### Taxonomy of Students

When teaching at and above the level of calculus, the differences between categories of your students are relatively minor. Sure, the engineering students are assumed to be hard workers and the math majors going into secondary education are assumed to be less capable. (Unfair stereotypes but widely held.) But overall the class is fairly homogeneous, especially in terms of academic culture and expectations.

In contrast, I catalog for you some of the students taking gen-ed math:

In contrast, I catalog for you some of the students taking gen-ed math:

**With-it Women**- These are much like Kristin from the now-defunct Mad Pony. These are some of the best students in my classes. While her priorities seem to revolve around college football, her sorority, and shoes, she has a good dose of common sense and of personal responsibility. This type of student recognizes that in some sense my class is an exercise in following directions. If you come to class, read the book, learn what the words mean, and do the homework (by which I mean actually try instead of scribbling down something that you hope gets credit), then you are well on your way to earning the grade you want.
**I Took Calculus in High School**- Sullen that they placed into gen-ed math, they believe that it is my fault that they can not do the problems in my class. Honest to God, I assigned the following problem:
You are selling lamps at a craft fair, and you want them to cost exactly $20.00 after adding on your state's 7% sales tax. What should be the before tax price? (Round to the nearest cent.)

And this type of student can't do the problem and then blames me for not teaching them how to do it. (The point of the lesson was on using the four-step approach to problem solving — it was assumed that college students had a basic knowledge of percents.) Or maybe they think that I am not teaching math because they can not succeed in my class without trying; they think that they are good at math because they had*calculus in high school*. **I Never Had to Try Before**- Closely related to the above category, except they gleefully admit that they are bad at math. Most of my students are in this category. They get upset when they get a 0 on a homework, telling me that they should get credit for turing it in. (Homeworks are graded on a 0-1 scale: either you get the point or you don't.) They don't bother to learn what the words mean or to read the book, and they can't figure out why merely coming to class isn't enough. Some of them don't bother to come to class, and they wonder why they're failing.
**Problems Outside School**- This is the student who shows up to class at 9am on a Wednesday smelling of alcohol. The one who explains that she can't take the test because a relative was murdered and the whole family is going to the accused's arraignment. Or the students who justify their absenses with a stack of papers from police and lawyers and courts. This is the student who commutes in from a rural area over an hour from here and who needs to help take care of her many younger siblings after the death of a parent. And the traditional-aged students with small children. (None of these examples are hypothetical.) This is more than your run-of-the-mill grandmother in the hospital.
**The Spooky Students**- Am I allowed to have favorites? If so, these are my favorites. I don't know why they're in gen-ed math: maybe it's because they've quietly slipped through the cracks. By spooky I don't mean goth fashion or other dark looks. Very quiet and not conforming to the norms on campus from a socio-academic standpoint. I asked my class what was the last mathematical pattern they'd noticed in real life or the last time they'd used math in real life. Probably 90%+ of them said they balanced their checkbooks or left a tip at a restaurant. The student in this category wrote about origami.