MQI Rubric
What is the MQI?
The MQI rubric captures the nature of the mathematical content available to students during instruction, as expressed in teacher-student, teacher-content, and student-content interactions. The Common Core-aligned observation rubrics provides a framework for analyzing mathematics instruction in several domains. With each domain, individual codes contain certain score points that categorize instruction into different levels of quality.
Domains
Common Core-Aligned Student Practices
This dimension captures the ways in which students engage with mathematical content. This includes:
- Whether students ask questions and reason about mathematics – e.g., students ask mathematically motivated questions, examine claims and counter-claims, or make conjectures.
- Whether students provide mathematical explanations spontaneously or upon request by the teacher.
- The cognitive requirements of a specific task – e.g., are students asked to find patterns, draw connections, determine the meaning of mathematical concepts, or explain and justify their conclusions.
Working with Students and Mathematics
This dimension captures whether teachers can “hear” and understand what students are saying, mathematically, and respond appropriately. Specifically:
- Whether the teacher accurately interprets and responds to students’ mathematical ideas.
- Whether the teacher remediates student errors thoroughly, with attention to the specific misunderstandings that led to the errors.
Richness of the Mathematics
Richness includes two elements: attention to the meaning of mathematical facts and procedures and engagement with mathematical practices and language.
- Meaning-making includes explanations of mathematical ideas and drawing connections among different mathematical ideas (e.g., fractions and ratios) or different representations of the same idea (e.g., number line, counters, and number sentence).
- Mathematical practices include the presence of multiple solution methods, where more credit is given for comparisons of solution methods for ease or efficiency; developing mathematical generalizations from specific examples; and the fluent and precise use of mathematical language.
Errors and Imprecision
This dimension refers to mathematical errors and distortion of content by the teacher. Specifically:
- Whether the teacher makes content errors that indicate gaps in the teacher’s mathematical knowledge.
- Whether teacher talk features imprecision in language and notation, for instance when teachers cannot articulate mathematical ideas.
- Whether there is a lack of clarity in the presentation of content or the launch of tasks.
MQI Rubric Research Basis
The MQI rubric was developed by Heather Hill and colleagues at the University of Michigan and Harvard University to reliably measure several dimensions of the work teachers do with students around mathematical content. The MQI rubric is based on a theory of instruction, existing literature on effective instruction in mathematics, and an analysis of the teaching of hundreds of diverse teachers in the United States.
The MQI rubric is based on the perspective that the mathematical work that occurs in classrooms is distinct from classroom climate, pedagogical style, or the deployment of generic instructional strategies. Similarly, the MQI rubric provides separate teacher scores for different dimensions of the mathematical work teachers do; for instance, the presence of mathematical explanations and practices is scored separately from student participation in mathematical explanations and practices. This makes the MQI rubric unique among instruments that measure mathematics instruction, many of which prioritize novel practices over a more balanced view of the numerous elements that comprise a mathematics lesson.
The MQI rubric was developed and piloted between 2003 and 2012. During that time, its authors examined the relationships between teachers’ mathematical knowledge for teaching, MQI rubric scores, and student outcomes, often finding significant and sometimes substantial relationships. The MQI rubric has also been subject to several studies that examine the best conditions for arriving at accurate and generalizable scores for specific teachers.
For more information:
- Hill, H. C., Kapitula, L., & Umland, K. (2011). A validity argument approach to evaluating teacher value-added scores. American Educational Research Journal, 48(3), 794–831.
- Hill, H. C., Umland, K., Litke, E., & Kapitula, L. R. (2012). Teacher quality and quality teaching: Examining the relationship of a teacher assessment to practice. American Journal of Education, 118(4), 489–519.
- Hill, H. C., Blunk, M., Charalambous, C., Lewis, J., 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, 430–511.
- Hill, H. C., Charalambous, C. Y., Blazar, D., McGinn, D., Kraft, M. A., Beisiegel, M., Humez, A., Litke, E., & Lynch, K. (2012). Validating arguments for observational instruments: Attending to multiple sources of variation. Educational Assessment, 17(2–3), 88–106.
- Hill, H. C., Charalambous, C. Y., & Kraft, M. A. (2012). When rater reliability is not enough: teacher observation systems and a case for the generalizability study. Educational Researcher, 41(2), 56–64.
- Kelcey, B., McGinn, D., & Hill, H. (2014). Approximate measurement invariance in cross-classified rater-mediated assessments. Frontiers in psychology, 5, 1469.
- Blazar, D., Braslow, D., Charalambous, C. Y., & Hill, H. C. (2017). Attending to general and content-specific dimensions of teaching: Exploring factors across two observational instruments. Educational Assessment, 22(2), 71–94.
Access the MQI Rubric Training
The MQI Rubric Training consists of modules that will teach you how to rate classroom video using the MQI rubric. Some of these modules are instructional videos that go into detail about how the rubric is intended to be used. Other modules are practice modules with self-grading quizzes that allow you to practice applying your MQI rubric knowledge to video of real mathematics instruction.
This particular training is a better fit for researchers or others who are interested in rating classroom video with the MQI rubric. It is recommended that educators looking to use the MQI rubric for teacher professional learning inquire about the MQI Coach Training instead.