Learning by discovery: what is learned?

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Abstract
It goes almost without saying that discovery learning is in vogue today, especially where mathematics and science educators are concerned. This observation is supported by the substantial curriculum efforts in mathematics and science [1, 2, 3, 4]†, and by the programmatic research endeavors on cognition [5], not to mention the numerous independent efforts by researchers over the country. The reason for tills is not entirely clear to me, however, so I would like to consider what is known about discovery learning that has some basis in experimental research. Specifically, I will attempt to a nswer the question, “What does the student learn when he discovers a principle or generalization in mathematics independently tha t he may not learn when taught these same principles or generalizations directly?” Then I would like to suggest some practical implications.

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