This post discusses the physics of coffee stains. “Just in case you’re wondering if it is a worthwhile use of processing power, time, and money to study a stain, consider this. Coffee isn’t the only substance that’s made of tiny particles suspended in a liquid. Blood, paint, ink…understanding the way these kinds of liquids behave could have huge implications in areas from medicine to high-tech manufacturing. For example, in the future we may be able to create tiny structures with unique properties by carefully dropping a liquid filled with nanoparticles onto a surface and evaporating the liquid. In order to do this, though, scientists need to be able to accurately predict a mixture’s behavior. This requires an understanding of the forces involved,” Kendra Redmond wrote in the post.
This post describes how “astronomers have found a way to ‘see’ all of the starlight produced in the history of the 13.7-billion-year-old universe.”
Article author Kendra Redmond wrote:
“If you want to know how much starlight is in the universe, you might try something like measuring all of the starlight you can see, and then estimating how much is out there that you can’t see. Scientists have performed refined versions of this type of analysis, but the estimates require lots of assumptions that may or may not match reality.
The Fermi-LAT Collaboration explored this question using an entirely new approach that doesn’t rely on the same types of assumptions. Instead of measuring starlight directly, they looked at the influence of starlight on high-energy gamma rays detected by the Large Area Telescope (LAT), an instrument on the space-based Fermi Gamma Ray Telescope.”
The team estimates that over the history of the universe, stars have produced about 4*1084 photons!
This post presents “a few short stories behind some of the biggest ideas in chaos and complexity theory,” including Lorenz and The Butterfly Effect, Mandelbrot’s Fractals, Complexity Theory & The El Farol Bar problem and a section about “symmetry versus roughness.”
The Nepantla Teachers Community Blog is a group blog that aims “to provide an honest and encouraging space to navigate sociopolitical situations that occur in mathematics education for the purpose of working towards justice in traditionally marginalized communities. By using the word political, we mean any situation that involves power dynamics,” according to its authors. There are six instructors on the blog’s leadership team — Esther Song (high school math specialist with the Chicago Public Schools), Chanel Keyvan (Assistant Principal at Oswego Community SD and former mathematics teacher at Oswego Community SD), Jennifer Dao (mathematics teacher at Evanston-Skokie SD), Jerica Jurado-Paz (mathematics teacher at Chicago Public Schools), Erin Berg (mathematics teacher at Lyons SD) and Crystal Penn (mathematics teacher at Fulton SD in Atlanta).
Here are a few interesting recent posts on the blog.
This post, which is part of the “Small Wins” series on the blog, was written by an anonymous writer Michelle, a math teacher who describes her experience with learning from her students “how to break the rules.” Her California school district has a policy that for remote Zoom learning, students must only use selfies, Bitmojis or nothing as their profile picture. But when she required that one student chance his profile picture because it didn’t meet those requirements, he said “I don’t see why I need to change my picture. I’m just trying to learn.” After he told her that his profile picture was of his favorite rapper who had died — and changed his picture back to it after she let him into the Zoom meeting — she allowed him to keep it as his picture.
What does my Zoom picture policing have to do with social justice and mathematics education? Everything. Especially in a Zoom environment, where most students’ cameras are off, it is even more difficult for students to express who they are as human beings. The limited avenues for self-expression are their Zoom picture and name, which are both mediated through Zoom as a platform. When Alberto changed his Zoom picture back to the picture of his favorite rapper, Alberto had demonstrated resistance in the mathematics classroom. How can students view themselves as mathematicians if they cannot bring who they are into the classroom? Who are students as mathematicians if they cannot resist and question what it means to be a student engulfed in a larger school system during a pandemic? As we discussed in our [Nepantla Teachers Community] over the summer, students are not simply stripped of their identities when they step into the mathematics classroom, even though many wish mathematics to be an apolitical space.
I asked myself, “Why am I following this distance learning policy so closely? Which students might this policy disproportionately harm? What actual consequences are there if students don’t follow this rule?” There are nuances and complexities within all of these questions. For instance, I am a first year teacher without tenure. There have been instances of inappropriate/offensive Zoom pictures. However, in the end, I decided to let Alberto keep his Zoom picture.
The “Student Voices in Remote Learning” series is also worth checking out. The most recent post in that series is from May.
Like other Part I and Part II posts on the blog, part I shares “a math teacher author’s real dilemma that they have recently experienced” and part II provides “an analysis of the powers at play and the author’s response (or lack of response) to the situation.”
In part I, Melissa Adams-Corral wrote:
In the summer before my third-year teaching, our district made a decision that I thought would be a game-changer: mandating dual language education district-wide. Previously, most schools in our district operated under bilingual education models that were focused on quickly moving children to all English instruction, with many schools refusing to offer clases bilingues at all. Moving to dual language meant that the district was taking an explicit stance advocating for students to continue to develop their English and Spanish side-by-side. I remember feeling very excited and hopeful about this shift…finalmente, I thought, policy would reflect the goal I had going into teaching—pride in bilinguismo, and meaningful, relevant language and content area instruction for mis estudiantes. It was a dream come true…that is, until I saw the model that all teachers were told to follow ‘with fidelity.’
