Math Class and Comics Blogs

Posted on October 7, 2019 by racheljcrowell

It’s that time of year again: For those in school, the fall semester is in full-swing and approaching the stretch where the winter holiday season doesn’t seem quite on the horizon. If you’re anything like me (averse to cold weather but living in an area that usually gets hit hard with snow and frigid temperatures), the quickly shortening days make winter weather seem like a looming possibility soon to be realized.

Since Vanessa wrote about an important and serious topic in her last post —  the climate strikes and sustainable mathematics — I’m in the mood to write about something a little more whimsical: comic books in math class.

For The Classroom Blog from Pop Culture Classroom, Jim McClain, the creator of the Solution Squad, a graphic novel about math-themed superheroes wrote “Using Comics to Teach Math!”

“I didn’t set out originally to create a graphic novel, or even a comic book,” McClain wrote. “I created Solution Squad to be heroes that I could use to replace the Marvel and DC characters I was using on my dozens of classroom activities. I had access to a wide variety of the worksheet sort of stuff early on in my career, and they were so mind-numbingly boring that I tried to jazz them up a little with the superheroes kids were watching on TV and in the movies at the time,” he added.

He describes some of the ideas behind his Solution Squad, such as using “characters themselves to embody math concepts.”

“The heroes are teenagers with math-themed powers. Absolutia controls temperature, which requires effort whether she raises or lowers it…Radical, whose symbol is a square root sign, can create invisible electromagnetic prisms whose bases are right triangles. He can move things, including himself, along the hypotenuse face of such a prism. Every construct he makes is itself an application of the Pythagorean Theorem,” he wrote.

Besides describing ways to use his book, McClain also mentions other resources, including The Manga Guide to Calculus and Prime Baby.

McClain also has a blog for the Solution Squad where he recently announced plans to complete Solution Squad Volume 2.

“Math Teachers Take a Page From English/Language Arts: Comic Books!”

Education Week recently published this piece by Catherine Gewertz. While there aren’t currently many graphic novels about math themes, math-focused ones are “just starting to get traction” and “it’s a real opportunity for teachers to shape the market,” John Shableski, the director of education development at Udon Entertainment, said to Gewertz.

The piece quotes teachers who describe using math-themed comic books along with other curricula. The piece ends with a discussion of misconceptions about comics in the classroom.

Cindy S. Ticknor, author of The Mysterious I. D. Vide & Newton’s Nemesis math comic book series, also writes Half a Blog. She has written a few “Math & The Characters” posts explaining why she gave the characters some of the traits that she did. For instance, in “Math & The Characters: Theo’s Mother,” Ticknor wrote about creating a character to help “the underlying narrative to reinforce growth mindset, or more specifically, mathematical mindset” as described in Jo Boaler’s Mathematical Mindset.

Posted in K-12 Mathematics, Math Communication, Math Education | Tagged , , | Comments Off on Math Class and Comics Blogs

Sustainable Mathematics

Posted on September 27, 2019 by Vanessa Rivera-Quinones

Hands cupped together holding soil and a plant On September 20, 2019, a series of strikes around the world demanding action against climate change began as part of Global Week for the Future. It inspired me to look into ways mathematics contributes to the growing challenge of sustainability. Sustainability is the ability of a system to meet the needs of the present generation without compromising the ability of future generations to meet their own needs. In her blog post “Planet Math”, Anna Haensch shared some of the resources in the math blogosphere to tackle climate change. As she mentions,

“… when someone suggests that mathematicians have a lot, they can contribute to our fight to save the planet, but for many people, it can be hard to imagine just why or how (other than gathering lots of data and making graphs that are totally scary).”

I agree! To add to the discussion, I wanted to highlight ways we can practice and incorporate sustainability in mathematics.

In our classrooms

One way we can use math for sustainability is to add it to our syllabus. If you are looking for ideas, the blog “Sustainability Math” by Dr. Thomas Pfaff (Ithaca College) has a collection of projects in statistics and calculus related to sustainability. Thomas Pfaff and Jason Hamilton expand on these ideas in the book “Mathematics for Social Justice: Resources for the College Classroom” by considering social justice and sustainability as the same system. They do this by discussing three sustainability issues: climate change, income inequality, and lead exposure and crime.

If you are a fan of differential equations like me, you can take a look the recent special issue of the CODEE Journal “Linking Differential Equations to Social Justice and Environmental Concerns”. It includes 11 ideas on how students can use applied mathematics to make a difference. Using mathematics to solve real-world problems in their differential equations classroom can shape student identities as Karen Kleen, Next CODEE Editor-in-Chief, shares,

“[The students] talked with me about working together on problems of population growth, and climate change, and other questions that involve finding answers to society’s and Earth’s issues. These students, who were all from underrepresented groups in STEM, showed how they are developing mathematical identities that includes being mathematical problem solvers to make a difference.” – Karen Allen Kleen

You can also share with your students the Society of Industrial and Applied Mathematics (SIAM) has a videos such as “Math Behind Sea Ice & Our Changing Planet” and “Renewable Electricity: Where are we now and where are we headed?” which explain in a few minutes how mathematicians contribute to global sustainability problems.

