A Conversation With Jim Propp

I recently had the tremendous pleasure of attending the 2019 BAHFest at MIT, an event in which very clever people deliver convincing arguments in support of absolutely ridiculous bad ad hoc hypotheses to a packed auditorium of nerds. Happily, this year one of those nerds was me, and one of the presenters was Jim Propp, a professor of mathematics at UMass Lowell, who you might know as the blogger of Mathematical Enchantments.

This was Propp’s second year presenting at BAHFest. You can (and should!) watch the video of his 2017 first-prize-winning presentation, “Dinosaur Extinction Caused By Gravitational Reversal Event,” and you can read this Q&A about how he develops his BAHFest material.

Since I write for a blog on math blogs, and cool math bloggers are my beat, I decided to call up Propp and have a chat with him about his experiences and inspirations in the realm of math outreach in blogging, BAHFest, and beyond.

Jim Propp also serves on the advisory council of the National Museum of Mathematics in New York City. Photo courtesy of Jim Propp.

Propp understands that blogging, writing, and generally contributing to math communication outside of the standard academic framework can be a challenge. Blogging takes time, and it is a reality that this type of writing is not as highly valued as research writing. And even if one has the time and support to blog, not all ideas are ready to be put into written word. I think this might be what people call writer’s block.

To help his thoughts gather momentum and clarity, Propp keeps a continually updating text document of ideas. I do something similar, but I email myself ideas and put them in my “ideas folder.” And this is a good thing, “let things sit for a long time and let them accumulate,” he says, “there will be time to blog later.” Documenting your ideas is a powerful practice.

I asked Propp what kind of advice he has for aspiring bloggers or math writers, he says “a piece of advice I got early on was that once a month is too seldom to post.” A sagacious suggestion to be sure, but one that Propp intentionally chose to ignore. Instead he posts precisely once per month, but always on the same day. “Regularity is helpful,” he says, so don’t be scared by these superhuman bloggers that post twice a week (I’m lookin’ at you Mathbabe).

Another suggestion that Propp likes to ignore is to “make pieces shorter.” Like one of his writing role models, Martin Gardner, Propp prefers long form essays that really take time to explore ideas. But although most of his posts are several thousands of words, Propp still likes the challenge of condensing his writing, and keeping a high “density of ideas per paragraph.” And this is part of what makes his blog so enchanting. Each essay opens an idea to its fullest, whether explaining the beauty of dimensional analysis or delivering a treatise on “Thirdsday.” Propp writes, “Hardly any of my Mathematical Enchantments pieces are “blogs” in the traditional sense; rather, they’re my way of testing out ideas, trying out ways of explaining those ideas, and more broadly, becoming a better expositor.”

I myself prefer a short paragraph without any ideas in it at all.

For newcomers to Mathematical Enchantments, Propp recommends the following posts:

Propp also hosts a list of practical style tips for blogging about math in WordPress, including some (sadly imperfect) workarounds for rendering LaTeX in HTML and getting those sweet math graphics into your post. If you’re looking for some more nuanced tips about the writing part of blogging, you might also enjoy Rachel Crowell’s recent post, “A roundup of advice for writing about mathematics.

Our conversation made me curious, dear reader. Have you ever considered starting a blog of your own? Why haven’t you done it yet? What feel like the biggest hurdles?

Propp has the eventual plan to publish thematic collections of his essays in book form, “I don’t know how to write a book,” he says, “but I know how to write a lot of them at once.” We will look forward to that, and in the meantime, you can reach out to Propp in the comments section on this blog, or find him on Twitter @JimPropp. And if you need me, I’ll be there too @extremefriday.

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Call for Co-Editor of the AMS Blog on Math Blogs

The AMS invites applications for a co-editor of the AMS Blog on Math Blogs. This blog’s editors are mathematical scientists who explore the world of blogs, which cover a wide range of math—research, applications, recreational—and write their take on blogs or particular posts.

