beginning my masters in teaching

• Things I am thinking about
  • Healing math trauma
  • Habits of mind
  • Math anxiety
  • Creativity and joy in math
  • Community
  • Curiosity
  • Access
  • Honors/standard/fundamentals (the levels of math offered at my school… we are trying to reimagine this)
  • Portfolios
    • Assessment
  • Communication
  • Identity
    • Disability
    • Gender
  • Art
    • Geometry of clothing/fashion
    • crocheting/knitting
    • Clay
    • 3D printing
  • Technology 
  • Journaling/Reflections
  • Productive struggle
  • Math literacy
  • Games 
• Questions
  • Why do we teach proof in geometry to ensure all students have access to and understanding of proof?
  • How can we foster an environment of collaboration and curiosity in mathematics?
  • How can we use proofs to teach students literacy skills in mathematics?
  • How can we use proofs to help teach students how to productively struggle?
  • What does a healthy mathematics community look like and how can we use community to heal math trauma and foster resilience in problem solving?
  • How do we decenter white male mathematicians in teaching geometry?
  • How can we use portfolios in mathematics to assess student growth and help students to see their own growth? 
  • How can we disrupt students’ internal narratives of fixed mathematics ability?
  • How can geometry be used to help students rediscover the power of play and creativity in problem solving?
  • How can teaching proofs be used to improve mathematical communication between students?
  • How can we use technology tools in teaching geometry and proof?
  • How can we incorporate art in teaching geometry? (Needs to be more focused) 
  • How can we use journals in mathematics to help students understand themselves as mathematicians, and their mathematical process?
  • How can mathematics be used to help students explore and understand identity and their place in the world?
  • How can we use games to foster creativity and collaboration in mathematics?
  • How can we reimagine the divide of students between varying levels of math courses?
• Possible project ideas
  • Workbook of selected proofs/puzzles that build on each other
  • Outline/Example of a portfolio based assessment system
  • Website/blog: Community Mathematics —> daily/weekly puzzles
    • Series of collaborative puzzles?
  • Unit/Lesson Plans
  • Something else??????
  • Design a project for students to do

Chosen Research Question (As it stands right now): What does a healthy mathematics community look like and how can we use community to heal math trauma and foster resilience and curiosity?

awards season

I gave each of my students an individual award for the end of the year. Below are the awards (slightly edited for anonymity).

1. Product of Zero Award: Most Persuasive
2. Absolute Value Award: staying positive when things are hard, bringing joy and humor to our class
3. Math Center Award: best use of resources and asking questions
4. D20 award: Best world builder
5. Denise chickulant award (named after the succulent in our class): positivity and adaptability
6. Proof Award: Excellence in class participation and mathematical explainations
7. Exponential award: Mathematical growth
8. x^2+y^2 = 1 award: well rounded, and rolls with the punches
9. Craftsperson Award: creativity and skill in many mediums
10. Secret Mathematician: Most likely to ask if we can not do math in math class
11. Tony Award: accomplishment in the dramatic and mathematic arts
12. Fractal Award: A mathematician who is meticulous, organized, and precise
13. Sunflower award: Most growth, and for being ray of sunshine
14. Chameleon award: makes the best of any situation
15. Technicion Award: Most likely to build a computer from scratch, and excellence in tinkering and finding the joy in a puzzle
16. Calculator award: Most likely to have done all the math in their head before half the class heard the question
17. Distributive property award: Best person to spill tea with
18. Best New Artist: Painting
19. Divide by 0 award: Best person to be stranded on a desert island/get you out of a bind
20. Apothem Award: for keeping us grounded, clever solutions, and also making us laugh
21. Cosine Award: For someone who is adaptable, practical, and perseveres through challenges
22. Prime number Award: For someone who demonstrates individuality, curiosity, and strength.
23. Probability Award: Most competitive at games of chance, as well as someone who always pushes themselves to improve
24. X^x: For excellence in volleyball, leadership, algebra skills, and positivity
25. Proof By Induction Award: For witty comments, persuasiveness, great communication, and clever mathematical solutions
26. Java Award: Most likely to be a vigilante hacker
27. Exponential Award: Most likely to make forbes 30 under 30
28. Rising Star Award: Given to a freshman who shows wisdom, discpline, and skill beyond their years
29. Parabola award: For excellence in 3 point shots, and for willingness to lean into difficulty and grapple with complex ideas and problems
30. GCF Award: For excellence in collaboration and making connections between concepts
31. Tangent Award: Most likely to steer the conversation in an extremely interesting (if unrelated) direction
32. 2022 Award: For someone who embodies the best part of this year together: fruits nacks, flexibility, fun, friendship, and a finding where you fit in this community.
33. Unmasked award: For authenticity, compassion, risk taking, and kindness.
34. Wordsmith: For excellence in fast typing and word puzzle solving, and general cleverness and collaborative skill
35. Canada Award: For excellence in leadership, athleticism, fidgeting, style, and perseverance
36. For excellence in collaborative problem solving, creative thinking, reading prowess, and openmindedness.
37. CPS (clicks per second) Award: For fastest gaming, googling, and wordle completing.
38. Blooket Award: For speed, accuracy, and good sportsmanship.
39. Desmos Award: Excellence in graphing, visualization, and precision
40. Linear Function Award: Someone who keeps us on track, and is consistent in their effort and enthusiasm
41. Rational Function Award: For someone who excels in logic, organization, and finding unusual methods of solving problems.
42. The Phantom Tollbooth Award: For embodying the spirit of Milo (the main character in The Phantom Tollbooth). This award is given to someone with extraordinary creativity, cleverness, and growth throughout the year.
43. (Breaking the) Glass Ceiling Award: for someone who defies expectations, holds themselves to high expectations, and advocates for their needs
44. Quadratic Award: For excellence in box factoring and mathematical explanations.
45. 18th Hole Award: For golf skill, kindness, compassion, and perseverance.
46. Piecewise function: For someone with many changes and bumps along the way through this year, but who managed to find a path through with positivity and humor.
47. The Lightbulb Award: For someone who asks great questions, and uses their understanding to help others understand. This award goes to someone who helps others see the joy in mathematics and problem solving.
48. High School Musical Award: For positivity, openness to trying new things, kindness, and commitment to the bit
49. Glee Award: for excellence in collaboration, community building, and communication

