Cornrow Curves Workshop
Part I: preparation at your computer lab
1) Make sure the main website http://www.rpi.edu/~eglash/csdt.html is bookmarked in the
browsers (IE or firefox)”favorites” -- if a student crashes the computer or accidentally closes
the browser it is easy for them to find it again.
2)
Make sure the browser has a recent plugin for flash. You can do this simply by checking to
see if the cornrow curves applet runs. You only need the java plugin if you may be using
Breakdancer or Rhythm Wheels later on.
3) It’s also a good idea to try creating a braid, and then clicking on “save” (in the applet’s menu,
not the browser’s menu). If save is working properly, you should be able to clear the applet’s
screen and then bring back the same braid. Sometimes security settings on the browser will
block a save (usually only in older versions of IE). Note that you are saving to the hard drive,
so kids will need to return to the same computer they used the day before if they are going to
be able to edit their work again. Alternatively, they could just write down the parameter values
and re-enter them on a new machine. If you are going to be printing (either from the “print”
option of the applet or by using a screen shot) it’s a good idea to try that out ahead of time as
well.
4) Finally, you might take a look at the screen resolution and browser text size settings; if those
are way off they can make life difficult. We have also found that occasionally a public lab
computer will have a mouse that has not been cleaned for so long that its performance is
“bumpy.”
Part II: Cornrow Curves
5) Start by having them click on the “history” section, and point out the four sections: “African
origins,” “Middle Passage,” “Civil War to Civil Rights,” and “Hip Hop.” Divide the class into 4
groups, and ask each group to read over their section (they may need some help in
understanding where one section begins and other ends: each section has a different number
and each page within the section has a letter—1a, 1b, etc). Explain that they will then
summarize what they think are the most important points from that section. It’s best to project
the page they are referring to on a big screen. Remind them about presenting something
orally—don’t mumble, project your voice, make eye contact, etc. You might have them
pretend they are trying to sell a TV show, or reporting on research to distinguished experts.
Remind the audience of their responsibility to listen, or ask them to come up with questions.
If students miss an important point, ask them about it – for example you may need to ask
group 1 what hairstyles represented in Africa (kinship, marital status, etc), and ask group 2
why heads were shaved (may have to go back to the group 1 question to get them to see
this), or why hairstyling was “resistance.” An important question for group 3 is why braiding
didn’t die out with hair straightening (little kids like you carried the tradition!). You might ask
group 4 why naturals and cornrows came back after the 1960s.
6) Go to the tutorial and take them through each page. Each time ask the group to figure out
what the correct value is for the simulation on that page. The kids often have fun trying to see
who will get the answer first. To make it more fair (so that one or two don’t get first each time)
you can have them silently raise their hands when they have an answer, but it also makes the
atmosphere more energetic to hear then yelling out answers. If you have time you can have
them take turns reading the text aloud on each page. Note that some pages also have
“follow-up” questions; these are really helpful in getting the kids to solve the posttest
questions. It’s a good idea to take a look at the post-test and see what to emphasize in the
tutorial; this is where a lot of learning can take place.
A fun exercise following the tutorial is breaking students into 4 groups and asking each to
demonstrate one of the geometric transformations using their bodies. At first they are
puzzled, but if you refuse to help they will figure it out—the scaling folks grow, the reflection
folks mirror each other, etc.
7) Take them to the software. Click on the image to show the various goal images available.
Then tell them we are going to run through one sim together. I like to use the middle braid of
the default image (my sister in law Denise) for that purpose: iterate = 20, X = -100, Y = 100,
Starting Angle = 12, Translate = 70, Rotate = -7, Dilate = 95. You can do all those as
question-response in that order except for Starting Angle – best to do starting angle last
(because there is no way you could have know that you would need that starting angle ahead
of time). Finally show them that by hitting the “add braid” button they can roll over the
previous values except for X,Y starting point. Ask them to reposition that new braid
themselves.
8) Now you can allow them to try one to simulate one of the other styles of their choosing.
9) Where to go from here? Lots of different directions:
--They can use it as a creative tool to make an art piece for a tee-shirt, or a logo for a
company, or just abstract art (which they could then colorize in Photoshop).
