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Using Mathematica, we recently developed MathEdu, an authoring tool based on a programming-by-demonstration paradigm. Students can use it in two ways: as a tutor that shows them how to solve specific problems corresponding to previously defined patterns, or to solve specific problems interactively with the tool while it controls the resolution process. MathEdu allows a degree of interactivity that no other tool with a similar purpose has achieved. We illustrate this last claim by briefly reviewing the most advanced tutoring systems currently representing mathematical concepts by means of symbolic information. We also describe the three core modules in MathEdu: MathSolver, MathDesigner, and MathTrainer.