He was the superintendent of the Houston Independent School District beginning in fall 2016. Carranza, who had signed a contract to serve for three years, served in this capacity until April 2018, when he was hired as New York City Schools Chancellor with a $345,000 salary. He announced his acceptance of the new job in March of that year. Observers in the Houston area were not aware that Carranza was seeking to exit his position with HISD: He publicly stated that he and the board members of HISD did not have problems with one another. Doris Delaney, a monitor of HISD appointed by the Texas Education Agency, wrote a report stating that the former superintendent in fact disliked and felt frustration in reaction to actions taken by HISD board members. The report stated that Carranza disliked how the board was unable to deliberate important issues, overstepped its authority, and included members with inappropriate political desires.
In 2018, the de Blasio administration initiated a plan to eliminate New York City's specialized high school exam, which is available to all middle school students in the city. In June 2018, defending the plan, Carranza stated that “I just don’t buy into the narrative that any one ethnic group owns admission to these schools.” Asian-American groups decried this as anti-Asian racism, considering that a disproportionately large number of students admitted to the city’s eight specialized schools are of Asian descent. They believe their children are being targeted for their success on the exam. Alumni, activists and Asian American groups argued that Chancellor Carranza failed to appreciate the socio-economic and other diversity among these students and internal to communities of Asian descent. Carranza refused to apologize for the remarks. In June 2019 nine members of the New York City Council wrote a letter to MayorBill DeBlasio asking him to dismiss Carranza, accusing him of having divisive actions. In response, twenty-three Councilmembers, including the education committee chair, sent a letter to the mayor in support of Carranza. In May 2020, it was reported that under Carranza, the Department of Education downplayed the coronavirus threat as it was closing schools. Students presumed sick from the virus were left unrecorded, and teachers and parents were deprived of information by supervisors on students and staff who were presumed sick. The teachers union contend that the DOE was not complying with state protocols. As of May 11, 74 NYC Department of Education employees had died due to Covid-19.