One of the most important tools that mathematicians and scientists use to cope with the daunting complexity of the world goes by the name of reductionism. That is, one first identifies the key parts of a complex system, then one strives to understand the parts, and finally one strives to understand how the parts fit … Read more
Many years ago I took a course on writing led by a wonderful man (whose name I now forget) who was a veteran of the newspaper business. He remarked one day on how difficult it is to write newspaper headlines, and that most newspapers had an editor who did nothing else but write headlines. Article … Read more
A good question and some interesting answers at MathOverflow. Hat-tip to Kareem Carr. (This post first appeared at my other (now deleted) blog, and was transferred to this blog on 25 January 2021.)
Once upon a time, an instructor (whom I shall call Professor “A”) went on sabbatical leave. As a result, another instructor (whom I shall call part-time instructor “b”) was called upon to teach Linear Algebra III, which was normally taught by Professor “A.” All 16 of the students who attended Linear Algebra III had successfully … Read more
Today is Galileo’s birthday, and it’s worth pausing for a moment to celebrate one of the founders of modern science, and one of the giants of its history. The standard biographies of Galileo are by the late Stillman Drake, one of the world’s greatest authorities on Galileo and his life (see here, here, and here). … Read more
Today I handed back the graded mid-term tests in my first-year electricity and magnetism course, and the results were OK. The 2-hour test consisted of five problems and then a final 7-part question that probed for conceptual understanding. In the past I have asked students to write a paragraph about this or that, but this … Read more
My good friend Manolo Santiago lived in Toronto in 1996 when he wrote this poem. Zen Valentine Before Valentine’s Day: Ride subway, walk briskly, look grim. On Valentine’s Day: Ride subway, walk briskly, carry flowers, look grim. After Valentine’s Day: Ride subway, walk briskly, look grim. (This post first appeared at my other (now deleted) … Read more
My basic attitude towards memorization in mathematics education is to memorize the absolute minimum, but memorize that minimum perfectly. Part of a mathematics teacher’s job, in my view, is to guide students to understand what this “minimum” is, and then encourage them to memorize it, helping them to find effective means for memorization. Effective means, … Read more
I’m teaching first-year electricity and magnetism this semester, and we are using the textbook College Physics by Knight, Jones, and Field. Students find it very clear, and it’s worked out well (we used the same textbook last year). The workbooks are very effective, as they walk students through concept development very nicely. As teacher resources, … Read more
I wrote about the power of abstraction earlier, and I just came across a beautiful passage on the same subject by one of my favourite authors, the prolific and master expositor, John Stillwell (see also here). It’s taken from the preface to Elements of Algebra: Geometry, Numbers, Equations, Springer1994: Algebra is abstract mathematics — let … Read more