Graduating with highest honors, Shumway received his BA degree from BYU in 1969 with majors in Spanish and music and a minor in French. His time at BYU was interrupted by a two-year mission for the LDS Church in Mexico. Due to growing doubts about the Mormon message, Shumway was not an especially good missionary, particularly because he found Mexicans more interesting than what he was supposed to teach them. Still, he considers the mission a pivotal experience which allowed him to become fluent in Spanish and helped pave the way to his academic career as a professor of Latin American Studies.

He completed his MA in 1971 and PhD in 1976 at UCLA with concentrations in Hispanic literatures and linguistics. After receiving his doctorate, he taught at Pepperdine University, Indiana University Northwest, Yale University, The University of Texas at Austin, and Rice University. At Yale he chaired the Latin American Studies program for three years and directed the Spanish language program for eight. In 1987, he received tenure at Yale and was promoted to Full Professor in 1992. After fourteen years at Yale, in 1993, he accepted an appointment at The University of Texas at Austin as the Tomás Rivera Regents Professor of Spanish. Two years later he became director of the UT Teresa Lozano Long Institute of Latin American Studies, a position he held for eleven years. From 2008 to 2010, he served as Chair of the UT Department of Spanish and Portuguese. In July of 2010, he was named Dean of Humanities and the Frances Moody Newman Professor of Humanities at Rice University, a position he held for seven years. He retired from Rice University in July of 2020 and now holds the title of Frances Moody Newman Professor of Spanish, Emeritus. He continues writing and lecturing, primarily in the Rice University Glasscock School of Continuing Education.

His scholarship explores Latin-American history and culture with particular emphasis on Argentina, Brazil, and Mexico. He has also written on advocacy and politics in the foreign-language classroom, and on the ideologies of Hispanism. His best known book, The Invention of Argentina (University of California Press, 1991) was selected by The New York Times as “a notable book of the year” and received Honorable Mention for the Bryce Wood Book Award of the Latin American Studies Association in 1992. EMECE Editores, Buenos Aires, published a Spanish translation of the book in 1993. An extensive revision of the book appeared in Spanish in 2005. The University of São Paulo Press published a Portuguese translation in 2009. The book is currently available in all three languages and as an e-book in both English and Spanish. In 2023, The Economist magazine, UK edition, recommended the book as one of seven essential titles to read about Argentina.

In 2012, he published with EMECE/Planeta in Buenos Aires Historia Personal De Una Pasión Argentina. Written in Spanish, the book consists of a series of essays, the two lengthiest ones being an autobiographical account of Shumway’s dialogue with Argentina and Argentine culture since first visiting the country in 1975, and the second, an exploration of Argentine liberalism and its detractors.

In addition to these accomplishments, Shumway is particularly proud of his former students. As a teacher, Shumway’s main goal was to become unnecessary, meaning that he hoped the subjects he taught would engage students to such a degree that they no longer needed him.  This has often proved to be the case since many of his former students either teach or have retired from prestigious universities while others are pursuing successful careers in journalism, government service, and business.