A central goal of the learning sciences is to discover principles that determine the optimal amount of instructional assistance to support robust learning (Koedinger & Aleven, 2007). We examined learning outcomes from providing and withholding stepwise instructional explanations as students studied worked examples and solved physics problems. We hypothesized that students would acquire more conceptual knowledge from withholding instructional explanations because they would be more likely to engage in constructive cognitive activities to understand the problem-solving steps, whereas providing instructional explanations might suppress such activities. Furthermore, we examined the roles of prior knowledge and student motivation in determining learning outcomes. Across three experiments, students in the withholding conditions showed greater conceptual learning than students in the providing conditions. Additionally, achievement goal orientations were more predictive of learning for the withholding conditions than the providing conditions. We discuss how the interactions between prior knowledge, motivation, and instruction can support learning and transfer. (Contains 5 figures and 1 table.)