Improving academic outcomes for economically disadvantaged students has proven challenging, particularly for children at older ages. We present two large-scale randomized controlled trials of a high-dosage tutoring program delivered to secondary school students in Chicago. One innovation is to use paraprofessional tutors to hold down cost, thereby increasing scalability. Participating in math tutoring increases math test scores by 0.18 to 0.40 standard deviations and increases math and non-math course grades. These effects persist into future years. The data are consistent with increased personalization of instruction as a mechanism. The benefit-cost ratio is comparable to many successful early-childhood programs.

Survey data are commonly cited as evidence of widespread misperceptions and misinformed beliefs. This paper shows that surveys generally fail to identify the firm, deep, steadfast, confidently held beliefs described in leading accounts. Instead, even those who report 100% certain belief in falsehoods about well-studied topics like climate change, vaccine side effects, and the COVID-19 death toll exhibit substantial response instability over time. Similar levels of response stability are observed among those who report 100% certain belief in benign, politically uncontested falsehoods—for example, that electrons are larger than atoms and that lasers work by focusing sound waves. As opposed to firmly held misperceptions, claims to be highly certain of incorrect answers are best interpreted as “miseducated” guesses based on mistaken inferential reasoning. Those reporting middling and low levels of certainty are best viewed as making close-to-blind guesses. These findings recast existing evidence as to the prevalence, predictors, correction, and consequences of misperceptions and misinformed beliefs.