Dr. John C. Nardo, Engaging Mathematics Institutional Partner and Professor of Mathematics at Oglethorpe University, published a new teaching manual that examines the theory and mathematics behind different voting systems and explores their history and fairness. The curriculum contained in the manual covers interdisciplinary topics in science, history, and writing, and provides exercises, homework problems, sample exams, and context for the mathematics of voting theory.
The teaching manual is available for download in ebook, PDF, and Microsoft Word format. Instructor solutions manuals are available upon request. Engaging Mathematics has published manuals that help teachers incorporate civic issues such as sustainability, climate change, and water pollution into statistics, algebra, modeling, and other mathematics courses. View all Engaging Mathematics teaching manuals.
Dr. Rikki Wagstrom, an Engaging Mathematics Institutional Partner and Associate Professor of Mathematics at Metropolitan State University, published a teaching manual containing two modules for use in either a standard Calculus I-II sequence or a one-semester applied calculus survey course. The first module, Calculus Exploration 1: Rates of Change, explores declining milkweed abundance in Iowa crop fields and the implications for monarch butterflies. The second module, Calculus Explorations 2: Definite Integrals, explores monarch reproduction, a crucial factor for survival of the species. Rikki’s manual builds upon her previous work that integrates sustainability into algebra courses.
This teaching manual is available for download in ebook, PDF, and Microsoft Word format at the Engaging Mathematics website. Engaging Mathematics has published manuals that help teachers incorporate civic issues such as sustainability, climate change, and water pollution into statistics, algebra, modeling, and other mathematics courses. New manuals will continue to be shared as the work of Engaging Mathematics continues. View all Engaging Mathematics teaching manuals.
Hosted by: Chris Arney, Janice Ballou, and Frank Wattenberg
Chris Arney and Frank Wattenberg are members of the Department of Mathematical Sciences at the United States Military Academy. The views expressed here do not necessarily reflect the views of the United States Military Academy, the United States Army, or the United States Government.
Webinar Date: Thursday, October 13, 2016 Webinar Time: 1-2pm (Eastern)
Many of us in the United States and around the world are aghast at the tone of this year’s United States presidential election. We are struggling to understand how and why our politics have reached the point that all that we hold dear about our country is in jeopardy. As STEM educators we have an enormous opportunity and responsibility. Our courses can help the debate in several ways:
Many of the most controversial topics–for example, climate change–involve the STEM disciplines. We can help inform the debate. Perhaps it is not too late to bring reason to public discourse.
Framing public policy questions in scientific terms can often lower the temperature of the debate. Perhaps spreadsheets can replace name-calling.
Perhaps most importantly, as scientists we can also study elections and public policy debate themselves. How did we get in this mess? How can we get out of it?
This year’s election season has sparked considerable hand-wringing and even soul-searching by professional journalists. Many worry that the quest for objectivity has enforced a false equivalency in their reporting. As educators we face some of the same problems as we seek to respect the opinions of all our students. In addition, our problems are compounded by the fact that we give our students grades.
We will focus on scientific modeling of how voters evaluate different positions on issues, how they decide for whom to vote, how candidates appeal to voters, and on what we can learn from surveys and polling about ourselves and our politics. We recommend taking the Pew Research Center’s brief Political Typology Quiz before the webinar.
This webinar will be largely discussion based. The organizers will briefly introduce some of the ideas below, but will spend most of the time talking about how these ideas can transform our classrooms and help shape a better and more civil future.
We will also touch on some of the ways in which technology has impacted the workings of the body politic and, especially, the impact of big data. We recommend the book Weapons of Math Destruction by Cathy O’Neil. The short YouTube video below is a brief introduction, especially the last few minutes.
In addition we will discuss the role that language–ranging from the post below commenting on the book to the words of candidates–has had dividing our nation and poisoning our politics.
As STEM educators we have contributed to the present situation. For example, the following problem is arguably the most pernicious of the many thousands of textbook calculus problems. (This particular version came from the web site calculus-help.combut versions appear in virtually every calculus textbook.)
The Next Generation Science Standards do somewhat better if they are understood and implemented well. Consider, for example, the highlighted words from the NGSS:
Engineering design at the high school level engages students in complex problems that include issues of social and global significance. Such problems need to be broken down into simpler problems to be tackled one at a time. Students are also expected to quantify criteria and constraints so that it will be possible to use quantitative methods to compare the potential of different solutions. While creativity in solving problems is valued, emphasis is on identifying the best solution to a problem, which often involves researching how others have solved it before. Students are expected to use mathematics and/or computer simulations to test solutions under different conditions, prioritize criteria, consider trade-offs, and assess social and environmental impacts.
