Teachers often have students publicly share their mathematical thinking as part of classroom instruction. Before reading further, we invite you to stop and think about this practice by writing down your responses to the following two questions:
Shari L. Stockero and Laura R. Van Zoest
Laura R. Van Zoest and Rebecca K. Walker
One curriculum change proposed by the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989, 109) is an increased focus on probability in the middle grades.
Laura R. Van Zoest and Ann Enyart
Discourse is one area of the nctm's professional teaching standards for School Mathematics (1991) that causes many teachers particular difficulty. Mathematics teachers have a long history as lecturers. Although “initiation-reply-evaluation” (Richards 1991) sequences between the teacher and students are not uncommon, genuine mathematical conversations are rare in most classrooms (Weiss 1994). Discourse can be a problem area for teachers when they do not realize how important it is and have not seen or experienced dynamic classroom discourse. Once a teacher has seen students defending their mathematical ideas, questioning other students' ideas, and helping clarify the mathematics to one another, the importance of discourse becomes clear.
Laura R. Van Zoest and Shari L. Stockero
We draw on research into the durability of sociomathematical and professional norms to make a case for attending to productive norms in teacher education experiences. We illustrate that productive norms have the potential to support teacher learning by (a) improving teachers' own mathematical understanding, particularly of specialized content knowledge; (b) supporting teachers to productively view and analyze classroom practice; (c) providing teachers an experiential basis for thinking about fostering productive norms in their classrooms; and (d) helping teachers to develop professional dispositions that support continued learning from practice. This work points to the importance of intentionally considering the norms cultivated in teacher education experiences, assessing their productivity, and strategically focusing on those that provide the best support for teacher learning.
Shari L. Stockero, Blake E. Peterson, Keith R. Leatham, and Laura R. Van Zoest
Identify student thinking that has potential to support significant mathematical discussion and pedagogical opportunity.
Blake E. Peterson, Shari L. Stockero, Keith R. Leatham, and Laura R. Van Zoest
Do your students ever share ideas that are only peripherally related to the discussion you are having? We discuss ways to minimize and deal with such contributions.
Keith R. Leatham, Blake E. Peterson, Shari L. Stockero, and Laura R. Van Zoest
The mathematics education community values using student thinking to develop mathematical concepts, but the nuances of this practice are not clearly understood. We conceptualize an important group of instances in classroom lessons that occur at the intersection of student thinking, significant mathematics, and pedagogical opportunities—what we call Mathematically Significant Pedagogical Opportunities to Build on Student Thinking. We analyze dialogue to illustrate a process for determining whether a classroom instance offers such an opportunity and to demonstrate the usefulness of the construct in examining classroom discourse. This construct contributes to research and professional development related to teachers' mathematically productive use of student thinking by providing a lens and generating a common language for recognizing and agreeing on a critical core of student mathematical thinking that researchers can attend to as they study classroom practice and that teachers can aspire to notice and build upon when it occurs in their classrooms.
Elizabeth A. van Es, Shari L. Stockero, Miriam G. Sherin, Laura R. Van Zoest, and Elizabeth Dyer
Recent advances in technology have resulted in an array of new digital tools for capturing classroom video, making it much easier for teachers to collect video from their own classrooms and share it with colleagues, both near and far. We view teacher selfcaptured video as a promising tool for improving mathematics teacher education. In this article, we discuss three issues that are essential for making the most of selfcaptured video: camera position, how much video to capture, and when to specify tasks for capturing, selecting, and using video. We propose that the act of deliberately participating in the self-capture process, as well as viewing and analyzing one's own video with colleagues, offers worthwhile opportunities for mathematics teacher learning.
Graham A. Jones, Carol A. Thornton, Ian J. Putt, Kevin M. Hill, A. Timothy Mogill, Beverly S. Rich, and Laura R. Van Zoest
This research extended the validation of a framework for assessing and describing children's thinking in multidigit number situations and used this framework to generate and evaluate different versions of an instructional program. The key constructs of the framework—counting, partitioning, grouping, and number relationships—appeared to be highly stable within each of the five levels and across the full range of thinking exhibited by 12 case studies. Results suggest that the levels may generate a hierarchy of thinking. Teachers were effective in implementing two versions of the framework-driven instructional program. Any differences could be attributed to the quality of problem-solving experiences, the level of student interactions, and, in essence, to differences in teachers' familiarity with the program.