This study examined the prevalence of teacher tracking in a population of 1,822 mathematics teachers in 184 high schools in a single state. Results showed that 70% of teachers were tracked by course level, course track, or both. Three fourths of high schools tracked at least 58% of their mathematics teachers. We also found significant differences in teaching assignments across quintiles of years of experience at a teacher’s current school. First-quintile teachers were the most likely to be assigned low-track or entry-level courses. In contrast, fifth-quintile teachers were the most likely to be assigned high-track or upper-level courses. These findings indicate that the tracking of mathematics teachers is a prevalent and persistent inequitable structure in most high schools.

A five-part proof progression can support diverse populations when engaging in proof-and-reasoning tasks.

Although high school geometry could be a meaningful course in exploring, reasoning, proving, and communicating, it often lacks authentic proof and has become just another course in algebra. This article examines why geometry is important to learn and provides an outline of what that learning experience should be.

The Common Core State Standards for Mathematics (CCSSM) explicitly states many specific theorems for students to prove across multiple domains (i.e., congruence, similarity, circles, and coordinates) in high school geometry. This study examined five high school geometry textbooks for how they approached proof of 17 theorems stated in the congruence domain focused on lines and angles, triangles, and parallelograms. Results showed that although textbooks provided 75 student opportunities to prove these theorems, no textbook provided student opportunities to prove all 17.Textbooks rarely had students write proofs from general conditional statements, and instead typically provided consistent hard scaffolding including the given, what to prove, and a diagram for all proof opportunities. Some of the textbooks used novel scaffolding such as partially completed proofs, flowchart proofs, second proofs, and hints in the back of the book. Textbooks need to continue shifting more responsibility to students proving the CCSSM theorems by incorporating more diverse scaffolding along with a process for removing the scaffolding as student learning progresses.

We define and investigate the concept of perfect donuts—rectangular donuts with a uniform width that is a natural number. Our investigation leads us to an interesting connection between the area of perfect donuts and the area of Pythagorean-triple triangles. We also provide ideas for further investigation.