Textbook problems have virtually no relationship to real problems–the problems voters and politicians must address. Textbook problems have textbook answers, whether the one best solution the textbook farmer seeks or the NGSS’s graphic showing a collection of solutions to individual problems, impossibly isolated from their context. There is no one best solution for most real problems. We will discuss how we can teach the topics we already teach with simple examples while emphasizing the complexity of real world settings–especially competing stakeholders and criteria and systems that are simply the sums of their parts.
SENCER educators in mathematics and other STEM disciplines can make use of a new report called GAIMME (Guidelines for Assessment and Instruction in Mathematical Modeling Education) for ways to incorporate applied mathematics into K-12 through undergraduate level curricula. Among the writing team is Sol Garfunkel, a member of the Engaging Mathematics advisory board.
The report, developed jointly by the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and its Applications (COMAP), is available to view and/or print at no cost. Professionally printed copies will also be available for $20 through the SIAM bookstore.
Dr. Frank Wang, a SENCER community member affiliated with the SENCER Center for Innovation – MidAtlantic region and professor of mathematics at LaGuardia Community College, was recently interviewed on the CASTpod podcast hosted by Harold Washington College in Chicago. On the podcast, Dr. Wang discussed the NICHE, or Numeracy Infusion Course for Higher Education, project funded by the National Science Foundation.
Prior to NICHE’s inception, LaGuardia launched an intervention for its students who needed help with basic skills mathematics. Because students often struggled with “abstract” approaches to math instruction, LaGuardia used SENCER strategies to teach mathematics through public health issues and the environment, which helped put the disciplinary content into a specific real-world context. Dr. Wang’s NICHE work is inspired by this previous SENCER intervention, and embeds quantitative reasoning in courses across the curriculum.
The interviewer, Kristen Bivens, asked Professor Wang what has been an exemplary application of quantitative reasoning in the project so far. He cited the work of Ester Isabelle Wilder, the NICHE PI, who shows her sociology students that, by the numbers, there are more homeless white people than black people in the United States. However, since the white population is larger than the black population in the United States overall, it is more meaningful in this situation to look at the rates of homelessness between the two, rather than the numbers alone. This is an important lesson in how statistical thinking and quantitative literacy can help us clarify and address civic problems, one that is also addressed in Dr. Cindy Kaus’s Engaging Mathematics teaching manual Introductory Statistics with Student Designed Community-Based Projects, which can be a helpful resource for educators interested in incorporating racial profiling data into their classes.
To learn more about Dr. Wang’s NICHE project and how it relates to SENCER and other areas, and to hear Dr. Wang’s advice on creating positive student attitudes toward math, listen to the interview.
“Evidence Matters: Using the Scholarship of Teaching and Learning to Tell the Story of Curriculum Development”
The Scholarship of Teaching and Learning (SoTL) is a form of research that involves a systematic investigation of teaching practices and student learning followed by peer review and public sharing of the work for others to build upon. This webinar begins with an overview of the key aspects of SoTL, situating it within a spectrum of scholarly work on teaching and learning. Two in-depth case studies, one involving service learning and the other involving sustainability, illustrate how SoTL can contribute to the process of developing, assessing, and disseminating curriculum. One particular SoTL component highlighted in this webinar is the role literature searches play in both shaping and refining questions as well as providing the background context required for publication. Resources for undertaking a SoTL investigation are made available to all participants.
The webinar will be held Thursday, May 5 from 12-1 pm (Eastern).
It will be hosted by:
Dr. Jackie Dewar (Professor Emerita of Mathematics, Loyola Marymount University)
Dr. Matthew Siniawski (Associate Professor of Mechanical Engineering, Loyola Marymount University)
Dr. Rikki Wagstrom (Associate Professor of Mathematics, Metropolitan State University)
Engaging Mathematics partner Victor Padron of Normandale Community College recently participated in the workshop Teaching Geoscience with MATLAB, hosted by Carleton College in Northfield, MN.
Victor reports that his experience in the workshop was very interesting and motivating. He developed two teaching modules for this workshop that are available to the public through a web repository of educational resources sponsored by the Science Education Resource Center (SERC) at Carleton College.
Here are the names of his modules with the corresponding links and summaries:
This is a teaching module, directed to undergraduate students in applied mathematics, introducing a Zonal Energy Balance Model to describe the evolution of the latitudinal distribution of Earth’s surface temperature subject to incremental levels of cumulative carbon emissions in the atmosphere. A strategy to avert “dangerous levels” of global warming is imbedded in the model. Students working with the module will write a MATLAB script to solve the model numerically and apply it with their own choice of the relevant parameters to obtain the solution that guarantee controlled levels of global warming.
