Expertise in Mathematics Instruction pp 63-84 | Cite as

# Coordinating Characterizations of High Quality Mathematics Teaching: Probing the Intersection

## Abstract

We present an analysis that probed empirically the relationship among three different views of exceptional mathematics teaching: (a) the operational definition of “highly accomplished teaching” of mathematics used by the National Board for Professional Teaching Standards (NBPTS) in the United States, (b) the effective use of cognitively demanding tasks in the mathematics classroom, and (c) the use of innovative pedagogical strategies. We analyzed samples of instructional practice—lesson artifacts and teachers’ commentaries on lessons—submitted by candidates seeking NBPTS certification in the area of Early Adolescence/Mathematics. The instructional samples were systematically probed for evidence of mathematical and pedagogical features associated with the views of cognitive demand and innovative pedagogy, and the features found in the submissions of applicants who were awarded NBPTS certification are contrasted with those who were not awarded certification. Our analyses detected a fairly strong interaction between the NBPTS view of accomplished teaching and the view of effective mathematics instruction associated with cognitively demanding tasks. Nevertheless, even in these lessons that teachers selected for display as “best practice” examples of their mathematics teaching, innovative pedagogical approaches were not systematically used in ways that supported students’ engagement with cognitively demanding mathematical tasks.

## Keywords

Mathematics teaching Teaching quality Cognitively demanding tasks Pedagogical innovation## Notes

### Acknowledgement

This study was supported in part by grant #ESI-0083276 from the National Science Foundation (NSF) to the Educational Testing Service (ETS), under the direction of Gail P. Baxter and Edward A. Silver. The authors are grateful to the National Board for Professional Teaching Standards (NBPTS) for granting access to the portfolio data and to members of the ETS staff, especially Rick Tannenbaum, for facilitating access to the data, used in this investigation. Any opinions expressed herein, however, are those of the authors and do not necessarily reflect the views of the NSF, NBPTS, or ETS. The authors acknowledge the contributions of Babette Benken, Kathy Morris, and Jon Star to the study reported herein, and also thank Angus Mairs, Douglas Corey, and Hala Ghousseini for their assistance with aspects of the data coding.

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