Creating Momentum Through Communicating Mathematics

By Matthias Beck, San Francisco State University, and Brandy Wiegers, Central Washington University

Given five minutes, can you turn to the person next to you and describe your research? How about over 15 minutes in front of a class of 10th graders? Thinking of one of your research graduate students, how would you prepare her/him to make such an activity equally beneficial for her/him and the 10th graders? For many of us, these are skills only nurtured through conference talks and time within the profession. The SF-State (CM)²: San Francisco State University Creating Momentum through Communicating Mathematics program worked to change this, creating a program that developed mathematics graduate students who could have this conversation and were better engaged in why they were studying mathematics and what role they wanted to have in the future of our profession. As an NSF GK-12 program, (CM)2 ran from 2009-2014, working with master’s level students in mathematics to engage them in mathematical discourse while also supporting their research and professional development. Over the course of the five-year program, a total of 43 SF State mathematics graduate students were involved in the project, spending considerable time and energy on K-12 activities in 13 schools in the greater San Francisco area. A key goal was to strengthen the graduate students’ communication, teaching, outreach, and teamwork skills by immersing them in mathematics classrooms and the San Francisco Math Circle. A second key goal was to make mathematics, especially algebra, and its career connections more relevant and explicit for 6-12th grade teachers and students. This post will share successes, lessons learned, and resources for you as a faculty member to build aspects of outreach, teaching, and professional development programs for your own students.

(CM)2 provided funding support for nine Ph.D.-bound graduate students per year, with the understanding that these students (the “Fellows”) would work 10 hours per week in an education-related environment. A lot of work went into preparing these students for that experience, with a year-long schedule starting with bi-weekly summer workshops focused on research and applying for Ph.D. programs, culminating in a two-week intensive training to prepare graduate students for the classroom. We reinforced the lessons from the summer throughout the year with weekly graduate student meetings and larger monthly meetings of graduate students with their partner K-12 teachers. Our goal was to ensure that the graduate students spent the summer focused on making research progress prior to the intensive school-year schedule. The partner teachers attended the second half of the two-week training, meeting their mentor students and starting to create lessons and schedules for the upcoming year.

At the first workshop, (CM)2 Fellows were asked to turn and explain their research to the student sitting next to them. Their goal was to prepare a lesson for middle/high school age students to help them learn about the graduate student’s research, and the first step in this process was to describe their work to a colleague at the same academic level. This was a struggle, as everything you might expect happened with the biggest issue being Fellows’ use of precise language specific to their area of research. They were so focused on showing how much they knew about their field that they failed to concentrate on communicating their work in context. When first presented with the exercise, the Fellows struggled, but with practice their explanations were more prepared for a K-12 classroom. From there we scaffolded the progression by having the graduate students explain their work to their mentor teachers, whom they would be spending the majority of their classroom work time with. This mentor team then worked for several workshop days to create a 15-minute sample lesson to share with the group of 9 mentorship teams. With feedback from the other graduate student and teachers, they worked over the next year to create grade-level appropriate mathematics activities that were related to their academic research. Over the year, the Fellows further developed these into 5-10 page lesson plans with an introduction to the mathematical content, an overview of the lesson structure and directions for implementation, worksheets, and a summary of how the lesson went, including recommendations for the future. These mathematics lessons were developed, shared between partnership teams, and papers to accompany them were posted online; you can still see many of these lessons at http://math.sfsu.edu/cm2/materials.php. Development of the lesson into such a report furthered the Fellows’ mathematical communications skills with writing practice.

Creating this lesson plan wasn’t the only aspect of the (CM)2 program. Once classes started, the graduate students quickly fell into a routine of weekly commitments, which included 10 hours of GK-12 student interaction (in class and at Math Circle), a one-hour GK-12 seminar, their own coursework and research, and continued work on their Ph.D. applications. Several of the fellows completed NSF graduate research fellowship proposal (GRFP) applications while participating in the fellowship program.

San Francisco Math Circle (SFMC) was key to the success of the (CM)2 program, providing the ideal stepping stone for graduate students to get involved with mathematics activities for middle and high school students. The program had been set up so that the graduate students worked in some of the schools we were using for our satellite programs (including Mission High School, Thurgood Marshall Academic High School, Lowell High School, and June Jordan School for Equity). While in the classroom, the graduate students created a mentorship relationship with the younger students whom they encouraged individually to attend Math Circle. The graduate students then served as instructors at the high-school Math Circle programs. We believe this improved the quality of instruction at the high-schools programs because the graduate students had the opportunity to incorporate more of their research into their Math Circle presentations and were better able to moderate their presentations for the correct level of students based on their experience in the classrooms of the students they were working with. In addition, the (CM)2 program sponsored nine teachers who were involved in the Math Circle. Overall, partnering with the (CM)2 program helped SFMC address not only the challenges in maintaining the diversity of the students in the Circle, but also that of increasing the number of qualified teachers willing to participate in a Circle with the students.

