Mathematics teachers make a number of decisions that shape their lessons, which therein impact their students’ opportunity to learn mathematics. Past research has often focused on teachers, students and the mathematical content as key classroom elements that drive teachers’ decisions. In this article, we propose that a fourth element–the curriculum–along with teachers’ curricular reasoning also hold considerable influence on teachers’ decisions. Using data collected from middle grades teachers’ curricular decisions, we share the Instructional Pyramid model for Curricular Reasoning to organize the interactions among these four key classroom elements and to delineate aspects of curricular reasoning. This model serves as a multi-dimensional framework to make sense of teachers’ curricular decisions. © 2021 Research Council on Mathematics Learning.

Grade 8 students were given a task that had pairs of shapes that had been transformed (i.e., preimages and images). Students were to identify which of the three rigid transformations--reflections, rotations, or translations--were used to map the preimage to the image. Students were also asked to give a justification for their choice of transformation. Using only a single transformation, the answer is that the preimage has been rotated to create the given image. However, Ava, a student in the class, identified a pair of shapes as representing both a rotation and a reflection. How many times have students answered a question similarly? Why do students think that this is a reflection? Is there something within the mathematics of reflections that students do not understand that causes them to respond that figures are reflections? In this article, the authors explore this misconception, give possible reasons why students struggle to differentiate between a reflection and rotation, and share ideas for teachers to elicit and discuss these misconceptions with students.