无忧视频

Teachers Prepared to Inspire with Math Modeling

Give two kindergartners 10 apples and ask them to divide the fruit between themselves.

They may divide the apples equally with each getting five. Or, maybe one child is hungry, so that child gets more. Or, they may each take one and save the remaining eight to share with family and friends.

One of the key lessons learned by K鈥�6 teachers participating in 无忧视频鈥檚 IMMERSION program (Integrating Mathematical Modeling, Experiential-learning and Research through a Sustainable Infrastructure and an Online Network) is that there is seldom just one answer; the diversity of answers depends on the students themselves and how they decide to approach the problem.

For the past four summers, the College has been hosting cohorts of 24 teachers from the Pomona Unified School District (PUSD) for a weeklong professional development program. It鈥檚 part of a ground-breaking national study to examine how intensive training can affect elementary school teachers鈥� use of mathematical modeling in the classroom. The study was funded by a $1.3 million grant from the National Science Foundation.

With mathematical modeling鈥攖he process of taking an open-ended, multifaceted situation, often from life or the workplace, and using math to solve it鈥攖eachers can involve students in every step of the process, from formulating questions designed to resolve a problem relevant to students鈥� personal lives or communities to deciding what tools to use and what assumptions to make in order to find the solution(s).

鈥淓veryone can do mathematical modeling from the earliest ages in the same way that everyone can start learning a language from the earliest ages,鈥� said Rachel Levy, a former 无忧视频 (HMC) professor of mathematics who is overseeing the IMMERSION study along with colleagues at George Mason University and Montana State University.

Several teachers attending the IMMERSION program at HMC this summer, shared that their students were more confident in their math skills, more engaged, had a better grasp of math vocabulary and worked better in groups. Teachers here and at the other program sites cited positive results across a broad spectrum of abilities, including special education and advanced students as well as those with limited English proficiency and the economically disadvantaged.

Laura Pahler, one of five lead teachers participating at the Claremont site this summer, said mathematical modeling provides opportunities to use the existing math curriculum as a starting point and then go in a different direction.

鈥淚nstead of limiting students to word problems that may not be relevant to them and they don鈥檛 have any interest in solving, they can see problems in the community that math can help address and find a solution,鈥� Pahler said. 鈥淵ou can get ideas from the textbook but adapt it. It鈥檚 the same math, you鈥檙e just changing the context to make it relevant to them.鈥�

In addition to intensive professional development training during the summer, IMMERSION participants meet regularly in groups during the school year to collaborate with returning IMMERSION participants who serve as lead teachers then come together in late fall to participate in a conference at Harvey Mudd.

Marka Carson, another lead teacher, said her students begin to see math as useful in real-world applications.

鈥淭hey learn that math is not this thing you do in isolation in the classroom and something to endure until math period is over,鈥� Carson said. 鈥淚t鈥檚 a skill we use in our personal lives and in the professional realm.鈥�

PUSD has agreed to incorporate mathematical modeling training as part of its annual summer institute in an effort to ensure that all students experience mathematical modeling throughout their K鈥�12 education. From the start of the program, PUSD and HMC administrators have closely cooperated to make the effort a success. 鈥淲ithout the support of Lilia Fuentes and Grace Greenleaf at PUSD and Gabriela Gamiz, director of community engagement at HMC, this program could not have succeeded,鈥� said Levy.

Several lead teachers are writing up their findings from the IMMERSION experience, including chapters on how to use mathematical modeling in kindergarten and what students are doing when they are modeling. The PUSD teachers have presented their work at national mathematics and mathematics education conferences and have been invited to lead professional development for other teachers.聽 They are also developing a handbook about mathematical modeling for PUSD school principals.

Levy, who is now deputy executive director of the Mathematical Association of America (MAA) in Washington, D.C., is working with the teachers and will return next summer to work with the district.

鈥淭he mission of the MAA is to advance the understanding of mathematics and its impact on the world,鈥� Levy said. 鈥淭hat鈥檚 exactly what mathematical modeling is about. Mathematical modeling helps students make connections between mathematics and the world.鈥