This session welcomes contributions from all areas related to history and philosophy of mathematics. This includes reports on research, survey talks, and issues related to the use of history and philosophy of mathematics in the classroom. The session will also include special sessions on mathematical communities and on the philosophy of mathematics. There will also be a group of talks in honor of Karen Parshall (one of the MAA Centennial lecturers) and also in memory of Jackie Stedall (a well known historian of mathematics who passed away in the early fall).
Bolzano's Measurable Numbers: Are They Real?
Does the Indispensability Argument Leave Open the Question of the Causal Nature of Mathematical Entities?
How Does the Mind Construct/Discover Mathematical Propositions?
What is an Adequate Epistemology for Mathematics?
Did American Professors Form a Mathematical Community in the Early 19th Century?
In celebration of the 100th anniversary of the MAA, the AWM sponsors this session to acknowledge and recognize the contributions, achievements, and progress of women mathematicians over the past 100 years. This century has seen great mathematical achievements by women, the most recent and most public being Maryan Mirzakhani winning the Fields Medal. To honor this and other advances in mathematics by women, this session welcomes talks about mathematics done by women and historical or biographical presentations celebrating women in mathematics.
A mathematics circle is an enrichment activity for K-12 students or their teachers, which brings them into direct contact with mathematics professionals, fostering a passion and excitement for deep mathematics in the participants. It is usually a weekly or monthly activity, but it can also be an intensive summer experience. Circles provide rich open-ended problems that enable students or their teachers to strengthen their problem-solving skills and deepen their appreciation for and excitement about mathematics. In honor of the MAA's 100th anniversary, we especially encourage talks that address a problem or topic involving the number 100 that was successful at your math circle.
Victoria Kofman, Quality Engineering Education, Inc.
This session is dedicated to aspects of undergraduate research in mathematical and computational biology. First and foremost, this session would like to highlight research results of projects that either were conducted by undergraduates or were collaborations between undergraduates and their faculty mentors. Of particular interest are those collaborations that involve students and faculty from both mathematics and biology. Secondly, as many institutions have started undergraduate research programs in this area, frequently with the help of initial external funding, the session is interested in the process and logistics of starting a program and maintaining a program even after the initial funding expires. Important issues include faculty development and interdisciplinary collaboration, student preparation and selection, the structure of research programs, the acquisition of resources to support the program, and the subsequent achievements of students who participate in undergraduate research in mathematical and computational biology.
Mathematics and art have a long historical relationship throughout the centuries. Ancient Egyptians and Greeks incorporated several mathematical relationships into their lives and art. In this session we encourage talks and presentations that connect mathematics and art. We would like to see a broad range of art: visual art, decorative art and performing art. The emphasis will be on college level mathematics that connects math and art in problems and projects that can enrich mathematics teaching. Puzzles, games and other activities that relate math and art are also encouraged.
Financial Mathematics encompasses all the mathematical and statistical tools, theories and techniques involved in the applied areas usually described as Quantitative Finance, Computational Finance, and Financial Engineering. Research in these areas of financial market modeling include derivatives pricing, risk-and-portfolio management and the theory of interest. Such works have resulted in Nobel Prizes in 1990 and 1997. This session welcomes presentations on any aspect of Financial Mathematics, including the history of this topic, the teaching of this topic, new applications or items of purely academic interest.
Social Security Benefit: Now or Later?
Video games are a part of popular culture and they show up everywhere and in different forms: computer or console, online or offline, on phones or other mobile devices. There are many applications of mathematics in the gameplay and creation of games that are popular today. This session seeks presentations that share some of the mathematical applications that appear in recent games. Presenters are encouraged to show college-level mathematics that might appear in a range of courses. This session will be of interest to gamers and instructors looking for innovative examples to use in their classes.
TCPS#9: What Can a Mathematician Do with a 3D Printer?
This session is dedicated to the intersection of 3D printing and mathematics: the creation of objects through the application of college-level mathematics or research-level mathematics, or the incorporation of 3D printing into the teaching of mathematics. In terms of the creation of objects on a 3D printer, of particular interest are those works that answer the question, "What can a mathematician do with a 3D printer?" This may include fractal images, knots, smooth manifolds, polyhedra, and demonstrations of theoretic or historical constructs. For teaching, of particular interest is the incorporation of 3D printing into college-level courses like geometry, topology, or multivariable calculus.
