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For many decades, educational communities, including computing education, have debated the value of telling students what they need to know (i.e., direct instruction) compared to guiding them to construct knowledge themselves (i.e., constructivism). Comparisons of these two instructional approaches have inconsistent results. Direct instruction can be more efficient for short-term performance but worse for retention and transfer. Constructivism can produce better retention and transfer, but this outcome is unreliable. To contribute to this debate, we propose a new theory to better explain these research results. Our theory, multiple conceptions theory, states that learners develop better conceptual knowledge when they are guided to compare multiple conceptions of a concept during instruction. To examine the validity of this theory, we used this lens to evaluate the literature for eight instructional techniques that guide learners to compare multiple conceptions, four from direct instruction (i.e., test-enhanced learning, erroneous examples, analogical reasoning, and refutation texts) and four from constructivism (i.e., productive failure, ambitious pedagogy, problem-based learning, and inquiry learning). We specifically searched for variations in the techniques that made them more or less successful, the mechanisms responsible, and how those mechanisms promote conceptual knowledge, which is critical for retention and transfer. To make the paper directly applicable to education, we propose instructional design principles based on the mechanisms that we identified. Moreover, we illustrate the theory by examining instructional techniques commonly used in computing education that compare multiple conceptions. Finally, we propose ways in which this theory can advance our instruction in computing and how computing education researchers can advance this general education theory.