Beyond the scope of the course

Hi.  Occasionally a student will ask me a question, or will make a mistake, that leads to a topic that is beyond the scope of the course.  Recently this occurred in college algebra where students confused algebraic functions and algebraic numbers.  This entire subject is beyond the scope of this course - we don't prove a function is not algebraic, but we merely state it without proof;  and we really don't care for this course whether a number is algebraic or not.

My philosophy is that I always try to answer a student's question, or try to correct a mistake, even though  this gets us outside the scope of the course.  Students will not be tested on whether a particular function is algebraic or not.  But I always have this nagging feeling that I'm providing more information than anyone really cares about.

Thinking about this dates back to when one of my sons was in middle school and says he was taught that only rational numbers can be exponents.  I then dashed off a letter to my son's teacher, reminding him that while logarithms were not part of the middle school curriculum, did he really want to teach the kids something that they would have to un-learn in a future class?  I try not to teach something that a future teacher may have to correct;  my son's teacher felt an irrational exponent was too much information for that grade level.

Which of us is right?

An algebra problem students struggle with

Hi.  I am amused when a student midway through the class will ask what grade he or she needs on the remaining material, so that the final grade will be say a B.  My amusement is because either it is a student in my algebra class asking this question, or a student in my statistics class where algebra is the prerequisite. 

I should use this example as additional ammunition to the question, "Why do we have to take algebra?  I'll never use it."

We do this in chapter 2; by chapter 8 students have forgotten

Every time I teach statistics, at least one student will ask me a question about chapter 8, whose answer is in chapter 2.

In chapter 2 we calculate the standard deviation of a sample. I invite the class to do one calculation of a sample of three numbers using each step of the formula: √ ∑(x_i - ̅x)² / (n-1). Then I show them how to do it with a single Excel function, =STDEV. At the end of chapter 2, every student can do this in Excel.

We discuss standard deviations in the subsequent chapters, such as when we do Normal distributions, but we don’t calculate any.

In chapter 8 we do hypothesis testing of two samples that are matched pairs, such as a husband’s data and a wife’s data. We take the difference between the two values in each pair, calculate the mean of the differences, and the standard deviation of the differences. And at least one student will ask how to do these standard deviations. The answer is: the same way we did them in chapter 2.

Even if you don't teach statistics, I bet you have a similar experience. Comments?

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.