# MQI Domains

The MQI instrument captures the nature of the mathematical content available to students during instruction, as expressed in teacher-student, teacher-content, and student-content interactions. Five domains of instruction are measured (click on the domains below for details).

Each recorded lesson is divided into equal-length (e.g., 5 or 7.5 minute) segments for scoring. Two raters independently give each segment a score for each of these five MQI domains. Using short segments allows raters to capture events as they happen, without resorting to memory or notes at the end of the lesson. Raters also each give the whole lesson an overall MQI score as well as scores for other factors such as the pacing of the lesson, the density of mathematics in a lesson, and the extent to which the tasks and activities assigned develop mathematics.

## MQI 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 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.

### Classroom Work is Connected to Mathematics

This dimension captures whether classroom work has a mathematical point, or whether the bulk of instructional time is spent on activities that do not develop mathematical ideas—e.g. coloring, cutting and pasting—or non-productive uses of time such as transitions or discipline.