At conferences and for community building

A big concern in academic social media is the environmental impact of travel. In the opinion piece “Reducing the Carbon Footprint of Academic Travel”, 12 scholars offer concrete ideas on how lower the environmental impact of academic travel and suggest some questions for consideration when planning an event, such as

  • Calculate the carbon impact of your event. What steps can you take to minimize that impact while achieving your goals?
  • How might decarbonization improve your event — whether in terms of intellectual exchange, equity and inclusion, or some other factor?
  • What goals for your event could be achieved by means other than an in-person meeting? How can your event make the most of its setting and the physical travel that it involves?

Some of the suggestions include minimizing the carbon impact of an event by serving vegetarian food, encouraging digital and not paper programs, minimizing swag and working with your venue to serve food and drink in reusable or compostable containers. Also, holding fewer conferences or minimizing overseas travel, organizing conferences at regional hubs near airports or as part of bigger conferences, and building carbon offsets into the conference budget.

These ideas extend to other aspects of academic life. For example, the use of virtual platforms (i.e. Skype, Zoom, Webex, Connect and GoToMeeting) to hold conferences, give talks remotely, and build communities through online discussion groups. There are several online communities such as Quantitative Undergraduate Biology Education and Synthesis (QUBES) Hub,  SIMIODE, and SUBgroups which encourage collaboration, resource sharing, and building community.

The intersection of research and sustainability

In his 2013 opinion piece, “The Mathematics of Sustainability“, Simon Levin, identifies three mathematical challenges towards achieving sustainability: developing the statistical mechanics of ecological communities, socio-economic systems, and the biosphere, modeling the emergence of an ecological pattern, and determining indicators of impending critical transitions between states. He also points out the great challenge of achieving cooperation with problems at a global scale, especially in the case of common resources, and the mathematical theory needed to tackle it.

“The greatest challenge facing us is to achieve cooperation in dealing with problems of the Global Commons, especially as regards public goods and common pool resources. This brings to the fore a different set of mathematical tools—control theory, game theory, voting theory, and mechanism opinion design — for identifying under what conditions cooperation is possible and how best to achieve it.” – Simon Levin

Also, SIAM hosts the Conferences on Mathematics of Planet Earth (MPE) which looks to offer a forum for mathematicians and computational scientists to discuss planet earth as a physical system, which supports life, organized by humans, and is at risk.  It will be held again in June 2020 and is co-located with the SIAM Conference on the Life Sciences. This conference is part of a larger initiative described in Evelyn Lamb’s post, “Strength in Numbers: Mathematicians Unite to Tackle Climate Change and Other Planetary Problems” whose goal is to “convince more mathematicians that climate change and other planetary problems are not only important but also interesting”. Besides, talk of “Green AI” has surged in the artificial intelligence community due to a recent paper by Roy Schwartz, Jesse Dodge, Noah A. Smith, and Oren Etzioni from the Allen Institute for AI. The ideas of the paper are summarized very nicely in Juan de Dios Santos’ blog post “Sorry, but your cat or dog AI is damaging the world”,

“The authors propose using efficiency, alongside accuracy and overall performance, as an evaluation metric for future AI implementations. Furthermore, the writers suggest that Green AI could turn the field into a more inclusive one. By doing so, not only researchers but students and others that don’t have access to state-of-the-art machines would have the opportunity to contribute to the field.”- Juan de Dios Santos

Big challenges need out-of-the-box thinking and a lot of collaboration. Be it in your classroom, research, or at your next conference, make sustainability part of the discussion.

Have suggestions of topics you would like us to consider covering in upcoming posts? Reach out to us in the comments below or let us know on Twitter! You can find me @MissVRiveraQ.

Posted in Applied Math, Artificial Intelligence, Biomath, Current Events, Data Science, Math Education, Mathematics and Computing, Sustainability | Comments Off on Sustainable Mathematics

Wolfram Blogging

Posted on September 23, 2019 by racheljcrowell

“A Very Brief History of Mathematics” is a recorded lecture recently posted to Stephen Wolfram’s podcast. A Boing Boing post describes it as “a fascinating lecture” but also “a spoken-word illustration of the problems with his incredible (and incredibly difficult) book A New Kind of Science which was…both brilliant and rambling and unstructured.” Want to listen for yourself? Here’s a link to Wolfram’s podcast episode.

In case you missed it, Wolfram made A New Kind of Science freely available online (with the option of downloading it) two years ago in celebration of the book’s 15th anniversary. He announced its free release while reflecting on that momentous occasion in a post to his blog.