This is a teaching module presenting an introduction to modeling ground water pollution, directed to undergraduate students in applied mathematics. It begins with a brief discussion of Darcy’s law concerning the flow of a fluid through a porous medium. A mathematical model that uses field data to track ground-water contamination is presented. Students working with the module will write a MATLAB script to obtain a numerical solution of the model and apply it to investigate a real event of groundwater pollution.
USMA uses robotics and artificial intelligence as interdisciplinary topics that cut across the curriculum, helping to unify the academic experience. The topics provide a great context for discussing a wide range of interrelated areas. For example, an assignment on self-driving cars raises questions in economics (Who is liable for accidents?), ethics (What would happen to cab drivers?), and logistics (Should cars driven by humans and self-driving cars be allowed on the same roads?).
Students need to have what Frank calls “intellectual integrity” to successfully program a robotic vehicle to pull into a garage and park itself, without crashing into the garage wall. The kits he uses with his cadets cost about $300 and give students experience with hands-on building and coding. It isn’t enough to get a problem 80% right. If the final product is going to be used in the real world, it needs to work; requiring rigor, tenacity, and attention to detail to perfect the design.
As part of his webinar, Frank led Yuxi Chen, who helped with filming and webinar production, as she built her own self-driving and self-parking robotic car. She used her hand to imitate the garage wall. An ultrasonic range finder mounted at the front of her car sensed the presence of her hand with sound waves, telling the car to stop before a collision.
Designing self-driving cars is a good starting point for cadets because its use in the real world is clear, and because it covers core content, such as linear functions. Another assignment Frank does with his students relates to sentries, or soldiers who stand guard, controlling access to a place. He describes the sentry job as both boring and dangerous–a bad combination for a human, but a perfect task for a robot.
The two big worries with robotic sentries are false positives (taking unnecessary defensive action) and false negatives (failing to take defensive action when there is a real threat). In his webinar, Frank discusses this in the context of a parking garage whose access is managed by a robotic arm. His students graph different scenarios, showing possible behavior patterns of approaching cars that are authorized or unauthorized to access the garage. Students also discuss the varying cost levels of defensive action. Blowing up an unauthorized car before it drives through the gate would be an extreme measure with high cost, whereas raising tire shredders or sounding alarms and flashing lights would be lower cost. This concept of cost, Frank mentions, is analogous to other situations, such as medicine. Different health interventions come at different costs than others.
For more on how Frank uses robotics and artificial intelligence with his USMA cadets, view his webinar.
Frank and his colleague Matthew Mogensen, an instructor of mathematics at USMA, also explored these topics with participants at the 2015 SENCER Summer Institute through a hands-on robotics workshop and panel discussion on the civic implications of robotics and artificial intelligence. Frank (firstname.lastname@example.org) and Matt (email@example.com) invite you to email them with questions about using robotics and artificial intelligence in the classroom, or to continue the discussion further.
Engaging Mathematics partner Victor Padron of Normandale Community College will be participating in the workshop Teaching Geoscience with MATLAB, hosted by Carleton College in Northfield, MN from October 18-20, 2015.
The workshop is designed to explore how teaching with MATLAB (a high-level technical computing language used by engineers, scientists, and mathematicians) can enhance the student learning environment in undergraduate Earth Science and related courses. MATLAB can be applied to solving problems and developing systems involving mathematical computation, data analytics and statistics, signal and image processing, geographical mapping, and more in the scientific and engineering domains. Workshop participants will help build a collection of teaching activities that showcase the utilization of MATLAB in the classroom.
Victor will be a panelist in a discussion on using MATLAB and data with students. He will present two modules based on versions of his Engaging Mathematics curricula on groundwater and global warming. Both require a computational environment such as MATLAB. The activities produced by the workshop participants will be posted on the workshop website and featured in a new web-based collection devoted to teaching geoscience with MATLAB. Links to these materials will be shared when they are made available. To learn more, visit the workshop website.
Victor Donnay’s plenary address during the 2015 SENCER Summer Institute had a clear goal—to show the connection between mathematics and the issues people care about.
Victor, who is the William R. Kenan, Jr. Chair of Mathematics at Bryn Mawr College and an advisory board member for NCSCE’s Engaging Mathematics initiative, has the same goal for his students.
Victor uses various assignments to make the connection between mathematics and real world issues clear. During his plenary, Victor shared three examples of such assignments with the audience.
