## Plotting Success in Math Education

by Jane Carter

The results are in—a Tufts program for middle school math teachers is producing positive effects in New England classrooms. The Poincaré Institute for Mathematics Education, funded by the National Science Foundation, focuses on improving student learning by providing instructors with a deeper understanding of mathematics and of how students learn.

The Poincaré Institute—a collaboration between the Tufts departments of mathematics, education, and physics, as well as TERC—has been funded since 2010. The institute is led by principal investigator Montserrat Teixidor i Bigas, Professor of Mathematics at Tufts, and co-principal investigators: David W. Carraher, Senior Research Scientist at TERC; Analúcia Schliemann, Professor of Education Emerita and Research Professor from Tufts; and Karen Berg from Dover Public Schools of New Hampshire. Along with a team of Tufts post-doctoral fellows, graduate students in math and education, and a staff of media specialists, they have worked with over 180 educators from public schools districts in Maine, Massachusetts, and New Hampshire.

The Poincaré Institute focuses on teaching, learning, and understanding student reasoning about algebra and the mathematics of functions in fifth through ninth grade mathematics curriculum. If you remember your mathematics education, you probably can recall timed memorization tests of multiplication tables as an elementary student, eventually learning how to solve for "x" in an algebraic equation at the middle school level, and finally learning how to graph and visualize those equations as you moved into high school. Previous research by members of the Poincaré Institute in the Early Algebra, Early Mathematics Project shows that if educators introduce algebraic activities, graphing, and conceptualizations of mathematical relationships at an earlier age, students gain a deeper understanding of the mathematics.

Poincaré researchers have analyzed the impact of the program in Massachusetts using 2011-13 MCAS results, the statewide standardized assessment for elementary and secondary education students. They found that more students in Poincaré districts are testing at a proficient or advanced level each year and that their improvement is significantly higher in comparison to what happens state-wide and in districts with similar demographics.

Currently, the Poincaré Institute is working with its third cohort of teachers in nine partner school districts and preparing to enroll a fourth cohort. Teachers from partner school districts enroll in three-semesters of graduate-level online and face-to-face courses taught in tandem with mathematics and education specialists. Professor Teixidor i Bigas says the Poincaré Institute teacher program is also novel in its approach. "Most of the [graduate] programs I have seen were either math or education or they have two courses in math and two courses in education, but not together" she says.

Alex Babinski, a Ph.D. candidate in mathematics, has helped teach the mathematics units offered by the Poincaré Institute. He and other graduate students are responsible for answering math questions in the course forums. "A lot of teachers are really concerned with teaching their grade, but we want to show them that they are a part of a continuous process," he says. The mathematicians involved emphasize pure math concepts to build "a solid mathematical foundation for the methods that they use." The Poincaré instructors use computer visualization tools such as Geogebra and Mathematica to bring those concepts to life at any grade level.

In addition to the math curriculum, the program includes approaches inspired by education research results. Caroline Hagen, program manager for the Poincaré Institute and Ph.D. candidate in education, says, "We spend a lot of time focusing on student thinking," says Hagen. Poincaré instructors prepare the teachers to "interview" their students to understand their thought process. "We don't want them just doing math, we want them to do the math and always circle back around to what their students are thinking and how it all connects and makes sense," says Hagen.

For the principal investigators, it is rewarding to see how the teachers change their perspectives throughout the course. Professor Schliemann says, "We introduce graphs in the Cartesian space which is something that usually they only see at the end of middle school, but we saw [fifth] graders learning about that. The teachers realize that their students can do much more than what they are normally being asked to do."

The teachers enrolled in the courses, like their students, have also been observed in their classrooms. The Poincaré Institute's external evaluators assess enrolled teachers using the Reformed Teaching Observation Protocol (RTOP), a standardized rating system that focuses on student-centered, engaged learning practices. The results showed steady gains in teacher performance during the coursework and significant gains six months after completion of the Poincaré Institute program.

Professor Schliemann says the program is a "deep collaboration between mathematics and education. Very often, in this kind of big program you have educators and mathematicians working in isolation. It doesn't work that way. It has to be a joint effort that combines the deep knowledge that the mathematicians could contribute and of what we educators know about how kids learn, about kids' ideas, about teacher preparation. This has really been one of my best experiences in the profession."

For more information, visit the Poincaré Institute website.*Jane Carter is a Communications Specialist in the School of Arts and Sciences.*