In the last few years, Wolfram has written about diverse topics on his blog. Here are some of his recent posts.

“A Book from Alan Turing… and a Mysterious Piece of Paper”

In this post, Wolfram wrote about receiving a copy of Dirac’s Die Prinzipien der Quantenmechanik that once belonged to Alan Turing. George Rutter, one of Wolfram’s former high school teachers, gifted him the book after Norman Routledge, Wolfram’s former high school math teacher and friend of Turing, gave it to Rutter.

Wolfram describes Routledge as someone who “was charmingly over the top in many ways, and told endless stories about math and other things. He’d also been responsible for the school getting a computer (programmed with paper tape, and the size of a desk)—that was the very first computer I ever used.”

The rest of the post discusses a four-page note from Routledge to Rutter that was tucked into the book and Wolfram’s last interaction with Routledge before he died. It also covers more about the book itself and mysteries surrounding who else may have owned it.

“Fifty Years of Mentoring”

Wolfram has been mentoring others in some form for “a shockingly long time: my first memories of it date from before I was 10 years old, 50 years ago,” he wrote. “Somehow I always ended up being the one giving lots of advice—first to kids my own age, then also to ones somewhat younger, or older, and later to all sorts of people,” he added.

He describes mentoring as different from teaching in that it’s “about answering the specific ‘What should I do about X?’ questions, and the general ‘What should I do given who I am?’ questions.” In the remainder of the piece, he discusses the commonalities between mentoring two populations which seem quite different but are actually “at some level, surprisingly similar”:  kids and CEOs.

“Testifying at the Senate about A.I.‑Selected Content on the Internet”

Wolfram was invited to testify at a hearing of the US Senate Commerce Committee’s Subcommittee on Communications, Technology, Innovation and the Internet. In this post, he explains the issues behind the hearing (determining whether Congress should consider pursuing options for algorithmic transparency or algorithmic explanation policies) and why peering inside the AI to see what’s happening isn’t a solution.

“If we want to seriously use the power of computation—and AI—then inevitably there won’t be a ‘human-explainable’ story about what’s happening inside,” he wrote.

The piece includes the full-text version of his testimony.

In addition to his blog, Wolfram also writes for the Wolfram Blog (which has multiple authors). Some recent posts to that blog include “Authorship Forensics from Twitter Data” by Daniel Lichtblau, “Embracing Uncertainty: Better Model Selection with Bayesian Linear Regression” by Sjoerd Smit and “Spherical Aberration Optics Problem Finally Solved Using the Wolfram Language” by Swede White.

Have ideas for topics or blogs you would like us to consider covering in upcoming posts? Reach out in the comments or on Twitter (@writesRCrowell).

Posted in Mathematics and Computing, people in math | Tagged , , , , , , , , | Comments Off on Wolfram Blogging

A tribute to Hispanic Heritage Month

Posted on September 12, 2019 by Vanessa Rivera-Quinones

It’s almost that time of the year again!

Hispanic Heritage Month (September 15 – October 15) is a national holiday in the United States that began as a way to promote the history, contributions, and culture of Hispanic-Americans. Its observation started with a week-long celebration in 1968 and was enacted into law to cover 30 days on August 17, 1988. As a Latinx mathematician myself, this month embodies a time of reflection of all we have achieved and the challenges still ahead of us. Most of all, it allows us to know the stories of fellow Hispanic and Latinx mathematicians that contribute to mathematics through their research, teaching, mentoring, and/or service.

During this month, Lathisms.org  features the profile of a Latinx/Hispanic mathematician daily, providing a biography and information on their research, teaching and service contributions. It was founded by Alexander Díaz-López, Pamela E. Harris, Alicia Prieto-Langarica, and Gabriel Sosa on 2016 and continues to grow each year (read more about its origin here). Last year’s calendar featured early-career mathematicians including graduate students and post-docs. You can visualize the locations,  institutions, and research areas represented by the 2018 honorees’ in this map. (Note: The data displayed is based on the honorees profiles and might have changed since the calendar launch.)

This year’s theme is Mathematics Education  and you can already see a sneak-peak to this year’s calendar on the AMS September Notices communication, “2019 Lathisms: Latinxs and Hispanics in the Mathematical Sciences”, which features the profile of four of the honorees: Dr. Hortensia Soto (University of Northern Colorado), Dr. Enrique Treviño (Lake Forest College), Dr. Vilma Mesa (University of Michigan), and Dr. James A. Mendoza Álvarez (University of Texas at Arlington).

It will also continue its podcast series featuring interviews with previous honorees led by Evelyn Lamb. What excites me the most about getting to know this year’s honorees is summarized in Evelyn Lamb’s post “The Dangers of a Single Story in Mathematics”,

“There really is no one kind of person who becomes a mathematician.”

