This Week at Global Math – 11/10/20


Curated By Chase Orton @mathgeek76

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Online Professional Development Sessions

No Webinar this Week.

Check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

You can also visit our new YouTube Channel to find videos of past sessions and related content.

Coming Next Tuesday: November 17th, 2020!

Park City Math Institute in the Time of the Pandemic

The Park City Math Institute (PCMI) is an intensive 3-week residential conference that’s been around in some form or another for 30+ years. The Teacher Leadership Program of PCMI offers a phenomenal professional opportunity for classroom teachers unlike anything else around. The global pandemic may have interfered with 2020, but come see what’s up for PCMI 2021!

Presented by: Monica Tienda and Barbara Lynch

To register for this webinar, click here.

From the Writing Team

Not Doing Math When You Should Be

I love math memes. Here is one that I recently saw:

I was amused by this meme because I knew that the result of the US Election was decided without the Nevada count: The President-Elect is Joe Biden, the Vice President-Elect is Kamala Harris, and the people of the United States voted out a failed fascist and overt racist. COVID can be stopped with masks and distancing, yet the sitting president* encourages mask-less gatherings (some of which become super-spreader events). The People of the United States deserve to vote, and voting by mail during a pandemic should not be a concern due to interference in the United States Postal Service. Families in the United States, irrespective of their citizenship status, deserve to remain together; we should not be caging children or losing track of the kids and parents separated from one another. As hard as it may have been to Cast your vote, it should have been easy to Decide your vote.
But. Over 71 million people voted for the pro-COVID, anti-USPS, cager/separator of children. donald trump has always been a loser. He aimed to enrich himself by running for president in 2016 without the goal of actually winning; it has been to the detriment of the United States, and the world, that he Lost at Losing and emerged electorally victorious. In 2020 he ran for re-election, but this time he wanted to win; as we now know, he lost like the loser he will always be. We cannot, as a nation, simply cast off those who voted for him despite these four years of intentional harm directed primarily at marginalized peoples. 71 million is simply too large a number. We also cannot “meet them halfway” on questions of fascism versus anti-fascism, or racism versus anti-racism. I don’t have game-changing advice on these voters right now. Not yet. Sorry.
What does “not doing math when you should be” mean? I have been doing math, incidentally, but it hasn’t been strictly school math.
There are a lot of current joyful happenings in the world of mathematics:

  • I hope that you are following BlackInMath during this #BlackInMath week
  • I was excited to see my former classmate-then-coworker Dr. Brandie Waid publish an NCTM MTLT article called “Supporting LGBTQ+ Students in K-12 Mathematics”
  • There is great work happening on mathematical gerrymandering that goes way beyond the “ChartThrob” casting of some white dudes on CNN and MSNBC whose math amounted (mostly) to arithmetic:

In the tweet above, I mention that the most impressive mathematical feat of this election, from my perspective, has been the voter organization of Stacey Abrams and others. With two competitive Senate races coming up in Georgia this January, I urge you to engage with the math that you should be doing.
To that end (who are the “others” besides Abrams, you may be wondering), here is a spreadsheet entitled “Georgia BIPOC-led voter outreach organizations (created by They See Blue Georgia)” via Cathery Yeh:

I want to go back to “doing math.” I want to dedicate more of my brain space to teaching and learning and shifting school mathematics (including a longstanding battle against Calculus, as Nas discusses below). I want to do types of math that go beyond Nevada’s slow counting—no disrespect to counting. And: Now that we have lodged a major victory in the presidential race, we need to do the math on how to keep pushing the United States forward. That starts with the Blue State of Georgia, and continues with, for example, understanding that so many of today’s 16/17 year olds can vote responsibly in the 2022 midterms.
We must engage in the types of math that ensure we live the words of John Lewis, as Vice President-elect Kamala Harris quoted in her acceptance speech, when both reminded us that “democracy is not a state—it is an act.”
What is the math that you should be doing?
Benjamin Dickman [@benjamindickman]