--They can photograph the hair of their family or friends. If they do that, make sure they take
the picture like a mug shot, 90 degrees to the front, side or top, and not at a weird angle—
also note that styles where there are lots of random little braids do not simulate well), or find a
style online (celebrities are always popular). We would be happy to include their photos in the
applet images as long as they send a copy of the signed permission form (see last page).
--They can try out some of the exercises from the “notes on math curriculum connections”
page (see below), or come up with their own math explorations. For example they can try to
figure out which parameters change and which remain the same as you move from one braid
to another. They can interview a professional braider and see if she can tell them about how
she is able to generate curved vs straight rows, or rapidly scaling vs non-scaling rows. The
possibilities are endless…
--They can move on to the Mangbetu Design tool. One of the nice things about the Mangbetu
tool is that it is based on the cornrows software, so they should be able to use the expertise
they gained with cornrows and apply it to Mangbetu. A couple of tips:
a. Have the kids repeat after you: Say bet (kids reply “bet”). Say wet (kids reply “wet”). Put
both words together and say “bwet” (kids reply “bwet”). Now say “Mangbwetu” (kids reply
“mangbwetu”).
b. Take the kids through the scaling heads example in the Mangbetu Design tool. Then ask
them, “Why do we find iterative scaling in both African American cornrows and Mangbetu
sculpture? The answer (which they usually can get to on their own) is that both come from
the same culture—that math can help us make the bridge back from American to Africa.
Some notes on curriculum connections with Cornrow Curves
General topics:


Cartesian coordinates
Transformational geometry
o translation--Cartesian distance, ratios between distances
o rotation--angle measures
o dilation--ratio and percentage
o reflection--Cartesian axes
Structured Inquiries:
1) Each plait (“y” shape) in the braid is scaled down by 90% of the previous plait.
a. If the first is 1 inch wide, how wide is the second? (answer: 0.9 inches).
b. How wide is the third? (answer: 0.81 inches)
c. How wide is the nth plait? (answer: 0.9n)
2) We can also look for some specific shapes
to explore: circles and spirals are probably the
best examples. Geometry of the circle, for
instance, can be explored by looking at the
relations between rotation and iteration. A
circular braid will be generated any time you
have a braid with rotation and sufficient
numbers of plaits (that is, sufficiently high
number of iterations). So you can ask
students to do an inquiry exercise: How many
plaits are required to create a complete
circle? It depends on the rotation--the higher
the rotation, the fewer plaits you need. If you
are only rotating by 1 degree in each plait,
then you will need 360 plaits to go full circle
(that’s only 359 iterations, because you get
one plait to start with; in other words there is a
“zeroth” iteration at start). A 10 degree
rotation will require only 36 plaits to make a
full circle. And so on. Having them discover this relationship on their own would be an
empowering exercise. Do these results change if you don’t use the default translation of 100%? If
you don’t use the default of 100% dilation? [TIP:use a small starting dilation, like 20%, so that
they can fit all of the braid on the screen at once]
3) Another good
exercise concerns
relations between
braids. As you
transition from one
braid to the next,
which parameters
change? Below is a
model in which
students can first
apply an empirical,
inductive approach,
estimating the starting
angle for each braid.
They can then
approach the same
problem analytically: there are 12 braids from zero to 90 degrees,
90/12 = 7.5. So the starting angle for each braid is 7.5 degrees
greater than the one before it.
PERMISSION TO BE PHOTOGRAPHED
_______________________________________ (the subject to be pictured) grants to
Professor Ron Eglash the right to use and authorize use of the photo or video in any
format or medium now known or hereafter developed, for the purposes of his computing
education project. No fees or ownership claims will be made by the subject now or later.
Subject(s)’ Full Name(s):
____________________________________________________________________
____________________________________________________________________
Date: _______________________________________________________________
[Photo Subject Name and Signature / or, Photo Subject Guardian Name and Signature]
For more information contact:
Dr. Ron Eglash, Associate Professor
Science and Technology Studies
Sage Labs 5502, Rensselaer Polytechnic Institute,
110 8th St, Troy, NY 12180-3590
www.rpi.edu/~eglash/eglash.htm eglash@rpi.edu
Work: 518-276-2048 fax: 518-276-2659