What a wonderful thing that is!  A theme of many of the past honorees’ profiles and interviews has been the importance of mentorship, early access to opportunities, and the big sense of responsibility to they feel towards making mathematics and inclusive environment for all.

“Hispanic Heritage Month means someone recognizes that we contribute to this country. It means that the sacrifice that my parents made for us was not in vain. It means that the work that my elementary teachers did for me is recognized. It is a mechanism to serve as a role model for others—regardless of gender, race, sexual orientation, religion, socio-economic status, level of education, etc. And, I get to do this in the same manner that it was bestowed upon me: through compassion. It means that as a Hispanic mathematics educator, I am valued.” —Dr. Hortensia Soto

In her blog post “For People Of Color, Succeeding In Academia Is A Political Statement” Melissa Gutierrez Gonzalez, a junior mathematics and philosophy student at Occidental College in Los Angeles, highlights some of impacts women and minority students face in academia.

“I couldn’t make a mistake, because if I did, what would others think of Mexicans? As someone who has always been a part of predominantly white institutional environments, ignoring the fact that I am acting as a representative for people of my ethnic background is incredibly difficult, because for many, I am the first Mexican they meet. For most, I am the first Mexican or Latino/a they meet in the mathematics field.”

These impacts are sometimes aggravated by the current political status of being an undocumented student. In “Requiem for a Dream”, Dr. Adriana Salerno shared the story of an undocumented mathematician and provides resources to support students affected by the changes in Deferred Action on Childhood Arrivals (DACA) program, which shields young undocumented immigrants from deportation. Representation and acknowledging the full identities of our students, teachers, professors, and colleagues matters. The importance of having faculty that can serve as role models for our students was highlighted in the following student quote from “Cluster Hiring Is Working for Us: Two Early Career Latinas in Math” by Dr. Selenne Bañuelos and Dr. Cynthia Flores,

“The fact that they were both Latina gave me the opportunity to communicate with them about my DACA status, and their support was invaluable to me.”

In the past years, there has been a growing recognition of how mathematics is political. For example, in her 2013 commentary, Dr. Rochelle Gutierrez proposes that,

“By virtue of mathematics being political, all mathematics teaching is political. All mathematics teachers are identity workers, regardless of whether they consider themselves as such or not. They contribute to the identities students construct as well as constantly reproduce what mathematics is and how people might relate to it (or not).”

When we are in the mathematics classroom, whether it is at the K-12 or college level, we are promoting more than mathematical knowledge, we are shaping the identity of  who is and can be successful in mathematics. This extends to other mathematical spaces such as workshops, conferences, and departments. As Dr. Pamela Harris shares in her recent blog post sometimes “It’s the little things” that make you question belonging in the mathematical community.

“It reminds me of little things that I have experienced and which have affected my self identity as a mathematician and made me question my place within the mathematical community. Itʼs the small actions or words or micro aggressions (regardless of intent) that take me out of doing mathematics and bring only selective parts of my identity front and center.”

What it means to be a Hispanic/Latinx mathematician is a multi-layered experience and we will not have a way to condense it all into a single narrative. Conferences such as SACNAS, Blackwell-Tapia Conference, Latinx in the Mathematical Sciences Conference (LatMath) play an important role in bringing together members of the Hispanic/Latinx community. Read some of the reflections on LatMath 2018 by previous participants Emily Alvarez, Dr. Adriana Salerno, and myself. These conferences hope to achieve true diversity in STEM, encourage and showcase the research being conducted by Hispanic and Latina/os at the forefronts of their fields, and to build a community around shared academic interests.

This Hispanic Heritage Month, let’s celebrate how far we’ve come, recognize the unique journey of the members of our community while continuing our work to make mathematics a place where all can belong.

Do you have suggestions of topics you would like us to consider covering in upcoming posts? Reach out to us in the comments below or let us know on Twitter! You can find me @MissVRiveraQ.

Posted in Current Events, Hispanic Heritage Month, Math Education | Comments Off on A tribute to Hispanic Heritage Month

Uncovering ‘What if?’ and ‘Why?’ in the A.I. era

Posted on August 31, 2019 by Vanessa Rivera-Quinones

Artificial intelligence, which has been extensively developed in the last few decades, cares about the power of a machine to copy intelligent human behavior.  As humans, we make decisions every day that rely on the cause and effects of our actions. For example, we know if we work out at the gym it will cause the number of calories we burn to go up. However, the implications this may have on our overall health is more difficult to address. This boils down to the difference between two statistical concepts: correlation and causation.

  • Correlation: measures the relationship between two things.
  • Causation: means that one thing will cause the other to happen.

The distinctions between the two can have important implications. In the website, “Spurious Correlations” by Tyler Vigen, you can explore a wide variety of correlations that are due to chance.  One of my favorites can be seen in Figure 1, which illustrates the correlation between math doctorates awarded and the Uranium stored at United States nuclear power plants. While these two variables have a correlation of 95.23%, it is highly unrealistic to think my degree caused an increase in the amount of Uranium stored in the United States.

