This study investigates Finnish, Norwegian, and Swedish first-year engineering students' task performance in mathematics and examines how it relates to their motivational values and beliefs about the nature of mathematics. In a set of seven mathematical tasks, female students outperformed male students, for example, in the simplification of symbolic expressions. Our findings also show that female students set more demanding learning goals for themselves. Further, they expressed higher intrinsic motivational values, whereas male students emphasised utility values, which correlated negatively with task performance. Problem-solving and discovering structures and regularities dominate engineering students' views of mathematics. The 'toolbox' view of mathematics is the best predictor of task performance; the stronger this view is, the poorer is the task performance. However, neither motivational values nor views about mathematics are especially strong predictors of task performance. Based on the findings of this study, it is recommended that, in engineering mathematics courses, greater emphasis is placed on learning fundamental reasoning strategies and discussing the theoretical foundations of the main results. This seems to lead to a better result even in applying mathematics than if one focuses only on learning how to use ready-made mathematical tools in concrete examples.