Some blogs covered may be associated with, for example, media and science journals, research mathematicians, or secondary school math teachers. The Blog on Math Blogs is written to inform and engage mathematicians and non-mathematicians alike, and to encourage all mathematicians to join the community of followers and to post comments. Sometimes blogs are revisited, as the Blog on Math Blogs editors give readers an ongoing “tour of the mathematical blogosphere.”

Blog on Math Blogs editors have covered biomath, current events, data science, game theory, math history, math education, math and the arts, women in math, publishing, statistics, computing and much more from the math blogosphere.

The position of co-editor requires excellent communication skills, a commitment to posting twice a month, and monitoring of comments. The posting itself is done with WordPress, a free and open-source content management system for blogs. Familiarity with WordPress is a plus; otherwise applicants must be willing to learn it (with AMS documentation and support).

AMS blogs are hosted on blogs.ams.org, and AMS staff liaisons help promote awareness of the blog and the blog posts on ams.org and on AMS social media. The co-editors are expected to commit for a three-year period, with an opportunity for both the co-editor and AMS to review the commitment each year.

Applicants are requested to provide a sample of their writing (from a blog or for a similar audience), CV, and their reason for interest in being co-editor, along with a vision statement for the blog (such as examples of math blogs of potential interest).

Send applications by May 17, 2019 to paoffice at ams dot org.

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On Technology And Harm

Caution sign on wooden pole in front of snowy landscape

Public domain photo courtesy of Yinan Chen/Wikimedia CC

Fictional stories about putting too much trust in technology often involve armies of killer robots. But what if some of today’s real threats of improperly checked technology are less thrilling but nevertheless harmful or even deadly?

On the bit-player blog, Brian Hayes writes about computation and mathematics. He also has a self-described “morbid fascination with stories of technological disaster.” He has written about a few disasters that tragically illustrate the results of putting too much trust in technology.

Two Boeing 737 MAX 8 airplane crashes 

Earlier this month, Hayes wrote an in-depth post about ongoing investigations of two tragedies involving new Boeing 737 MAX 8 airplanes. The first is the crash of Lion Air Flight 610. That plane departed Jakarta, Indonesia on October 29, 2018. After a flight control problem, that plane crashed into the sea, killing 189 people. The second is the crash of Ethiopian Airlines Flight 302, which departed Addis Ababa (the capital of Ethiopia) on March 8, 2019. Just six minutes after takeoff, the plane crashed, killing 157 people.

“The pilots reported control problems, and data from a satellite tracking service showed sharp fluctuations in altitude. The similarities to the Lion Air crash set off alarm bells: If the same malfunction or design flaw caused both accidents, it might also cause more. Within days, the worldwide fleet of 737 MAX aircraft was grounded. Data recovered since then from the Flight 302 wreckage has reinforced the suspicion that the two accidents are closely related,” Hayes wrote.

Preliminary analysis suggests that problems occurred with the a type of onboard software called the Maneuvering Characteristics Augmentation System, according to Hayes’s post.

Pressure surge and a series of fires and explosions

Last October, Hayes wrote about the role that technology played in the Merrimack Valley gas explosions and fires in Massachusetts on September 13, 2018. “By the end of the day 131 buildings were damaged or destroyed, one person was killed, and more than 20 were injured. Suspicion focused immediately on the natural gas system. It looked like a pressure surge in the pipelines had driven gas into homes where stoves, heaters, and other appliances were not equipped to handle the excess pressure,” Hayes wrote. He added that the National Transportation Safety Board (NTSB) had released a preliminary report supporting that hypothesis.

Hayes wrote about a disturbing finding:

“The cause of the accident was not a leak or an equipment failure or a design flaw or a worker turning the wrong valve. The pressure didn’t just creep up beyond safe limits while no one was paying attention; the pressure was driven up by the automatic control system meant to keep it in bounds. The pressure regulators were “trying” to do the right thing. Sensor readings told them the pressure was falling, and so the controllers took corrective action to keep the gas flowing to customers. But the feedback loop the regulators relied on was not in fact a loop. They were measuring pressure in one pipe and pumping gas into another.”

