Division by zero

Hi.  One topic I cover in week one of a college algebra course is division by zero.  We are going to see this later on in the chapter on rational functions, so I think we ought to settle this issue sooner rather than later.  Most people reading this blog are well-aware that division by zero is an undefined operation in the rules of real and complex number arithmetic.  3/0 = undefined.

This is often quite a surprise to my students, who apparently never learned this anywhere in their K-12 educations.  Truthfully, I can't remember learning it in my K-12 education either.  I think my fourth grade teacher is on Facebook, and I'm going to ask her if she remembers teaching it.

I invite my students to try 3/0 on as many calculators as they own.  Sometimes the calculator will show "Error" (which is descriptive, but is not a correct answer), and sometimes it will show zero (which is worse).  Students are even more surprised when I tell them both of these calculator results are incorrect.  However, we also experiment on calculators with Order of Operations problems, so students discover that not every calculator follows those rules.

I can picture Reverend Jim on the TV show Taxi:  "3/0 = undefined?  You're blowing my mind!"  I'd love to hear from some K-8 teachers or some high school algebra teachers on whether they teach division by zero.

First post - please be gentle

Hi.  It's probably about time that I join the blogging world.  I have been teaching online college math for about four years.  I started out with pre-algebra, worked my way up the math hierarchy, and now mostly teach college algebra and statistics.

I teach for several for-profit colleges.  Sometimes "for-profit" has a poor reputation.  I am not involved in the recruiting, advising, and counseling end of education, and perhaps this poor reputation is not undeserved.  But as an analogy, I never like dealing with car salesmen, but I still drive a car.

The first question I asked during my first interview was how does an online school know its students are not cheating.  Unless there is some in-person proctoring by a certified third-party (which is possible - I have taken online courses as a student that did this), an online school can not know.  But plenty of cheating goes on in a brick and mortar school too, from paying someone to submit assignments and using cell phones or crib sheets during exams, so please don't be "holier than thou."

I have two bases of comparison of my online courses at online schools versus the content of brick and mortar schools.  The first is that my son who attends a state university took a very similar statistics course to the one I teach.  Although my course is fewer weeks than his, my course seems to cover approximately the same topics.  Second, I recently took an online liberal arts course as a student at a different state university, and I was decidedly unimpressed with how little my professor was involved in the class, how infrequently she communicated with students, and how she apparently didn't read the students' posts at all because she never commented on some of mine which clearly exceeded that scope of the course.  So I have some confidence that my online students are not getting an inferior education.

I look forward to sharing some of my online math experiences, discussing math and teaching, and learning from this vast blogging community.