Squeegees and Square Inches: Differential Instructional Design and Enactments for Student Explorations of Area Measure and What They May Reveal About Teacher Perspectives on Equity

Abstract

This work is a comparative case analysis of two elementary mathematics teachers and their attempts to help their third and fourth-grade students understand the foundations of area measure from a spatial reasoning perspective: that area is a two-dimensional space formed as the product of lengths with associated implications for the properties of area units and their symbolizations, and how the area formula for a rectangle (length x width) relates to its dynamic formation. Through my analysis, the teachers’ design and instructional enactment is shown to influence student mathematical meanings as evidenced by in-the-moment activity. And I highlight how the teacher activity in the classroom might be revealing something about the teachers’ tacit assumptions and goals around equity that were shared in 1:1 interviews with me as the researcher. I used a combination of phenomenological thematic analysis of interview transcripts and interaction analysis of classroom instruction to identify teacher’s perspectives on equitable mathematics instruction, examine students’ opportunities to learn in the classroom based on the form and function of teacher assistance, and articulate the mathematical meanings students develop in the two classrooms attributed to different forms of teacher assistance.