I'm thinking about some mini-app ideas for statistics. Here's one idea: we calculate probabilities by finding the area of a portion of a normal (bell) curve. Students need to label the mean (center point on the bell curve), figure out what portion of the bell curve we actually want and shade it in, and then figure out how to type that calculation into their calculator.
For example, if the mean is 3.1 and we want the probability of being 3.5 or higher, the picture would look like this:
First, I would like the mini-app to ask for the mean, ask for the parameters (let the student enter 3.5, then choose more or less), and draw the curve with the shaded portion.
The calculator only finds probabilities BETWEEN two points, so it can find the area between 3.1 and 3.5. So the student needs to figure out that the area we want would be half the curve (0.5) minus the area between 3.1 and 3.5. So I'm envisioning the app highlighting half the curve, and then crossing out the part between 3.1 and 3.5 to illustrate the subtraction, then print on the screen "0.5 - area between 3.1 and 3.5"
If the area were more than half the curve, you'd have to take 0.5 and add a piece, so I'd like to see that visually as well.
This is a really dry example of an incredibly applicable calculation that is the backbone of inferential statistics. (It is how ACT and SAT scores are normed, and underlies most of the statistics in the media and in academic research.) But it is a calculation that really trips students up. I'd love to have this interactive app to help us get past the calculation and into some really cool research projects.