The dichotomy of our Fellows’ work, including both in-class and out-of-school Math Circle experiences, provided an informed balance that helped them become better mathematicians and teachers. The in-class work provided a model for how to work with students of this age, giving reinforcement to expectations of behavior and any aspects of student discipline. Here are three sample testimonies from Fellows that show the diversity of experiences and highlights this program provided for the participating graduate students:

“I’m serious about becoming an educator. Readings and discussions in 728 were terrific, and I learned more about teaching from working with […] than I did last year teaching on my own. My work at […] and SFMC were more valuable to me than the paychecks..”

“(CM)² has also enhanced my preparation to enter the Ph.D. programs. Being in this program has increased my confidence and excitement to start my Ph.D. program through the support from Matt and Brandy as well as the teachers and other fellows. In addition, the financial support has opened up opportunities by removing financial barriers […] As an underrepresented minority, this program has given me so much in terms of academic support, encouragements, and resources. Through (CM)², I have become more aware of the low numbers of underrepresented minorities in higher education and I’m ecstatic to be a role model to others.”

“In all honesty, I was not interested in working in the high school or in math circle to begin with but obviously took this fellowship for financial and moral support. Now, I’m looking sadly at the end of my time working at […] High and with […] and […] and the other teachers. I’ve learned so much, even if I never teach again, well, I may start up my own math circle someday, but even if I don’t, it has been a very personally rewarding experience.”

The out-of-school work provided creative outlets for the graduate students to discuss their research and higher level mathematics that didn’t need to be connected to curriculum goals or other K-12 benchmarks. We also saw success reflected in comments we received from partner teachers:

“Having another person in the room with deep math knowledge is good for the students and definitely helps with the amount of material covered. As to my pedagogy, I’m sure it has had an effect but I haven’t tried to define what it is. It has caused me to think more about what engages the students. I tend to push moving through the concepts, but now I am thinking more about ways to get the students involved. I don’t believe this necessarily has to be a show of how the concepts are relevant to the students lives. Coming up with intriguing problems where the students don’t feel shut out and turn off because of prior assumptions of them having a particular skill set seems to work well. Just having someone for me to interact with intellectually has been good, and I think it will help in improving course content.”

“Having another pair of knowledgeable eyes in the classroom has pushed me to think about and to be able to articulate what my motives and intentions are for each lesson. […] is always thinking beyond the math concept to its implementation and I have benefited from his sharing his insights. Also, the students love it when we come up with different interpretations on a topic.”

Our GK-12 program provided us with an invaluable opportunity to create a community of scholars, from elementary students to university faculty — vertical integration at its best. Working with our graduate students, their partner teachers, and their K-12 students was both great fun and an interesting challenge; everyone could learn something from the other participants (and that most certainly included us). We are somewhat heartbroken that the NSF cut the overall GK-12 program. The impact of our program went beyond the students; e.g., the San Francisco State mathematics department continues to offer a graduate-level writing-in-the-discipline course, which was initially developed as part of (CM)2. Some of our current graduate students continue to be involved in the San Francisco Math Circle, including teaching and leadership positions. We hope we’ve inspired you to bring an aspect of this or a similar program into your work and encourage you to contact us for further information. Finally, we thank the graduate students and teachers who we worked with for their contributions and support of our program.

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1 Response to Creating Momentum Through Communicating Mathematics

  1. Avatar Jacob Koczwara says:

    I think it extremely invaluable to discuss mathematics with younger students. High school level students that have an interest in mathematics but aren’t necessarily sure that’s what they want to do with their lives should be pushed towards the field. To continue progress with mathematics and expand our understand of the field itself and to expand our understanding of the world around us we need fresh minds and new perspectives. New students who are interested in mathematics are critical for this to continue. While the current mathematicians and professors are continuing to expand the field a large number of new minds studying and expanding the field would be invaluable. This is because with new perspectives we can continue to push the boundaries of what we know and what we understand. What we know and what we don’t know will be expanded with these new minds. We never know who will be the next Newton or the next Gauss. Young students and their minds are our most valuable resource to continue pushing the boundaries of the field of mathematics and if we can interest them in pursuing careers in mathematics that would be amazing. These able new minds might give us invaluable insists into our universe and the world we live in and that would be invaluable to the field of mathematics and the human race in and of itself.

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