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SIGMAA Activities

SIGMAA on Mathematics and the Arts (ARTS SIGMAA)

Minicourse

Visualizing Projective Geometry Through Photographs and Perspective Drawings

Part A: Thursday, August 1, 3:40 p.m. – 5:40 p.m., Duke Energy Convention Center, Room 204
Part B: Friday, August 2, 3:40 p.m. – 5:40 p.m., Duke Energy Convention Center, Room 204

Description

This Minicourse will introduce hands-on, practical art puzzles that motivate the mathematics of projective geometry—the study of properties invariant under projective transformations, often taught as an upper-level course. This Minicourse seeks to strengthen the link between projective geometry and art. On the art side, we explore activities in perspective drawing or photography. These activities provide a foundation for the mathematical side, where we introduce activities in problem solving and proof suitable for a sophomore-level proofs class. In particular, we use a geometrical analysis of Renaissance art and of photographs taken by students to motivate several important concepts in projective geometry, including Desargues’ Theorem and the use of numerical projective invariants. No artistic experience is required.

Organizer:
Annalisa Crannell, Franklin & Marshall College,

 

SIGMAA on the History of Mathematics (HOM SIGMAA)

Contributed Paper Session

History of Mathematics in a Math Circle

Part A: Thursday, August 1, 9:00 a.m. - 10:40 a.m., Duke Energy Convention Center, Room 237 & 238
Part B: Thursday, August 1, 1:30 p.m. - 4:30 p.m., Duke Energy Convention Center, Room 237 & 238

Description

Math Circles are outreach programs led by mathematicians for K-12 students or teachers. Math Circles combine significant content with a setting that encourages a sense of discovery and excitement about mathematics through problem solving and interactive exploration. Great problems can often be solved by a variety of approaches working in concert. During this session, presenters will share mathematical topics, activities, and problems of a historical nature or have a historical component for use in a math circle. This can include such ideas as working a class of problems using historical methods, discovering methods of calculation from a former time or culture, discovering how mathematical concepts were discovered or used historically or culturally, or building a hands-on model that is a replica of a historical item or depicts a historical mathematical idea. If space allows, non-historical math circle topics will also be considered.

Organizers:
Amy Shell-Gellasch, Eastern Michigan University
Philip Yasskin, Texas A&M University

 

Other Mathematical Session

Reception for Read the Masters Session: Euler's Introductio in Analysin Infinitorum

Thursday, August 1, 3:40 p.m. - 5:40 p.m., Duke Energy Convention Center, Room 201

Description

Leonhard Euler's Introductio (1748) is a key text in the history of mathematics. In it, Euler provided the foundation for much of today's mathematical analysis, focusing in particular on functions and their development into infinite series. At this event, a brief description of what is entailed in engaging historical texts, especially through small reading groups, will precede an open reading session of a portion of the Introductio (in English translation, with guiding questions) by attendees in small groups, followed by a general discussion. No experience with the history of mathematics is required.

Organizers
Erik Tou, University of Washington Tacoma
Daniel Otero, Xavier University
Lawrence D'Antonio, Ramapo College
Robert Bradley, Adelphi University
Amy Shell-Gellasch, Eastern Michigan University

 

SIGMAA on Inquiry-Based Learning (IBL SIGMAA)

Business Meeting, Reception, and Guest Lecture

Thursday, August 1, 4:30 p.m. - 5:50 p.m., Duke Energy Convention Center, Room 200

 

Invited Paper Session

Equity and Justice in the Context of Inquiry

Thursday, August 1, 1:30 p.m. - 4:20 p.m., Duke Energy Convention Center, Room 200

Description

Research is indicating that inquiry pedagogies have the potential to offer rich learning experiences that address some of the ways in which the collegiate mathematics education systematically under-serves some populations. And yet, we also know that elements of these environments, if implemented without care, can contribute to the alienation of exactly the students instructors are hoping to support. For example, being asked to talk in class can trigger stereotype threat for students of color, and unstructured discussions may create spaces in which privileged voices dominate. In addition to implementation issues, as researchers we must develop and apply methods that allow us to see the experiences of marginalized students even when these experiences can be hidden by averages or statistical methods.

