Geometry Solids Project: Creating a Die

I am looking to attempt this project with my students starting in a few weeks. I am still working out details and testing it, but I would love feedback.

Objective: 

Students design and create a non-cube die of their choosing using either 3D printing, crocheting, (or something else?)

Definitions: 

Polyhedron: a solid formed by plane faces

Dice: A solid object that can be rolled and land on one of n-sides. Each side is labeled a number or other symbol(s). 

Deliverables

ItemFormatDetailsDueDone?
ProposalGoogle FormWhat polyhedron?What material?Who you are working with (if anyone)? 
*Everyone must submit a form, even if you are working in pairs*
Digital 3D Model.spl fileUse tinkercad.com to design your dice. It must include the polyhedron listed in your proposal, but you may combine it with other polyhedrons.
Play with the number of sides, steps and other settings to create your die.
Paper/cardboard NetFlat net and folded netDrawing of net(s?) and calculations (perhaps showing multiple approaches for calculating?)Find Area (in general terms, and then with a specific size that you plan to make)
SummaryPaper
 AND 
Google Classroom
Stats/Calculations: 
-Surface Area of Net (General and specific)
-Volume of paper (General and specific)
-Print/Crochet speed (in. of material/minute?)
-Length yarn/filament used 
-Something with the probabilities/fair and unfair dice???

Reflection: 
-It is impossible to create a perfect physical polyhedron. In what ways is yours an approximation? In what ways is yours an accurate representation?
-What did you learn during this project about your medium? About polyhedrons?
-Discuss the math behind constructing your die
-What surprised you during this project?
-What are you most proud of from this project?
DiePhysical ObjectPossibilities:
1. 3D printed
Crafting Days: Research/learning about how 3D printers work, beginning prints

2. Crochet/Knit
Crafting Days: Time to work on your project and troubleshoot together

3.Something else that you think would be cool? Talk to your teacher!
After Project SurveyGoogle formGetting your feedback!
  • Questions for those reading this:
    • How does this read? Is it logical? What questions are you left with?
    • How would you assess this? What would you include in a rubric?
    • What should the presentations/celebration at the end of the project look like?
      • Possibilities: gallery walk, verbal presentation, giving feedback to each other, playing dice games…?
    • Any ideas for extensions to this/other mathematics to explore
Photo by Matthias Groeneveld on Pexels.com

motivation when I’m tired

(Alternatively titled: A teaching philospohy)

In trying to understand who I am as a teacher
I found a misconception I had been holding on to:
I thought the pull to teaching was math.

(And I do love math
I am grateful to have it as a partner in this endeavor
I love its definitiveness and ambiguity

Give me good pattern any day of the week and I’ll be happy
Or an algorithm
a visualization
a comparison
a mapping
a graph
a prediction
a puzzle

Math is a language where you can express
both more
and less
than you can with words.

Math carries a precision that syllables and sentences never can
Yet fails to articulate the finest points of humanness)

But to say I am tied to teaching because I love math
is a knot that will unravel under tension.
I would not have ended up here if I had not accompanied a bouquet of trans folks
On legs of their expeditions:
Through crushing expectations
Through meeting themselves
Through glimmers of expansive freedom
Through letting the world in to meet them.

I teach in order to hold a place for these gender explorers and defiers
For these norm breakers
For these students looking for someone to see them, to know them.


I stumbled into teaching with my crochet hook and calculator
with enormous and hazy and overwhelming dreams
To chip away at these walls against which my back is pressed
To exist where they said we couldn’t
To make space
for us.



Black trifold board poster with a rainbow geometric stripe from the bottom left to top right. Title in silver: lgbteacher: being out in the classroom as an act of radical honesty. 
Bottom right is a timeline with pictures. Middle contains titles with flap doors that reveal to more
final project for my first grad school class in teaching in 2019

themes from writing feedback: fall 2021

At the end of the term, my school has a thing called narrative comments: individual written feedback by each teacher to each student.  A typical structure (and the one I chose) was 3 sections: commendations, recommendations, and comments. Below are some excerpts from my first term of comments. 

Commendations

  • You do a great job of leaning into the challenges in class. We have had many concepts that were tricky and nuanced, but you have always been willing to jump in and start trying to make sense of them.
  • You do a great job of pulling apart diagrams/breaking complex problems into smaller, more manageable problems.
  • You always come to class with a great attitude and a willingness to work with anyone.
  • You are very good at working slowly and methodically through problems and keeping your work organized. This will serve you well and we continue to delve into more complex problems.
  • You do a great job of asking for help with focused and specific questions. This shows me that you have put a lot of thought into your work before looking to other resources for help.
  • I was very impressed with your work on the unit 4 assessment, and the thoroughness of your proof map. Your best work comes out when you have the time to dig deep into a complex problem.
  • You use your time in class efficiently, and take advantage of extra class time to start homework. This is a great habit that allows you to get your questions answered before you leave.
  • Over the term I have seen a large growth in your skills tackling difficult problems. You seem more willing to dive into the complexity, rather than shy away from it. 
  • Your work is always thorough and well thought out. Your homework could be an answer key. I appreciate your ability to communicate so clearly and precisely in your work.
  • You are patient and kind to group mates when they find a problem more difficult than you do. You do an excellent job of balancing listening to others’ thoughts and contributing your own.