In the first assignment Victor shared, students are instructed to take a homework problem and describe in one paragraph how the mathematics involved might be used to address a real world issue. Students post their paragraphs online and read three others posted by their classmates. From this assignment, something like the concept of related rates in calculus transforms from a general question about how quickly two planes move away from each other into a question about how vocabulary growth rates differ for children born into different socioeconomic classes.
In Victor’s second assignment, students find an article about mathematics in a newspaper or on the web and post it to the class website with a one-paragraph summary. They then read three other summaries and write comments on them. This assignment exposes students to real-world, relevant, and newsworthy mathematics.
In the third assignment, which serves as a final project in Victor’s multivariable calculus course, students pick a world topic that interests them and a topic they learned from the course and show how they are connected. Students present their work at a reception where they can discuss their projects with a general audience.
Victor is also highly focused on issues of environmental studies and sustainability. He chairs the college’s Sustainability Leadership Group, directs the Environmental Studies program, and has taught numerous courses that integrate sustainability with mathematics.
In his mathematics of sustainability courses, he focuses on social, economic, and environmental issues, because all three have an impact on sustainability. His students have studied the Rwandan genocide, population growth models, and tipping points.
Victor worked with TED-Ed to create a short animated video on how tipping points relate to the mathematics of climate change. In the video, titled “Our Chaotic Climate,” chaotic billiard motion explains how a two-degree increase in Earth’s average temperature can lead to substantial consequences.
Victor also incorporates service learning into his mathematical modeling and sustainability course, allowing students to work to make a real difference on their campus and in their community. Student projects range from examining the energy footprint for a renovation of the science building to measuring the level of safety of bike routes. Two of Victor’s students were publicly recognized for their efforts in helping Haverford Township apply for a grant from the Pennsylvania Energy Department Authority to help fund a geothermal energy system for the Community Recreation Environmental Center, a direct result of their service-learning project that explored the center’s options for alternative energy sources.
Students react well to being able to make a difference through their course work. As one of Victor’s students said, “The end results of all the projects were pretty satisfying; it made you feel like you were making a contribution and that you might actually be able to affect something.”
Reactions from the plenary audience were largely positive as well. Overheard were comments from attendees along the lines of, “I never knew this was math!” Victor’s plenary did a great job of showing how mathematics relates to current world problems and topics in many other disciplines, from environmental sustainability to social justice. He helped SSI 2015 attendees see that mathematics is accessible, exciting, and important.
For more from Victor’s plenary, please access these resources:
During the 15th Annual SENCER Summer Institute held last week at Worcester Polytechnic Institute, the Engaging Mathematics initiative led a hands-on session in which participants tried out lessons and curricular units that faculty from the Engaging Math project have developed, all of which illustrate how to connect important topics in mathematics to a variety of civic issues. We are pleased to share these lessons and associated materials here on our project website, so that even if you weren’t able to join us in Worcester, you will still be able to access and use the Engaging Mathematics lessons in your own classroom, with your own students.
The lessons cover civic topics in environmental science, health, social justice, and sustainability, and are applicable to statistics, college algebra, pre-calculus, calculus, and mathematics for liberal arts courses. For an outline of the agenda of the hands-on session, links to lessons and materials covered by session presenters, and links to our Engaging Mathematics Advisory Board member Victor Donnay’s plenary slides, references, and handouts, please see the document below:
March will be a busy time for Engaging Mathematics–we will be represented at several upcoming meetings!
Wm. David Burns (Engaging Math Principal Investigator) and Victor J. Donnay (Engaging Math Advisory Board member) will be speaking at the jointly held Chicago Symposium Series on March 13 and the SCI-Midwest regional meeting on March 14. Both meetings will be held at Northeastern Illinois University.
For the Chicago Symposium series, David will be speaking about “Multidisciplinary Trouble” and offering “Some Thoughts on the Future Directions of Education and Our Democracy”. Victor will be giving a keynote address and offering an interactive session on mathematical lessons that involve sustainability themes, in which all meeting participants can work through problems and develop their own lessons for implementation on their home campuses.
At the regional meeting, David will address the academic structural and cultural barriers to pedagogical progress in STEM fields, and Victor will speak about using service learning involving sustainability in math classes.
Frank Wattenberg (Engaging Math Co-Principal Investigator) will be speaking at the 27th International Conference on Technology in Collegiate Mathematics (ICTCM) from March 12-15 in Las Vegas, Nevada. Frank is organizing a session with three talks on math courses that incorporate meaningful civic applications–the types of math courses that the Engaging Mathematics initiative is working to develop.
We are certainly looking forward to March, and are grateful for the exciting opportunities these meetings offer for our project.
Photo credit: Yann Caradec. No changes were made to the original photo. License.