That safety board subsequently released a safety recommendation report about the product development and review of natural gas distribution systems. For NiSource, Inc., the company whose subsidiary (Columbia Gas of Massachusetts) owned and operated the distribution system involved in the disaster, the report’s recommendations include such measures as applying “management of change process to all changes to adequately identify system threats that could result in a common mode failure” and developing and implementing “control procedures during modifications to gas mains to mitigate the risks identified during management of change operations. Gas main pressures should be continually monitored during these modifications and assets should be placed at critical locations to immediately shut down the system if abnormal operations are detected.”

Cathy O’Neil, who is author of Weapons of Math Destruction, blogger at mathbabe.org and a Bloomberg opinion columnist, has written extensively about algorithms and the issues that accompany them. You can find her posts about algorithms here. (Check out the other posts on this blog about O’Neil and mathbabe.org, along with Anna’s coverage of O’Neil’s MAA-AMS-SIAM Gerald and Judith Porter Public Lecture, “Big data, inequality, and democracy” on the 2019 JMM blog.)

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Do Evaluations Really Add Up?

Photo by creditdebitpro
via FlickrCC

First, let’s start with the classic article, “How to Improve Your Teaching Evaluations Without Improving Your Teaching” by Ian Neath from the mid 90’s, in which 20 tips are furnished for gaming your end-of-semester evaluations. Despite the funny title and sort of gimmicky conceit — and at this point somewhat out of date research — it is a serious paper in a serious academic journal. We know more now than we knew then, but a lot of the broad strokes are still the same. Often more than teaching and student outcomes, the class size, maleness, quality of students, and other non-pedagogical factors, play an outsized role in Student Evaluation of Teaching (SET) scores. But there’s more.

In a recent slam-dunk of a meta-analysis by Uttl et al. in 2017, the authors provide strong evidence that when controlled for prior knowledge and sample size “student evaluation of teaching ratings and student learning are not related.” Yup, that’s it, there is no correlation between the learning and the SET scores. Based on this the authors suggest, “institutions focused on student learning and career success may want to abandon SET ratings as a measure of faculty’s teaching effectiveness.” In a post for the Berkeley Blog, the statistician Philip Stark talks about some the “statistical considerations” of SET scores.

So we can be reasonably convinced that instructors who get very good evaluations aren’t necessarily bringing better learning outcomes to bear. But maybe they are bringing…something else?

In “Availability of cookies during an academic course session affects evaluation of teaching,” published by Hessler et al. in 2018, the authors prove just that. All things being equal, the presence of cookies leads to higher SET scores, or as the authors so succinctly put it, “the provision of chocolate cookies had a significant effect on course evaluation.” And again, they conclude that it might be unwise to use SETs in important promotion and tenure decisions.

Since then, the research about Student Evaluations of Teaching continues to roll out and continues to undercut my confidence in the system. Most recently, “Gender Bias in Teaching Evaluations” a study by Mengel et al really lit up the internet. This study includes analysis of almost 20,000 student evaluations and makes some important observations about the presence of bias in SETs.

A really nuanced discussion of Mengel et al. appears in a post on the Rice University Center for Teaching Excellence Blog. The tables in the original paper are a bit hard to digest, but this post distills some major ideas into an easy to read infographic, and gives good bulleted summaries of the main points. Some takeaways are that bias is more apparent in math than in other subjects, junior women are subject to more bias than senior women, and bias in evaluations follows some in-group patterns, that is, men tend to rate men more favorably and women tend to rate women more favorably. The most appreciable loss is dealt to female PhD students teaching classes of predominantly men, who see -0.26 on a 5 point scale compared to their male counterparts. This number isn’t huge, but still troubling when you consider the particular importance of SETs for young people just beginning their career.

I recently learned that SETs at Villanova this year will also allow students to comment on instructor bias in the classroom. You can read about it in a Wall Street Journal editorial (sorry, paywall), or in this twitter thread from Jeffrey Sachs.

Many universities have started to move away from using SETs as tools in determining promotion and tenure cases. In the US, the University of Southern California caused a stir in spring of 2018 when they announced that they would no longer use SETs in promotion and tenure decision. Since then others have also begun to opt out, and others have begun to offer training on how to correctly interpret the scores once they’ve been collected. Jacqueline Dewar wrote a comprehensive blog post for the AMS blog On Teaching and Learning Mathematics about how we might interpret our SETs.

