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Two experiments were conducted, contrasting a minimally guided discovery condition with a variety of instructional conditions. College students interacted with a computer-based tutor that presented algebralike problems in a novel graphical representation. Although the tutor provided no instruction in a discovery condition, it constrained the possible actions sufficiently that students could always discover the algebraic transformations they needed to learn. In Experiment I, with ample practice for each new transformation, students performed better in the discovery condition than any instructional condition. In Experiment 2, with only a little practice for each transformation, students performed worst in the discovery condition. The authors suggest that the high levels of practice in the 1st experiment made students more efficient at discovering the algebraic transformations. When the cognitive demands were manageable, the discovery students may have more often encoded the algebraic transformations in mathematically correct ways.