O.R. 'BLOSSOMS' in high schools

By Richard C. Larsen

Imagine high school students in a math class – algebra, geometry, pre-calculus or calculus. And imagine that they have an entire class devoted to collaborative, experiential learning of some operations research application. What a wonderful way to encourage young people about the relevance of math and to attract young scholars to our profession! And, as explained below, we need your help!
Consider MIT BLOSSOMS – Blended Learning Open Source Science or Math Studies – a free online video-on-demand resource available for high school math, science and engineering classes ( BLOSSOMS is part of the new OER movement (Open Educational Resources), first started at MIT with its OpenCourseWare (OCW) program. The BLOSSOMS Web site provides interactive video lessons on STEM (Science, Technology, Engineering and Math) topics created by university professors and students, as well as high school teachers. BLOSSOMS is led by a team at MIT, with university and high school partners in Jordan, Pakistan and Lebanon, along with other U.S. universities and high schools. Right now there are 40+ lessons in the BLOSSOMS video library, and a number that will more than double during the coming year. These lessons will soon be mapped to the USA uniform “Common Core” high school educational standards.

We already have OR/MS applications. Consider “Taking Walks, Delivering Mail, An Introduction to Graph Theory,” a BLOSSOMS video by Dr. Karima Nigmatulina, an O.R. Ph.D. from MIT ( The lesson starts with Euler’s Seven-Bridges-of-Konigsberg Problem, introduces graph theory and then advances to the Chinese Postman problem. The video proceeds in short segments, each being five minutes or less. By the end of each segment, the video teacher (Karima) offers a challenge to the class, with all the students assumed to be sitting in their regular seats with the regular in-class teacher in charge. Then the video fades to black, is paused by the teacher, and class activities take over.

At the end of the first segment of Karima’s video, she challenges the class to find a solution to the Seven-Bridges-of-Konigsberg Problem – find a path that starts and ends at one location and crosses each of the seven bridges exactly once. In a video teacher’s guide, Karima suggests to the in-class teacher that she/he divide the class into four groups, give each group a map of Konigsberg with its bridges (a pdf downloadable file), and the teacher promises a reward to the student team that first finds a solution. Of course, there is no solution! But the students at this point are engaged, frustrated and want to learn more. That is exactly where you want them!

At that point, the in-class teacher starts the second video segment, and Karima introduces basic notation and concepts of graph theory and explains the degree of nodes, odd and even, and how that relates to the problem at hand. This segment later fades to black with another challenge to the students. And so on and so on.

We call this non-lecture interactive pedagogy a “Teaching Duet.” It usually involves much experiential collaborative learning. Already high schools have contacted us, telling us that they plan to use Karima’s BLOSSOMS video to introduce students to discrete math, a subject that apparently they fall asleep over via more usual teaching methods. Karima’s video requires two, full in-class sessions to complete, though the teacher may choose to select only portions for a one-hour experience.

We have other O.R.-related BLOSSOMS videos, such as two in geometrical probability at a level appropriate for high school students who have not formally studied probability. Consider Professor Gil Strang’s video on random triangles He asks, “Of all random triangles, would you be surprised to discover that over 50 percent are obtuse vs. acute?” And then, in Teaching Duet mode, he and the class – together – discover the true fraction of random triangles that are obtuse. I do the “Broken Stick Experiment,” where I select two random numbers scaled over the length of a yardstick, mark the yardstick with chalk at the two selected random points, and then take out a scary saw to cut the yardstick into three pieces ( The question is, “Before we do this experiment, what is the probability that we can configure the three pieces of the yardstick to create a triangle, with each piece being a full leg of that triangle?”

MIT Professor Arnie Barnett and MIT O.R. doctoral student Anna Teytelman provide a final example of OR/MS-related BLOSSOMS video. They ask, “Is Bigger Better? A Look at a Selection Bias that is All Around Us” ( I leave it to you to discover the content of their video and whether Anna and Arnie should be nominated for Academy Awards!

In the pipeline, we have BLOSSOMS OR/MS-related videos planned for Little’s Law, the Diet Problem and Voting Methods. But we need many more associated with O.R. And here is where you come in. In addition to our formal partners, we have BLOSSOMS video creators from Teachers Without Borders, from other U.S. universities and even from as far away as Singapore. We need the world to design and create BLOSSOMS video modules. We welcome your participation. If you think you may be interested and have an idea related to the application of some O.R. concept that is suitable for a high school math class, please send me a no-obligation e-mail with your idea. We can start a dialogue and move from there. Who knows, six months from now you may be located next to Arnie Barnett’s video with Anna Teytelman – in our ever-increasing BLOSSOMS video repository. And you could influence the lives of thousands of young people worldwide.

Richard Larson ( is the Mitsui Professor for Engineering Systems and the director of the Center for Engineering Systems Fundamentals in the Engineering Systems Division at the Massachusetts Institute of Technology.