CHAMPAIGN, Ill. - In a unique research project funded by the National Science Foundation, education professor Gloriana González at the University of Illinois is developing animated cartoons to help geometry instructors become better teachers.
A group of high school teachers from high-need schools will use the cartoons to learn strategies for recognizing students' prior knowledge and building upon it in mathematics instruction.
Educators have found that students' approaches to solving mathematics problems may be very different, influenced by the various forms of prior knowledge they have - including their knowledge of mathematics concepts, their unique backgrounds and experiences, and the contexts of the problems.
Titled "CAREER: Noticing and Using Students' Prior Knowledge in Problem-Based Instruction," the project is funded by a grant of more than $850,000 from the NSF's Early Career Development (CAREER) Program.
Considered some of the agency's most prestigious awards, the CAREER grants support the work of researchers who effectively integrate research and education within their organization's mission.
"Students' prior knowledge, or 'funds of knowledge,' includes ways of doing mathematics that may not be publicly recognized because students draw upon their experiences within their family, cultural group or regional context," González said. "We want teachers to recognize these different types of prior knowledge and become aware of the ways in which their students are doing mathematics that could be aligned with - or could be in conflict with - school mathematics."
González's team has created two animated stories about teaching concepts related to perpendicular bisectors; two additional stories about teaching dilations are in production. Each story includes several vignettes with alternative scenarios.
In order to make the cartoons as realistic as possible, the team conducted focus groups with high school geometry students.
"We wanted to make the cartoon animations realistic, in the sense of how they portray students and what could happen in a classroom," González said. "We tried to look at problems that could trigger these different types of prior knowledge and show ways that a teacher could trigger that knowledge, too.
"We realized that a lot of the ways in which students solved the problems were not methods we had anticipated. It confirmed our hypothesis that students bring contextual information that shapes the way they approach mathematics problems," González said.
A student in the School of Art and Design at Illinois created the animations.
Using a recording studio in the School of Music, Illinois students, including some from the theater department, performed the voices of the cartoon characters. Staff members in the school also assisted with sound editing.
A group of 10 mathematics teachers from different high schools will participate in the project, meeting a total of 20 times over the next two academic years.
The teachers will view and discuss the cartoons and collaboratively develop common lesson plans that they will present to their students. The teachers will be videotaped in their classrooms and will review and analyze excerpts with the other teachers as a "video club," a popular form of professional development for educators.
Using information gained during the first year, the research team plans to create a second set of animated vignettes, which the teachers will use the following year to revise the lessons plans and teach the material again.
Another objective of the project will be collecting data on students' learning and the effectiveness of the problem-based lessons at teaching mathematics concepts.
González plans to use all this information to create a professional development model for teachers, to be published in professional/research journals and on a website along with facilitation guides and other materials.
"This is the first time that a project has combined animation and videos to promote teacher learning," said González, who is a former middle- and high-school mathematics teacher and has a background in professional development. "We're really excited about the opportunity to combine these and the Lesson Study model.
"There's evidence that it's very useful for teachers to work together and pay attention to student thinking," González said. "We want to use the expertise that teachers have and help them share some of the strategies that are effective in their teaching practice."
An advisory board that includes education experts from Illinois State University, Indiana University, North Carolina State University, Northwestern and the U. of I. also is working with González on the project.
González presented a poster about the project at the NSF's 2014 Principal Investigator Conference, held this past August in Washington, D.C.