"Fairminded critical thinking" (FCT) is an alternative to traditional critical thinking conceptions as it places greater emphasis on ethical reasoning. Argumentative writing can provide a means to observe and cultivate such thinking qualities. This study introduces a non-linear instructional model to teach FCT, and through a small-scale intervention, explores its potential for developing four FCT intellectual standards in argumentative writing (intellectual accuracy, depth, breadth, and logic) with a group of Chinese university English (EFL) users. Adopting a one-group, pretest-posttest exploratory design, writing samples were assessed with a locally created rubric tool which was also triangulated through an adapted content analysis. Overall, pretest writing samples showed that some thinking skills had already been developed, yet there was a tendency toward one-sided argumentation and the use of informal evidence to justify claims, frequently culminating in a persuasive defense of one position. On the posttest, logic was the only intellectual standard that showed a more noticeable improvement, potentially attributed to the teaching model, representing development of a more moderated, multi-sided articulation of logic. These findings provide impetus for a discussion of how FCT can be further taught and assessed. Theoretical and methodological implications of FCT as a non-traditional approach to critical thinking and argumentation are discussed.