This model required that certain content areas be taught in one language only and that teachers practice and enforce strict separation of languages in the classroom. My bilingüismo doesn’t work that way—it flows effortlessly, trying to stop it is like putting a wall in the middle of a river. I grew up in a bilingual home in Miami, where my language never needed to be split in two. During the summer, I would spend weeks with my primos en Honduras, singing along to Boyz II Men and Shakira, watching movies and telenovelas. Back at home in my city, bilinguismo and latinidad was lo normal. I became a bilingual teacher in large part because my language y mi cultura are a large source of my joy, pride and hope. I imagined bilingual teaching as being the work of supporting children as they grew from similar raices.”
When she followed the policy “with fidelity,” which required that her mathematics classes be taught only in English, Adams-Corral noticed a disturbing pattern. “In every math discussion, students who were comfortable speaking in English dominated. And mis estudiantes who preferred to read and write in español? They were silent. I could call on them and ask them questions, but they would shake their heads no, refusing to speak up. I would remind them that they could share their thinking in any language, already moving away from ‘total fidelity.’ But they would sit there and wait.”
Part II tackles the response, starting with Levels of Oppression, a reflection tool created by Mariame Kaba. I’ll leave it to you to check out Part II, because it’s meant to be read after reading and pondering part I.
Have ideas or comments to share? Reach out in the comments or on Twitter (@writesRCrowell)!
For me, the end of the year always is a time for reflection. If you haven’t yet, I encourage you to read Rachel’s round-ups of AMS blog post Part I and Part II.
In the AMS December Notices, Dr. Katherine Thompson wrote her opinion on the role of blogs in our mathematical community in The Place of Blogs in the Modern Math World. As Thompson mentions, while there are many considerations to still be figured out (e.g. structure, defining their success, lack of peer review) these are an extremely versatile tool that is here to stay. I was excited to see Blog on Math Blogs has 631 subscribers and an average number of shares over the last 10 posts of 110.2. I am grateful to all of our readers for their support.
Inspired by this piece and by Dr. Jennifer Quinn’s blog (see my last post), I wanted to take inventory of the lessons learned this year from Blog on Math blogs.
This blog has been a wonderful way to keep learning about fascinating mathematics and the people behind it. The blogs I have toured stood out to me because of their sheer dedication to share and be seen. As you may have realized by now, there is a whole world in the math blogosphere that I have sought to discover. One of the greatest pleasures has been learning from the breadth of content and styles that you get when you allow people the space to be their most creative selves.
This year we toured twenty blogs, wrote about different topics and themes ranging from mental health, crime-fighting, traffic modeling, Black History Month, among others, and interviewed seven bloggers.
Authors have shared their passion for mathematics and beyond, advocated for change, and given us a glimpse of their interests and passions. It begs the question, what will be the role of math blogs in the future? In my opinion, math blogs have opened the door to content that might be inaccessible otherwise (for both mathematicians and non-mathematicians alike). I am grateful for the opportunity to interview authors who joyfully share their blogging journey. If you ask me what the role of blogging and what is its importance is in our community, I think some of our interviewees have given fantastic answers to that question. Below you will find some of my favorite excerpts from the interviews.
“The name of the blog is “Logic ForAll”, now this is what I want, all people using logic formalized or not in the daily activities. But the name is also a pun, because in Brazilian Portuguese we have a dance and a style of music called “forro’ “. I only realized very late that the music (which is great and very danceable) comes from a mispronunciation of the English expression “for all”. So I wanted my blog to be like the music, fun and enjoyable and for all. Also, if possible full of little puzzles and games that it didn’t matter if you didn’t get them. It’s not about competition, it’s about fun!” – Valeria de Paiva in LogicForAll: A Tour
“I’d like to reach non-mathematicians that are curious about what a mathematician does, and how a mathematician works on proving theorems.
I’d also like to reach mathematicians, particularly “mathematicians in training,” who may want to read stories from the point of view of a more senior mathematician. I’m hoping they will relate to these stories or learn useful information about, say, what it’s like to be tenured or what it’s like to be a working mathematician and a parent in a household where both parents work and split childcare evenly. I hope the ‘realism’ in the writing helps people understand that we all struggle sometimes, that we have all gone through tough times and happy times during our careers and that almost all of us fight impostor syndrome.” – Álvaro Lozado-Robledo in Field Guide to Mathematics
“I’ve learned a lot from my interviewees. All of them taught me something. One thing stands out: their definition of success is very different from the usual one. It had more to do with having a balanced life and a satisfactory experience with research and teaching, than with awards and competition. They were compassionate, they thought of their students when thinking of teaching and their collaborators when thinking of research. It’s a very human take on professional success, and it’s what I aspire to.” Contanza Rojas-Molina in Rage of the Blackboard: A Tour.