Chart that illustrates how math doctorates awarded correlates with Uranium stored at US nuclear power plants over time.

Figure 1: Example of a spurious correlation by Tyler Vigen.

When we think of causality we want to prove that there is a direct relationship between two variables. This can be harder than expected since, as the famous phrase goes, “correlation doesn’t imply causation”. One of the first examples I encountered  as a student was based on the question: Do storks deliver babies? Many parents may wish the answer was yes to avoid explaining where babies come from to their kids. While the number of storks and human births exhibit a positive correlation (see “Stork Deliver Babies”  by Robert Matthews), again this is not true.

I like this simple example that Adam Kelleher uses in his article “If Correlation Doesn’t Imply Causation, Then What Does?”. Think of your daily commute, if your alarm doesn’t go off or there is traffic, you will be late for work. There are many events on your morning routine that could also make you late for work (i.e. traffic is fine but you spilled coffee on your way or your alarm goes off and you oversleep). We think of all this as noise and as the author mentions, “it takes care of the host of “what-if” questions that come up from all of the unlikely exceptions we haven’t taken into account”.

In the new era of big data, how do we discover the underlying relationships between big datasets and which relationships can we trust? “The Book of Why” by Judea Pearl and Dana Mackenzie, which was recently reviewed in the Notices of the AMS by Dr. Lisa R. Goldberg, tackles the question of how we can use the theory of causality to model and interpret data. In the review, the concept of “The Ladder of Causality” is summarized nicely:

“The bottom rung is for model-free statistical methods that rely strictly on association or correlation. The middle rung is for interventions that allow for the measurement of cause and effect. The top rung is for counterfactual analysis, the exploration of alternative realities.”

Figure 2: Illustration of the ladder of causality in “The Book of Why” by Judea Pearl and Dana Mackenzie.

To achieve intelligence, Pearl proposes a machine’s reasoning should move through the ladder illustrated in Figure 2.  Machines should move from seeing associations in data to doing and planning interventions to obtain a desired outcome, towards  becoming counterfactual learners  that can imagine what does not exist yet and infer from observed data. As mentioned by Pearl in an interview by Kevin Harnett from Quanta Magazine,

“If we want machines to reason about interventions (“What if we ban cigarettes?”) and introspection (“What if I had finished high school?”), we must invoke causal models. Associations are not enough — and this is a mathematical fact, not opinion.”

Reaching the top of the ladder of causality may still be out of our grasp. As our understanding progresses, I would love to see how we integrate the qualitative and quantitative aspects of building a world around data. As Andrew Gelman points out in his review of the book,

“If you think you’re working with a purely qualitative model, it turns out that, no, you’re actually making lots of data-based quantitative decisions about which effects and interactions you decide are real and which ones you decide are not there. And if you think you’re working with a purely quantitative model, no, you’re really making lots of assumptions (causal or otherwise) about how your data connect to reality.”

In my perspective, as humans, we are only able to imagine when we consider both. For machines to answer “what-if?” and “why?” they must do so as well.

Posted in Artificial Intelligence, Data Science, Statistics | Comments Off on Uncovering ‘What if?’ and ‘Why?’ in the A.I. era

Mathematical oncology blog posts

Posted on August 29, 2019 by racheljcrowell

In July, The Mathematical Oncology Blog was launched. This community blog, which focuses on mathematical and computational oncology, is looking for contributors. Presently, the blog has several posts and seems to be off to an great start.

I find it convenient that links to manuscripts are included at the tops of some of the posts — such as “Quantifying Tumor Heterogeneity” by Elana Fertig and “Space Accelerates Evolution” by Jeffrey West. I am also excited to see that so far, the contributors on the blog have chosen to cover varied topics.

For instance, in “The Colors of Cancer,” Thomas Hillen uses a paint analogy to argue against the “popular myth that the pharma companies have a Golden-Bullet-drug against cancer in their drawers and refuse to use it as to maximize profits” (emphasis is Hillen’s). He then takes his argument further by explaining why “even more so, it is not even theoretically possible to have such a Golden Bullet drug against cancer.”

Taking a totally different approach and critiquing the modeling in a Nature Communications paper published in 2017, Fred Adler’s “All pithy maxims about modeling are wrong, but some are useful” on the blog begins with this:

“In science, criticism is perhaps the highest compliment, showing that we take work so seriously that we are inspired to spend time thinking about and formulating how work can be improved. It is in this spirit that I lay out some of the many issues that I have with the model of Zhang et al (2017) developed by my friends and colleagues at the Moffitt Cancer Center. This model has been widely cited as providing support for the appealing idea of adaptive therapy in prostate and other cancers, the approach of adjusting therapy continuously in response to tumor status in order to maintain long-term control by delaying or avoiding resistance. However, I have been arguing for some time this model is severely flawed in its assumptions, the way it implements those assumptions, and in the presentation and interpretation of results. I take this opportunity to present a brief outline of these flaws. How much they weaken the justification for adaptive therapy is a broader question, as is the question of whether I have wasted my career trying to write models that avoid flaws of this sort.”

