Photo Credit: Jenn and Tony Bot (CC BY-NC 2.0)

Engaging Mathematics Co-PI Hosts Webinar on A Future Shared with Robots

Should insurance companies be allowed to use your purchasing history to set prices on your policies? Should self-driving cars be allowed on public roads? What are the implications of robotic police?

These are some of the questions Frank Wattenberg explores during his webinar, Robotics and Artificial Intelligence – Shaping a Future Shared with Robots. Frank is a professor in the Department of Mathematical Sciences at the United States Military Academy (USMA) and a Co-Principal Investigator of NCSCE’s Engaging Mathematics initiative.

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 ( and Matt ( invite you to email them with questions about using robotics and artificial intelligence in the classroom, or to continue the discussion further.

Photo credit: Jenn and Tony Bot (CC BY-NC 2.0)

Engaging Mathematics Leads Hands-On Session and Delivers Plenary Address during 15th Annual SSI

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:

Download (PDF, 101KB)

Engaging Mathematics Advisory Board Member Co-Edits Book on Mathematical Modeling and Interdisciplinary Education

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.

Photo credit: Tom Brown