Thursday, December 19, 2019

Playful Math 133

Welcome to the 133rd installment of the Playful Math Carnival.

133 is the 6th octagonal number. How many carnivals until the 7th octagonal? What kind of pattern do the 6th polygonal numbers make? (Play with some figural number GeoGebra.)

133 is also semiprime - the product of two prime factors. (Which two?) What is the next semiprime number? 133 is also a Harshad (aka Niven) number, a number divisible by the sum of its digits. It's an unusual stretch where 3 of four consecutive integers are Harshad - which are the other two? There's also a new to me fact: 133 is the number of partitions of 55 into distinct odd parts, which seems equivalent to the number of symmetric Ferrers graphs with 55 nodes. I haven't made sense of this yet, though! 133 is happy in base 10, so a good number for this holiday edition.

Last fact and shout out to Megan Schmidt: 133 is a square spiral corner number! Is that connected to any of the patterns discussed above?
 Literal math playing...

  • Dave Coffey gave a presentation on Math Play with a Purpose at Global Math. He talks about redeeming Bingo, among other things.
  • Speaking of Bingo, two of the groups at this semester's Family Math Nights made actual math games out of a Bingo premise. Meg and Madison made Food Bingo, which makes it about attributes of food. Erica and Claire had Star Bingo which used better number cards and some choice to enhance the game.
  • There was one game that I liked more than the PSTs who ran it! Give Hamburger a try.
  • Probably the breakout and most original game of FMN was You Must Cross the River. Eddie and Climie brought this D&D style game.
  • One of my HS preservice teachers tried to gamify Which One Doesn't Belong... I think Danielle is on to something.
  • Denise Gaskins, the founder of this here blog carnival, shares one of her many Hundred Chart Games.
  • Marilyn Burns shares her two dice sum game, which is a classic for a reason. She shares using it in 2nd and 7th grade!
  • Kent Haines assembled a Holiday Gift Guide for math games that might be too late for shopping this holiday from this post, but you'll want to keep this list.

The 133rd Space Shuttle mission 
was the last (39th) for Discovery. 
They installed the Leonardo Module 
to the International Space Station.

Some playful interactives...

  • NRICH shared a puzzle that is part about area, but made challenging through Cuisenaire Rods. Great lesson.
  • Kevin Forster shared Factris which is a multiplication/factoring version of Tetris. 
  • Scott Farrar made a cool GeoGebra activity implementing Always/Sometimes/Never with quadrilaterals. 

 The C-133 Cargo plane over San Francisco Bay.

Math stories...

Xenon 133 is an isotope 
that is inhaled to study respiration, 
among other medical imaging uses.

Math art to round us out...

  • Isohedral rounded up some of my favorite animated math artists in this post.
  • Very excited that Clarissa Grandi has a math art activity book coming out.  Look at her website and you'll see why I'm excited.
  • Nathaniel Highstein did an Islamic Geometry project with his students. Scroll down this thread to see their work and how he tiled them!
  • Paula Beardell Krieg has been killing it, but if I was picking one recent post it's this one about the gyrobifastigium. You heard me.
  • Simon Gregg tweeted some mathart that turned into WODB and latin squares and more, as only Simon can do. But what better captures the spirit of Playful Math?

Math art from the Public Domain Review.

The previous Playful Math was at Arithmophobia No More and the next is at Math Misery?. Would you like to host? Contact Denise Gaskins, or see the Playful Math homepage. People don't submit a ton of posts anymore, but I enjoy looking back at what I've found helpful from the math ed community and sharing it all together. So many resources and so much fun to be had.

Happy Holidays, or New Decade Blessings, or Sweet Playful Math!


Listening to Ibram X Kendi read his book, How to Be an Anti-Racist, and these are some notes along the way.

The introduction starts out with his humble admission of a speech he shared for a Martin Luther King Jr Day competition/celebration which he now views as racist. This leads into his focusing on the word racist, and how it has become viewed as an attack or a slur instead of a descriptor. Anything that blames a whole group for its problems is or can be racist. The struggle is to both be fully human and to treat others as fully human.

Which I love as basically the central problem of human existence. In a recent Zadie Smith interview, she responded to a question:
"You recently wrote about Toni Morrison that the thwarting of human potential was her great theme. What is yours? My own feeling is that it’s about the failure to be human. Everybody’s born and everybody exists. But to be fully human takes a little bit of effort. I think my novels are about the challenge of actually being human and not avoiding the responsibility of being human, which is very heavy. There’s a responsibility of the single person, the responsibility of the married person and of the person with children, the person without, of the dog lover — each tiny path has its kind of demands upon you, which are incredibly hard to fulfill."

Dr. Kendi points out that racist acts or statements are often followed with denial. When we say we're not racist, we're joining in denial and warping the meaning of the term as a descriptor. The distinction is not between racist and not racist, but between racist and anti-racist. Not racist, Dr Kendi points out, is a denial, and racists are the first to deny. So denials are no way to distinguish. Denial is akin to colorblindness, and antiracists aren't ignoring important characteristics of people that have affected their lives. They are seeing the effects and working to counteract racist thought and action. 

Each chapter covers a different specific kind of racism and antiracism. Starts with definitions, tells stories, often personal, sometimes historical, and supports with science and statistics. Then he illustrates the definitions with examples of what a racist and antiracist do or say. It's a robust structure that really supports the book's aim, which is really just the title.

Group vs individuals is a major theme of the book. Racism is the historical most harmful way of grouping individuals that we have manufactured. Dr. Kendi makes clear that every time we think or use 'because they are <fill in race>' we are being racist. To be anti-racist is to break those narratives, to treat people as individuals, to work against the consequences that racism has caused. One of the major shifts in this way of thinking is that black people can be racist if they are engaged in this kind of thinking and action. His motivating example is his own anti-black racism, and he shares anti-white racism from his story as well. Including himself in this analysis is humility and truth speaking in action, and it is powerful. 

In most of the diversity and inclusion learning I have had up until this point, the focus has been on the inequities produced by individual and systemic oppression of non-white (even as that definition has shifted) people. In this view, the minority groups can not be racist because they have no authority or power to oppress. Bias has come to be the identifier for individual racial preference, explicit or implicit.  Dr. Kendi's vision is more powerful to me because it addresses the cause of the oppression and fights against the core of what went wrong as racism was constructed.

Recently, a friend and colleague asked me for resources for anti-racist math education resources and I couldn't really think of any. I made a Google Doc to gather the resources I do now about: Please feel free to add or comment. We do have people in the math ed community working toward this and I know I don't know the half of it.

As Dr. Kendi discusses education, he is particularly concerned with the "racial achievement gap". The whole concept is, necessarily, in his framework, a racist idea. To be antiracist is to believe that individuals face greater challenge in schools and each learner is capable of achievement. Here is a blogpost where he details the enraging history of the idea and the tests which maintain it today.

I've taken long enough to write this that Mindshift has a post today about these ideas applied to education.

This book was specifically helpful to me this semester. One of my classes was driving me a little crazy. Pre-service teachers who were not engaged, who didn't listen to instructions, who didn't seem to care even when it involved working with kids. But this book made me realize I was treating them monolithically. I was not treating them as individuals, I was not seeing and encouraging the work of those who were engaged, and I was lowering expectations. I am a spoiled college teacher with low numbers of classes and small class sizes and I was struggling with this most fundamental of my responsibilities. This realization helped me have a better attitude, helped me individualize my thinking towards the learners. 

I love the synergy between this view of antiracism and call to action. It feels of a piece with the call to rehumanize mathematics from Rochelle Gutierrez from Sam Shah's and Hema Khodai's Humanizing Mathematics Conference