Go Formative: Unit 2 Review (Day 39)

As a Southern Californian, I will start this post by congratulating the local basketball team, the Los Angeles Lakers, on winning the franchise's seventeenth championship last night.

Meanwhile, my car finally broke down today. I first purchased my car in 2007, and ever since the major repairs it needed four years ago (which I described on the blog at the time), I knew that it was living on borrowed time. Today's damage (the oil leaking in several places) will cost thousands of dollars of fix, and so it might be better for me just to purchase another car.

None of this of course has anything to do with today's lessons. Let's start with the teachers' department meeting on this Late Start Day. One thing mentioned there is the upcoming district assessment, to be given either the week before or the week after Thanksgiving break. I notice that one word used to describe these tests is "benchmarks." This immediately reminds me of my Benchmark Tests song --that's right, I am always looking ahead for songs that I can sing in class!

The main assignment for eighth grade is a review assignment on the Go Formative website, for the upcoming Unit 2 Test. One of the other eighth grade math teachers created this assignment by taking some of the questions from the APEX test itself.

As we discussed, neither this review nor the test will contain any questions from Lesson 2.2.1, slope. It turns out that slope is taught more thoroughly in Unit 3, and so it's better for us to wait until then to test the students on slope.

In first period, I try to go over each Go Formative question, doing one question for the students and then having them try the next question. But we only get through eight of the 20 questions on the assignment. I stumble on Question 9, which asks students to get information from a graph, but it's difficult for me to see the graph in Go Formative. I assume that the graph will look better on the actual APEX test.

And so I fix this by fourth period. I simply skip over the hard-to-see questions in order to reach some of the later ones. This time, I make it to Question 14.

The seventh grade schedule is slightly different. Today is actually the day of the Unit 2 Test -- they had their own Go Formative assignment to do last week. But many of the students struggle to complete the Go Formative work -- and it's easy to see why. It's not actually based on Unit 2 in APEX, but on a completely different curriculum. In this old text, all four rational number operations appear in the same unit, whereas in APEX, only addition and subtraction appear in Unit 2, with multiplication and division being saved for Unit 3.

In second period, since so few students had completed Go Formative, I decide to go over it first, to be sure that they're ready for the Unit 2 Test. But then I gave up once I saw multiplying and dividing. By third period, I tell the students just to forget about Go Formative and proceed directly to the test.

Meanwhile, the Queen of the MTBoS has spoken! Fawn Nguyen makes her first post in five months -- and since she is (or was) a middle school teacher, I do wish to link to her. I'm adding the "MTBoS" label, since I'm one middle school teacher linking to another:

http://fawnnguyen.com/momath/

At our core, we sense when something is not equitable, not right. We want to speak up when someone is not abiding by the guidelines that are meant for all of us.

And Nguyen herself links to the blog of high school teacher Sam Shah (Continous Everywhere but Nowhere Differentiable -- yes, he's a Calculus teacher):

https://samjshah.com/2020/10/11/concerns-about-momath/

Both Shah and Nguyen are concerned about "MoMath" -- a New York Museum of Mathematics. They are concerned that when schools visit the museum on field trips, wealthy full-paying schools are treated much better than poor schools:

To me, one of the most problematic charges in the letter is that students from Title 1 schools who visit MoMATH often get lessons that end up being 20-25 minutes instead of the normal 45 minute sessions. The letter states “We cannot remain silent while the Museum chooses to offer sub par services forthe least fortunate students who are vastly more likely to be people of color.” I hope that with this letter, those at the Museum take a close look at their practices to ensure there is equity for all the students visiting the Museum. To me, more than anything else, this is of paramount importance before the museum opens its doors again. 

This discussion is getting very close to politics -- and indeed, I'm about to start reading Eugenia Cheng's latest book. We know that Cheng also writes about politics, especially in her last two books.

So once again, let me give my disclaimer -- those who wish to avoid politics, or disagree with the politics of Cheng (or Nguyen or Shah), should avoid all posts with the "Eugenia Cheng" label. I try to avoid deeply political posts, especially when I'm teaching five days a week in a math classroom. But once again, I feel that these topics are directly related to our math classes and our students, and so it's fair game to mention them during the school year.

OK, I've made my decision about our side-along reading of Eugenia Cheng's newest book. I'll start with Chapter 1 today and Chapter 2 later this week, but I'll cover the middle Chapters 3-5 only on Twitter rather than this blog. And even for the chapters that I do blog, it's going to be a much briefer summary of each section of the chapter, rather than several pages of her quotes and my responses. So without further ado, let's begin:

Chapter 1 of Eugenia Cheng's x + y is an introduction. Here are the sections of this chapter:

• Being a woman means many things: Cheng writes about what it is like to be a woman in the male-dominated field of mathematics.
• What is mathematics? Mathematics isn't just about numbers and equations -- it's also the study of shapes (yay Geometry!), patterns, structures, interactions, and relationships.
• How does mathematics do things? Cheng quotes Sir Tim Gowers, who says that mathematics is all about problem-solving and theory-building -- although the latter is often ignored.
• What is the problem? The problem is that some words like feminism are tricky to define -- indeed, feminists and anti-feminists often define it differently.
• A mathematical approach: Cheng begins by proposing a theory -- and mathematical theories begin by defining the key terms.
• The process of math: Mathematical theories start not necessarily with calculating answers, but by spotting patterns.
• The idea of category theory: Cheng's specialty is category theory --featured in her first book How to Bake Pi -- and here she repeats a category-theoretic diagram from her Art of Logic, where an image with arrows is used to demonstrate both the factors of 30 and levels of privilege in society.
• Dimensions: Just as mathematicians use a new dimension for analyzing complex numbers, we can use a new dimension to study the concept of gender.
• How we make progress: To make progress with a mathematical theory, we must evaluate both its practical and theoretical sides, and Cheng does the same with gender.
• Dream worlds: Math is more about getting the right answers -- it's also about dreaming up new worlds in which different things are true.

Hmm -- perhaps MoMath in New York would be wise to include a Eugenia Cheng exhibit somewhere in their museum. This exhibit can show her privilege cube -- especially since (according to Shah and Nguyen) the museum is itself promoting "rich" privilege over poor.

One thing Cheng writes is especially relevant to me as a teacher:

"Similarly, if we think about a pattern of women not speaking up in meetings, and female students not asking questions in class, the similarity at an abstract level could be summed up as 'women not speaking up in mixed-gender environments.'"

And this is certainly something I plan on watching out for. It's one reason that I like to choose students at random -- it's to avoid situations where only the boys are calling out answers and the girls are afraid to participate. (And it also helps during this hybrid plan, where students in the classroom are answering questions and I forget all about the students logging in from home.)