Talk Math With Your Friends (TMWYF) is a weekly virtual mathematics colloquium. The speaker will present for 45 minutes, followed by 15 minutes of questions and discussion. Talks will be recorded and posted, subject to the consent of the speaker.
Click the button below to join us live via Zoom each Thursday from 3:30-4:30 Eastern (12:30-1:30 Pacific). More information is on our Zoom Info page.
A major hurdle in the study of mathematics education is that "knowing", "understanding", and "learning" are inherently unknowable states; there is no mechanism that allows a researcher or instructor to see into the minds of students. This naturally results in a reliance on students' written and spoken utterances, observable actions, and performance as key sources of insight into students' engagement with mathematics.
This talk discusses the theoretical implications of a misalignment between written, enacted, and attained mathematics curriculum goals in the K-16 space through the lens of a student's first week in a graduate real analysis course. I use Sfard's theory of commognition to nuance misalignment in curricular goals and introduce two novel tools based on Sfard's realization trees (I have named these discursive maps and evoked trees) that can aid in the study of advanced mathematical thinking in students. I will use the first page in chapter one of Rudin's "Real and Complex Analysis" (3E) to motivate the discussion.
All are welcome to this talk; it will be accessible to anyone with a basic familiarity with single variable calculus up to integration. All other relevant background information will be provided. The audience will be given an opportunity to create discursive maps and/or evoked trees, so please join on a device where you can either draw on a touch screen, or where you are comfortable with using a mouse to write. If you choose to contribute a drawing to this session, your name will be anonymized automatically.
For the interested audience member, I provide some questions to consider prior to the talk that emphasize the potential for differences in what is expected of students' thinking by expert mathematicians and how students describe their own thinking:
Read the first page of the abstract integration chapter of Rudin where a brief introduction is made to Lebesgue's theory of integration. What is the highest level of mathematical content that you believe a student will need to be familiar with to follow this introduction?
In what prior courses do you believe that a student should have gained familiarity with the content that you have identified in response to question one?
What connections do you anticipate a student will need to make to K-16 content to make sense of this introduction? What connections do you make to prior K-16 content to make sense of this introduction?
Please feel free to discuss your thoughts by email at bsalaam at uga dot edu, or share them during the discussion portion of the talk.
2/10 - Michael Barany
3/3 - Dan McQuillan
3/17 - Adriana Salerno
3/31 - OURFA2M2
4/14 - Mandy Jansen
5/5 - Nicole Joseph, Ashli-Ann Douglas, Mariah Harmon
5/12 - Bolanle Salaam
Rescheduling - Shraddha Shirude
Rescheduling - Vanessa Sun
After a tumultuous time studying mathematics in college, Vanessa Sun has been writing about both her positive and negative experiences in math as healing, as an expression of her joy and the pain of losing her love of mathematics, and as a call to action for those in the math community to listen to the needs of their students and colleagues. In this session, Vanessa will be baring her soul, reading some of the poems and memoirs she has written, as well as discussing the stories behind them.
The purpose of this session is to think about integrating the use of rough drafting and revising practices into mathematics instruction. K-12 teachers report that rough drafting and revising in mathematics class can create safe spaces for students to share their thinking, focus on understanding over answer-getting, and emphasize that learning is a constant, on-going process of evolving thinking. I will share ideas from K-12 classroom teachers about how they integrate rough drafting and revising into their mathematics lessons to spark discussion.
This study used Black Feminist Mathematics Pedagogies to understand the experiences of 48 10th and 11th grade Black girls in secondary mathematics classrooms. Elevating their voices produced Black girl-authored knowledge revealing that they often experienced uncaring teachers, curriculum and classes that were not interesting, and unsupportive learning environments. Such experiences limited their perceptions about the usefulness of mathematics beyond school and their future careers. Findings also showed that their prior and current experiences in mathematics did not contribute to positive mathematics identities. Implications for teachers, general educators, Black girls, and their families are discussed followed by Appendix C that includes actions mathematics teachers can take now to begin supporting the Black girls in their classrooms.
The Online Undergraduate Resource Fair for the Advancement and Alliance of Marginalized Mathematicians (OURFA2M2) is an annual online conference organized by current and recent undergraduate students. We designed the conference to connect underrepresented and marginalized mathematics undergraduates with career-building resources, to provide them with a space for and by students, and to build their confidence through representation and encouragement. Our conference attracts over 350 registrants, including both students and professional mathematicians, for networking and a variety of personal, professional, and technical talks.
In this talk, we will draw on both our personal experiences and what we learned from organizing the conference. We will identify the ways in which current mentoring of undergraduates is lacking, and propose ways faculty can work toward solutions. We will also share how faculty and other professionals can improve their advocacy for marginalized mathematicians and other organizing efforts.
Origami is an ancient art that continues to yield both artistic and scientific insights to this day. In 2012, Buhler, Butler, de Launey, and Graham extended these ideas even further by developing a mathematical construction inspired by origami — one in which we iteratively construct points on the complex plane (the “paper”) from a set of starting points (or “seed points”) and lines through those points with prescribed angles (or the allowable “folds” on our paper). Any two lines with these prescribed angles through the seed points that intersect generate a new point, and by iterating this process for each pair of points formed, we generate a subset of the complex plane. We extend previously known results about the algebraic and geometric structure of these sets to higher dimensions. In the case when the set obtained is a lattice, we explore the relationship between the set of angles and the generators of the lattice and determine how introducing a new angle alters the lattice. (Joint work with Deveena Banerjee and Sara Chari.).
A total labeling of a graph G is an assignment of the integers 1,2,...,v+e, to the v vertices and e edges of G. The weight of a vertex is the sum of its "label" with the sum of its incident edge labels. The total labeling is vertex-magic (or a VMTL) if the weight of each vertex is a constant, called the magic constant for the VMTL. The questions are easy to state and reasonable to solve. Many results and proofs are quite elegant. There are many remaining open problems that are accessible to undergraduate students. This talk will discuss several past undergraduate research successes and possible future projects.
Today, it is ordinary and in many cases expected for mathematicians to engage with work and people from other countries and often other continents. Mathematicians often travel long distances for their vocation, and it is not unusual for careers to be built through international migration. I will identify Global Mathematics as a distinct historical phenomenon in the modern history of mathematics and argue that it should be understood as a recent, provisional, contingent, and precarious development, explaining in the process what makes this argument significant for historians of mathematics. Global Mathematics today is threatened by disease, climate change, geopolitics, racism, economic disparities, shifting assumptions about mathematics and higher education, and numerous other recent and long-running considerations. Asking why mathematicians have aspired (and continue to aspire) to make and maintain global connections and what their efforts to achieve this aspiration have cost (and continue to cost) the mathematics profession and its surrounding societies, I will challenge the TMWYF community to reconsider the values and implications of Global Mathematics in the past, present, and future.
Do you have some interesting math you would like to share with a wide audience? We are currently soliciting abstracts for future talks.