While inquiry pedagogies and equity research have great potential for interconnections, combining them as pre-existing perspectives can miss key issues. Inquiry in general might have potential for equity, but colorblind approaches to this framing of the classroom will hide the different meanings made by students in those classrooms and cannot address the pervasive issue that students of color are disproportionately tracked out of some mathematical spaces and into others. Similarly, to the extent that some equity research has had to use instructor-centered pedagogies as a backdrop, different assumptions in inquiry pedagogies might produce significantly different observations. As a result, equity and inquiry must be theorized and researched together in order to engage these emergent questions about using inquiry to rehumanize mathematics and offer justice for all students. The scholars in this session have all contributed to this ongoing research agenda; this session will put their work in direct conversation in support of extending this research agenda.

Organizer:
Brian Katz, Augustana College

Potential Speakers:
Sandra Laursen, University of Colorado Boulder
Chris Rasmussen, San Diego State University
Stacy Brown, CalPoly Pomona
Rochelle Gutierrez, University of Illinois
Jessica Ellis Hagman, Colorado State University
Estrella Johnson, Virginia Tech
Christine Andrews-Larson, Florida State University
Gail Tang, University of LaVerne
Emily Cilli-Turner, University of Washington Tacoma
Aditya Adiredja, University of Arizona
Robin Wilson, CalPoly Pomona
Brian Katz, Augustana College

 

Contributed Paper Session

Inquiry-Based Learning and Teaching

Part A: Thursday, August 1, 9:00 a.m. - 10:40 a.m., Duke Energy Convention Center, Room 230 & 231
Part B: Thursday, August 1, 1:30 p.m. - 4:30 p.m., Duke Energy Convention Center, Room 230 & 231

Description:

The goal of Inquiry-Based Learning (IBL) is to transform students from consumers to producers of mathematics. Inquiry-based methods aim to help students develop a deep understanding of mathematical concepts and the processes of doing mathematics by putting those students in direct contact with mathematical phenomena, questions, and communities. Within this context, IBL methods exhibit great variety. Activities can take place in single class meetings and span entire curricula for students of any age; students can be guided to re-invent mathematical concepts, to explore definitions and observe patterns, to justify core results, and to take the lead in asking new questions. There is a growing body of evidence that IBL methods are effective and important for teaching mathematics and for fostering positive attitudes toward the subject. This session invites scholarly presentations on the use of inquiry-based methods for teaching and learning. We especially invite presentations that include successful IBL activities or assignments that support observations about student outcomes with evidence or that could help instructors who are new to IBL to try new methods.

Organizers:
Victor Piercey, Ferris State University
Susan Crook, Loras College
Brian Katz, Augustana College
Eric Kahn, Bloomsburg University
Amy Ksir, United States Naval Academy

 

Panel Session

Jumping into IBL Teaching: Reflections by First-Time Practitioners

Friday, August 2, 3:00 p.m. - 4:20 p.m., Duke Energy Convention Center, Room 263

Description

Curious about Inquiry-Based Learning (IBL) but not sure where to start? So were they! In this panel, faculty who have recently taught an IBL-style course for the first time will reflect on their experiences. Panelists will share a typical day in the classroom along with lessons learned about what worked well and what they would change in the future. Courses represented will range from entry-level to upper divisional.

Organizers:
Angelynn Alvarez, SUNY Potsdam
Sarah Wolff, Denison University
Robert Kelvey, The College of Wooster

Panelists:
Emily Barnard, Northeastern University
Judit Kardos, The College of New Jersey
Sarah Nelson, Lenoir-Rhyne University
Kristen Pueschel, Penn State University New Kensington
Adam Giambrone, Elmira College

 

SIGMAA on Math Circles for Students and Teachers (SIGMAA MCST)

Contributed Paper Session

History of Mathematics in a Math Circle

Part A: Thursday, August 1, 9:00 a.m. - 10:40 a.m., Duke Energy Convention Center, Room 237 & 238
Part B: Thursday, August 1, 1:30 p.m. - 4:30 p.m., Duke Energy Convention Center, Room 237 & 238

Description

Math Circles are outreach programs led by mathematicians for K-12 students or teachers. Math Circles combine significant content with a setting that encourages a sense of discovery and excitement about mathematics through problem solving and interactive exploration. Great problems can often be solved by a variety of approaches working in concert. During this session, presenters will share mathematical topics, activities, and problems of a historical nature or have a historical component for use in a math circle. This can include such ideas as working a class of problems using historical methods, discovering methods of calculation from a former time or culture, discovering how mathematical concepts were discovered or used historically or culturally, or building a hands-on model that is a replica of a historical item or depicts a historical mathematical idea. If space allows, non-historical math circle topics will also be considered.

