For graduate students to succeed, acquiring skill at evaluating arguments is crucial, but reaching mastery at argument evaluation necessitates perspicacity and a willingness to challenge recognized authorities, published articles, and heretofore accepted “truths.” Teaching university students to become more effective at critique, however, has seldom been the focus of academic study within the context of English as a foreign language (EFL). In this action research, a critical-question approach was employed in an English for Academic Purposes (EAP) class designed to instruct graduate-level science majors to critique popular science articles. Instructional focus shifted, as the action research progressed, from general critical questions to scheme-relevant critical questions drawing upon Walton's argumentation scheme theory. Students' skill development level was assessed through group oral critiques and individual critique essay writing. Subsequent discourse-based interviews with five students revealed nuances in skill development. Results indicated that students' oral critique skills improved over time, whereas substantial enhancements in the targeted goal of their critique essay writing did not materialize. This study showcases how EFL university students' exposure to societal, rhetorical and power dynamics within a specific sociocultural context can impact their performance in critiquing written English text.