A student, Stuart, related perimeter to pixels and the professor, Beth, moved back and forth between "reserved believing" and "reserved doubting" and "doubting" teacher actions (Elbow, 1986; Harkness & Noblitt, 2017) while assessing the merit of his conjecture in the moment. Video allowed the researchers to…

Getting students to think about the relationships between area and perimeter beyond the formulas for these measurements is never easy. An interesting, nonroutine, and accessible problem that will stimulate such thoughts is the Lattice Octagon problem. A "lattice polygon" is a polygon whose vertices are points of a regularly spaced array.…

Circumscribable quadrilateral is the one that contains a circle tangent to each of its side and it is assumed to be convex. The way teachers could use their own mathematical curiosity to engender the same in students, thereby showing a simple but relentless habit of questioning could lead is illustrated.

Teachers assume that by the end of primary school, students should know the essentials regarding shape. For example, the NSW Mathematics K-6 syllabus states by year six students should be able manipulate, classify and draw two-dimensional shapes and describe side and angle properties. The reality is, that due to the pressure for students to…