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The One Question Calculus Final

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By  Lew Ludwig  (Editor-in-Chief),  Denison University As the semester begins and we prep for classes, the practice of backward course design is a powerful way to get the most of the learning experience for our students. With this in mind, I thought I would share one of my favorite exam questions for a first semester calculus course, which appears below. I call it �the one question calculus final.� Now of course this is tongue-in-cheek, as the one question has over 15 questions. Nonetheless, this one question tour de force covers the full range of a first semester calc course. To substantiate this bold claim, I found a comprehensive list of typical topics in such a course at Wolfram Mathworld Classroom . The chart below cross-references each alphabetically listed topic with its specific question. While some questions touch on a range of topics, the cross-referencing refers to the primary reference. Why I like this question: I really like this question because it requires...
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4 Ways to Promote Gender Equity in Your Classroom

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By  Jessica Deshler ,  West Virginia University There is something beautiful about the structure of mathematics that we can all appreciate, but it�s equally beautiful because it can be creative and messy. So is the teaching of mathematics. As mathematicians, we know and understand the complexities involved in our discipline, but sometimes overlook the underlying complexities of our classroom environment when preparing to teach. You�ve likely heard about the leaky pipeline � the phenomenon that describes the loss of women from STEM fields at various points in the academic pipeline. Because many undergraduate women leave the STEM pipeline after taking a mathematics course , our discipline can especially benefit from classroom practices known to help retain and support these students. You might wonder whether the gender breakdown in our classes or variation in our students� cultural and social backgrounds matter. We posit that these do matter, and that they can impact whether stu...
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CLOSING THE HOLES ON SWISS CHEESE KNOWLEDGE

Over the years, I have argued often on this blog that one of the really weak spots in education was the failure of students to close the holes on what I call �Swiss Cheese Knowledge.�   Thus, on the first day of class last week, I drew a block on the board and put holes in it.  I then explained the drawing to my students. When you leave class every day, your knowledge looks like a block of Swiss cheese.   It appears entirely solid.  However, it is full of holes�things you missed, things you misunderstood, things you did not quite catch.  I know the knowledge feels solid, but it really is not.   If you do not take action, those holes just get bigger as time passes and your memory begins to fade.   Having taught for nearly 50 years, I know where the holes are likely to be.   I can and will write test questions to expose those holes.  In many ways, testing is just an attempt to measure the quantity and size of the holes ...
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