Few issues on the educational scene have proven as vexatious as the achievement gap between the "haves" and "have nots" in society. The achievement gap has proved both substantial and persistent, despite the good intentions and considerable efforts of thousands of educators and notwithstanding the "No Child Left Behind" Act and other reform initiatives. Numerous factors associated with this predicament have been suggested. The goal of the research reported here was to investigate the issues that prompt teachers to favor low-critical thinking (CT) activities over high-CT ones when teaching low-advantage learners. In the resulting data analysis, nine of 11 candidate issues were associated with statistically significant pedagogical-preference effects, but the effect sizes were small. The data make it possible to frame an account of the conditions under which teachers favored high-CT activities or low-CT ones for teaching low-advantage learners. A pedagogical-preference effect in which teachers favored high-CT activities over low-CT ones was associated with the issues "high-stakes tests," "influence of administrators," and "nature of the subject." A pedagogical-preference effect in which teachers preferred low-CT activities over high-CT ones was associated with the issues "learners' level of prior knowledge," "time constraints," "influence of parents," "influence of colleagues," "learners' level of motivation," and "learners' level of ability." (Contains 1 figure and 1 table.)