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<p>These explorations allow students to discuss topics and discover the ideas of calculus for themselves in groups of 3 or 4. The teacher should be present to help, of course, but this discussion leads to deeper understanding of calculus and to more rigorous mathematical work. Struggling and making mistakes is essential to better thinking, and when you have students do this in a classroom 2 or 3 times a week, they learn that initial confusion is normal for math problems, and they can surmount their initial confusion. Explorations build interest, understanding, camaraderie, and confidence.</p>
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