The Mathematical Quality of Instruction (MQI) is a Common Core-aligned observational rubric that provides a framework for analyzing mathematics instruction. Observers rate instruction across five domains: common core-aligned student practices; working with students and mathematics; richness of mathematics; errors and imprecision; and, classroom work is connected to mathematics. Although originally designed for research use, the MQI can be used as a tool to support teachers' professional development.
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Beisiegel, M., Mitchell, R., & Hill, H. C. (2018). The design of video-based professional development: An exploratory experiment intended to identify effective features. Journal of Teacher Education, 69(1), 69–89. https://doi.org/10.1177/0022487117705096
Charalambous, C., & Litke, E. (2018) Studying instructional quality by using a content-specific lens: The case of the Mathematical Quality of Instruction framework. ZDM Mathematics Education, 50, 445-460. https://doi.org/10.1007/s11858-018-0913-9
Hill, H. C., Litke, E., & Lynch, K. (2018). Learning lessons from instruction: Descriptive results from an observational study of urban elementary classrooms. Teachers College Record, 120(12), 1-46. https://doi.org/10.1177/016146811812001207
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., Kapitula, L., & Umland, K. (2011). A validity argument approach to evaluating teacher value-added scores. American Educational Research Journal, 48(3), 794–831. https://doi.org/10.3102/0002831210387916