Awards named for colleagues

1. For someone who has worked hard to make connections in the community, and goes out of their way to make sure everyone feels welcome. You are someone listens without judgment, and who is always trying to understand the perspectives of others.
2. For a leader and in the community with big visions, high expectations, and good humor.
3. For being unafraid to stand up for the right thing
4. For Kindness and compassionate leadership
5. For a lover of calculus
6. For perseverance, good humor, curiosity, and tenacity
7. For someone who is kind, consistent and clever
8. For creativity and Enthusiasm
9. For someone who is prepared, organized, thoughtful
10. for curiosity, collaboration, singing, and style

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

Item	Format	Details	Due	Done?
Proposal	Google Form	What 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 file	Use 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 Net	Flat net and folded net	Drawing 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)
Summary	Paper  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?
Die	Physical Object	Possibilities: 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 Survey	Google form	Getting 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.

final project for my first grad school class in teaching in 2019

long and short term goals and dreams

But who’s to say which is which

• Create a math elective
• Decorate/organize classrooms and office
• write a play
• create knit/crochet clothing
• create a gender retreat or pen pal network or mentoring network or something related to giving the trans youths a place to explore gender
• write pretty math puzzles
• make cool escape room puzzles
• crochet cool things
• knit cool things/learn to knit
  • One of the knitting projects designed by Tom Daley (https://bytomdaley.com/)
• Research the crossover of fiber art and math
• journal/post updates more consistantly
• write poetry
• Create art with trash
• Learn more about 3d printing
• Write a letter to students thanking them for being my first group I’ve thought for a full year
• Do a workshop on gender/trans competency for faculty
• Learn to roller skate more
• Find a way to get back into dance

Defining our purpose: the trajectory of my math department

There is a lot of discussion around what the math department at my school will look like over the coming years. I rarely contribute to the discussions, sometimes out of anxiety but mostly because I am listening to what others have to say. I want to fully understand where we stand right now and how we got there before I can begin imagining where I want us to go. Here are some things that have come up when I have been thinking about this.

I want us to be a place:

Where you problem solve and model and visualize and predict

Where you learn to communicate precisely

Where you practice seeing patterns and connections

Where you use logical and organized thinking

Where you analyze and critique the world you live in, and brainstorm solutions

Where you come out in the end fundamentally believing in your ability to struggle productively

Where you lean into the unknown and the confusing with curiosity and creativity

Where you learn to ask questions far more than you find answers

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.

• 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.

small poems (1)

I push myself constantly for growth.
But what if I just maintain for a while?
Enjoy the view from here?

assorted thoughts from my notes app (pt. 3)

1. Statistics for how many calls I get per day to sub for various schools, despite working full time (I stopped keeping track after 3 days)
2. “I am better adapted to a world with technology” (most of the time)
3. “When teaching I give away the answer too fast”
4. A selfie from when I was feeling cute
5. Outline for my murder mystery review activity
6. Things to do with my mom during break
7. “I need more structure for self care”
8. “My body is a plane of a non Euclidean geometry”
9. “I love looking for patterns in data”
10. “Proofs are about seeing connections”
11. A list of ideas of things I would love to create from writing a book to
12. How do you be introspective without being overly self critical (edited from original longer jumbled thought)
13. “Adapting to a genre vs conforming to it”
14. “Bad healthcare’s effect on my relationship with my body: Its too expensive to check in, So I tune it out. I tune out the creeks and throbs, the stiffness and pressure”

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.