How do you help students and teachers become passionate about mathematics? You put them in a circle. "A Math Circle, that is," says Associate Professor of Mathematics and Mathematics Education, Diana White.
Math Circles engage mathematics professionals in providing K-12 students and their teachers with informal opportunities to explore, create, and communicate substantive mathematics; increase their problem-solving skills; and develop or deepen enjoyment of mathematics. The program focuses mainly on middle-school teachers, with additional workshops for elementary and high school teachers, and to date over 450 teachers from dozens of school districts across the state have participated in Math Circles at CU Denver.
White has directed the Rocky Mountain Math Teachers' Circle since 2010. While there are now over 100 Math Teachers' Circles across the country, the CU Denver program is one of the ten or so oldest and most well-established, having now hosted more than a dozen summer workshops and over 50 academic year sessions for teachers. During the 2016-2017 academic year alone, White and her team's regular, monthly Math Teachers' Circle sessions reached approximately 100 teachers from 28 school districts across Colorado. In total White approximates 150 contact hours with teachers in 2016. Adding to the impact, White says that over 75% of the participating teachers are from high-needs districts. Conservatively estimating that each teacher involved in Math Circles reaches 100 students per year, White estimates that well over 90,000 local K-12 students have been impacted by the program since 2010.
Problems that teachers' explore are taken from all areas of mathematics and generally easy to state and access, but can lead to advanced mathematics. Most problems are ones that even mathematicians would struggle to answer quickly, and the focus is much more on the process of exploration than on finding a specific answer.
"With the advent of the Common Core, many teachers are being asked to teach mathematics in ways that differ significantly from how they learned, and to facilitate mathematical habits of mind in their students that they themselves may not have had the opportunity to develop. Math Teachers' Circles provide an opportunity for teachers to experience mathematical problem solving as learners," White notes. "They learn to embrace the struggle inherent in the inquiry-process, to be okay not knowing an answer right away, and to enjoy and value the process of exploring mathematics as open-ended discipline full of new discoveries."
While the program began for teachers, those same teachers soon wanted to offer similar enrichment opportunities for kids. This led to teachers from the Math Teachers' Circle leading Math Circles for students. In this context, two teachers led sessions over 70 contact hours with students last year. In the fall, RMMTC hosted its second Julia Robinson Math Festival (JRMF) on the CU Denver campus for 196 students from 5 schools across the greater Denver metro area, and this spring the group co-hosted a JRMF for approximately 80 kids at Franktown Elementary School.
Not satisfied to keep her influence local, White lets her impact with Math Circles ripple out across the nation. Since late 2014, she has directed the National Association of Math Circles (NAMC), a program of the Mathematical Sciences Research Institute that provides training, resources, and support to the more than 200 Math Circles across the country. As part of an ongoing NAMC Math Circle - Mentorship and Partnership Program, White organized and co-facilitated a three day workshop at CU Denver the past two Septembers. Together they trained 39 novice Math Circle Leadership Teams on the academic and administrative components of leading Math Circles, bringing together a total of over 80 mathematicians and educators from around the country. White also co-organized the Fall 2016 Circle on the Road Conference for approximately 100 Math Circle and outreach leaders. White travels frequently to lead other Math Teachers' Circles around the country and mentor their facilitators.
White also conducts research and evaluation, give presentations, and write papers related to Math Circles. In the past seven years, White has published more than twelve papers, given 32 national and one international presentation related to Math Circles, and presented 14 times at other Math Teachers' Circles across the country. She's also been PI or co-PI on over $840,000 of external funding related to Math Circles–including 2 NSF and 2 NSA grants and a wealth of funding from national and professional organizations and foundational funding.
"These efforts all impact our potential pipeline of future undergraduate students, and fall under the CU Denver mission to apply knowledge to improve the health and well-being of Colorado and the world, and our vision to be a leading public university with a global reputation for excellence in learning, research and creativity, community engagement…" says White.
White spoke to Education Week in 2016, giving these extended comments on the program:
Education Week: So what goes on during a math circle?
Diana: Mathematics professionals lead sessions with either K-12 students or teachers that really focus on the process of doing mathematics, on mathematical problem solving, and on understanding mathematics as a discipline of inquiry where you're conjecturing and communicating and exploring mathematics with other people as opposed to, like in a lot of school mathematics, you're often just learning set procedures. This is really more like a mini-mathematical research experience where you're learning to do mathematics just like a mathematician would, only obviously the people learning it don't have the same massive background with math coursework, and so they're doing it at a level that's appropriate to the background that they do have.
Education Week: How does a math circle differ from a traditional K-12 math class?
Diana: In a typical K-12 math class, there's set content that a teacher is responsible for covering at a given grade level. Whether that aligns with the Common Core State Standards or whatever state standards their state happens to be using, there's specific content and benchmarks for each grade. In a math circle, the focus isn't on any particular content per se but much more about the process of doing mathematics and solving mathematical problems. So it can be taken from content that wouldn't typically be seen in K-12 mathematics. You might see some stuff with number theory or cryptography or other areas of geometry that aren't done in K-12 mathematics typically.
Education Week: Can an average or below-average math student benefit from a math circle?
Diana: Just testing at an average or below-average level isn't necessarily a real indicator of that student's creativity or that student's potential in mathematics. That could be a reflection of the mathematical experiences they've had to date much more so than aptitude or what they could develop into.
To find out how to donate to the Rocky Mountain Math Teachers' and Students' Circles Funds click here. Teachers and students interested in learning more about Math Circles on the Auraria Campus can find more information here. The 2017 Summer Math Teachers' Circle Workshop will be held in Durango, CO from June 12-16, 2017! For more information, click here.