School: Redesign Homework


Around this time of year, I always think about how I’m going to re-design my teaching for the fall semester.  It doesn’t matter whether I’m teaching or not, I think about it.

A recent conversation with Dave Gray of XPLANE, Inc. got me thinking about his heuristic matrix from the book Gamestorming which he wrote with Sunni Brown. A heuristic matrix looks a lot like the grid from a spreadsheet, and which I used several years ago to redesign homework.

That grid looked something like this…

Screen Shot 2017-08-08 at 8.44.24 PM

I identified a bunch of broad categories that I wanted my students to learn about.  In this example, based on the broad theme of teaching about Ancient Greece, I have categories like religion, and aspects of art history, politics, literature, philosophy, and science and technology.

I then identified a variety of styles that I wanted my students to learn to write in. These formed the individual columns of the heuristic matrix.    These included paragraphs dealing with compare and contrast writing, where the same paragraph alternates between two different viewpoints or styles. There was also descriptive writing, involving a top-to-bottom explanation of a thing or a place.  Narrative writing, the description of a beginning-to-end process, was another category. Persuasive paragraphs offer reasons for holding an opinion, and attempt to persuade the reader to accept a particular viewpoint.  Exposition attempts to define or explain a person’s ideas or opinions without forcing them on the reader.  Reading comprehension, on the other hand, asks students to engage with an actual historical text.  Self-directed research is another category — independent projects of various kinds.

I haven’t filled in the heuristic matrix completely. Some of this is left as an exercise to the reader (which is to say, perhaps, that I’m lazy or that I don’t wish to think all of this through, or maybe that I don’t wish to share all of my thought process at once).  But the overall structure should be discernible.

I tried to do something similar with a mathematics heuristic grid for a lower grade, perhaps grade 2, grade 3, or grade 4.

Screen Shot 2017-08-08 at 9.53.21 PM

I’m not a mathematics teacher, so you’ll notice that the grid isn’t completely filled in.  But you’ll see what I’m trying to do… I’m trying to come up with a variety of mathematics exercises and activities that don’t revolve exclusively around the traditional “do these 20 problems to learn a type of procedure” worksheets or homework lists.  This is about inventing new forms of assignments and identifying how these can be used to teach or refresh skills that lie outside the usual curriculum norms.

And it’s important to note that YOU don’t have to fill in a grid completely, either. You may only generate one or two useful ideas from a heuristic matrix.  Yet if a few of those ideas have the chance to reinvigorate your teaching, that may be worth i.


Autumn Maker School: Picture IDs


I’m running a program on my blog from October 2 to December 21: Autumn Maker School. The goal is to make ten useful things this fall, with a fairly broad definition of ‘useful’: So far I’ve made a 1) Volvelle, a 2) disk for braiding friendship bracelets, a 3) computer program to calculate the area and perimeter of a hexagon, and a 4) digital image of the Egyptian deity Khonsu.  Today brings us to number five (5): a student ID card.

My school secured a fairly prestigious invitation to a major institution early this summer, and the time is rapidly approaching for us to take a group of students to go.  A snag arose — every student needs a picture ID.  We’re a middle school, and a small one at that; I know 97% of the students on sight.  We need picture ID cards?

Making one for every kid in the school, and every adult, doesn’t even begin to qualify for minimum orders for most such cards. We need seven, ten at most.

So over the last few days, I made them. Heavy cardstock paper from the Design Lab, our color printer, the photography software on the Macintosh computers in our computer lab, some digital layout software, a big sheet of paper and some cardboard to make the background for the photographs, the kids and adults that needed photo IDs, a laminating machine, and my boss’s signature.  Seven cards, two hours spread over three days.


Making twenty or twenty-five would have been almost as easy — another hour, tops. Making sixty? A hundred seventy-five? Not so easy.  I’ve found the right solution for the scale at which I must work, at which I am working — but scaling up would be challenging.

No picture of this project, of course — there’s no point in providing either pictures of the students at my school on a private blog; or in making it possible for anyone to duplicate the school’s ID cards exactly.

But then, how to prove that it’s done?

