EDUCATIONAL IMPACT OF REUT (RESEARCH EXPERIENCES IN MATHEMATICS FOR UNDERGRADUATES AND TEACHERS) PROGRAM IN CALIFORNIA STATE UNIVERSITY, CHICO
FOMIN, SERGEI
CALIFORNIA STATE UNIVERSITY, CHICO
DEPARTMENT OF MATHEMATICS AND STATISTICS.
Prof. Sergei Fomin
Department of Mathematics and Statistics
California State University, Chico.
Educational Impact of REUT (Research Experiences in Mathematics for Undergraduates and Teachers) Program in California State University, Chico
Synopsis:
Within the last 11 years, we have completed three very successive REUT programs funded by NSF. Our programs targeted secondary teachers with a strong interest in mathematics or math education and students who have completed their junior year. The participants were engaged in research problems with a high potential for publication and to create a research experience that broadens participants’ perspective both of mathematics as a discipline and of research as an exciting exploratory process.
Educational Impact of REUT (Research Experiences in Mathematics for Undergraduates and Teachers) Program in California State University, Chico.
Sergei Fomin
Department of Mathematics and Statistics, California State University, Chico, Chico, CA
Abstract
Within the last 11 years, we have completed three very successive REUT programs (2004-2006, 2006-2010, 2012-2016) funded by NSF. Our program targets secondary teachers with a strong interest in mathematics or math education (RET) and students who have completed their junior year with coursework appropriate to the research project (REU). From both populations, we recruit members of underrepresented groups. Our program is designed to engage participants in research problems with a high potential for publication and to create a research experience that broadens participants’ perspective both of mathematics as a discipline and of research (whether mathematical or not) as an exciting exploratory process. By doing so, we hope to achieve the following specific objectives:
- Encourage undergraduate students, especially those from underrepresented groups, to pursue careers in sciences and engineering, including teaching.
- Help to better prepare students to pursue advanced degrees and careers in the sciences.
- Provide in-service teachers with a research experience that will foster excitement about mathematics, increase content understanding, and inspire pedagogical innovation in their classrooms.
- Promote and enhance mathematical research involving undergraduates at CSUC. We feel that both teachers and undergraduates benefit from working together on a research team. Participants develop connections not only with faculty but also with participants who have very different backgrounds, experiences, and career paths. Students have the opportunity to develop a direct relationship with a math educator; they benefit from the experience teachers have in communicating mathematical ideas and may be inspired to consider the possibility of teaching as a career. Secondary teachers also benefit from the experience of close contact with outstanding undergraduates and see firsthand what some of their current students will be doing in a few years. Both populations benefit from their complementary mathematical backgrounds, which allow them to help one another in their research exploration. A teacher’s broader mathematical experience can provide the insight to make a conjecture, while a student’s recent exposure to college-level mathematics could provide the specific tools to “make the epsilons and deltas work.” We provide a research experience that enhances the skills necessary for careers in any of the sciences, while adding both depth and breadth to the participant’s mathematical knowledge, skill, and understanding. The depth comes primarily from participation in a research team working on a potentially publishable research problem, while breadth is added by activities that integrate all research teams, by in-service teacher/undergraduate interactions, and by synergistic activities such as weekly research talks. Mathematical activities are supplemented with social activities conducive to creating a productive and comfortable research environment.
Introduction
Within the current REUT grant we have completed the REUT summer programs in 2012- 2015 and obtained one year no-cost extension until April 2016. Prior to the current grant we had very successful grants that supported twelve participants for each of 2004 to 2010. Our program targets secondary teachers with a strong interest in mathematics or math education (RET) and students who have completed their junior year with coursework appropriate to the research project (REU). From both populations, we will recruit members of underrepresented groups. We include about three students from CSUC each year; the remainders are recruited externally. Teachers are recruited primarily from CSUC’s service region which is roughly the size of Ohio and contains over 650 schools in 165 districts.