Artem Kaznatcheev, who is part of the group that launched the blog, has also written posts about cancer on the Theory, Evolution and Games Group Blog at the University of Oxford. That blog is in its ninth year. Just a few of the posts Kaznatcheev has written about cancer for TheEGG include “Hamiltonian systems and closed orbits in replicator dynamics of cancer,” “Symmetry breaking and non-cell-autonomous growth rates in cancer” and “Abstracting evolutionary games in cancer.”

On the SpringerOpen blog, Jorge Gómez Tejeda Zañudo wrote “Using physics, math and models to fight cancer drug resistance.”

Know about particular blogs or topics you would like us to consider covering in upcoming posts? Reach out to us in the comments below or let us know on Twitter! You can find me @writesRCrowell.

Posted in Applied Math, Game Theory | Tagged , , , | 1 Comment

Let’s Talk About Viral Equations

Posted on August 21, 2019 by Vanessa Rivera-Quinones

Recently, there was a viral post about solving the equation below:

Many mathematicians and social media powerhouses have weighed in on what the answer should be. But, why has this equation led to a lot of debate? This is not the first time that an equation or math problem has become an internet sensation and I suspect it won’t be the last (see “10 viral math equations that stumped the internet”). Depending on the order of operations you apply to this equation you will end up with an answer of 16 or 1.

Every time a new viral equation storms the internet, I casually scroll through all the responses.  What draws my attention the most is the way people interact with these types of posts. Many seem to jump at the opportunity to flex their math muscles while others reach for their calculators. The perception seems to be that this basic math question should have solely one answer and however disagrees is wrong. The answer to this viral equation, as Steven Strogatz explains in his recent article, depends on what conventions you are using.

What jumps at me is that, when presented with solving an equation, it’s is rare to discuss how we write mathematics and why we interpret it in a particular way. Mathematical grammar matters and conveying the “right” statement of a problem relies on using the symbols that have become our language. As told in this 2013 article “What Is the Answer to That Stupid Math Problem on Facebook?”  by Tara Haelle, ‘Consider how often people debate grammar. Math has syntax just as language does—with the same potential for ambiguities. And just as word-based riddles exploit the ambiguities of language, so do these math problems’. As Hanna Fry mentions, ‘This is like a maths version of the sentence “He fed her cat food”. Does it mean the man gave some food to a cat? Or – slightly darker- fed some cat food to a woman. It’s impossible to tell from the information we’ve been given’. We have allowed the perception that math is unambiguous to reign. But different from a language, being right or wrong in math, tends to be associated with how smart a person is. This mindset ultimately is what leads to these heated debates and causes a divide. As expressed in this essay  by Kenneth Chang, “It implies that the point of mathematics is to trip up other people with stupid rules.”

Don’t get me wrong, mathematicians spend a lot of time trying to be as unambiguous and precise as possible. However, math can be written in ways that make the reader interpret its meaning in unintended ways. Last year, I taught a course that was aimed at future elementary school teachers. This class was a great way to see how we can build our interpretation of math when most of the tools we use are suddenly are unavailable. Students struggled with playing with assumptions, definitions, and ultimately engaging with mathematics in a playful way. We explored the number systems that were used in different cultures, build proofs using physical objects, and played with what makes and breaks definitions. Yet, the idea that there is only one way to interpret a problem stayed throughout the course. The more time I’ve spent teaching (and learning) mathematics the more dangerous this perception feels. It hides away the fact mathematics was built, written, and interpreted by humans, and sometimes this leads to fun internet debates.

Mathematics has a rich history of how we’ve built the conventions that we use every day. In his blog “What is 00, and who decides, and why does it matter? Definitions in mathematics”, Art Duval shares why definitions (I would also extend this notion to conventions) are useful and highlights how we can still have choices to make even for precise definitions.  For example, Terry Moore’s short TED video, “Why is ‘x’ the symbol for an unknown?”, illustrates that even some conventions have origin stories outside of mathematics. But often, students learn acronyms like PEMDAS (parenthesis, exponents, multiplication, division, addition, and subtraction) without knowing the history of these conventions. We may not have the time to unpack the history of all the conventions that we use but we can highlight how they help us communicate math. Next time a viral equation floods the internet, don’t fret! This can be the perfect opportunity to share a bit of the history of our conventions and the importance of how we write (and interpret) mathematics.

Posted in History of Mathematics, Math Communication, Recreational Mathematics, Uncategorized | Comments Off on Let’s Talk About Viral Equations

Introducing Vanessa!