Organizers:
Amy Shell-Gellasch, Eastern Michigan University
Philip Yasskin, Texas A&M University

 

SIGMAA on Mathematical and Computational Biology (BIO SIGMAA)

Contributed Paper Session

Mathematics and the Life Sciences: Initiatives, Programs, Curricula

Part A: Thursday, August 1, 9:00 a.m. - 10:40 a.m., Duke Energy Convention Center, Room 207 & 208
Part B: Thursday, August 1, 1:30 p.m. - 4:30 p.m., Duke Energy Convention Center, Room 207 & 208

Description

The 2015 CUPM Curriculum Guide to Majors in the Mathematical Sciences identified the life sciences as a key path through the mathematics major to graduate programs and the workforce. Topics include scholarly contributions addressing initiatives, programs, curricula, and course materials at the interface of mathematics and the life sciences that have been implemented and tested at institutions of higher education.

Organizers:
Timothy D. Comar, Benedictine University
Raina Robeva, Sweet Briar College
Carrie Diaz Eaton, Bates College

 

SIGMAA on Mathematical Knowledge for Teaching (MKT SIGMAA)

Panel Session

Mathematical Knowledge for Teaching as an Integrated Application in Core Mathematics Major Courses

Thursday, August 1, 3:00p.m. - 4:20 p.m., Duke Energy Convention Center, Room 263

Description

Core courses in the math curriculum often include problems attending to specific application areas such as science, engineering, and business. These problems serve to emphasize the utility of the mathematics in the areas, to legitimize the application area as requiring deep mathematical thinking, and to help students understand the breadth of career opportunities for mathematicians. The MAA META Math project (NSF DUE 1726624) is focused explicitly on adding “secondary teaching” to the list of legitimate application areas of mathematics by creating resources and training on the integration of curriculum materials for every math major course. In this session, panelists will share course materials and classroom activities that have been developed and successfully integrated into a traditional undergraduate major course with the goal of inspiring future teachers to engage in deep thinking about how the mathematics is connected to secondary school content. There will also be at least one panelist representing META Math researchers who are measuring the impact of these materials on the attitudes, recruitment, and retention of students preparing to become teachers as well as the attitudes of mathematics instructors toward their students who are pursuing a career in teaching.

Organizer:
Doug Ensley, Shippensburg University
Elizabeth Fulton, Montana State University

Panelists:
Elizabeth Burroughs, Montana State University
James Tanton, Mathematical Association of America
Rick Hudson, University of Southern Indiana
Lisa Berger, Stony Brook University

 

SIGMAA on Quantitative Literacy(SIGMAA QL)

Town Hall Meeting

Quantitative Literacy and Social Justice

Friday, August 2, 3:00 p.m. - 4:20 p.m., Duke Energy Convention Center, Room 201

Description

At the 2019 Joint Mathematics Meetings, Dave Kung and Kira Hamman called for a need to teach mathematics and quantitative literacy with an eye toward social justice. As part of their presentation, they not only reiterated the importance of promoting quantitative literacy for social justice (and vice versa), but they also pushed the audience to consider diverse and potentially divisive issues ranging from who “receives” quantitative literacy on their campus to how students are positioned in mathematics classrooms. Their remarks accentuate that the relationship between quantitative literacy and social justice is complex, and that there is much for the mathematics and quantitative literacy communities to consider as we teach in an era of alternative facts, dueling memes, and politically charged classrooms.

SIGMAA-QL would like to invite all members of the mathematics community who are interested in issues of social justice as well as pathways toward a quantitatively literate society to a town hall discussion at MathFest 2019 to follow up on some of these questions. In particular at this session we hope to start a much needed conversation about the roles people of mathematics can play in promoting quantitative literacy for social justice (and vice versa). Issues we would like to discuss range from teaching mathematics for social justice, to the role of QL in charting a path towards a more just society, to the future of SIGMAA-QL as an ambassador of mathematicians interested in these issues. The organizers will come in with questions to initiate and facilitate the conversation, but we invite everyone interested to come and make their voices be heard.

