there?

All the same, Provenzano’s points echo my own sense of Maker work in schools. Hands-on practice with tools, with materials, with construction and design process, all help make students and teachers into more well-rounded, more competent and capable people. They’re more skilled at solving problems outside their own usual wheelhouse,  because they’ve solved problems involving physical materials and invisible forces (like the flow of electricity through a circuit, or the arrangement of parts so a thing stands on its own).  I think this is a great book for teachers or librarians starting out, who have curiosity about how to get a program started; and I’d happily recommend Provenzano to come to your school or library to help your MakerSpace get started.

Giordano Bruno: Wheels in Wheels

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I’ve been reading Scott Gosnell’s translations of Giordano Bruno, on Gordon’s recommendation over this holiday.  Giordano Bruno was an Italian, a Dominican monk, a university professor, a heretic, a scientist, and probably a magician of some great capacity, and was executed on February 17, 1600.

CipherDisk2000.jpg

Caesar cipher (Wikimedia)

He was also an expert on memory palaces, and used the work of Raymond Llull, the 13th century logician, as a basis for developing his own ideas.  At the core of both Llull’s work and Bruno’s extension of that work is a paper machine similar to a Caesar cipher wheel, to find multiple combinations of images and attributes, to invent memory pictures for study and recall… More

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