Recommendations

  • Continue to push yourself with communicating mathematically. There is a lot of specific notation in geometry, but it all serves a purpose. Becoming as comfortable as possible with notation (in diagrams and written out) will help to avoid confusion or miscommunications in your work.
  • When you face a problem that feels overwhelming, try breaking it down into smaller pieces. Another strategy is to list out everything you know in the problem. It will surprise you how much information you already know
  • Work on improving the organization of your work in order to communicate more clearly. Your process should be able to be read and understood by someone else.
  • Work on understanding and using math notation when marking up diagrams. In geometry, these figures hold so much information, and it will help if you write on diagrams rather than trying to keep the information in your head.
  • Practice slowing down when working. With some assignments or problems, you seemed rushed to get it done, causing you to miss some of the details. It will help your understanding to slow down, and take the time to make sure your work is organized well and you understand all the pieces. 
  • Practice approaching problems from different vantage points. See what ways classmates look at problems, and try to understand the similarities and differences in the approach, and why both may work. This will help you be more flexible when approaching unfamiliar problems.

Comments

  • You have done a wonderful job of adjusting to so many changes this year, including switching classes. I am so proud of you for advocating for what you needed, and taking care of yourself. It has been wonderful to see your confidence in math growing.
  • I really appreciate your honesty when giving me feedback on what works and what does not work for class. Our class is better because your suggestions, and because of your presence and participation.
  • I want you to know that your effort and hard work is seen, and remind you of the resources that are here to support you.
  • I appreciate how honest and communicative you are about how you are doing and what difficulties you are having.
  • You have all the makings of a great mathematician. You think critically and question information that is given to you, you persevere through difficulty, and you do it all with humor and joy.
  • Continue to hold yourself to high standards, but remember you are allowed to make mistakes as part of the learning process.

a mathematician crochets

As I have learned to crochet, my first thought is (as it is for all people, I assume): what is the mathematics involved in this beautiful fidget medium. Here are some questions I have asked so far (with answers, if I have found them):

Side note: Nothing would make me happier than other people engaging with these questions/trying to find answers/asking their own questions…. (:

  1. how do you tell how many yards of yarn there are in a ball, without just measuring it all?
  2. how do you tell how many yards of yarn a project will take, without just making it?
  3. knot theory things… (this is probably about a million questions, I know approximately nothing about knot theory, and am fascinated)
  4. weight vs. volume? Potential formula???
  5. making regular polygons?
    1. found this beauty: https://www.revedreams.com/crochet/yarncrochet/single-crochet-shaping-3-polygons/
    1. making platonic solids? I need to do it. There are only 5, after all. I can do that.
  6. mathematics of winding patterns for various yarn ball things…skeins, cakes, big ol’ knot, etc…
  7. mow does tightness of balling/density effect the ratio of final yarn length to weight (or some other measure)?
  8. how does material effect all of this? (density?) (Which size hook to use?)
    1. how does the size hook effect the final area of the piece?
      1. does that match with sizing? If so, US, UK, or metric? (side note: Why are there 3 different systems (according to the conversion chart that came with my hooks))
  9. How do types of stitches play into all this (single crochet, double crochet, half-double crochet (side note: terrible name. better name would be 1.5 crochet maybe?)

an ode to zero

You beautiful Nothing
You steadfast and headstrong emptiness
You magnificent subtlty

You hide in the corner
always observing
contributing nothing but your presence
But your presence is everything

You are shy
You are dangerous
We must tread carefully around you
A misstep could lead us to chaos
But we must trust you

You are assertive when it comes to grand gestures
You take control
You are persuasive
But when we contemplate the details, you remain quiet
adding nothing

You do not fit into binaries:
neither positive nor negative
neither prime nor composite
You are your own

You hold space for those who have not yet arrived
You hold the memory of where others once were

You are nothing.
A powerful and immensely important
nothing.

labels and definitions

Much of mathematics is understanding precisely what a word means, the intricacies of what makes this thing unique from other thing. How is a square different from a rectangle? What differentiates a prime number from relative primes? I appreciate this precision and I enjoy exploring the edge cases and being able to place my hands firmly on those edges.

Outside of mathematics, things are different.

To use labels, we operate under the assumption that we have the same working definition of a word. In my experience, that is a bold assumption to make.

My understanding and definition of queerness, masculinity, gender expression are not the same as yours, which makes it difficult for me to claim labels, because while I know what these mean to me, I don’t know what associations and assumptions you will bring to them.

These are not concepts defined with precision. And that is the beauty of them.

critical points

1. In math, critical points of a function are the points of a function where the derivative is 0 or undefined. In other words, they are the places where the function is horizontal, or there are points or gaps where there is no tangent line. Often times these points are turning points: they are where a function changes from increasing to decreasing, or vice versa. Not always, but often. In calculus, these points are called “critical” because they offer us a roadmap of the function and it’s behavior. They give us a nice summary of what is going on. And they also include points of interest such as maximums or minimums.

2. The word “critical”, outside of math, has a few meanings:

  • 2a. Very important, crucial
  • 2b. To point out the flaws, to critique
  • 2c. Something that offers analysis of a work
  • 2d. Having the potential to become disastrous (ie critical condition)

So this blog, this collection of thoughts, plays on both of these definitions. These are thoughts that are critiques and analysis, of things that are important to me. They are writings about my personal turning points to give you a roadmap of my mind, where I have been, and where I am now.