Research Background Algebra Cubed is an outreach project of the University of Kentucky, sponsored by the National Science Foundation to promote educational interactions of doctoral students from what is often referred to as the STEM (science, technology, engineering, and mathematics) fields with secondary schools. This engagement is expected to impact content and pedagogy knowledge of teachers in the teaching of mathematics as well as cognitive and affective domains of students in the learning of mathematics. Algebra Cubed fellows go to work with mentor teachers in two middle schools and two high schools. Meanwhile, fellows interact with students of their mentor teachers through such activities as answering questions in class and tutoring students after class. We have engineered the rich interaction of fellows with teachers and students to promote teachers’ teaching and students’ learning. Can interaction of this nature really improve teachers’ understanding of content and pedagogy in the teaching of mathematics? Meanwhile, can interaction of this nature really improve attitude and achievement of students in the learning of mathematics? Theoretical Framework Algebra Cubed has two components relating to teachers and students. For the teacher component, Algebra Cubed is designed based on the premise of the theoretical framework of Wenger’s (1998) “community of practice” defined as “shared histories of learning” with a focus on learning as social participation (p. 86). Central to this framework is the regular professional interaction among members of a community that promotes constant reflection on content knowledge and classroom practice as well as constant renegotiation of what it means to teach algebra. For the student component, Algebra Cubed is designed based on the premise of the theoretical framework of role models within social learning theory (Bandura, 1977). Central to this framework is that significant others can inspire and motivate students to pursue higher educational and occupational goals. Graduate students as significant others offer unparalleled advantages in that they essentially belong to the same generation as school students.

Research Method We used a pre- and post-test design to measure gains of teachers (N = 10) in their mathematical knowledge for teaching and of students (N = 586) in their mathematics achievement. We designed a survey questionnaire to measure changes (through pre- and post-survey) in teachers’ pedagogical understanding of critical issues in mathematics education and students’ attitude toward mathematics. The role model scale on the student questionnaire was a good indication of the impact of the fellows on students. We then related the variance in the role model scale with the variance in attitude gains and achievement gains of students in a multiple regression approach to analysis of covariance. Satisfaction of teachers with the fellows was a good measure of the impact of the fellows on teachers. We then related the variance in the satisfaction scale with the variance in gains in content knowledge and pedagogical understanding of teachers in a non-parametric statistical framework because of the small teacher sample.

Initial Findings Our preliminary data analyses have already shown significant impact that fellows created as role models on students and as colleagues on teachers. The role model scale scores were related to gain scores in attitude toward mathematics and mathematics achievement. School students who accepted more these graduate students as role models experienced bigger improvement in attitude toward mathematics and mathematics achievement. Teachers on average were satisfied with the professional interaction and relationship with the fellows. The satisfaction scale scores, however, were not related to gain scores in content knowledge and pedagogical understanding.