T his research project examined the changing beliefs, knowledge, and classroom practices of teachers who participated in a professional development seminar entitled Developing Mathematical Ideas (DMI). In a year-long, 48-hour seminar, teachers:

(a) studied elementary mathematics to deepen their own understanding of it,

(b) studied the development among children of the ideas central to elementary mathematics, and

(c) experienced a teaching and learning environment focused on the joint exploration of ideas.

What happens when, over the course of one year, teachers’ attention is focused on an exploration of the fundamental mathematical ideas of the elementary curriculum? What happens as teachers gain experience of themselves as mathematical thinkers, and of children as mathematical thinkers? What happens when teachers gain experience of classrooms – both teacher seminar classrooms and elementary classrooms – in which student ideas are expressed, explicitly represented, and built on to formulate stronger ideas?

In addressing these questions this study followed two DMI seminar groups and the classroom practices of seminar participants. The data include:

• Video recordings of the seminar meetings of two different DMI seminar groups that met during the 1996 -1997 school year. Each seminar group was videotaped 8 of the 16 times they met during the year, at approximately 1-month intervals.
• Teacher portfolio writing from all participants at each of the 2 seminar sites.
• Video recordings of mathematics classes in the elementary classrooms of each of 6 of the teachers participating in one of the seminar groups. Four visits were made to each of the classrooms, 3 were scheduled during the year that the teachers were participating in the DMI seminar (fall, winter, and spring 1996 –97), and the 4th visit was scheduled in the fall of the following year (1997-98).
• Tape recordings of after-class interviews with these same 6 teachers.

The data provide converging evidence that virtually all of the teachers came to believe that they and their students have ideas about the subject matter they study, and that these ideas belong, front and center, in the classroom. Virtually all of the teachers learned mathematics in the seminar context, and for roughly half of the participants there is evidence that outside of the seminar teachers continued to learn mathematics through an examination of the work of their own students in their own classrooms. Finally, for all 6 of the teachers for whom there are classroom observations and interviews, there is strong evidence that teaching practices changed in a particular direction. Teachers’ classroom practices increasingly supported the articulation and representation of students’ mathematical reasoning and ideas, and through the teachers’ own engagement with the mathematics, increasingly supported students’ rigorous investigation of the ideas expressed.

The results of this study are reported more fully in a forthcoming book Teachers’ Professional Development and the Elementary Mathematics Classroom: Bringing Understandings to Light. The book is written for a broad audience – both school-based and university-based – and is currently available from Lawrence Erlbaum Associates.

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