Our program is designed to engage participants in research problems with a high potential for publication and to create a research experience that broadens participants’ perspective both of mathematics as a discipline and of research (whether mathematical or not) as an exciting exploratory process. By doing so, we achieve the following specific objectives:
- Encourage undergraduate students, especially those from underrepresented groups, to pursue careers in sciences and engineering, including teaching.
- Help to better prepare students to pursue advanced degrees and careers in the sciences.
- Provide in-service teachers with a research experience that will foster excitement about mathematics, increase content understanding, and inspire pedagogical innovation in their classrooms.
- Promote and enhance mathematical research involving undergraduates at CSUC. Both teachers and undergraduates benefit from working together on a research team. Participants develop connections not only with faculty but also with participants who have very different backgrounds, experiences, and career paths. Students have the opportunity to develop a direct relationship with a math educator. Students also benefit from the experience teachers have in communicating mathematical ideas and may be inspired to consider the possibility of teaching as a career. Secondary teachers benefit from the experience of close contact with outstanding undergraduates and see firsthand what some of their current students will be doing in a few years. Both populations benefit from their complementary mathematical backgrounds which enables them to help one another in their research exploration. A teacher’s broader mathematical experience can provide the insight to make a conjecture, while a student’s recent exposure to college-level mathematics could provide the specific tools to “make the epsilons and deltas work.” CSUC is an ideal location for hosting a combined REUT. The goals of the REUT mesh closely with CSUC’s mission statement, and hence there is strong institutional support for such a program. In particular, teaching is the institution’s primary mission and CSUC embraces a teacher/scholar model in which the main purpose of research is to improve the undergraduate experience. Through the initial grants the participating faculty have gained experience in directing summer research and seen that, not only does this add life to their own research programs, it also benefits our students and department. Inspired by their example, other faculty members are including students in their research projects. Moreover, our REUT plants the seeds for the future by providing our newest faculty members with the chance to work with undergraduates in their first few years at CSUC. In this way, continued funding of our site enhances diversity by simultaneously serving two NSF-defined underrepresented populations, namely, faculty and students at an undergraduate institution.
Another guiding mission for CSUC is teacher preparation and support of the K-12 community. Many high school mathematics teachers in CSUC’s large rural service area already have strong ties to the department and college. The majority of early-career teachers received their B.S. or credential at CSUC. The university is also a home to the Chico Mathematics Project (CMP), which is charged by the State with providing professional development for in-service mathematics teachers at all grade levels. In addition, CSUC has a Master’s program in mathematics education, populated entirely by in-service mathematics teachers who attend the program during three consecutive summers. Several of the fifteen teachers funded through the previous REUT grants have connections with these programs. In fact, three of the fifteen completed Master’s theses based on their REUT research and a third is an alumnus of our Master’s program. Thus, our REUT fits strongly within the teacher-scholar model and complements and extends the broad range of mathematical activities occurring in Chico during the summer.
Nature of Participant Activities
We provide a research experience that enhances the skills necessary for careers in any of the sciences, while adding both depth and breadth to the participant’s mathematical knowledge, skill, and understanding. The depth comes primarily from participation in a research team working on a potentially publishable research problem. The breadth is added by activities that integrate all research teams, by in-service teacher/undergraduate interactions, and by synergistic activities such as weekly research talks. Mathematical activities are supplemented with social activities conducive to creating a productive and comfortable research environment.
In both academic and industrial positions, scientists and mathematicians are expected to be able to think critically and independently and they are also expected to participate as part of a team. We believe that an REUT experience at CSUC allows participants to hone their own organizational, communication, and critical thinking skills while simultaneously learning how to work as part of a research group. Each summer we organize our REUT participants into three research teams, each of which will include one in-service teacher. Each participant is expected to work both individually and as a contributing member of his or her research team.
