Unfortunately we don’t have other videos, so I’ll attempt a description. The key was to start with very concrete numbers and use the wireless submission of answers to the teacher to foster conversations about the pattern that the students observed in their classmates’ answers. The software’s ability to store and replay the animations was critical, both for students to review their own work and for the teacher to view, select, and replay student work for class discussion. Also, the ability to hide the rows or columns of an array in order to get students thinking about the general case was important. A student using cubes to create a physical array could hold his or her hand over the middle of the array in order to convey the notion of generality, but we think that the new version of the software that enables creation of an N dimensioned array will make the concept even clearer.

All of the above! The students used the animation tool to reason about the problem, sometimes practicing several times before submitting an animation to the teacher. The teacher viewed the student work on her machine and chose representative examples to display publicly for the class in order to foster discussion. The student work is displayed anonymously, but we’ve noticed with younger students that they often want to claim their work. (The 2nd graders seemed less concerned with correctness than older students.) The teacher also viewed student work in order to identify students who needed additional help.

Just to add to Kimberle’s answer: Part of the classroom process was to replay selected animations for the class to foster classroom conversation. We would replay a student’s work while she described what was happening on the screen and her thinking process. A useful aspect of the animation system in this situation was a speed control knob, so that we could slow down what was happening and let students contemplate and discuss each step.

Not at the moment, but we’re hoping to have a downloadable version of the software available by the end of the summer or early next fall, on both the project website, http://tma.mit.edu, and the related project’s website, http://ink-12.mit.edu.

One of the only challenges with the younger students was their remembering to tap on the Record button. (We’ve used this software with older students, who didn’t seem to have that problem as often.) So we implemented a “Forgot to Record?” button that created an animation of all their interactions. (The software stores all their interactions behind the scenes anyway, in what we call an interaction history. The Record button just lets students choose what section of that interaction history they want to be explicitly visible.) The disadvantage of relying on this button is that all a student’s extraneous interactions were included as well, e.g., erasures. That extra information is incredibly valuable for a teacher, but from the student’s point of view, the extra steps can be distracting. But at least the students didn’t lose their work and could review what they did and create a cleaner version if they wanted to. (A very loud cheer went up in the classroom when we announced this new feature a few days into the trial!)

Thanks for your comment, Courtney. Interacting with the technology was, perhaps surprisingly, never an issue for the students. I think we can take some credit for that, as we worked hard to make sure the interface was easy to use. But it also reminded us how young students are digital natives; not only are they used to interacting with technology, but they generally have good help-finding skills (e.g. asking a friend or trying a bunch of things) when they get stuck. What they struggled with more was understanding the relationship between a representative and the math, but that’s why we are doing this work.

Miriam -
We are doing an in-depth analysis of the use of the underlying CLP system in a 5-week unit on multiplication and division in a 3rd grade class. We are in the process of that analysis now. We have also published several papers that are linked to from the website of the related project INK-12: ink-12.terc.edu.