Mistakes as Tools for Learning in U.S. Mathematics Teaching: Studying a Video-Enhanced Researcher-Teacher Collaboration for the Integration of Research into Practice

Investigator: Rossella Santagata

Purpose of the Study

This project, funded through a grant from the Spencer Foundation, investigates a video-enhanced researcher-teacher collaboration model that encourages joint reflections on culturally ingrained teaching strategies and promotes "collaboration in the borderlands between research and practice." The aspect of teaching targeted is the fundamental problem of handling students' mistakes. 

Teachers in high-achieving countries are reported to use a constructivist approach and to regard mistakes as having a positive function. Students in Japanese mathematics lessons, for example, are called to the front of the classroom to share their own problem solutions with their classmates. Teachers require that not only correct but also wrong solutions be shared. These are sources of useful discussions. Despite widespread agreement within the U.S. education community on the important role of mistakes in learning, U.S. mathematics teachers' instructional decisions involving mistakes have been documented as quite different from those observed in Japanese classrooms. In a project conducted earlier, a representative sample of eighth-grade U.S. mathematics teachers, videotaped as part of the Third International Mathematics and Science Video Study, were observed to avoid the discussion of students' errors, to mitigate their responses using such expressions as "You are close," and "You are almost right," and to ask the same question to the next student until they received the correct answer. Trying to protect their students from failure, U.S. teachers lowered the cognitive demands of problems, turning them into risk-free sets of procedures.

This project explores why constructivist approaches to handling students' errors have not taken root in the U.S.

Research Questions

1. From Theory to Practice: Does a video-enhanced professional development (PD) model that encourages researcher-teacher joint reflections on culturally ingrained teaching practices, as well as exposure to innovative practices, facilitate teachers' integration of research-based strategies into their daily lessons?
2. From Practice Back to Theory: What can be learned about the role of mistakes in U.S. mathematics teaching and learning from the experience of teachers working with low-performing students?
3. Exchanging Professional Knowledge: What form does the collaboration between researcher and teachers take? What can be learned from this collaboration that will inform the design of PD programs for U.S. teachers targeting mistake-handling strategies specifically and research-based instructional strategies more broadly?

Study Design and Methods

A group of four teachers in grades 4-6 at a low-performing urban school are participating in this study.

The lead researcher and the teachers are engaging in joint reflections on research findings and video-based examples of both traditional U.S. mistake-handling practices and research-informed instruction. Video is being used to document teachers' attempts to introduce new strategies in their classrooms and to study both the successes and the challenges that the teachers encounter.

Potential Benefits

• By the end of the study, teachers will have developed a portfolio of lesson plans, videos, and commentaries that document their experience.
• This collaboration will increase teacher awareness of culturally-ingrained practices, expose them to alternatives, and support them in their attempts to try new strategies.
• Teachers will begin to treat mistakes as signals of the need for students to restructure their knowledge and plan discussions of mistakes to facilitate students' metacognitive awareness and their adoption of more efficient strategies.
• Findings will provide a model for researcher-teacher collaboration that can be used by others to facilitate the contextualization of scholarly knowledge into classroom practices.
• The findings will serve as basis for the design of PD programs targeted to larger numbers of teachers and focused on effective use of mistakes in mathematics teaching.