Well, provide a procedure, of course:

  • Measure an existing ID — wallet card, driver’s license, etc.
    • Many of them are about 2″ x 3″ in the US, to fit into a wallet slot-pocket
  • Produce a base template that is 2x that size in one direction — so it can be folded over.
  • Use color, text, contrasting elements and fonts/typography to include:
    • a blank space for the student picture
    • a blank space for the student’s name
      • a blank space for the student’s grade
      • and hometown
      • and other data
    • a place for the head of school to sign
    • emergency contact information
    • school contact information
    • school logo
  • Create a photo studio in front of a computer
    • extra lighting
    • background in relatively neutral color
    • photography software & web-cam
  • Take the photos
  • crop and lighten the photos
  • Paste the photos into the template
  • Print the templates/digital cards onto cardstock
  • cut out, score and fold the ID cards
  • laminate the ID cards
  • cut out the cards from the laminate


It was an elegant and interesting process, but it had some challenges, too.  I’m glad it’s over with.

It did lead me into some interesting awarenesses, though.  I was authorized to produce seven cards.  But I produced ten or so, in the process of learning how to make them.  Did I counterfeit them? No, because they were never signed — and I never pretended that they were anything other than experimental.  They were even marked “DRAFT” in large letters, and watermarked as such.  At what point did they become “legal IDs”? Are they legal ID cards before an authority figure looks at them and accepts them as valid?

It’s a complicated set of questions, really.  And in some ways being a magician doesn’t make answering them any easier.  I mean, in a very real way I just created the illusion of an ID card — and then through a combination of competence, confidence, persuasion and usefulness convinced a bunch of people to agree to the proposition that it was My School’s Official ID Card.  

Which, when you come right down to it and think about it carefully, is a bizarre and magical thing to achieve.

Autumn Maker School: Khonsu, Re-membered


This post is part of my Autumn Maker School project. The idea is to make ten useful things.  As Stacey has figured out, my definition of ‘useful’ is pretty broad-based, because I have my work cut out for me in so many different ways.  The more people who become makers, the happier I’ll be.

Khonsu disassembled//’m currently teaching my unit on graphic design to my sixth grade students, and they’re having a lot of trouble with the pen tool. The pen tool incorporates both straight lines and Bezier curves in the same system — click to put down a point, click again to make a straight line, click again and again to make more straight lines and eventually a closed shape that can be filled with color, and then click and drag to change straight lines into curves. I am not particularly skilled at this.  I don’t think anyone will ever pay me to be a digital artist. But I wanted my students to understand that if you want to create a complex image, you have to create the individual parts.  In this case, the individual parts were a shirt, and a kilt (in gray), four arms, bicep and wrist bands, anklets, an ankh, pieces of a collar, pieces of a nemyss (the headdress of ancient Egypt, and of the druids), the Moon, and the moon sphere —and the parts of Khonsu’s face. Once I was done assembling it, they said, “Wow, that’s really good!”  But I have to admit, I don’t think the lesson was made clear enough. It was too complex an image for them to grasp — too hard for them to see how a line-drawing of Khonsu transformed into a series of components, each of which had to be drawn separately.  Admittedly, it’s a difficult lesson to understand. But it’s also a difficult lesson for us as teachers to understand.  We’ve all heard the old adage, “A picture is worth a thousand words.”  But it takes a special kind of educator to understand that a quality picture, even one that looks as disassembled as the one on the top, takes as much time to create as a 1000-word essay.  And all I did was try to copy, digitally, an image in a century-old book about the Egyptian gods. Khonshu//

We live in a society that, at least for the moment, runs on imagery and symbolism nearly as much as it runs on words and mathematics.  And we like to pretend that you have to learn everything about words and mathematics in order to be successful in this world. And that if you’re not good at math or reading/writing, then you’re terrible and your life will be awful.


But I’d like to suggest that there’s an important lesson here.  The students in my sixth grade classes today saw these two images. They saw the complete image, and then they saw it dismembered and pulled apart, and then they saw it re-assembled.  And then they went right back to trying to use the pen tool to draw airplanes with differently-colored parts, and faces with eyebrows and hair and noses, without bothering to try to break those images down into components.   The students SAW the components, saw that this picture was made up of a number of components, SAW that each component was individually drawn, and then chose to use their pen tools as if they were using an actual pen or pencil in a paper notebook.

We have so divorced our children from their drawing skills, from their visual representational skills, that they don’t know how to disassemble their visual cues of the world into their component parts.

Autumn Maker School: Hexagon Program


This post is part of a larger series called the Autumn Maker SchoolThe idea is to make ten things, mostly useful or to self-teach certain skills, and then write about them.  The first post was about a graphic-design project, the Astrological Volvelle. This is the second project.