Team Activities: We help the participants progress from dependent learners to independent investigators by modeling and explicitly discussing Polya’s four stages of problem- solving: understanding the problem, devising a plan of attack, carrying out the plan, and reflecting on the work. Our activities are structured to facilitate the smooth progression from one stage to the next at a pace appropriate to the competence of each participant.
Following that model, in the initial stage, each research team leader offers a mini-course related to the team’s mathematical focus area. This allows the team leader to give participants relevant background material, introduce computer software, evaluate the competence of each participant, foster a supportive team environment, and in general ensure the group has the necessary tools to carry out the research project. The team leader concurrently introduces open research problems and students are encouraged to begin their own exploration right away. As a first step towards independence, the team selects their research problem. At this point they are given research/expository articles to read in order to better understand their problem. The articles are then discussed in a group setting. These informal discussions help the faculty member ensure that the whole team “understands the problem” and is thus ready for the next stage.
In the second stage, the faculty member takes a step back and gradually moves from group director to group member. The team is responsible for “devising a plan of attack,” which includes developing research directions and allocating responsibilities. The faculty member contributes to discussions and helps guide the group in fruitful directions without imposing his or her own ideas. He also ensures that each individual is contributing to the development of the team’s plan and has a reasonable share of the responsibilities in carrying out the attack. This stage culminates in a presentation of the team’s research problem and plan of attack.
In the third stage, the faculty member steps back even further. Having helped guide the group in the development of a plan, the faculty member now allows the group to carry out that plan with minimal assistance and acts primarily as an advisor as the team becomes self-sufficient and takes ownership of all aspects of their particular problem. Here, both teachers and undergraduates are confronted with their lack of experience in doing mathematical research. They can help each other to overcome this hurdle and learn to be independent mathematical explorers.
In the fourth and final stage the group “reflects” by jointly authoring a written report and preparing a presentation on their research including: a clear statement of their problem, their plan of attack, any obstacles which were encountered, results they obtained, and perhaps directions for further investigation. In this stage the faculty member’s role is primarily to give advice and answer questions that may arise. The reflective stage often continues after the term of the REUT as students work with their team leader to revise a manuscript for publication and prepare to present their research at professional conferences.
Synergistic Activities: Fostering an appropriate research environment is an important part of our program. A successful research team consists of participants who have the following characteristics: they are comfortable expressing their ideas, they aren’t afraid of looking foolish they feel they can disagree with other team members, and they know each other. Social interactions are thus an essential component of our REUT program. Space for all participants is reserved at special apartment style dorms on campus to facilitate ongoing unstructured social interaction. Social contacts are further cemented through a weekly series of lectures by prominent invited speakers, each followed by a dinner or reception, and some other social event such as a movie, bowling, or a visit to the Thursday Night Farmer’s Market.
We would like our participants to gain not only a deep understanding of a mathematical focus area, but also to develop breadth in their mathematical knowledge and experience. To this end we feel it is important for the three research teams to interact not just socially, but also mathematically. All participants are expected to attend talks given by other participants and the six-week term ends with a full group discussion of the experience.
The research environment at CSUC is particularly well suited to a research program for undergraduate students and teachers. There is a strong tradition of undergraduate research. In addition to serving as an REUT site since 2004, as a founding member of the MAA’s NREUP program we have hosted a total of fifteen undergraduate researchers from underrepresented minority groups since 2003. Local students also participate with funding from CSUC “Research and Creativity Awards.” Students from these programs have made numerous presentations at national and regional conferences and published several papers as detailed in our results section. Participants complete the program with a substantial written paper and make oral presentations to an audience that includes eminent guest speakers. Past guests include researchers like Robion Kirby of UC, Berkeley, Joel Hass of UC, Davis, and Konstantin Kornev of Clemson University, Laurent Pilon of UC Los Angeles, etc.
CSUC also has a strong tradition of externally funded and innovative programs for teacher preparation and professional development. The more than thirty teachers in our summer Master’s program are inspired by the example of Brooke Kennedy and Joel Pyzer who completed their Master’s theses based on research carried out during their RETs with us. The multiple multi-week summer institutes for over 100 teachers every year of the Chico Math Project provide another excellent venue for integration of the REUT into a broader range of mathematical activities occurring in Chico during the summer.