Organizers:
Gizem Karaali, Pomona College
Mark A. Branson, Stevenson University
Catherine Crockett, Point Loma Nazarene University
Victor Piercey, Ferris State University
Luke Tunstall, Trinity University

 

SIGMAA on Recreational Mathematics (REC SIGMAA)

Business Meeting and Reception

Friday, August 2, 5:00 p.m. - 5:50 p.m., Duke Energy Convention Center, Room 206

 

Invited Paper Session

The Serious Side of Recreational Mathematics

Friday, August 2, 1:30 p.m. - 4:20 p.m., Duke Energy Convention Center, Room 200

Description

Recreational mathematics covers a wide variety of themes: card tricks, board games, puzzles, origami, and art are just a few. The use of “recreational” gives the impression that research in these topics is more of a pastime than an investigation with depth to it. However, when you look below the surface, there is a surprising amount of complexity to the subjects being studied. This invited paper session will include experts in the many topics in recreational math showing how starting with a fun puzzle, game, or story can take one on a trip to deep mathematics.

Our goal is to show the myriad of topics gathered underneath the recreational umbrella rather than highlight one topic. The gamut of this runs from the combinatorial questions in designing unique puzzles and using origami in designing robots, to the powerful logic in Knights and Knaves puzzles, the geometric structures hidden in the game SET, and using number theory to create new tricks with playing cards.

Organizer:
Robert Vallin, Lamar University

Sponsor: SIGMAA on Recreational Mathematics

Speakers:
Art Benjamin, Harvey Mudd
James Sellers, Penn State University
Liz McMahon, Lafayette College
Steve Butler, Iowa State University
Bob Bosch, Oberlin College

 

Contributed Paper Session

Recreational Mathematics: Puzzles, Card Tricks, Games, Gambling and Sports

Part A: Thursday, August 1, 9:00 a.m. - 10:40 a.m., Duke Energy Convention Center, Room 206
Part B: Thursday, August 1, 1:30 p.m. - 4:30 p.m., Duke Energy Convention Center, Room 206

Description

Puzzles, card tricks, board games, game shows, gambling, and sports provide an excellent laboratory for testing mathematical strategy, probability, and enumeration. The analysis of such diversions is fertile ground for the application of mathematical and statistical theory. Solutions to new problems as well as novel solutions to old problems are welcome. Submissions by undergraduates or examples of the use of the solutions of these problems in the undergraduate classroom are encouraged.

Organizers:
Paul R. Coe, Dominican University
Sara B. Quinn, Dominican University
Kristen Schemmerhorn, Concordia University Chicago
Andrew Niedermaier, Jane Street Capital

 

SIGMAA on Research in Undergraduate Mathematics Education (SIGMAA on RUME)

Invited Paper Session

Equity and Justice in the Context of Inquiry

Thursday, August 1, 1:30 p.m. - 4:20 p.m., Duke Energy Convention Center, Room 200

Description

Research is indicating that inquiry pedagogies have the potential to offer rich learning experiences that address some of the ways in which the collegiate mathematics education systematically under-serves some populations. And yet, we also know that elements of these environments, if implemented without care, can contribute to the alienation of exactly the students instructors are hoping to support. For example, being asked to talk in class can trigger stereotype threat for students of color, and unstructured discussions may create spaces in which privileged voices dominate. In addition to implementation issues, as researchers we must develop and apply methods that allow us to see the experiences of marginalized students even when these experiences can be hidden by averages or statistical methods.

While inquiry pedagogies and equity research have great potential for interconnections, combining them as pre-existing perspectives can miss key issues. Inquiry in general might have potential for equity, but colorblind approaches to this framing of the classroom will hide the different meanings made by students in those classrooms and cannot address the pervasive issue that students of color are disproportionately tracked out of some mathematical spaces and into others. Similarly, to the extent that some equity research has had to use instructor-centered pedagogies as a backdrop, different assumptions in inquiry pedagogies might produce significantly different observations. As a result, equity and inquiry must be theorized and researched together in order to engage these emergent questions about using inquiry to rehumanize mathematics and offer justice for all students. The scholars in this session have all contributed to this ongoing research agenda; this session will put their work in direct conversation in support of extending this research agenda.

