Linking teaching, learning, and assessment.

The sixth standard in the Professional Standards for Teaching Mathematics (NCTM 1991) focuses on analyzing and interconnecting teaching and learning. The standard calls for the analysis of teaching and learning to be ongoing by "[o]bserving, listening to, and gathering other information about students to assess what they are learning." Teachers examine the "[e]ffects of the tasks, discourse, and learning environment on students' mathematical knowledge, skills, and dispositions."

The purposes of this analysis are several (p. 63):

* ensure that every student is learning sound and significant mathematics and is developing a positive disposition toward mathematics;

* challenge and extend students' ideas;

* adapt or change activities while teaching;

* make plans, both short- and long-range;

* describe and comment on each student's learning to parents and administrators, as well as to the students themselves.

Thoughtful classroom teachers have always recognized that teaching and learning are a continuous loop, each at different times influencing and leading the other; however, few programs make the interconnectedness of teaching and learning a primary focus of evaluation. Teachers informally observe students and use, with varying degrees of expertise, the information they gather to make decisions. "Tests" have been the usual approach to evaluation, and accountability has been documented by a standardized pencil-and-paper measure given once at the end of the year. The 1990s may prove to be a decade of change in assessment.

North …