A thing that really frustrates me about all of this is that women, POC, and other underrepresented groups who get lower SET scores by no fault of their teaching, are fooled into thinking they are a “bad teachers” when they’re really perfectly good. Consequently, they redirect the energy they would have otherwise spent on research in trying to fix their teaching, thereby increasing the likelihood that they will be viewed as less serious researchers. This, in a word, sucks.

The end of the semester is barreling towards us, which means SETs will be dropping soon. Has your institution had the talk about SETs? What will you do to prepare your students? Are you bringing cookies on SET day? Do you love SETs? Tell me everything over on Twitter @extremefriday.

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A roundup of advice for writing about mathematics

April is Mathematics and Statistics Awareness Month, a time for increasing the understanding and appreciation of those fields. One way to communicate the joy and importance of math and stats? Through our writing.

Just last month, the Early Career Section of the Notices of the AMS published several articles on the theme of writing, including “Outward-Facing Mathematics: A Pitch” by Jordan Ellenberg, “To Write or Not to Write… a Book, and When?” by Joseph H. Silverman, “Preparing Your Results for Publication” by Julia Hartmann, “The Art of Writing Introductions” by John Etnyre and “Writing, and Reading, Referee Reports” by Arend Bayer.

“There’s really only one form of outward-facing math I personally know well: writing about math for general-audience publications, which I’ve been doing for more than twenty years now. And I meet a lot of graduate students and early-career mathematicians who are interested in doing it too. So let me tell you some of the lessons I’ve learned,” wrote Ellenberg. He gave this advice on getting started:

“Social media drives attention, but no one has yet figured out a great way to tweet or Snap about math. That’s why blogging is still alive for mathematicians, even as blogs have withered somewhat on the whole. I think best practice for getting started is to blog on a platform like Medium or WordPress, then use social media to bring readers to your writing. When you want to pitch a piece to a more formal publication, they’ll want to see what your writing looks like: with the blog, you’ll have something to show them.”

Etnyre’s piece focuses on writing introductions to mathematics research papers, but much of his advice is relevant for anyone who wishes to write well about mathematics.

“A common problem writers have, especially early in their career, is to overestimate what everyone will know about their work and how it fits into the research world,” Etnyre wrote. (I think this common problem often also occurs when mathematicians write about mathematics outside of the realm of their own research.) He added this advice:

“Assuming that everyone will understand the context of your work, and why it is really interesting, is not a good idea. Most work is focused on some part of a bigger program or problem, and even experts in a field might not, in any given moment, recall the subtleties and details to every interesting problem in their field. So tell them, and all the other readers who will have no chance of appreciating the context without some help from you. Explain the big picture.”

Hartmann’s piece is also intended for folks who are writing research papers but contains advice that’s useful for anyone considering writing about mathematics.

“Decide what the story is you’d like to tell. There is usually more than one way to present a result and the work that leads to it…Talk about your work to other people. Consider giving a talk at your home institution. This will force you to come up with a way to “pitch” your story. You might also receive helpful feedback on your results and comments on connections to other existing work. During the process of writing, you may find that your conception of the story has changed, and this may change the idea of how to best present it,” she wrote.

The “On writing” section for Terence Tao’s blog includes links to many pieces (written by him and others). Many of these are geared toward people who are writing research papers, but some of this advice could be helpful to folks who want their mathematics writing to take the form of blog posts, news articles and more.

Francis Su’s 2015 MAA Focus piece “Some Guidelines for Good Mathematical Writing” shares both basics and advice “toward elegance.” While the piece is written at a level that’s accessible to students, it also contains gems that will serve even experienced math writers. For instance, he advises that writers “Decide what’s important to say. Writing well does not necessarily mean writing more” and “Observe the culture. Good communication is inseparable from the culture in which it takes place.”