Posted on August 14, 2019 by racheljcrowell
Woman holding a flower bouquet

Vanessa Rivera Quiñones at her defense in April 2019. Welcome to the blog! Photo courtesy of Vanessa Rivera Quiñones

Starting this month, Vanessa Rivera Quiñones (@MissVRiveraQ) will be co-editing the blog with me! She received her Ph.D. in mathematics this year from the University of Illinois at Urbana–Champaign and she’s currently looking for a job in Belgium.

Last year, Vanessa wrote three guest posts on the AMS Graduate Student Blog: “Communicating Mathematics to a Broader Audience,” “Towards Embracing Diverse Mathematical Communities” and “Staying Organized to Improve Productivity.” She is currently in the process of launching her own math blog.

Vanessa brings to this blog her broad interests in such areas as mathematical biology, data science, interdisciplinary research, science communication and teaching. She’s also passionate about exploring the intersection of those fields with equity, inclusion and social justice.

Vanessa says she views math blogging as “a nifty way to get ideas out there” and discuss “topics that don’t come up as naturally” within the mathematical community. She’s eager to jump into writing about a wide range of topics, including those outside of her areas of expertise and finds writing about different topics to be a great way to learn more about them.

Her doctoral research, which involved collaborating with a biology laboratory, focused on using differential equations and other mathematical tools to study the disease dynamics of the Daphnia-Metschnikowia system. She also participated in several other research programs. During a Research Experiences for Graduate Students (also at the University of Illinois at Urbana–Champaign) opportunity, she studied “Variable Annuities with Guaranteed Minimum Benefits.” She also participated in the Research in Industrial Projects for Students program at the Institute for Pure and Applied Mathematics (IPAM) where her group (sponsored by Standard and Poor’s) researched ‘Pricing and Risk in the Credit Markets: Investigation of Credit Default Swaps.” Her project at the Iowa Summer Institute in Biostatistics was the ‘Study of Glaucoma Change Probability for Open-angle Glaucoma.”

Vanessa was born in Puerto Rico and she went to college at the University of Puerto Rico at Río Piedras, where she earned a bachelor’s degree in pure mathematics with a minor in finance. She says that she didn’t have a lot of mathematical role models at the beginning of her undergraduate studies, but when she got involved with SACNAS and other organizations aimed at underrepresented students, that really helped.

It’s critical to “look for stories that portray a lot of people that do math,” Vanessa says. She finds that while today’s students have access to certain websites (such as “Mathematically Gifted & Black”) and other resources that weren’t available when she started her undergrad, it’s still challenging for many of them to find role models. She says that meeting mentors with different backgrounds not often seen in mathematics can help students find the representation they crave. Some ways she thinks instructors can do this are by opening up with students about different aspects of their identities outside of mathematics and by encouraging students to connect with mathematicians of varied backgrounds at conferences.

Just a few of Vanessa’s writing plans include creating blog tours similar to this one and highlighting blogs covering interdisciplinary, collaborative research. She also says she “would love to see more blogs about books aimed at the general audience and explaining mathematical concepts in an accessible way.”

“I admire a lot the work of Tai-Danae Bradley, Nicky Case Explorables, and MathMunch. I think as mathematics becomes more interdisciplinary, the efforts made by QUBES Hub with their blog of bringing together quantitative biology, mathematics, and education is another important contribution,” Vanessa says.

Outside of math, Vanessa enjoys dancing, drawing and Zumba.

Know about new blogs we haven’t covered yet or want us to take another look at one of your favorite blogs that hasn’t been discussed here in awhile? Please reach out in the comments or on Twitter!

Posted in Applied Math, Biomath, Data Science, Math Communication, Math Education, people in math, women in math | Tagged , , , , , , | Comments Off on Introducing Vanessa!

Math Instruction for Students Learning English

Posted on August 1, 2019 by racheljcrowell

As of 2016, 4.9 million students — or 9.6% of students in U.S. public schools — were identified as English Language Learners (ELL), according to the National Center for Education Statistics. While different folks advocate using different terms to describe those students (for instance, some advocate using the term “multilingual students” instead, this Education Week blog post notes), at least one thing is certain: We need to think about how to set those students up for success in school, including in math classes.

“The Challenges of Teaching Math to English Learners”

“Many educators share the misconception that because it uses symbols, mathematics is not associated with any language or culture and is ideal for facilitating the transition of recent immigrant students into English instruction. To the contrary, language plays an important role in learning mathematics. Teachers use language to explain mathematical concepts and carry out math procedures,” Rusty Bresser wrote for the Math Solutions blog.

“The challenge of teaching math to English learners lies not only in making math lessons comprehensible to students but also in ensuring that students have the language needed to understand instruction and express their grasp of math concepts both orally and with written language. ELLs have the dual task of learning a second language and content simultaneously,” Bresser added.

