This study addresses a longstanding question among high school mathematics teachers and college mathematics professors: Which is the best preparation for college calculus—(a) a high level of mastery of mathematics considered preparatory for calculus (algebra, geometry, precalculus) or (b) taking calculus itself in high school? We used a data set of 6,207 students of 216 professors at 133 randomly selected U.S. colleges and universities, and hierarchical models controlled for differences in demography and background. Mastery of the mathematics considered preparatory for calculus was found to have more than double the impact of taking a high school calculus course on students' later performance in college calculus, on average. However, students with weaker mathematics preparation gained the most from taking high school calculus.

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### Philip Sadler and Gerhard Sonnert

### Gerhard Sonnert, Melissa D. Barnett and Philip M. Sadler

Students’ attitudes toward mathematics and the strength of their mathematics preparation typically go hand in hand such that their specific effects are difficult to disentangle. Employing the method of propensity weighting of a continuous variable, we built hierarchical linear models in which mathematics attitudes and preparation are uncorrelated. Data used came from a national survey of U.S. college students taking introductory calculus (*N* = 5,676). A 1-standard-deviation increase in mathematics preparation predicted a 4.72-point higher college calculus grade, whereas a 1-standard-deviation increase in mathematics attitudes resulted in a 3.15-point gain. Thus, the effect of mathematics preparation was about 1.5 times that of mathematics attitudes. The two variables did not interact, nor was there any interaction between gender and these variables.