In “Mathematics for Human Flourishing,” Su discussed the importance of valuing public writing about mathematics:

“I would like to encourage institutions to start valuing the public writing of its faculty.  More people will read these pieces than will ever read any of our research papers.  Public writing is scholarly activity: it involves rigorous arguments, is subject to review process by editors, and to borrow the NSF phrase, it has broader impacts, and that impact can be measured in the digital age,” he noted.

Posted in Math Communication, Math Education, people in math, Publishing in Math | Tagged , , , , , , , , | 1 Comment

On the National Girls Collaborative Project’s blog

Painted portrait of Émilie du Châtelet

Public domain portrait of Émilie du Châtelet by Maurice Quentin de La Tour. Image posted on Wikimedia (under a Creative Commons license) by user RockMagnetist.

In the U.S., March is Women’s History Month. The vision of the National Girls Collaborative Project (NGCP) is to “bring together organizations throughout the United States that are committed to informing and encouraging girls to pursue careers in science, technology, engineering, and mathematics (STEM),” the organization states on its website. The organization currently consists of 33 collaboratives that serve 41 states by facilitating collaboration between 36,400 organizations that serve 20.15 million girls.

The NGCP blog includes posts about a myriad of topics. Here are a few of their recent posts that I think are interesting: Continue reading

Posted in Issues in Higher Education, K-12 Mathematics, Math Education, Mathematics and Computing, people in math, women in math | Tagged , , , , , , , | Leave a comment

Putting Math In Context

Image courtesy of Toshimichi Miki via FlickrCC.

So, I’ve been eavesdropping on math history Twitter for the better part of a year now and there is one thread of conversation over there that I’ve been wanting to talk about, namely, the question of whether math – the numbers, variables, and equations themselves – can be inherently sexist, racist, or otherwise politically charged. Then this morning I was reading this incredibly stale and annoying op-ed in the New York Times that, in addition to other defects that I’ll let you uncover on your own, ends with this cringeworthy sentiment, “Math is one of the few institutions we have left free of doublespeak or embellishment or biased opinion. Its words are supposed to mean exactly what they say. Let’s keep them that way.” And I thought, ok, today’s the day.

My first entry to this conversation was captured in a blog post here on the Blog on Math Blogs in 2016, where I reviewed a Scientific American blog post by Michael J. Barany, math historian. In his post, Barany puts our current mathematical climate in context by describing historical mathematical gatekeeping, “elite mathematics today, while much more inclusive than it was one or five or fifty centuries ago, remains a discipline that vests special authority in those who, by virtue of gender, race, and class, are often already among our society’s most powerful.”

But from there it’s hard to say whether math is politicized, or whether mathematicians themselves are politicized, and whether or not those concepts are entirely distinct.

Then a thoughtful pivot to this discussion came across my Twitter feed from Alexander R. Galloway, who writes a blog that hits some nice points in technology and philosophy. Despite the fact that its title sounds like a pretty well-worn argument, the post “Are Algorithms Biased?” is full of thought-provoking and fairly new-to-me arguments and rebuttals about the politicization of math. Unlike Barany’s post above that is more rooted in the practice of math, Galloway’s post is firmly planted in the objects of math themselves.

Galloway’s Response #7 to the claim that “math is just a tool” — something along the lines of “there are no racist algorithms only racist coders” — especially resonated with me. I’m not quite sure I can fully get behind his position, but I can see how the tool and the user (as in the case of guns and shooters) can’t always be fully decoupled.

To see an example of racist and classist numbers in action, a 2011 paper by Barany discusses “savage numbers” — he defines these as “number-like or number-replacing concepts and practices attributed to peoples viewed as civilizationally inferior” — and their critical role in positioning the British on top of the heap of emerging science in the Victorian era.

The question of whose mathematical contributions count and why — most poignantly the de-colonization of math — is an interesting one. Academic mathematicians certainly know that the future directions of math are largely shaped by journal editors and funding bodies and all of their intrinsic biases, preferences, and motivations. Tangential to that topic, this blog post by C.K. Raju outlining his allegations of intellectual theft by Michael Atiyah and subsequent silencing by the AMS is a really wild ride.

Another blog in this realm that you might want to check out is The Renaissance Mathematicus by Thony Christie who often writes about the misrepresentations of math and science in the historical discourse. In one post he gives a scathing rebuttal to the notion of a western intellectual birthright.