“So my biggest piece of advice is to make it enjoyable and sustainable for yourself. There are no guarantees that even very good writing will end up getting widely read, but if you enjoy it and find that it helps you learn new things or understand your own ideas better through the act of writing them down, it’ll be worth it.” – Evelyn Lamb in Farewell, Roots of Unity
“I have learned that blogging pushes me to continue to play and innovate. I often start on one curiosity to find myself down a rabbit hole with the Cheshire Grin. These rabbit holes are what often guide me on life long adventures in learning. When I discover something new, I often go on the quest for who discovered it first – I have this picture in my mind of people rediscovering patterns throughout human history. Another lesson I have learned: I dropped posting for a while when my mom moved in for chemo in January through May. I cherish the time that we had together, and I would say to any blogger that ebbs and flows are part of life, so allow them to be part of your blogging as well.” – Sophia Wood in Fractal Kitty: A Tour
“Something that is important to all of us is that we want people to know that this is a heart project. Because of what we’ve experienced growing up and working in education, we have decided to do something to make a change. Our motivation and inspiration comes from the vision of a future where little Black girls know they rock math and boldly say it with pride. We overcame our math trauma and became something wonderful, so we hope to ease the path for those coming after us. We believe that Black women rock math because Black girls rock math! Now it’s time for the world to know.” – Kaneka Turner, Deborah Peart, and Dionne Aminata in #BlackWomenRockMath: An Interview
“I have been told that what I post has resonated with folks—not just mathematicians, not just teachers, but many people experiencing this wild and crazy pandemic year. If they find any comfort, then I consider it a success.” – Dr. Jenny Quinn in Math in the time of Corona: A Tour
I look forward to continuing to discover the treasures in the math blogosphere next year. Until then, thank you for showcasing your math, for reading our posts, and joining Rachel and me as we tour the math blogosphere. Stay safe and happy holidays!
Have an idea for a topic or a blog you would like for me and Rachel to cover in upcoming posts? Reach out in the comments below or on Twitter (@VRiveraQPhD).
As I mentioned in my Part 1 post, I’ve been seeing a lot of posts on other AMS blogs that have piqued my interest and really got me thinking about a variety of different subjects. As we approach the end of this interesting and oh-so-challenging year, I offer you a roundup of some thought-provoking posts on other AMS blogs.
Earlier this year, the decision was made to broaden the scope of the BookEnds blog by AMS Consulting Editor, Eriko Hironaka. If you haven’t already read about that decision and would like to, this post by Nicola Poser discusses it.
In “Interacting With Ordinary Differential Equations,” a guest post by Stephen Kennedy (Carleton College), AMS/MAA Press Acquisitions, he writes about “changing content and delivery” methods for ordinary differential equations in the context of the online interactive textbook Interacting with Ordinary Differential Equations by Sandy and Max Saperstone.
Galvez-Reyes writes about her concerns with navigating the graduate school application process and the organizations she’s found — such as Cientifico Latino and Women+ of Color Project —that provide mentorship and support. She closes with these words:
“While there is no doubt that the application process is daunting, it can also be a chance to find your people. People who will cheer you on, pick you up when you’re down, and remind you of your worth when imposter syndrome threatens to take over. It’s important to not only have mentors ourselves but also to pass on the knowledge to those coming after us. Like Toni Morrison so perfectly put it, ‘When you get these jobs that you have been so brilliantly trained for, just remember that your real job is that if you are free, you need to free somebody else. If you have some power, then your job is to empower somebody else. This is not just a grab-bag candy game.’ Reach back and help those trailing you. Pass on information you wish you had, resources you needed, job listings you know about. Mentorship and community are integral parts of succeeding in spaces that weren’t designed for people like us. Despite the lack of consideration for us and our experiences, we have an ever growing community willing to help each other into these spaces.”
Saul wrote about his experience working with children under federal custody with the Office of Refugee Resettlement (ORR), which is now on hold because of COVID-19.
“The children love it. Their eyes light up. They intrigue each other. Language and social barriers tumble. And their minds are active. The work is similar to leaving food and water in the desert for thirsty immigrants. We are not offering them a complete diet or significant sustenance. But we are keeping their minds alive until their situation stabilizes,” he wrote.
Have an idea that you would like for us to cover? Want to share what you’re most excited about for JMM 2021? Reach out in the comments or on Twitter (@writesRCrowell).
Lately, I’ve been seeing a lot of posts on other AMS blogs that have piqued my interest and really got me thinking about a variety of different subjects. As we approach the end of this interesting and oh-so-challenging year, I offer you a roundup of some thought-provoking posts on other AMS blogs.
Katz wrote about Trans Day of Remembrance and the LGBTQ+Math Day, which was held virtually at the Fields Institute.
“An event like this contributes to the visibility of queer people and our accomplices/allies, and a major theme of our conversation was the fact that each of us, by virtue of existing, queered spaces by being in them, from the rugby pitch to mathematics conferences. But for this post, I’d like to reflect on the ways that I saw our queer identities influencing our mathematics,” Katz wrote.
On the day of the conference, I was only able to watch bits and pieces of the talks, so I’m glad that Katz mentioned that the talks are going to be available on YouTube in coming weeks.
