I think my favorite part of teaching is helping the students who really struggle with math/stats.
There’s a huge range of familiarity and comfort with math in 251. That’s likely because you only need two years of high school algebra to take it (or, failing that, MATH 108). The stuff we start with isn’t too conceptually hard or even computationally hard—the mean, median, standard deviation, etc. However, the notation for these calculations seems to be what trips some people up.
Example: I’m sure we’re all familiar with the mean and how it’s calculated. Suppose we had a dataset with values 3, 5, 2, 6, and 7. To find the mean, we add up all the values and then divide by the total number of values, which in this case is 5.
But here’s the formula to do that:
If you’re not familiar with summation notation, this calculation, as simple as it is, might look really intimidating, right? And I’d guess that students who have taken MATH 108 as their highest math class at the U of I haven’t been exposed to summation notation. I know we never saw it in MATH 143 (which is a horrible class in general, but I won’t go into that). Personally, I don’t think it was ever explicitly explained until I took MATH 176 (Discrete Math).
Unfortunately, I’ve heard from a LOT of students who are re-taking STAT 251 or who had taken stats in high school that a lot of the “basic” notation we use right at the beginning of class was never really explained. It was just knowledge that they were assumed to already know, and so was glossed over rather quickly.
That really bothers me.
That’s why my favorite part of teaching is actually helping to make sense of these “everybody should already know this” concepts…these concepts that, in actuality, not everybody already knows. I’ve had a lot of students who have taken stats in the past say that no one has ever explained those things to them and that they really appreciated a basic “here’s what this capital sigma means and how to calculate stuff with it” and other such explanations.
And that makes me happy. Not happy enough to alleviate my anger over the lack of standardization across all sections of STAT 251 at UI, but happy.