In early January Engaging Mathematics partners flew to San Antonio to discuss their work at the 2015 Joint Mathematics Meetings (JMM). The Engaging Mathematics initiative was invited to the JMM to contribute a poster for projects supported by the National Science Foundation’s Division of Undergraduate Education.
Initiative partners also presented individual work. Dr. Rikki Wagstrom (associate professor of mathematics at Metropolitan State University, SENCER Leadership Fellow) and her math education student Jodin Morey gave talks on curricula they developed for Engaging Math. Rikki’s curriculum focuses on the Midwest’s declining milkweed populations and the potential impacts for monarch butterflies. Jodin’s compares greenhouse gas emissions from automobile fuels.
Dr. Lynn Gieger (associate professor of mathematics at Oglethorpe University) gave a talk exploring how flipped classrooms impact student attitudes and achievement in a liberal arts mathematics course.
The Joint Mathematics Meetings, the “largest mathematics meeting in the world”, is co-presented by the American Mathematical Society and the Mathematical Association of America. To learn more about the JMM, click here. To see the Engaging Mathematics poster exhibited at the meeting, click here. Follow the initiative on Twitter at @MathEngaging.
Dr. Rikki Wagstrom, SENCER Leadership Fellow, associate professor of mathematics at Metropolitan State University, and Engaging Mathematics institutional partner, authored a chapter in the Mathematical Association of America’s recent book Doing the Scholarship of Teaching and Learning. Her chapter is titled “Using SoTL Practices to Drive Curriculum Development” and describes how SoTL, or the Scholarship of Teaching and Learning, influenced her Mathematics of Sustainability course development.
SENCER Leadership Fellow Jacqueline Dewar and Curtis D. Bennett edited Doing the Scholarship of Teaching and Learning. They provide the following commentary on Rikki’s chapter:
In this chapter, Rikki Wagstrom describes how she applied SoTL processes to aid in the development and evaluation of a new curriculum that integrated civic issues into a pre-requisite course for college algebra. She helps readers to understand several critical aspects of the process of doing SoTL by describing her approach to searching the literature and telling how her search led her to a useful model, one that prompted her to revise the site of her investigation and helped her re-shape her research question. She provides insights into the concerns that can arise in the selection of faculty to teach experimental and control sections, and the tough decisions that have to be made about how much data to collect.
For the Engaging Mathematics initiative, Rikki plans to develop four new modules for Mathematics of Sustainability. The modules will cover disappearing milkweed populations in the U.S. and the potential impact on Monarch butterfly populations, wind energy modeling and profitability, comparisons of greenhouse gas emissions generated by different automotive fuels, and the interplay between population growth in the U.S. and declining per capita carbon footprints. Each module will be a self-contained, portable unit suitable for use in college algebra, pre-calculus, and liberal arts mathematics courses.
To order a copy of the book, click here. You can follow Engaging Mathematics on Twitter at @MathEngaging.
What does it take to be outstanding at mathematical modeling, and how does modeling relate to real world issues across disciplines of study? For 16 years, teams of high school students and college undergraduates have competed in the Consortium for Mathematics and Its Applications’ (COMAP’s) Interdisciplinary Contest in Modeling (ICM) to find out.
COMAP recently published a book about the contest edited by Drs. Chris Arney and Paul J. Campbell. Chris is an ICM director, United States Military Academy math professor, and advisory board member for the Engaging Mathematics initiative. In addition to co-editing the book, Chris also wrote a number of the book’s chapters. Paul is a mathematics professor at Beloit College.
The book, titled The Interdisciplinary Contest in Modeling: Culturing Interdisciplinary Problem Solving, presents a history of the ICM, including descriptions of past problems, a list of outstanding teams, and commentary from participants, advisors, judges, and directors. Also included is advice on how to prepare a team for the contest and how to develop curricula on modeling, as well as discussions on the current state of interdisciplinary education. Wm. David Burns, the executive director of NCSCE and principal investigator for Engaging Mathematics, authored one of the book’s chapters on interdisciplinarity titled “‘Multidisciplinary Trouble’ and Learning: A SENCER Approach.”
In the book’s preface, Dr. Solomon Garfunkel, the executive director of COMAP and an Engaging Mathematics affiliate, writes:
All of us who do this work [of the ICM] appreciate mathematics for its beauty. But all of us also appreciate the power of mathematics to help us understand and deal with the complexities of our world. We are educators and we want our students to see knowledge not compartmentalized into a discrete set of disciplines, but with all of its interconnections.
For more information on the book, including instructions about how to purchase it, click here. Click here to register for the 2015 ICM.