Also, if you missed Trans Day of Remembrance or weren’t aware of it, I have a suggestion. Please consider spending some time thinking about the trans lives lost this year (and in years past) and what we can do to embrace trans folks within the mathematics community and beyond.
For instance, Juliette Bruce, a NSF postdoctoral fellow at the University of California, Berkeley and a postdoctoral fellow at MSRI who spoke about “Computing Syzygies” at the conference, tweeted that she is working with others in Spectra “to create a working group seeking to address the harm that current standard publishing practices often do to the trans community, as well as to advocate for the adoption of more trans inclusive publishing practices.” I look forward to learning more about that group’s work and any recommendations they make on trans-inclusive publishing practices within mathematics. Also, on the inclusion/exclusion blog, a group of guest authors just wrote about “Building Gender and Sexuality Allyship in the Mathematics Community.”
I’m a sucker for stories about foster parenting. Come for Adiredja’s recounting of planning to “just be revising papers till tenure” while adjusting “into my new role as a queer single parent,” stay for Adiredja’s description of life with foster daughter M. Here’s a snippet:
“The first time I met M, she told me that her favorite school subject was math. I believed it was a sign! Of course, later I found out M had googled me and learned about my job. Did I tell you this girl was smart?”
Lawrence wrote about her concerns as a Black mother of two Black kids and asked “When have you opened a door for a Black colleague or gone out of your way to encourage a Black student? When have you spoken out against racist systems that are in place in math departments in every corner of America? What are you doing to diversify the faculty in your department?”
This post describes a project of the Association for Women in Mathematics in which “a commemorative deck of cards has been created. Using one side of the cards, several different variations of a mathematical game called EvenQuads can be played. The other side of the deck features portraits and short biographies of 64 exceptional women mathematicians. This deck helps bring women mathematicians, both historical and modern, into the spotlight.”
Have an idea you would like for us to cover? Let us know in the comments or on Twitter (@writesRCrowell).
Math in the Time of Coronais a blog created by Dr. Jennifer Quinn to reflect on teaching during a pandemic. She is a professor at the University of Washington Tacoma and president-elect of the Mathematical Association of America (MAA). As she describes on the website, this is “a blog in response to a global pandemic from an eternal optimist. Musings on emergency remote teaching (of mathematics), maintaining humanity, and building community in isolation.”
There is a new post every day, and while they can vary a lot in topic and length, each of them brings a sense of comfort as her authenticity shines through her writing. Also, the posts are not solely about mathematics showcasing to me a new way of humanizing mathematics. Some of my favorite posts include:
The very relatable experience of the technology hiccups that come up unexpectedly during class and the ways we improvise in October 28 Day 234: Flummoxed.
September 7 Day 183: Taking Inventory, which encouraged me to reflect and take inventory. It inspired me to ask myself what I’ve accomplished, lost, learned, wonder about as this semester comes to a close. I will leave the answers for another post.
I am more grateful than you can know that you are a part of my life. You make my pulse race when a solution is revealed. You inspire me towards creativity and persistence. You provided the foundation upon which I built my career. And you bring comfort—even when I don’t know that is what I need.” – Dr. Jennifer Quinn
I was so appreciative of the thoughts behind the blog that I reached out to Dr. Quinn to know more about the inspiration behind her writing.
a) VRQ: Can you tell our readers a bit about yourself and your blog?
Figure 1. Self-portrait of Dr. Jennifer Quinn. Credit: Dr. Jennifer Quinn.
JQ: I am a Professor of Mathematics at the University of Washington Tacoma and president-elect of the Mathematical Association of America (MAA). Expository writing has played an important role in my professional life: first, as co-author with Art Benjamin of the award-winning book Proofs that Really Count: The Art of Combinatorial Proof, then as co-editor (also with Art) of MAA’s Math Horizons, and finally as Chair of the MAA Council on Publications, at the time overseeing its three print journals, one electronic journal, two magazines, and eight-book series. At JMM 2020, I was moved by a recurring call to humanize our discipline and I bring that lens to my current writing. By showing myself to be authentic, flawed, and yes, at times struggling, I hope others can see that they belong in mathematics with me and together we can help one another survive and achieve.
b) VRQ: What motivated you to start blogging during the “Corona times”?
JQ: I never planned to write a blog. I sort of fell into it. Let me explain:
I started journaling the day after the announcement that the University of Washington’s three campus’s classes would suspend face-to-face interactions and teach remotely. Mostly my posts were on Facebook. Some were on MAA Connect, the MAA’s member platform. Maybe it’s because I was on the leading edge of the emergency transition. Maybe its because I felt a duty to other mathematicians going through the same ordeal. Regardless, I kept thinking, writing and voicing my doubts, concerns, successes, and vulnerabilities.
Then Beth Kalikoff, friend and director of the UW Center for Teaching and Learning, asked if she could use one of my posts in the Center’s new Teaching Remotely blog. I agreed but had no response when asked, “where can we link our blog post so people can read your other reflections?” Over the next 24 hours, Math in the Time of Corona was born. I started by posting past reflections chronologically and vowed to continue writing until there was no longer a need. I posted almost every day through the end of spring quarter 2020. After a summer hiatus, I restarted daily posts on September 28 with the beginning of Autumn teaching.
c) VRQ: What is the most interesting thing you’ve learned through daily blogging?
