### Combinatorics: Making learning mathematics more accessible

**You have twenty new books. You want to take three of them to read on your trip. How many different possibilities are there for which three you could take with you?**

This question is a classic example of a problem in Combinatorics, the domain of mathematics devoted to counting. Although the problem is fairly difficult to solve, most people would agree that the problem is quite easy to understand. Like this example, many challenging problems in Combinatorics can be stated in simple language, without the need for technical mathematics vocabulary or notation. This presentation will discuss a study devoted to understanding whether and how this "statement simplicity" renders Combinatorics problems accessible to students with varied backgrounds and proficiency levels in mathematics. The study combines quantitative and qualitative approaches of large-scale assessments (ENEM) and task-based interviews in which students work on selected problems.

**Fernando Carnauba** is a doctoral candidate in Mathematics Education at Teachers College, Columbia University. He earned an MA in Economics at the University of São Paulo and was a visiting student researcher at the Lemann Center in 2014. Fernando is a cofounder of Instituto Canoa, where he serves as Pedagogical Director.