Organizer:
Brian Katz, Augustana College

Potential Speakers:
Sandra Laursen, University of Colorado Boulder
Chris Rasmussen, San Diego State University
Stacy Brown, CalPoly Pomona
Rochelle Gutierrez, University of Illinois
Jessica Ellis Hagman, Colorado State University
Estrella Johnson, Virginia Tech
Christine Andrews-Larson, Florida State University
Gail Tang, University of LaVerne
Emily Cilli-Turner, University of Washington Tacoma
Aditya Adiredja, University of Arizona
Robin Wilson, CalPoly Pomona
Brian Katz, Augustana College

 

SIGMAA on Mathematics and Sports (SIGMAA Sports)

Business Meeting, Reception, and Guest Panel

Undergraduate Research in Mathematics & Sports

Friday, August 2, 6:00 p.m. - 7:30 p.m., Duke Energy Convention Center, Room 263

Description

We will discuss ways in which faculty have mentored undergraduate projects related to mathematics and sports. Faculty will describe the various types of student research that was conducted, including interdisciplinary work, applied mathematics, sports analytics, and mathematics education. We hope that this will serve as a springboard for ideas on future work that can be conducted regarding mathematics and sports. We welcome all faculty and students to share their experiences and contribute to our discussion.

Panelists:
Daniel Dobbs, Trine University
R. Drew Pasteur, College of Wooster
Tetyana Berezovski, St. Joseph’s University

Moderator:
Diana Cheng, Towson University

 

Contributed Paper Session

Mathematics and Sports

Saturday, August 3, 9:00 a.m. - 12:00 p.m., Duke Energy Convention Center, Room 206

Description

The expanding availability of play-by-play statistics and video-based spatial data have led to innovative research using techniques from across the mathematical sciences, with impacts on strategy and player evaluation. Other areas of interest include ranking methods, predictive models, physics-based analysis, etc. Research presentations, expository talks, and contributions related to curriculum or pedagogy are all welcome. With a broad audience in mind, talks should be accessible to undergraduate mathematics majors, and projects involving undergrads are particularly encouraged for submission.

Organizer:
Drew Pasteur, College of Wooster

 

SIGMAA on Teaching Advanced High School Mathematics (SIGMAA TAHSM)

Business Meeting, Reception, Sliffe Award Winners Celebration, & Guest Lecture

Using History and Education Research to Shape the Calculus Curriculum

David Bressoud, Conference Board of the Mathematical Sciences

Friday, August 2, 6:00 p.m. - 7:30 p.m., Duke Energy Convention Center, Room 237 & 238

Abstract

This talk will explain how the historical development of calculus should be used to inform its instruction. The standard order of the four big ideas—limits then derivatives then integrals then series—is wrong both historically and pedagogically. In addition, the standard models for derivatives and integrals, slopes of tangents lines and areas under curves, erect obstacles in the path of many students. Drawing on history and recent research in undergraduate mathematics education, this talk will make the case for calculus introduced first as problems of accumulation (integration), then ratios of change (differentiation), then sequences of partial sums (series), and finally the algebra of inequalities (limits).

Biography

David Bressoud is currently Executive Director of the CBMS. He was President of the MAA and the winner of the MAA Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2018 for Distinguished Service to Mathematics and the Leitzel Lecturer, among other awards.

 

SIGMAA on Undergraduate Research (UR SIGMAA)

Guest Panel and Lunch

Saturday, August 3, 11:30 a.m. - 1:00 p.m., Duke Energy Convention Center, Room 237 & 238

Description

Choosing good research problems to work on with undergraduate students is an art. In creating a research experience, a mentor must ask themselves a variety of questions. Can my students work in my research area, or do we need to explore a new area together? Will my students be able to start thinking about problems in my chosen field immediately, or will they need to learn some background material first? What kinds of questions will be too hard, leading to a frustrating lack of progress? What kinds of questions will be too easy, leaving my students with too much free time on their hands? In general, what are some good qualities to look for in a research problem for students? A panel of successful undergraduate research mentors will share their experiences to begin a broader conversation on this topic that can continue over food and drinks, provided by the UR SIGMAA.

Panelists: TBA

 

Year: 
2019

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