JQ: I find writing to be therapeutic as I reflect on the state of my life, my work, my profession, and the world. I am always surprised at which posts are embraced by readers and which are ignored. It seems to be a combination of timing, clever title, good picture, and who you mention. The June 11 post detailing my method for giving oral finals in Spring is, hands down, the most popular post on the blog garnering more than 10% of all views. It has been visited three times more frequently than the second most popular post, a logic puzzle based on Zoom placements featuring screenshots from Art Benjamin, Jeanette Shakalli, Nancy Neudauer, and me. (The puzzle was fun but is essentially obsolete because of the recent upgrade to Zoom 5.3).
I have been told that what I post has resonated with folks—not just mathematicians, not just teachers, but many people experiencing this wild and crazy pandemic year. If they find any comfort, then I consider it a success.
d) VRQ: Are there any reflections/wisdom you would want to share with our readers about “Math in Corona times”?
JQ: The full impact and injury of the global pandemic is yet to be seen. Covid-19 has up-ended education from K-20+. It will disrupt scholarly productivity for years to come. Those lucky enough to have the health, mind space, and lack of care-taking responsibilities to continue in isolation will be fine. Everyone else will fall further behind. I keep returning to the words I first wrote on March 13, 2020. They are as true now as they were then. “Don’t panic. You don’t have to be an expert. Just use what you know and adapt. Ask for help. Offer help. Breathe.”
So far I have remained true to my original vision of writing about emergency remote teaching, maintaining humanity, and building community. As our isolation drags on, I imagine adapting the blog to suit the needs of the times. I would love a day when the title Math in the Time of Corona no longer makes sense and then I will happily change it. May that day come soon.
Have an idea for a topic or a blog you would like for me and Rachel to cover in upcoming posts? Reach out in the comments below or on Twitter (@VRiveraQPhD).
Musing Mathematically is a blog written by Nat Banting, a mathematics teacher, and mathematics education lecturer at the Department of Curriculum Studies at the University of Saskatchewan, Canada. His blog, which began back in 2011, is centered around the ideas behind teaching and learning.
As he describes on his website, “his academic interests include the ecological and biological roots of cognition (particularly pertaining to the instigation and observation of student problem-posing), the decision-making of teachers and students with(in) high-density mathematics classrooms, and student (and teacher) impressions of probability.” In this tour, I will give a glimpse of some of my favorite recent posts on the blog.
In this post, Banting discusses his thoughts on the ideas presented in the book Building Thinking Classrooms by Peter Liljedahl. In this context, a thinking classroom, as defined by Liljedahl himself, means,
A classroom “that’s not only conducive to thinking but also occasions thinking, a space inhabited by thinking individuals as well as individuals thinking collectively, learning together, and constructing knowledge and understanding through activity and discussion.” – Peter Liljedahl, Building a Thinking Classroom in Math
It has 14 elements, that if your curious, you can see in this wonderful sketchnote by Laura Wheeler. Banting states in his post, ‘I don’t have a thinking classroom’. I was taken aback a bit by this, since I for one, believe many of the mathematics teachers I know strive to create thinking classrooms. He does, however, mention that the statement comes with three qualifications which I encourage you to read. The one that caught my attention the most was the second one in which he points out how the idea of “Thinking Classroom” get’s simplified to “any class with students standing at whiteboards in random groups.”
The structure above serves as an example of two of the elements of a “Thinking Classroom”: vertical non-permanent surfaces(VNPS) and visibly random groups(VRG). I found this very insightful since with a lot of active learning scenarios. I know, I’ve counted on these structures creating a conducive environment for learning that is lost in traditional lectures. As Banting puts it elegantly,
“However, those structures do not teach; they amplify potential teaching moments. We, as teachers, still need to harness them, and Peter develops many ways to do so in the sections of the book. And so when it is proposed that I run a “Thinking Classroom,” I am always careful to interrogate what the proposer has in mind, because I think we have the responsibility to ensure that the term “Thinking Classroom” doesn’t strictly refer to the structure(s) of VNPS and VRG and leave the teaching behind.”
In this post, Banting begins sharing his encounter with the following question:
If you chose an answer to this question at random, what will be the chance it would be correct?
D ) 25%
What I appreciated about the post is the idea that, while questions like this are can lead to a lot of mathematical arguments, it is not the answer itself the end goal. As he mentions,
“The point of the exercise is not to complete the exercise, it’s to dwell a while in the complexities it offers. By constructing the argument, you interact with notions of odds, randomness, probability, and the like.
To engage help students to step out of the usual problem-solving approach (i.e. recall a similar situation and apply it to a new context), Banting proposes shifting the focus of answering a question to puzzling with it by not offering any questions at all (see Figure 1).
Figure 1. Sample questions from quiz from ‘Probability Quizzes with No Questions’ by Nat Banting.
