How Today’s Pros Solve Math Problems: Part III

By Keith Devlin NOTE: This article is the final installment of a four-episode mini-series posted here starting in mid-January. In writing it, I have assumed my readers have read those three earlier pieces.   At the end of last month’s post, I left readers with a (seemingly) simple arithmetic problem. I prefaced the problem with...

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Gaps in Student Understanding of the Fundamental Theorem of Integral Calculus

By David Bressoud I have long held the belief (Bressoud, 2011) that we should revert to the original name, the Fundamental Theorem of Integral Calculus (FTIC), for what in the 1960s came to be known as the Fundamental Theorem of Calculus (FTC). The reason is that the real importance of this theorem is not that...

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How Today’s Pros Solve Math Problems: Part II

By Keith Devlin CHANGE OF PLAN: When I wrote last month’s post, I said I would conclude the description of my Nueva School Course this time. But when I sat down to write up that concluding piece, I realized it would require not one but two further posts. The course itself was the third iteration...

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A False Dichotomy: Lecture vs. Active Learning

By David Bressoud On January 31, I published a piece in The Conversation, “Why Colleges Must Change How They Teach Calculus.” The following is one of the statements that I made in this article: Active learning does not mean ban all lectures. A lecture is still the most effective means for conveying a great deal...

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How Today’s Pros Solve Math Problems: Part 1

By Keith Devlin Last month, I wrote about my recent experience teaching a three-day mini-course in the Nueva School January electives “Intersession” program. What I left out was a description of the course itself. I ended with the below diagram as a teaser. I said that, when reading in the usual left-right-down reading order, these...

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Getting to Know the IP Guide

By David Bressoud In 2015, the MAA’s Committee on the Undergraduate Program in Mathematics (CUPM) produced its latest Curriculum Guide. Extensive as this was, including specific recommendations for most courses and programs offered in departments of mathematics, the steering committee that it left out a big part of what is needed for effective teaching. Spurred...

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Déjà Vu, All Over Again

By Keith Devlin I gave a short course at a local high school recently. Three days in a row, two hours a day, to fifteen students. To my mind, it was a huge success. By the end of the course, the students had successfully reverse-engineered UPS’s core routing/scheduling algorithm. In fact, they spent the last...

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Indicators for STEM Education

By David Bressoud The National Academies have just released the Board on Science Education report on Indicators for Monitoring Undergraduate STEM Education (available at http://sites.nationalacademies.org/DBASSE/BOSE). This report is a response to the concern raised by the President’s Council of Advisors in Science and Technology that despite the many initiatives that are seeking to improve the...

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