Measuring the Quality of Math Instruction

In this sidebar to a longer Ed. article on teaching Common Core math, David McKay Wilson reports on the Mathematical Quality of Instruction tool (MQI) for evaluating K-8 mathematics teaching. Developed by Heather Hill at the University of Michigan and Harvard’s Graduate School of Education, the MQI is designed to give observers a better lens and get teachers self-assessing and bringing more mathematical substance to students. The MQI

measures five key components of math instruction:

• Richness of the mathematics – Does the teacher explain ideas well and make connections between different ideas (e.g., fractions and ratios) and different representations of the same idea (e.g., a number line, counters, and a number sentence)? Does the teacher include different solution methods, generalizations from specific examples, and fluent and precise mathematical language?

• Working with students – Is the teacher “hearing” and understanding what students are saying mathematically, responding appropriately, and remediating misunderstandings thoroughly, with attention to the specific misunderstandings that led to the errors?

• Errors and imprecision – Is the teacher making mathematical errors and/or using language and notation imprecisely (for example, telling students that 0.5 percent is one-half when it’s really one-half of one percent)?

• Student participation in meaning-making and reasoning – Are students asking questions and reasoning about mathematics (e.g., examining claims and counter-claims or making conjectures)? Are students providing mathematical explanations, finding patterns, drawing connections, determining the meaning of math concepts, and explaining and justifying their conclusions?

• How classroom work is connected to math – Does the work have a mathematical point, or is the bulk of instructional time spent on activities that do not develop mathematical ideas (e.g., coloring, cutting, and pasting) or on transitions and discipline problems?

“Teachers Need Help, Too” by David McKay Wilson in Ed., Winter 2013 (p. 28-29), http://www.gse.harvard.edu/news-impact/2013/01/do-the-math; Hill can be reached at heather_hill@gse.harvard.edu and the website for the MQI is 

http://isites.harvard.edu/icb/icb.do?keyword=mqi_training&pagei... 

From the Marshall Memo #469