For example, in a ten-question quiz, seven out of those 10 questions will have the correct answer be C, you may ask students to circle the correct response and ask them to reflect about what are the chances that, in fact, that would happen? What I love most about this idea, is that it throws the student into grappling with uncertainty in a very familiar scenario. You can use mathematics as a way to demystify this feeling of uncertainty. As Banting mentions,
“Mathematics is suggested as a way to dissect the feeling of uncertainty, and this act of justification becomes the focal point. I mean, of course it does. What is left to argue about the solutions of questions 1-7? They were simply the vehicle to encounter an experience, and, in this way, those seven “questions” were never the questions to begin with.”
Since I am a big fan of board games and art, I also enjoyed looking at Project: QuaranTiles and hope to try them out soon. In addition, to Musing Mathematically, he is also the curator of FractionTalks.com, a really neat website that fosters creative ways to visualize fractions. I loved exploring this website, especially, since oftentimes one of the most memorable early mathematics experiences for students is learning fractions! The ideas behind this website also lead to great implementations of these for the classroom such as Marie Brigham’s Fraction Talk War for fourth-graders and the creation of the Fraction Wars Cards by Carla Dawson.
Have an idea for a topic or a blog you would like for me and Rachel to cover in upcoming posts? Reach out in the comments below or on Twitter (@VRiveraQPhD).
The Mean Green Math Blog: Explaining the whys of mathematicsis a blog by Dr. John Quintanilla, a professor of mathematics at the University of North Texas (UNT). It has been around since 2013, and its name, ‘Mean Green’, is an ode to one of the symbols of UNT. This blog is for future mathematics teachers, alumni, colleagues, friends and family, along with teachers who mentor other teaches. As he describes on the blog, the purpose of the blog is to dive into the why behind the math.
“This blog does not aim to answer common student questions like “How to factor this polynomial?” or “How do I solve for in this equation?” (There are plenty of excellent websites out there, some listed on my Resourcespage, that give good step-by-step instructions of such problems.) Instead, this blog aims to address the whys of mathematics, providing readers with deeper content knowledge of mathematics that probably goes well beyond the expectations of most textbooks. As well as an audience of current and future secondary teachers, I also hope that this blog might be of some help to parents who might need a refresher when helping their children with their math homework. I also hope that this blog will be interesting to students who are interested in learning more about their subject.”
In this post, I will share some of the posts that caught my attention, in particular, those aimed at engaging students.
Engaging Students Series
As part of a capstone course for secondary mathematics teachers, he asked his students to come up with ideas on how to engage their students with mathematics topics. What appealed to me the most about this assignment was the structure provided to the students. Instead of lesson plans, students had to come up with three different ways to catch their students’ interests. As you’ll see in the examples, the type of engagement activities varies for each topic. With the permission of the students, we get to see their work and draw inspiration from their ideas! Below are some of my favorites,
Former student, Haley Higginbotham, shares how as a teacher she would create an activity to involve her students. She presents a visual proof of the Pythagorean theorem using a hands-on activity. What I found super interesting her answer to the question: how has this appeared in high culture?
“The Pythagoras tree is a fractal constructed using squares that are arranged to form right triangles. Fractals are very popular for use in art since the repetitive pattern is very aesthetically pleasing and fairly easy to replicate, especially using technology.” (see figure below).
Pythagorean tree created by Guillaume Jacquenot. Picture obtained from Wikimedia Commons.
She concludes by discussing how to incorporate technology in the activity and shares how she would use an activity that allows students to drag the different sides to see that the Pythagorean relationship holds no matter how the sides of the triangle change.
The next idea comes from former student Andrew Sansom. In this case, he explores an interesting word problem that students can do to practice solving linear systems with matrices. He discusses and walks the reader through the solution to the following problem,
“The Square in Downtown Denton is a popular place to visit and hang out. A new business owner needs to decide which road he should put an advertisement so that the most people will see it as they drive by. He does not have enough resources to traffic every block and street, but he knows that he can use algebra to solve for the ones he missed. In the above map, he put a blue box that contains the number of people that walked on each street during one hour. Use a system of linear equations to determine how much traffic is on every street/block on this map.”
Based on the diagram above, you can build an equation for each intersection that has the sum of people walking in and out as equal, rewrite the system in standard form, represented as an augmented matrix, reduce the matrix using Echelon form, and voila! You find that the best place to advertise is in Hickory Street between Elm and Locust Street. He also provides his thought on the are the contributions of various cultures to this topic and shares some of the history of solving systems of linear equations. Below is an excerpt,
“Simultaneous linear equations were featured in Ancient China in a text called Jiuzhang Suanshu or Nine Chapters of the Mathematical Art to solve problems involving weights and quantities of grains. The method prescribed involves listing the coefficients of terms in an array is exceptionally similar to Gaussian Elimination.
Later, in early modern Europe, the methods of elimination were known, but not taught in textbooks until Newton published such an English text in 1720, though he did not use matrices in that text. Gauss provided an even more systematic approach to solving simultaneous linear equations involving least squares by 1794, which was used in 1801 to find Ceres when it was sighted and then lost.”