I am not always very smart when it comes to teaching programming.  I’m going very slowly, and it’s challenging both to me and to the students.  I keep throwing a program up on the projector screen for them to look at, and then I discover that it’s wrong. Argh. It worked fine when I made it the other night, why isn’t it working now?

Mostly it’s that I barely understand what I’m doing, yet.  In three years, I’m going to be amazing.  But first I have to live through these three years of agony.

Here’s the code I wrote tonight.  It is not elegant.

# Hexagon Calculator
# by Andrew B. Watt

#imports arguments from system library
from sys import argv
# turns three arguments into the script name, the side, and the units
script, side, units = argv
# turns the side value into a number from a text string, makes it a variable.
side1 = int(side)

# Reports the values of the three given arguments
print "This script calculates values for hexagons using", script
print "The units are called:", units
print "The side length is:", side

# Brings in the math system more completely
import math
# calculates the perimeter of the hexagon.
perimeter = side1 * 6
# Stores the square root value of 3 to use in the area equation
sqRt = math.sqrt(3)
# calculates the area of the hexagon.
area = 3 * sqRt * (side1 * side1)/2
print "The area of the hexagon is %r square %s." % (area, units)
print "The perimeter of the hexagon is %r %s." % (perimeter, units)

The purpose of the code is to calculate the area and perimeter of a hexagon. Happily, I can report that this code worked successfully.  But it took me a long time to get it right, and ten run-throughs, before it operated properly.

Here’s what it does:  it calculates the perimeter and the area of a hexagon, and feeds it back to you using the unit type you designated at the beginning of the operation.  Including my comments, it takes up twenty-five lines of code.  Not including my comments… It’s twelve lines of code.  I could probably make it 8 lines of code, but I was also learning how to use the import math function, and the argv function.

But better — I now understand how argv works in the python computer language, and I understand how I can access higher mathematical functions in python.  It took me a long time to understand that the name of the file was itself an argument in the command. Now I understand how to use additional variables in order to store a broader range of information, and how to use argv to access the name of the file itself when I write a program.  What I’m going to use that for, or how I’m going to teach the use of that to my students, I don’t know.

Their own efforts are coming along nicely.  We’ve written a short script that generates the caesar cipher codes for their email messages.  It’s not a secure code at all, but it gets them thinking about security and about the difference between secure and insecure channels — which is no bad thing, to my mind.  They wrote short computer programs which calculate the area of a triangle, the area of a circle, and the area of a square or rectangle — and then they built that code into a type of meta-code, which asks the user what sort of polygon they want to solve for, and then uses the data they give it to calculate area, perimeter/circumference, and so on.  We got into if-elif-else constructions on that one.  Now I can have them write a program where they tell the computer what sort of polygons they’re working with, right at the command line, using argv.

But again, I say, I am not fast at learning programming, nor at teaching it.  I’m learning these little bits and pieces, and gradually learning how to string them together to do things.  I’m not yet clear how how being able to tell a computer to do these things, in the right sequences, makes computers do cool things.

Still, I feel that I’m learning the basics.

Computers: a short assignment in programming


I’ve been teaching programming for two years.  I’m really not very good at teaching programming, which is why I haven’t talked about it here very much.  At first, I used JavaScript programming, because there was a great tutorial on  But, I’m increasingly unnerved by larger questions about what school is for — and the way in which Khan Academy and other online tutoring programs are establishing a check-box grading system for everyone.  But also — it’s clear that there’s now a well-established tutorial system for JavaScript which my students have access to, and are using.  And other programming languages are not as well-established or understood in schools.  So I’ve been teaching python, using the tutorials provided by, and  I’ve particularly enjoyed teaching my students to create the code necessary to replicate the effects of the Caesar Cipher, a simple letter-substitution code-system, using Al Swiegart’s book Hacking with Python: Codes and Ciphers, available at

I’ve also been writing short programs, and trying to get kids to reverse engineer the structure of those programs.  This has not been entirely successful, but it’s gradually leading them (and me) into an understanding of best practices for teaching code.

Here’s the program that was our first quiz, today:

# Circle Calculator
 # by Andrew Watt
 radius = input("what's the radius of the circle? ")
 units = input("what units are you using (in double-quotes): ")
 diameter = radius * 2
 area = 3.14 * radius * radius
 circumference = 2 * 3.14 * radius
 print "the radius of the circle is %r %s." % (radius, units)
 print "the diameter of the circle is %r %s." % (diameter, units)
 print "the area of the circle is %r %s squared." % (area, units)
 print "the circumference of the circle is %r %s." % (circumference, units)
Python output

Here’s the  output from running this small python program, shown twice with different variables.