I Can Touch the Math!
How You Too Can Join the 3D Printing Craze!
In the Scholarship of Teaching and Learning (SoTL), faculty bring disciplinary knowledge to bear on questions of teaching and learning and systematically gather evidence to support their conclusions. Scholarly work in this area includes investigations of the effectiveness of pedagogical methods, assignments, or technology, as well as probes of student understanding. The goals of this session are to: (1) feature scholarly work focused on the teaching of postsecondary mathematics, (2) provide a venue for teaching mathematicians to make public their scholarly investigations into teaching/learning and (3) highlight evidence-based arguments for the value of teaching innovations or in support of new insights into student learning. Appropriate for this session are preliminary or final reports of post-secondary classroom-based investigations of teaching methods, student learning difficulties, curricular assessment, or insights into student (mis-)understandings. Abstract submissions should have a clearly stated question that was (or is) under investigation and should give some indication of the type of evidence that has been (or is being) gathered and will be presented. For example, papers might reference the following types of evidence: student work, participation or retention data, pre/post-tests, interviews, surveys, think-alouds, etc.
Does Calculus Help with Algebra?
Critical thinking is self-directed, self-disciplined, self-monitored, and self-corrective thinking. It entails effective communication and problem solving abilities. "We think critically when we have at least one problem to solve. One is not doing good critical thinking, therefore, if one is not solving any problems." (Richard Paul, Think Magazine, 1992). Mathematics is solving problems. The session will focus on the role of active learning in mathematics, and how a teacher can use it to cultivate critical thinking. We invite instructors to share their experiences and provide useful tips and tricks on implementing active learning strategies and overcoming obstacles to active learning in general. Examples and ideas can come from any type of course, from undergraduate non-major service courses and early-major mathematics courses to late-major and even graduate-level classes. Speakers are encouraged to include assessment data on the effectiveness of their active learning strategies or empirical feedback from students and/or faculty about their strategies.
From the simplest modeling equations to the most complex proofs, students often lack the writing abilities to properly communicate their solutions. In order to help students achieve coherent arguments that are both logical and sequential, math-writing skills need to be developed. Students in introductory math classes must be able to find the solution to a problem by writing down all the necessary steps and reasons for each step leading up to the answer. Students in advanced math classes must be able to delineate hypothesis from conclusion in proving statements and be able to use the definitions, assumptions, and related results accurately in justifying their proofs. In this session, we invite participants to share useful approaches to teaching students not only how to reason critically, but also to communicate in writing in a way that fully demonstrates conceptual understanding. We encourage instructors that actively practice mathematical writing across all levels of the curriculum to share best practices for student writing objectives. We are interested in hearing about specific problems and/or projects, as well as the assessment tools for these projects, which have been used to address the issue of writing mathematics.
As president Obama stated regarding STEM, "We need to make this a priority to train an army of new teachers in these subject areas." In response to this need, many institutions have developed programs that provide STEM certification or other credentialing for pre-service elementary education majors. This session solicits presentations regarding programs that have been developed to provide this type of credentialing. As mathematics plays a significant role in these programs, the mathematical aspects of these programs should be highlighted. Presentations about programs under development are also encouraged.
Essential to the learning of mathematics is that students engage in "authentic" mathematical activity, or what mathematicians would recognize as "doing math." However, too often deficit explanations (i.e., students' lack of background knowledge, lack of math ability, lack of motivation) have been used to deny students access to authentic experiences. This session is a vehicle to promote a more equitable orientation to the learning of mathematics for all students in a range of learning situations (not just the "top" kids in ideal situations). We invite talks illustrating viable, evidence-based strategies that promote access to authentic mathematical activity through inquiry that honors the diversity of students' mathematical knowledge. Topics may include 1) innovative, equity- and inquiry-oriented methods of teaching and learning in remedial, developmental, or introductory courses and courses for non-majors; 2) lessons that allow students to use mathematics to address important equity and social justice issues in their communities; and 3) programs that provide students with opportunities to engage in the kinds of authentic mathematical activities and research projects that embrace the knowledge and experiences they bring to school.