Predicate Logic and Popular Culture Series
Similar, to the goal of the last series of posts, the Predicate Logic and Popular Culture series has a great number of examples (with different sources and complexity) to make predicate and propositional logic more appealing to students. As part of his Discrete Mathematics class, he presented students either with a logical statement (which they had to translate to actual English) or gave them a famous quote to translate into predicate logic. This was so fun that I ended scrolling for a while just to find my favorites. Below are some that caught my eye,
I was captivated by the idea of using song lyrics to practice! Especially, since in this example is a song from a Mexican band, Mana, which I listened to growing up.”Let W(t) be the proposition “At time t, you want me as I am,” and let R(t) be the proposition “At time t, you reject me for what I was.” Translate the logical statement:
$$\forall t <0, (\neg W(t) \wedge R(t)).$$
This matches a line from the Spanish-language song “Tengo Muchas Alas / I Have Many Wings.”
If you’re looking for an exciting new blog to check out, look no further. Kaneka Turner, Deborah Peart, and Dionne Aminata recently launched #BlackWomenRockMath. In an interview conducted over email, we discussed why they started the blog, what they have planned for it and more. (The following interview has been lightly edited.)
Rachel Crowell: Why did you decide to start a blog now?
Kaneka Turner, Deborah Peart, and Dionne Aminata: We have been working together for about 2 and a half years and have had the opportunity to present together at conferences on varied topics around mathematics. We recognized that we have a lot in common and that our beliefs around equity in mathematics are aligned. During the pandemic, many things have been brought to light, and it is clear that Black communities are impacted at an alarming rate. Collectively, we have a deep and profound understanding of and experience with racism and decided that now was the time to speak up. Individually we have always had a lot to say, but by approaching it together we found the boldness to say so much more. We hold one another accountable and desire to lift up other Black women so they can find their voices. This is the platform we are hoping to create.
RC: What are some of your main hopes and goals for the blog?
KT, DP and DA: Our main goal is to create a community that recognizes the brilliance of Black women in math education and sets the stage for securing a legacy for Black girls to be inspired and walk in confidence as doers of mathematics. We hope to disrupt systems and break patterns, so Black women have the opportunity to lead and Black girls have the opportunity to shine. We hope everyone will begin to see the power we hold and the brilliance we share and open doors for so many who have gone unseen or unheard for far too long.
RC: Who are you hoping will read the blog?
KT, DP and DA: We are hoping that educators, school leaders, and parents are reading the blog, but we also hope that people with the power to support our mission to make a difference will also take notice. Educators and people in the field are the obvious choice, but we also want the community at large to recognize that our voices need to be heard because we (Black women) have valuable contributions to make in the field of math education.
In the first post on the blog, you wrote “A little over 2 years ago our paths crossed when we joined Illustrative Mathematics as lead writers for the K-5 Math Curriculum. This was a rare space and opportunity. We immediately recognized the weightiness of our roles and the need to support each other. The reality is, Black women are not typically asked to use their expertise in mathematics to co-design a national math curriculum. We were not brought to IM to address the diversity, equity, and inclusion components of the curriculum. We were hired for what we know about mathematics, and this was unprecedented.” How did you feel to be asked to use your expertise in math to co-design a national math curriculum?
KT: I felt honored to be selected because I was familiar with IM’s work and believed it was important to align with a company that had a reputation of producing quality materials. I didn’t know they had a plan to focus on supporting marginalized communities through their materials, but I was glad to know that I would be connected with this positive presence in math education.
DA: I believed that I needed to take this opportunity, especially if they were planning to serve students in marginalized communities. My work had always been with students of color or students living in poverty, so I thought it was vitally important to offer my perspective to support the development of materials for these children. I was hopeful that IM’s vision aligned with mine, a vision of a future of mathematics with a shift in curriculum towards inclusion.
DP: When I was offered the position, I was in disbelief. It seemed too good to be true. I had always thought of curriculum writers as something other than me; it never occurred to me that I could be one. It was exciting to be a part of something that would reach thousands of students. It was rewarding work from the beginning because I felt inspired by the people with whom I would have the chance to collaborate. It was a dream come true because I had wondered how I could be a part of a larger mission to impact math education for more students. Changing lives 1 class at a time was great, but I longed for such an opportunity as this.
RC: What are some of your favorite math or math education blogs?
KT, DP and DA: We don’t have a long list of math education blogs that we subscribe to, but we agreed that Krisin Gray’s blog “Math Minds” and Theresa Wills’ “Where THERE’S A WILLS, there’s a way” are both favorites. During the time we have been writing, we have read several books as a team around content and pedagogy. We have also started to listen more and more to podcasts, which is something we plan to launch for BWRM in 2021.
RC: Is there anything else you would like to share?
KT, DP and DA: Something that is important to all of us is that we want people to know that this is a heart project. Because of what we’ve experienced growing up and working in education, we have decided to do something to make a change. Our motivation and inspiration comes from the vision of a future where little Black girls know they rock math and boldly say it with pride. We overcame our math trauma and became something wonderful, so we hope to ease the path for those coming after us. We believe that Black women rock math because Black girls rock math! Now it’s time for the world to know.
