Gonçalves is originally from Esposende, in Portugal. Her father owned a shoe company and her mother was a teacher. Her father died when she was young, of primary amyloidosis, leading her to aim for a career in medicine. However, this disruption in her life caused her schoolwork to suffer, and her scores were not high enough for medical school. Instead she went into mathematics at the University of Porto, inspired by one of her high school teachers.[2]
After taking a summer course in measure theory from Cláudio Landim at the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro, Brazil, she went to IMPA for her doctoral studies.[2] She completed her PhD there in 2007. Her dissertation, supervised by Landim, was Central Limit Theorem for a Tagged Particle in Asymmetric Simple Exclusion.[3]