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Faculty members

Borko, Hilda

Hilda Borko
Hilda Borko
Academic Title 
Professor
Program Affiliations 
CTE: Mathematics Education
CTE: Teacher Education
(MA) LDT
Assessment By Teachers
Classroom Dynamics
Design Experiments
Learning Design
Mathematical Problem-solving
Mathematics Education
Professional / Staff Development
Teacher Community
Teacher Education and Certification

Toward a Scalable Model of Mathematics Professional Development: A Field Study of Preparing Facilitators to Implement the Problem-Solving Cycle

The Problem-Solving Cycle (PSC) model of mathematics professional development encourages teachers to become part of a collaborative and supportive learning community. As they participate in the PSC, teachers think deeply about both mathematics content and instruction, and they explore their instructional practices with their colleagues through the use of video and other classroom artifacts. One iteration of the PSC consists of three interconnected professional development workshops, all organized around a rich mathematical task. During Workshop 1, teachers collaboratively solve the mathematical task and develop plans for teaching it to their own students. Shortly after the workshop, the teachers implement the problem with their own students and their lessons are videotaped. In Workshop 2 teachers explore the role they played in implementing the problem. In Workshop 3 teachers critically examine students’ mathematical reasoning.

The Problem-Solving Cycle model provides a structure for mathematics teachers to work together and share a common mathematical and pedagogical experience. Our previous research suggests that it is a promising model for enhancing teachers’ knowledge and supporting changes in classroom practice.

In our current project, initiated in Fall 2007, we are working with a group of middle school mathematics teachers in a large urban district to foster their leadership capacity, and specifically to prepare them to facilitate the Problem-Solving Cycle. We will provide 2½ years of preparation and support for teachers who have been designated as “mathematics instructional leaders.” These instructional leaders will in turn implement the PSC with the mathematics teachers in their schools. We will document the range and quality of the instructional leaders’ implementation of the PSC. We will also analyze the impact of the professional development process on the mathematical knowledge and classroom teaching of the instructional leaders and the mathematics teachers with whom they work. In addition, we will analyze the impact on their students’ mathematics achievement. By the conclusion of the project, we anticipate that the participating schools will have the infrastructure and capacity to carry out the PSC indefinitely, using their own resources. In addition, the project will produce a highly refined set of PSC facilitation materials—with a strong emphasis on supporting a linguistically and culturally diverse student population—that can be widely disseminated.

My research explores teacher cognition and the process of learning to teach, with an emphasis on changes in novice and experienced teachers' knowledge and beliefs about teaching, learning, subject matter, and their classroom practices. I am particularly interested in factors that facilitate and hinder teachers' learning of reform-based practices, and in policies and practices that can support teacher change. Currently, my research team is studying the impact of the Problem-Solving Cycle -- a professional development program for middle school mathematics teachers that we designed -- on teachers’ professional community and their knowledge, beliefs, and instructional practices.

  • Ph.D. Educational Psychology, University of California, Los Angeles, 1978
  • M.A. Philosophy of Education, University of California, Los Angeles, 1973
  • B.A. Psychology, University of California, Los Angeles, 1971
  • California State Elementary Teaching Credential, June, 1972 University of Southern California, specialization in Mental Retardation

2007-present Professor, School of Education, Stanford University, Stanford, CA

1991-2007 Professor/Associate Professor, School of Education, University of Colorado, Boulder, CO

1985-1991 Associate Professor, Department of Curriculum and Instruction, College of Education, University of Maryland, College Park, MD

1980-1985 Associate/Assistant Professor, Division of Curriculum and Instruction, College of Education, Virginia Polytechnic Institute and State University, Blacksburg, VA

1978-1980 Educational Evaluator, System Development Corporation, Santa Monica, CA