Want to give feedback or suggest ideas for future blog posts? Reach out in the comments or on Twitter (@writesRCrowell).
We are almost midway through Hispanic Heritage Month (September 15 – October 15)! This month marks a national holiday in the United States that began as a way to promote the history, contributions, and culture of Hispanic-Americans. The month wouldn’t be complete without recognition, reflection, and celebration of the contributions of Hispanic and Latinx individuals in the mathematical sciences.
In last year’s post, A Tribute to Hispanic Heritage, I talked about several initiatives, articles, and blog posts that shared some of the history and the challenges still ahead for members of the Latinx/Hispanic community. This year marks the fifth anniversary of an initiative close to my heart, Lathisms (Latinxs and Hispanics in the Mathematical Sciences, www.lathisms.org).
“Since 2016, Lathisms has featured 122 diverse mathematicians, highlighting one per day during US Hispanic Heritage Month, which is celebrated September 15–October 15. The website, which has been visited more than 250,000 times since its inception, also features some of the honorees in podcast interviews by Evelyn Lamb, and each honoree is featured in freely downloadable posters.”
I encourage you to read the profiles of each honoree unraveled daily on the website along with this AMS notices article five of this year’s honorees.
This year, I wanted to highlight another fantastic organizationTODOS: Mathematics for ALL. As described in their website, TODOS mission is to advocate “is to advocate for equity and high-quality mathematics education for all students— in particular, Latina/o students”.
“TODOS: Mathematics for ALL is a professional organization that advocates for equity and excellence in mathematics education for ALL students – in particular, Latina/o students. Founded in 2003 and with over 800 members from across the country, TODOS Members know that Equity and Excellence in Mathematics Matter! We promote Social Justice in Mathematics education and provide high-quality resources to help reach our Mission and Goals.”
TODOS was established in the years 2000-2003 as a result of the Equity and Diversity Advisory Committee (EDAC) sessions at the National Council of Teachers of Mathematics (NCTM) annual meetings. The themes of these sessions revolved around organized issues of teachers of Hispanic/Latino students.
The website of the organization is full of resources for mathematics educators, parents and families (in both English and Spanish), webinars, a podcast, a blog, and many more. In this tour, I give you a glimpse of some of TODOS blog posts. I’ve learned so much by reading these posts and found their resources insightful.
In this blog post by Carlos López Leiva, Silvia Llamas-Flores, and Kyndall Brown, the authors describe the importance of naming an identity, in particular the naming of the Latina/o community in the United States. They state very clearly at the beginning of the post that rather than propose solutions, they hope to open the conversation around naming identities.
Naming an identity is something many of us may feel strongly about, especially as it relates to our relationship with the United States. As stated in the post, naming my identity has been a way to name the community I belong to. However, as an identity that captures a group with a lot of diversity, we may never have a consensus on a single word that captures all of our experiences. However, the post highlights that naming those identities depends on the historical and current context in meaningful ways and that as educators we must acknowledge the identity of our students beyond mathematics as a way to make our interactions more meaningful.
“As educators, we must challenge places of marginality (Aguirre et al., 2013). We must also learn about, acknowledge, and nourish the intersectional identities of the students with who we work.
When we self-identify, we often make use of language to name those identities according to a context. In the case of Hispanic, Latina/o, Latin@, Latinae, and/or Latinx people in the U.S., the changes in these names or words have been linked to linguistic and political perspectives.”
These terms (Hispanic, Latina/o, Latin@, Latinae, and/or Latinx people) have changed as a way of challenging paradigms on many different axes of identity such as gender, race, land, residency status, language, among others. The authors conclude with a call to unity towards inclusivity and ask the readers to share with them which term is more relevant to identify this diverse group and what should that decision be based on.
In this post, Carlos LópezLeiva, Kyndall Brown, and Silvia Llamas-Flores, dive into the world of Ethnomathematics, as they define (and describe) it as,
“Ethnomathematics is a term introduced by Ubiratàn D’Ambrosio (1991) from Brazil to describe the techniques used to explain, understand, and cope with reality in order to survive across diverse communities. Ethno relates to the members of distinct groups identified by cultural traditions, codes, symbols, myths, and specific ways of reasoning and inferring (D’Ambrosio, 1985). So, ethnomathematics refers to the way that members of various cultural groups mathematize their own reality because it examines how both mathematical ideas and practices are processed and used in daily activities (D’Ambrosio and Rosa, 2017, p. 288).”
Finally, as the elections draw near, in their post, The Mathematics of Voting and its Consequences: Ideas for Mathematics Lessons, they present resources on the historic link between democracy and voting, current issues that relate to inequity in voting, and mathematics lessons on voting. For example, using mathematical modeling to explore the link between voting and the Common Core Standards of Mathematics.
Have an idea for a topic or a blog you would like for me and Rachel to cover in upcoming posts? Reach out in the comments below or on Twitter (@VRiveraQPhD).
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