Their objective for the class was to get this program to work, while only having the output from the terminal program, that looked like this, to work from.    It took the whole class, which I wasn’t expecting; they’ve been typing in these commands for days, and seeing the results of the programming they’d done… why wasn’t it working?

Turns out, the answer had a lot to do with how programmers teach programming, i.e., for other programmers who already know a language, vs. how a teacher who’s been teaching other subjects for years teaches programming – that is, me.

My goal of the exercise was to see that they knew how to define variables, use the mathematics functions of python, and use the “print” command to show results to the user.  I also wanted them to be able to run the “input” command.

The results were… not what I wanted.  Nearly everyone got how “input” and “print” worked, and nearly everyone was able to set up the mathematics correctly.  But they couldn’t get the strings to work. Their programs looked like this:

# Circle Calculator
 # by [various students]
radius = input("what's the radius of the circle? ")
 units = input("what units are you using (in double-quotes): ")
 diameter = radius * 2
 area = 3.14 * radius * radius
 circumference = 2 * 3.14 * radius
 print radius
 print diameter
 print area
 print circumference

In other words, their programs would tell you what the results of the calculations were, but wouldn’t show what each printed variable result was.   If you didn’t know that the program was going to print in the order of radius, diameter, area, and circumference, you wouldn’t get a sense of what the results meant.

And this means that I have to do a better job of explaining how replacements work within python code.  This wasn’t something I’d spent a great deal of time thinking about, but clearly I do need to think about it.  A great deal of that challenge, it turned out, hinged on the fact that I’ve had several dozen hours to think about how programs work, and they haven’t.  I’ve learned enough of the language to become competent at making these small quiz-like programs: “can you use this function? How about this one? How about this one?”  But I hadn’t thought that this was something that needed teaching.  And clearly it does.

What did they actually know? What didn’t they know?  The answers were illuminating.

Most of the kids got how the mathematics system worked.  But variables were tricky, and the difference between variables that held strings (“text”) and variables that held numbers was confusing. They’re used to using one of those purposes for variables, not others.

This makes me think about the way that I teach Latin, though. I work kids through the structures of sentences a lot:

Marcus udus est. Claudia sicca est.
Marcus is wet. Claudia is dry.

Claudia dormit.  Marcus scribit.
Claudia is sleeping/Claudia sleeps/Claudia does sleep. Marcus is writing/Marcus writes/Marcus does write.

Marcus ambulat in villa. Claudia currit in horto.
Marcus walks in the house. Claudia is running in the garden.

A lot of what I do in Latin is help kids think about sentences as formulas that allow one to plug in different variables — a noun here, and an adjective there, change to masculine or feminine or neuter as needed.  The first two sentences, Marcus is wet, Claudia is dry, can use any pair of nouns and adjectives.  The next two sentences can use any combination of noun and verb. The next two sentences can use any combination of noun, verb and place-name.

It occurs to me that the more that I can teach my sixth graders this year to think of sentences as equations with strings or variables, the easier time I will have teaching them programming in seventh grade next year.  And that’s enough to spark ambition, really.  I think I can get them over this hurdle.

Search Term Track Back June 2015

1 Comment

I learned this from Sam at Digital Ambler, who is one of the most sophisticated modern writers about Geomancy that I know of. And “This” in this case, is the reconnection of the blog to its ten or twelve most popular posts in the last 30 days.

