Proofs and Wolfram Alpha

In my Introduction to Proofs course, I discussed the proof the following: The cube of an integer is of the form 9k, 9k+1, or 9k+8, for some integer k. The problem is from the text I use, How to Think Like a Mathematician: A Companion to Undergraduate Mathematics The big idea here is to to note that any integer can… Read more →

Teaching teachers to teach

An article in last Sunday’s New York Times discusses the complex issue of teacher preparation. The writer of the article includes a lengthy discussion of math teaching in particular. I found it to be quite interesting – the work of math educators doesn’t usually make it to mainstream media. Hopefully the Times will continue its coverage of key education issues… Read more →

Online math courses and academic integrity

For the past three years, I have been teaching an online math course every semester. To ensure that the students taking the class are really the ones who signed up, I have always used in class midterm and final exams. I check their ID and my grading system system reflects a heavy weighting toward the in-class tests. I encourage students… Read more →

Counterexamples in Calculus

One way I motivate critical thinking in my Intro to Proofs class is by using counterexamples. The book, Using Counter-examples in Calculus by Mason and Klymchuk, provides an accessible set of ideas to think about. Producing counterexamples is an important step to thinking about proofs in general, especially for students who are used to computations. What I really liked about… Read more →

The paradox of higher math standards in high school

Those of us who regularly deal  with entering college freshmen are all too familiar with their inadequate math preparation. But in fact, high school mathematics has been ramped up quite a bit in terms of content. What happened? An article in the American Physical Society discusses this paradox. The author of the article, Dr. Joseph Ganem,  is a professor of… Read more →

Efficient Math Commands for Wolfram Alpha

Wolfram Alpha is a free, online, computational engine. It provides some of the power of a computational algebra system (CAS) such as Maple or Mathematica without having to learn the proper syntax. However, it takes a little bit of practice to get WA to give exactly what you want. Here, I’ll give a list of queries that are commonly used… Read more →

Free Multimedia Algebra Review

There are seemingly an infinite number of free math resources on the Internet. However, very few provide the comprehensive content that are usually found in textbooks. One of these rare sites is Hippocampus. It is part of the Monterey Institute for Technology and Education and provides free multimedia ebooks for a variety of high school subjects and introductory college level… Read more →

Research meets teaching

When I was asked to give a talk on some aspect of the history of mathematics a couple of years ago at Suffolk County Community College, I tried to bridge my research and teaching interests by presenting on the history of numerical algorithms. My Ph.D. was in numerical analysis and this was an opportunity to use my research background to… Read more →

Teaching Reading in a Math class?

An often asked question from my students is “but this is a math class – and you want me to read and write?” When teaching my upper division Intro to Proofs class, I find a certain discomfort among students in extracting information from a math text. Most students are used to skimming over some examples and finding one that matches… Read more →