alice in summerland

learning and teaching math in alice


Title inspired by Will Smith’s Switch.

I finished my second tutorial today! I’m going to further test the world I built tomorrow since that will be the finishing world displayed on the website, and I’m going to read over the tutorial before I ask Peggy and Chitra to look at it.

This world is a little more complex than the inequalities one in that there were some sketchy algorithms that I needed to explain, especially for the 4! permutations case. Here are some of the slides that helped piece out these different algorithms for the 2, 3, and 4 cases, and note that there are obviously more slides explaining how to code this:

2-person switch

With 2 people, it’s easy to show the switch in terms of Alice. Since the switching code only takes 3 lines (and 2 more to change the counter), I can show the animation in 3 subsequent. First, the order is Alice in the first spot and Jared in the second. Alice moves to the temporary spot in the back. Jared moves over to the first spot. Alice moves to the second spot. Switch done. Looking back I could have also used red and blue squares like I do in the other two cases below, but I think I like the realization of the actual Alice people.

3-person switch

The 3-person switch gets more complicated. I use the colors to represent people and numbers are the indices, which obviously don’t change. The algorithm goes like this: Switch items 1 and 2, 0 and 1, 1 and 2, 0 and 1, then 1 and 2. In other words, keep the item in the 0th position constant and switch the 1st and 2nd, and then put the new item in the 1st position as the new 0 position. Repeat for all 3 colors. The way  I explained it on the Powerpoint makes sense to me, but I’m still not sure if it would make sense to a middle schooler.

4-person switch

The 4-person case is a hot mess, though I do use 4 slides to explain it. Let’s look at the first column, where we can call first permutation 0, …, and the last permutation 5. In permutations 0, 2, and 4, we switch the items in indices 2 and 3. In permutations 1 and 3, we switch the items in indices 1 and 2. Permutation 5 is more complicated. Let’s call the first column column 0, …, and the last column 3. In columns 0 and 1 we switch the items in indices 0 and 1. In column 2, we switch the items in indices 2 and 3. In column 3, we do nothing because we’ve finally exhausted all of the possibilities. What I just said is essentially pseudocode for what I wrote in the program. Since all of these cases come together to make 8 nested loops at its worst, I’m sure the programmer has a headache already at this point. Not sure how to cure that, though, at this point…

In other business: Wednesday lunch. Two of the professors who have been leading the lunches, Richard Lucic and Robert Duvall gave a talk about their new class CS 196: Application Capstone, which is obviously such an awful name for the fun that seems to go on in that class. Actually as I just found that website to link it, I was amused by the grading scheme: 25% engagement; 25% skills; and 50% assignments. I wonder how many people didn’t get an A+ in that class. Although different than other grading schemes, this model does seem to fit the class.

The class seems awesome. Kind of like Stanford’s “Facebook Class”, but for iPhones. Students work in groups to create applications in demand by certain clients, and the three apps that were chosen in the pilot class in the spring were: an interactive marine sciences textbook, along with videos, pictures, and research papers relevant to the course (and this model can and will be applied to other courses as well); an interactive medical questionare to help diagnoses from anywhere; and I don’t think they showed us the fourth one. Anyway, it sounds cool and I definitely want to take this class after I take CS 108 or at least once 108 is no longer a pre-requisite.

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