Available Lectures on Thinking
- Teaching the joy of thought
- Transforming anxiety into hatred: Rethinking this standard model of reaching reluctant students
- Inquiry Based Learning: Math and beyond
- Getting students to think
- Abandoning Dead Ends: Resuscitating the Heart of Mathematics
- The Way to Create Ideas
- The Other Lessons: What students keep for life
- Math for Most People: What, Why, and How
Teaching the joy of thought
Non-science majors often fear or dislike mathematics. My challenge is to get students to discover that (1) a math class can be valuable to them and (2) thinking in a new way can open their eyes and minds to a new world. Meeting this challenge involves enticements, twenty-year lessons, connections with the broader culture, learning from mistakes, and concentrating on what the students are doing. You can find a brief preview of this lecture here.
Back to TopTransforming anxiety into hatred: Rethinking this standard model of reaching reluctant students
Mathematics contains great ideas and employs powerful methods that transcend mathematics. Topics such as infinity, the fourth dimension, probability, a nd chaos spark everyone’s imagination. Our challenge is to convey intriguing ideas of mathematics and important strategies of thought in a lively, fun, and enticing manner. Let's replace anxiety with confidence and hatred with delight.
Back to TopInquiry Based Learning: Math and beyond
When students prove theorems on their own and present their results to their peers, interesting things happen. Expected outcomes include students’ developing theorem-proving skills and the ability to tell whether a proof is correct or flawed. But beyond those mathematical skills, this type of experience frequently involves important consequences on students’ self-reliance, independent thinking, and willingness to make mistakes.
After the coercion of education has subsided in the lives of students, they are free to abandon the less pleasant aspects of their schooling. Then they can view the unpleasant past as an ordeal endured. They rarely will spontaneously undertake the odd numbered exercises as entertainment to wile away the cold winter evenings.
Back to TopGetting students to think
Each mathematics class can be a valuable and mind-opening experience for students; however, it can also be boring and useless. How can we make each class truly important for the intellectual growth of our students? This process involves enticements, twenty-year lessons, connections with the broader culture, learning from mistakes, concentrating on what the students are doing, and enjoying every minute of it.
Back to TopAbandoning Dead Ends: Resuscitating the Heart of Mathematics
Students study the best paintings, the most glorious music, the most influential philosophy, and the greatest literature of all time. Mathematics can compete on that elevated playing field, but we must offer all students our grandest and most intriguing ideas. Infinity, fractals, and the fourth dimension; topology, cryptography, and duality—these ideas and many more can compete well with any other subject for depth and fascination. In addition, the powerful methods of analysis that generated these fabulous ideas can enrich every student’s ability to think. Mathematicians have a great story to tell and that story could and should be an important part of the education of all students.
Back to TopThe Way to Create Ideas
Frequently people view creativity as a mysterious result of magical inspiration. But that concept has two defects: first, it's wrong; and, second, it's useless. Viewing creativity as magical is a useless perspective, because with that view, all we can do is to sit and wait hopefully. This talk will present a list of practical steps that you can take that will result in new insights, new ideas, and new solutions. This method releases the creativity in us all.
Back to TopThe Other Lessons: What students keep for life
“Education is what survives when what has been learned has been forgotten.”—B.F. Skinner. The vast majority of our students soon forget the vast majority of the mathematical details they learn in class—(sometimes, in fact, before the final). But mathematical analysis has produced some of the greatest triumphs of human thought and creativity. Let’s design our courses and curricula so that what survives in our students, after they forget, clearly improves their lives. Let’s make students’ mathematics course the most important course they take to help them develop their ability to think.
Back to TopMath for Most People: What, Why, and How
Mathematical thinking has produced some of the greatest triumphs of human thought and is full of creativity, intrigue, and imagination. Most students and adults who are not technically oriented have an impression about mathematics, but ‘creative,’ ‘intriguing,’ and ‘imaginative’ are not the adjectives most used to convey that impression. So our delightful challenge is to make mathematical ideas accessible, fascinating, and inspirational to everyone.
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