If you’re in for a long read about philosophy and access to mathematical ideas and technology, I am happy to point you towards McKenzie Wark’s A Hacker Manifesto.

For shorter reads, you can also eavesdrop on the conversation about socio-historical mathematics on the #MTBoS. And as always if you have anything to contribute, endorse or disagree with, please hit me up on Twitter @extremefriday.

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Babies, math class and parents with STEM careers

Old balance scale with weights

Let’s tip the scales to make STEM more inclusive of parents. Photo credit: Nikodem Nijaki via Wikimedia CC

CNN, the Washington Post, BBC News and other publications recently covered a viral news story about a U.S. mathematics professor. The story didn’t focus on mathematical research or groundbreaking teaching techniques. Instead, it was about a professor holding a student’s baby during an algebra class. People are even calling the professor — Nathan Alexander of Morehouse College in Atlanta — a hero, BuzzFeed News reported.

There are a myriad of ways that I could jump into this conversation, but I’ll start here: That people consider it heroic for a professor to hold a baby for one 50 minute math class so a college student can take better notes says quite a bit about the world we live in. Might I suggest a few different (and less dramatic) ways to describe that professor’s actions?

  • Kindhearted
  • Invested in student success
  • Going above and beyond to help a student and their family

I don’t want to discount Alexander’s actions by any means, but if we choose to call them heroic, that puts them on a pedestal. “Why is that a problem?” some folks might ask. Here’s my answer:

Heroic actions are ones that we expect very few people to take. We call them heroic because they are so out of the ordinary that we’re surprised to hear they happened. But the fact of the matter is, there are many students with babies/toddlers/older children, childcare is expensive and its easy for that care to fall through at the last minute. Wouldn’t those students have a better chance at success if society started treating childcare issues as common ones that shouldn’t get in the way of learning or successful careers?

On a related note, these recent articles cover the intersection of STEM careers and parenting (especially motherhood):

“Nearly half of US female scientists leave full-time science after first child” by Holly Else, Nature, February 19, 2019

“Parenthood drives women out of science, US survey reveals” by Michael Allen, Physics World, February 21, 2019

“After a baby, 28% of new parents leave full-time STEM work” by Rachel Bernstein, Science, February 18, 2019

Strangely, while there are tons of articles, non-profits and other initiatives focused on connecting kids with STEM, the climate is such that many of their parents are leaving STEM careers.

In 2018, the Journal of Humanistic Mathematics released a “Special Issue on Mathematics and Motherhood.” In that issue, Pamela E. HarrisBecky HallEmille Davie Lawrence and Carrie Diaz Eaton wrote “Math Mamas: Changing the Narrative.”

“Motherhood and mathematics are not commonly discussed unless you identify as a ‘math mama.’ So why would the mathematics community need an entire issue of a journal discussing experiences by mathematical mothers? Moreover, why would we, as editors, not present an issue on parenthood and mathematics? The simple answer is that we are mothers who are mathematicians. We realized we were not anomalies but comprise a productive part of the mathematics community. So we sought to uncover hidden narratives like ours, full of hope and courage, involving women breaking the stereotype of what a mathematician and a mother should be,” they wrote.

This year, the AMS welcomed a new Math Mamas blog, which is edited by Emille Davie Lawrence (who is editor-in-chief), Amanda Ruiz and Rachelle DeCoste.

In the first post for the blog, Emille wrote “Welcome to the first post of our new blog ‘Math Mamas’!  We, the editors, were hoping to create a space where we can share our experiences, learn from each other, and discuss how our identity as women underrepresented in mathematics interacts with our role as a parent. Research shows that academic men benefit professionally from having children, yet women are penalized for having children. Therefore, the community we hope to create through this blog centers mothers and non-binary parents, particularly those who are raising or are considering raising children. We hope that our conversations will help all genders understand the joys and challenges of balancing life as a working mathematician and as a parent.  Mathematics is the more formal part of our lives. Motherhood is the less structured and messier part of our lives. Each of these enriches and impacts the other. These roles are not separate and parallel. Instead, they are constantly intersecting which sometimes makes both jobs better and other times brings about unique difficulties.” Her second (thought-provoking) post is “The Road to Success.”