Recruitment and Selection
Normally, our summer projects are accessible to juniors and high-school teachers are also comfortable with this level of math requirement. Our experience shows that six weeks program is sufficient for participants to resolve a well-chosen research problem. At the same time, this time frame is short enough to accommodate high-school teachers who typically have shorter summer recesses. Our past students have been very active in publishing and presenting REUT results which demonstrate that the six week time frame has been successful. Moreover, faculty mentors are committed to providing mentoring during the following academic year. We are rather successful in recruiting participants from underrepresented groups as well as from colleges where STEM opportunities are limited. We are close to 50 percent participation both for women and underrepresented minority groups in our REUT.
In running the NREUP programs we have pursued several avenues for recruiting students from underrepresented groups including, for example, advertising our program at the web site of the Society for Advancement of Chicanos and Native Americans in Science. Our most effective recruiting tool is a direct appeal to undergraduates at nearby institutions such as UC Davis, UC Berkeley, and Stanford. To increase participation, we also directly approach our sister institutes such as CSU, Monterey Bay and CSU, East Bay that have a very diverse student body. We note that, as one of the founding sites of the NREUP program, CSUC has acquired a reputation as a summer destination for students from underrepresented groups such that faculty frequently refer minority students to us without specific efforts on our part. For these reasons, we are confident that we can carry through on our commitment to greatly increase the already healthy level of participation of women and minority students in our summer research programs.
By holding three positions each year for CSUC students, we also guarantee representation of another NSF-defined underrepresented group, namely students of an undergraduate institution. We regularly have a large proportion of our students from non- research institutes.
We have also had no difficulty in attracting qualified teachers to our program, receiving four applications for each available position. In recruiting teachers, we have taken advantage of CSUC being renowned as a summer destination for teachers through the Chico Math Project (CMP) and the summer Master’s program for in-service teachers. Each year we send applications to every teacher in the CMP database of 650 schools in our service area as well as all alumni and students of the Master’s program. As is clear from the comments above, past participants are also our best recruiters.
These specific recruiting efforts are complemented by a web site with information for prospective participants. To apply, students submit letters of recommendation from faculty members, transcripts, and a personal statement describing why they are interested in the program. Teachers are also required to submit statements and CV’s.
Intellectual Merit of REUT
In addition to facilitating the solution of research problems in mathematics we provide a model for the integration of research experiences of teachers and undergraduates. The program assessment gauges the success of this model by measuring not only the impact on career decisions of undergraduate participants, but also the major changes in participants’ perception of research in general and mathematics in particular. Methods for measuring this impact on participants’ mathematical world-view are of interest not only to the NSF, but to science and mathematics educators. As such, this program fits into CSUC’s strong tradition of externally funded and innovative programs for teacher preparation and continuing education in mathematics. Moreover, it builds on the department’s history of involving undergraduates in research.
Broader Impacts of REUT
This project supports two significant NSF guiding strategies. First, the integration of research and education is carried out at several levels. Not only are students involved in research, but also high-school teachers and CSUC faculty are provided with an example of how to integrate research activities into the teaching and learning of math. By structuring our program after Polya’s steps for problem solving we are disseminating an effective pedagogic approach to mathematics education. Second, the project also serves to broaden the participation of underrepresented groups through specific efforts to recruit women and underrepresented minorities.
Further, the REU/T at Chico will promote faculty research programs and also open avenues for the inclusion of undergraduates in those programs, thus simultaneously serving two NSF-defined underrepresented populations, namely faculty and students at an undergraduate institute.
Acknowledgements
The author would like to acknowledge the significant contribution of Dr. Thomas Mattman and Dr. Kathy Gray to the success of the program. The author would like to acknowledge the National Science Foundation for support of this project (NSF DMS Award # 1156612).