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Tool Name
Mathematical Quality of Instruction (MQI)

Evaluation Type
Classroom Observations

Mathematics specific

Elementary Grades only
Middle Grades only

Use of Evaluation

No URL is currently available for this instrument.

This product was developed by the Learning Mathematics for Teaching Project.

Product Description
The MQI observation protocol assesses the following: richness of the mathematics, responding to students' mathematical ideas, classroom errors, and student cognitive demand. Classrooms are scored on the following scale: not present, partially present, and characterizes the lesson. The MQI was created to validate the Mathematics Knowledge for Teaching instrument, also developed by the Learning Mathematics for Teaching Project.

General Target Population Information
This product was developed for Grades K–8 mathematics teachers.

Stage of Teacher Development
All Stages


This observation protocol was used in the following research studies: Gates Measures of Effective Teaching study; National Center for Teacher Effectiveness study lead by Thomas Kane and Heather Hill; and the Investigating the Effect of Professional Development, Mathematical Knowledge for Teaching and Instruction on Student Outcomes study funded by the National Science Foundation and lead by Heather Hill, Geoffrey Phelps, Robin Jacobs and Douglas Corey. 

The protocol has been deemed through research to be both valid and reliable for these purposes. The protocol is currently being used in the Understanding Teaching Quality (UTC) study conducted by ETS, the Rand Corporation, and the Institute for Social Research at the University of Michigan. Drew Gitomer, Ph.D., and Courtney Bell, Ph.D., of ETS are leading the study, which is funded by a four-year grant from the Bill & Melinda Gates Foundation.

Research and Resources

Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430–511.

Learning Mathematics for Teaching. (in press). Measuring the mathematical quality of mathematics teaching. Journal for Mathematics Teacher Education.

Learning Mathematics for Teaching. (2006). A coding rubric for measuring the mathematical quality of instruction (Technical Report LMT1.06). Ann Arbor, MI: University of Michigan, School of Education.

Additional Research

Heather Hill, Ph.D., and Charalambos Charalambous are conducting research to ensure the reliability and accuracy of MQI.

Additional research is currently under way by Courtney Bell, Ph.D., and Drew Gitomer, Ph.D., of ETS.

Free, online training for raters will be available in fall 2010. In-person training is available by special arrangement.

Contact Information
Heather Hill
Harvard Graduate School of Education
Phone: 617-495-1898

Support Available
Online training for raters will be available in fall 2010. In-person training is available by special arrangement.