I’m excited to read future posts from the Math Mamas blog. Do you have stories to share about STEM careers and parenthood or suggestions for making STEM more inclusive of parents? Share your thoughts in the comments below or reach out to me on Twitter @writesRCrowell!

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A tour of Dan Meyer’s blog

While I was recently cruising through the mathematical blogosphere, I landed on a post I enjoyed on Dan Meyer’s dy/dan blog. The post, titled “Stats Teachers: 2019 Is Your Year,” discusses proposed tax rates and using classroom examples to help students become “smarter about taxes in a day than fully half of Americans have been in their entire lives.”

In 2016, Meyer’s blog celebrated its 10th anniversary. Please join me on a tour of just a few of the many interesting posts available there.

“That Isn’t a Mistake” and the follow-up post “[Mailbag]: What Do You Do with the Ideas You Used to Call ‘Mistakes'”

In the first post, Meyer compares mistakes, which he defines as “the difference between what I did and what I meant to Do” and incorrect answers. He offers teachers this challenge:

Our students offer us windows and we exchange them for mirrors. The next time you see an answer that is incorrect, don’t remind yourself about the right way to talk about a mistake. It probably isn’t a mistake. Ask yourself instead, ‘What question did this student answer correctly? What aspects of her thinking can I see through this window? Why would I want a mirror when this window is so much more interesting?’

In the second post, Meyer remarks on reader-submitted questions and comments about implementing this approach to responding to incorrect answers in the classroom. Here’s one of my favorite sections:

“I don’t have any problem saying a student’s answer is incorrect, that they didn’t correctly answer the question I was trying to ask. But my favorite mathematical questions defy categories like ‘correct’ and ‘incorrect’ entirely:

  • So how would you describe the pattern?
  • What do you think will happen next?
  • Would a table, equation, or graph be more useful to you here?
  • How are you thinking about the question right now?
  • What extra information do you think would be helpful?

How can you call any answer to those questions a mistake or incorrect? What would that even mean? Those descriptions feel inadequate next to the complexity of the mathematical ideas contained in those answers, which I interpret as a signal that I’m asking questions that matter.”

A High School Math Teacher’s First Experience Teaching Elementary School”

Come for the story of an interesting adventure; stay insights such as these:

From Meyer: “Children are teenagers are adults. I was struck hard by the similarities between all the different ages I’ve taught. People of all ages like puzzles. They respond well to the techniques of storytelling. Unless they’re wildly misplaced, they come to your class with some informal understanding of your lesson. They appreciate it when you try to surface that understanding, revoice it, challenge it, and help them formalize it.”

From Joshua, a commenter: “Everyone has their right to an aesthetic preference for particular areas/topics/levels of math. The cool thing about math is that (almost) every topic can be really fun to investigate because it is open to a deeper exploration of pattern, structure, and connections to other areas. A weakness of math education is that again, almost every topic can be presented in a way that is closed, shallow, isolated, and boring.”

“[Fake World] Limited Theories of Engagement.” 

Just one of several interesting posts in his “Fake-World Math” series.

His “Guest Bloggers” series about his student teaching days

The “Starter Pack” page, in which he shares his own highlights from the blog

As always, thank you for reading! If you want to reach me with any comments or suggestions, reach out in the comments below or on Twitter @writesRCrowell.

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We Need To Talk

So Boring. Image via Flickr CC @Adikos.

We have a problem. I feel like we’re just not communicating properly. I hear you, but I don’t understand you. I appreciate that you have something to say, I just don’t like the way you’re saying it. I’m not angry, it’s just that I know you can do better. Don’t worry, I’m not going to leave you. But, dear speaker, I just wish you would do better.

In 1992 the physicist N. David Mermin wrote an article for Physics Today, in which he describes Physics talks saying, “the only pleasure it affords is the relief that washes over you as you realize, finally, that perhaps the end is in sight.” In math, we tend to suffer from a similar disaffectedness. Talks that just go on and on interminably and it’s not clear that a single person in the room knows what’s going on. Sometimes it even feels like that’s just the acceptable norm.