A common focus of university administration is student retention and graduation. First year mathematics courses- remedial and general education- have relatively high drop/fail/withdraw rates, which place them under scrutiny by administration. In this session, we would like to hear what you have been doing to improve pass rates and student persistence in first year courses with traditionally high DFW rates. We hope to focus on department efforts (rather than specific classroom approaches) to support students in these first year Mathematics courses. Presentations could include complete multi-section redesign, restructure of curriculum, efforts to standardize. We would like to hear about successful, in progress, and unsuccessful efforts. Presentations with a description of the initiative along with data supporting the success or failure are encouraged.
Poor retention in the STEM fields is often tied to students' initial difficulties and/or lack of motivation in mathematics courses early in their academic career. In this session, we would like to hear about efforts to help struggling students in first year mathematics courses for STEM students or to help motivate students in these courses. We are particularly interested in departmental efforts, rather than specific classroom teaching activities. We would like to hear about successful, in progress, and unsuccessful efforts. Presentations with a description of the initiative along with data supporting the success or failure are encouraged.
Often modeling is associated with differential equations courses as a motivator for learning and as a way of showing how mathematics is applied in other disciplines such as physics, biology, and economics. Modeling can be used (1) as a way of leading up to the mathematics being taught, (2) during the instruction on the mathematics and techniques, and/or (3) after the mathematics has been taught. These three times—before, during, or after—for using modeling have the potential to support students and motivate their learning. We invite colleagues who use modeling, especially with real data, to share their experiences with special attention paid to the timing of the modeling activities with respect to associated differential equations concepts and techniques. This session is sponsored by SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations and presenters will be invited to submit their modeling scenarios for peer-reviewed publication at www.simiode.org.
Inquiry-Based Learning in ODE Classes: Stable or Unstable?
There has been a significant amount of investigation into the flaws of traditional calculus courses and possible improvements, from the Calculus Reform movement beginning in the late 1980s to the recent MAA study finding significant attrition during the calculus sequence. This session shines a spotlight on recent efforts from instructors to make a productive change. In this session, we ask instructors to share creative ideas for instruction from the calculus sequence. We are interested in general approaches and/or specific activities that a) help students engage in the mathematics of calculus in innovative ways and/or b) promote group work and conversation about the mathematical content. Submitted abstracts should include a description of the approach/activity, how it meets these objectives, and observed strengths and weaknesses compared with the traditional approach. We encourage presentations in which the audience can experience the innovative teaching and learning.
Where is the Differential in Differential Calculus?
The mathematical preparation of secondary teachers has received substantial attention by mathematicians and mathematics teacher educators for many years, but how do university instructors and program coordinators know their efforts are making a difference? While the program evaluation process, which can include accreditation reports (e.g., CAEP) and teacher candidate surveys, encourages faculty to seriously consider this question, it is tempting to focus program evaluation on outcomes such as: graduation rates, teacher placement rates, and scores on teacher licensure exams or performance-based teacher assessments (e.g., edTPA). In this session, we invite mathematics content and methods instructors and program coordinators to share ways they gather and analyze data for the purpose of making decisions about their programs. Presentations should focus on one or two program goals directly linked to the mathematical preparation of secondary teachers. Examples include: How do you know that teachers can promote mathematical thinking and learning in ways consistent with the Common Core Standards for Mathematics (NGA Center & CCSSO, 2010)? How is your program addressing the recommendations in the Mathematical Education of Teachers II document (CBMS, 2012)? How does your program work with mentor teachers to develop candidates' use of formative assessment?
This session invites presenters to share demonstrations, using geometry software or tablet applications, which help students to understand aspects of undergraduate geometry. These demonstrations should be suitable for Euclidean and non-Euclidean geometry courses as well as for courses frequently referred to as "modern" or "higher" geometry but not those related to differential geometry or (low-level) graduate courses. Presenters must perform the full demonstration (or a key portion of it) and discuss the aspects of the demonstration that help students to understand an associated theorem. Information regarding prerequisite topics and related areas with which students have difficulty should be discussed as should problems, if any, experienced in using the software or tablet application. Presenters are invited to discuss how they have modified the demonstration over time as well as to share information about software or tablet explorations performed with students that have helped students understand the associated theorem. Abstracts should include the name of the software or application, the platform (computer or tablet), and the associated theorem as well as a brief description of the demonstration. Presenters must provide their own laptop or tablet.