In that post, he explains that ELL students often struggle in math class when they don’t understand the vocabulary, syntax and grammar used in instruction. He also provides specific examples of this.

“How Do We Support English Learners Success in Mathematics?”

This post on the National Council of Teachers of Mathematics (NCTM) blog invites us picture what many ELL students go through.

“Imagine that throughout your whole life, the only language you’ve heard or spoken is Spanish. You’re from a rural town in Honduras, the only home you know, and then at age six your family moved to the USA. Once there, you were signed up for 1st grade at the local elementary school, and you were thrown right into an English-speaking classroom. While at school, you received some English language support, but what you heard all day long at school is English,” wrote Evgeny Milyutin.

‘Take another look, you used to love math class in Honduras; yet, in your American classroom you feel bored, exhausted and frustrated. In fact, instead of feeling smart and capable, you’re actually starting to believe you’ll never be a good student in your American math classroom,” Milyutin added.

Milyutin reminds us that ensuring that ELL students attending public schools receive a proper education isn’t merely a goal to aim for, but, instead, a mandate. “Federal law requires that school districts ensure that ELLs can ‘participate meaningfully in schools’ educational program[s],’ and that schools strive to bridge language barriers…More recently, legislation has gone as far to require that districts use strategies and programs to help ELLs that are backed by scientific evidence,” Milyutin wrote, citing the Education Week article “Teaching English-Language Learners: What Does the Research Tell Us?”

In the second half of the article, Milyutin shares a list of what to do — and what not to do — when teaching ELL students mathematics. The list is based on an interview Milyutin had with Lisa Meyer, director of programming for Dual Language Education of New Mexico.

“ELLs Count on Language Support in Math”

This post was included in a publication of the ASCD (formerly the Association for Supervision and Curriculum Development).

Megan Rowe, a math teacher at Borah High School “in a linguistically diverse district outside Boise, Idaho” told article author Laura Varlas “Language is the entirety of the mathematics classroom. From the language I use when I’m teaching to the language students use when they’re reasoning among their peers—I don’t know how you could ever teach mathematics now without focusing on language.”

“Once you start looking at math through the lens of language, you see linguistic demand everywhere,” Bill Zahner, a San Diego State University professor and former high school math teacher told Varlas.

The rest of the article describes how educators can help ELL students, such as “building a baseline” and “weeding wordy problems.”

Posted in Issues in Higher Education, K-12 Mathematics, Math Communication, Math Education | Tagged , , , , | 1 Comment

A Blog On Blog On Math Blogs

Posted on July 22, 2019 by annahaensch

Your blogger blogging, one last time.

Folks, I’m packing it in. After 97 posts and nearly 5 years of covering the math blog beat, the time has come for me to pack up my blogging tools and hit the high road to adventure.

I’ve really enjoyed blogging so much, but there is a funny thing I’ve observed over the years. The posts I like the most or am the most proud of are often not the ones that get the most traffic. Since this is my final and farewell post, I wanted to share the three favorite posts that I’ve written here. What makes them my favorite? Usually it’s that I feel like I’ve told a good story, or learned a lot in researching the post, or that I just find myself talking to friends often about the topic. I hope you enjoy these posts (perhaps, again).

  • Black Hat, White Hat, a tale of cybersecurity and a hero blogger who saved the internet.
  • The Blockchain Party, an explanation of some of the math behind bitcoin and the blockchain, published in 2017 at the pinnacle of bitcoin mania.
  • Do Evaluations Really Add Up?, an inspection of some (mostly bad) attitudes on the internet about about student evaluations of teaching.

When I joined Evelyn Lamb as a co-editor of this blog in 2015, the internet felt like a different place. We were still in the golden age of math blogging, the art of podcasting was on the rise, and Twitter was a platform for the people. Since then, the landscape has shifted, but the #MTBoS remains a rich and wonderful place.

Accordingly, as one might notice from my blog posts, my interests have shifted away from basic problems in math and become more directed towards the ways that bloggers are using the tools of math to make a societal difference in issues like gun control, vaccination, climate change, gerrymandering and elections.

To be clear, when I say basic problems in math, I’m talking about things like the Erdős Discrepancy Problem and the Graph Isomorphism Theorem. So maybe basic isn’t quite the right word. But you know what I mean. There are still some incredible bloggers writing about various explorations in mathematical pedagogy, visual artists working with core ideas in mathematics, and all manner of opining on the intrigue of academia.

As for this blog, stick around, there’s more to come from the Blog on Math Blogs! Later this summer, the talented Rachel Crowell with be joined by a brand new to the blog Vanessa Rivera Quiñones. I’m looking forward to their posts, and I might just pop back in for the occasional guest post. In the meantime, you can find me on Twitter @extremefriday.

Posted in Uncategorized | 6 Comments