A few years ago one of those really validating bits of research came out confirming that boring speakers really do go on longer than exciting ones. Being exciting is hard. We can’t reasonably expect exciting speakers all the time. But keeping an eye on the time is not only easy, it’s a minimum display of respect that you can demonstrate for your audience.

The matter of giving a talk that your audience can actually understand, is a different thing altogether.

If you’ve been invited to give a colloquium talk, Sara Malec blogged 5 tips to give a good colloquium talk for the PhD Plus Epsilon Blog. For seminar talks, Jordan Ellenberg gives tips for giving talks on his blog Quomdocumque, and on What’s New, Terry Tao explains the important difference between writing a talk and writing a paper.

It’s been my experience that in the culture of mathematics, there is a certain fear of giving a talk that can be perceived as too elementary, causing speakers to whiplash too far in the other direction. Myriad are the talks I’ve seen aimed at the “experts” in the room, and typically the “experts” in the room consist of a cohort of 0 to 1 individuals who would likely be very happy to speak with you privately for 20 minutes after your talk.

And I guess it’s ok for only one person in the room to understand you by the very end, but everyone in the room should understand the first 5 minutes, half of people should understand the first 30 minutes (I know, ambitious) and, ok, from there I guess you can go nuts. And I use the word “understand” quite loosely here, give us definitions, give us notation, give us a chance. I’m talking to you, colloquium speaker who opened with “Let G be the k-dimensional Grassmanian on V.”

And I say this all with an understanding that a Colloquium, an Algebra, Combinatorics, and Geometry Seminar, and a Number Theory Seminar will likely have a different expectation of prerequisite knowledge.

As the imaginary Professer Mozart in Mermin’s article suggests, “strive to place as far as possible from the beginning the grim moment when more than 90% of your audience is able to make sense of less than 10% of anything you say.”

Having said all of this, the burden doesn’t rest entirely on the shoulders of the speaker. It’s also important to be a good audience member. When I was a graduate student someone pointed me towards the “3 Things” exercise that Ravi Vakil wrote about many years ago. The idea is, from any good talk you should be able to write down three things. Whether definitions, questions, ideas, theorems, or the like, these should be things that are interesting to you. In a way, these things represent hand-holds. These are places where, regardless of how divergent your research area is from the speaker, you are able to catch a little relatable tidbit that you can put in the context of your own knowledge.

This worked well for me as a graduate student. It certainly made me more attentive during talks, and had an added (perhaps unintended) bonus, that when I wasn’t able to find three things in a talk, I would walk around feeling righteously indignant for having sat blamelessly, martyrlike, through a terrible talk.

I always write down one clear goal and circle it. In likelihood I won’t remember a talk I saw 2 years ago, but I can easily flip back in my notebook and recall what someone was up to back in 2016. Bonus points if you can articulate at least one obstruction to achieving the goal.

Since then, in my wisdom and maturity, I’ve added two more components to the exercise. I try to write down a single one-sentence “goal” at the end of the talk. If a talk is good (and I pay close attention) it should always be possible to write down at least one goal or large overarching purpose of the research described. I also try to write down one purposeful question. If you haven’t done it before, this is good training for being a session chair, a position in which (in my opinion) it is your duty to be armed with a question after every talk, just in case.

And finally, as I always tell a young friend of mine when she complains about going to church, they can make you go, but they can’t make you listen. If it’s boring, congratulations, you’ve just earned yourself 45 minutes to daydream and think about other problems that are more interesting to you, or failing that, daydream about your fantasy tiny home or whatever.

A seminar is like a special gift exchange between the speaker and the listener. So please join me in this pledge to always take only the allotted time, throw your audience a lifeline early and often, strive to be exciting — and failing that, aim for just being excited — and commit to hunting for interesting things for as long as you possibly can. If you have some more thoughts about this, ideas about giving better talks, tips and tricks for being an active listener, or if you totally disagree with me, feel free to let me know @extremefriday.

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