The Cases for Discrete Math

Since my first middle school viewing of “Stand and Deliver,” I dreamed of taking calculus in high school and, much later, instilling the same excitement for college-level mathematics in my own middle school algebra students. Beyond Hollywood fantasies of rising from arithmetic to perfect AP Calculus scores in under two years, the expectation of taking calculus in high school has become all but normalized over the last few decades. Significantly, high school calculus is often promoted as a mechanism for both engaging historically underrepresented students in STEM and in increasing access to STEM careers. To both these ends, and with no disrespect to Jaime Escalante or my own wonderful calculus teacher, I propose an alternative: all students should be required to take a full year of college-level discrete math as their terminating high school mathematics course.
Arguments against the push to take calculus in high school often cite the rapidly growing number of seniors enrolling in calculus out of a desire to bolster their college applications despite inadequate mathematical preparation or interest. Consequently, as reported by the Mathematical Association of America, a large percentage of students who successfully pass the AP Calculus Exam retake Calculus I in college because university math departments often claim that even students earning high AP scores are still poorly prepared for college-level mathematics. With significant research and discussion around the detriments of tracking students, I am less interested in these elitist pushes toward reserving calculus for only the most mathematically “gifted” high schoolers.

Having been lucky enough to teach both a conceptual calculus course last year as well as the start of a discrete math course to seniors within our wholly de-tracked high school, I argue that discrete math is both the more equitable as well as the more rigorous option for students regardless of their post-high school plans.
Case 1: For High Schoolers Interested in STEM Careers
The entryway into coding afforded by the typical discrete math course renders it an obvious selection for students pursuing a wide range of STEM careers. Its appeal to students of pure mathematics, however, has historically been a bit more varied. Only ten or so years ago, my undergraduate math department—troubled by low student retention in the subject—opted to make discrete mathematics a required course for mathematics majors, their stated goal being to more adequately prepare students for advanced study in mathematics through rigorous exposure to proofs.
Despite skipping multivariable calculus and lower-division linear algebra, I found that my familiarity with formal logic as a result of taking discrete math enabled me to successfully complete the core upper-division courses for the major. In this way, discrete math provided more extensive exposure to the types of problems and reasoning I would experience as an advanced math student than my AP Calculus class. By contrast, students at my university who had excelled in calculus but had not taken discrete math or other courses building formal logic skills frequently expressed frustration at their upper-division math courses’ unexpectedly heavy emphasis on proofs. Offering discrete math at the high school level will not only provide more students with the requisite skills for success in future math classes but also a more representative view of what the field entails.
Case 2: For High Schoolers Not (Yet) Interested in STEM Careers
With broad applications in economics and other social sciences, calculus is often marketed to high school students seeking careers outside of STEM as a “necessary evil” that will benefit them in future research endeavors. By including units on combinatorics, Bayesian probability, and formal logic, discrete math similarly provides students with essential tools for analyzing “real-world” phenomena through a mathematical lens. An intuitive understanding of conditional probability, for instance, might go so far as to help patients decide on the best course of treatment. The importance of teaching logical deduction to all students prior to their high school graduation is particularly uncontroversial. (For a fun read on the topic, Professor Eugenia Cheng makes a compelling case in The Art of Logic in an Illogical World). 
Unlike calculus, however, the comparatively minimal prior content knowledge required for even college-level discrete math courses provides new entry points for students who have experienced limited past success in the subject. While the most common arguments advocating against high school calculus take issue with students’ insufficient exposure to intermediate algebra and trigonometry, discrete math defines all core concepts within the scope of the course. This quality allows students to explore a range of low-floor, high-ceiling non-routine problems early on with minimal anxiety. 
In all these ways, discrete math presents a unique combination of accessible, rigorous, and transferable skills and concepts that will universally benefit students regardless of their future career interests. If you are convinced and interested in designing a discrete math course (and possibly collaborating), check out this open-source textbook as well as this cool graph theory resource
Nasriah Morrison [@nasriahmorrison]


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