  • how to make tattwa cards, tattwa cards pdf, pics of tattwa cards — yep, all of these different searches found the same thing, my post where I provided a PDF you can print out of the design of the Tattwa cards, which are useful for elemental scrying work and other techniques.  Which is weird, because I don’t think I’ve ever seen anyone use these cards, only talk about them. 
  • pagan calendar — There’s a pagan calendar which I created and host through Google Calendar, and the links to add it to your own calendar are in this webpage. This particular calendar is strongly rooted in a Roman pagan tradition, since much of my ‘pagan poetry‘ revolves around Roman-ish spirits of various types, adapted to a modern American experience. 
  • libra 2nd decan, libra decan 2 month of july.— I made an astrological image for the second decan of Libra, which you can find here. The second decan’s traditional image is “the strong African returning from a voyage with the fruits and rewards of his labor,” which I’ve depicted as a man standing on a dock, surrounded by chests and boxes, dancing.  I did this image as a present for my father for his birthday several years ago.  Libra’s Decan 2 is not in the month of July, however.
  • the horse could talk, the horse may talk The story of Nasruddin teaching a horse to talk appeared on this blog in 2009.  The figure of Nasruddin is, depending on whom you ask, either a folk-tale character from the Middle East, or an important teaching persona in Sufi tradition, or just a character that you use when you want people to know it’s a joke when you start.  
  • first decan of virgo — 
  • magic to win lottery, how to use magic square for gambling?, use magic to win lottery, magic to win lotto, how to win lotto by spell blogYes, I did use magic to win the lottery.  And yes, I feel that I did win, although you may not agree.  I also learned that the powers that I worked with to win the lottery are either tricksters, or jerks, depending on how you look at it.
  • y4d88 — This code, Y4D88, led people to this particular post, the 88th day of year 4 of my tai chi practice.  I wonder what they were looking for? It’s not a solstice poem, nor a geomantic image, nor nothing particularly important.  Anyway, this is what they found.
  • geomancy love judge, larn geomantic – I assume these people want to be learning Geomancy, and hopefully they mean western-style geomancy rather than Chinese-style geomancy; because that’s what I know.  I imagine they’re after this post, which is adapted from one I originally posted on Tumblr, that lays out how to learn geomancy, but they might be interested to know that I’ve also taught geomancy. Both of these reference a poem I wrote, called Geomantic Quatrains or Quatrains on Geomancy.
  • historical trends in emotional intelligence — You’re probably after my notes from the lecture by Peter Salovey. I don’t know what’s useful to you there, but that’s why you got directed here.  I took these notes at a conference on learning and the brain in 2010, which I believe was held at Avon Old Farms School here in Connecticut.
  • visual aids in teaching ideas — I’ve written a great deal about this subject in my blog, because visual thinking is an important part of what and how I teach these days. But this is probably a good place to begin, or you could start here, with the idea of lenses, or with a sample of it in Latin class.
  • winter solstice poetry — Southern Hemisphere person?  I don’t know if my poetry is appropriate to the southern hemisphere, but this is what I’ve got about the Winter Solstice here and here.

Search Term Trackback: April


Digital Ambler does this thing at the start/end of each month, where he lists the most common search terms for people who come to his blog, and explains where on his blog to find that material.

  • tattwa cards — apparently there are a lot of people out there looking for Tattwa Cards, because this has rapidly overtaken the Tree of Life and the Palace of Memory as the most important thing people are looking for when they come to this site. They’re here — a set of Tattwa Cards as a PDF that you can print out on a color printer and then cut out.
  • pony cliffs ashfield Pony Mountain is in Ashfield, MA, near Chapel Brook, which is one of the Massachusetts Reservations. I’ve done work there, and I like climbing there from time to time.
  • how to draw tree of lifeStill a popular favorite.  It’s amazing to me that there are people who go through a magical curriculum and never learn this.  I mean, this is kinda basic, right? Right?
  • tai chi one step at a time — I don’t think it’s possible to learn Tai Chi one step at a time.  I think mostly you learn three or four steps at a time, practice them obsessively, and then maybe pick up a few more steps.  It took me eight or ten weeks to learn the form, and I’ve been at it, off and on, since 1998.  However, you can try following the Tai Chi Poem.
  • memory palace lesson plan — I wrote a great deal about how to introduce a Palace of Memory project to a group of middle school students; the core documents and links to them are assembled here.  I’ve moved away from this in recent years, because the needs of my students and school has changed; but I remain convinced that it has both power and relevance.
  • how to add google calendar wiccan holidays — I put together a Graeco-Roman-Wicca themed Google Calendar a long while ago, which appears to be still-functioning; there are instructions attached to the post.  THere’s also quite a lot of poetry on this website for use with those festal days.
  • St Patrick primary source — I gathered together a good deal of information about St. Patrick, once upon a time, who turned out to be far more interesting than his legends about driving out the snakes would indicate.  I don’t know how many of the links are still active.
  • Mandala compass — I like making Mandalas, and because of my interest in geometry and teaching I frequently use a compass to do so.  Here’s some work that’s relevant to that.
  • Memory palaces for learning music — I don’t have a memory palace for learning music, because I’m not that good at learning music.  However, I think that you should/could arrange it as two separate “halls” with seven radiating corridors for the Circle of Fifths.  I hope this provides the necessary clues to get you started, along with other materials about the Palace of Memory, as indicated above.

Older Entries