Doherty - Important features of computer modeled systems

As Kafai notes, there is a problematic lack of diversity in professional math and science. This comes as no surprise, however the reason proposed is new to me. That the representations of content and the way in which we manipulate and access that content may specifically reflect the people at the professional level instead of the best or only methods of the discipline. This puts a different spin on the results in Wilensky and Resnick’s work on understanding levels. While they clearly show that the general public, as well as specialized professionals, have difficulty with negotiating the notion of levels within systems, they also show that new representations of those systems aid in understanding. Thus, perhaps with different representation, not only would a wider population have access to thinking in a way that suits them, but the subtle intricacies of  complex content would also be better understood.

In each of the examples suggested by Kafai, Wilensky & Resnick and Simpson, Hoyles & Noss, there are common features that nonetheless are uncommon in traditional instruction. Each feature provides higher levels of student agency in learning as well as flexibility of representation within a structured model.

• Non-static visual representation – Most commonly content is seen without movement or change. Textbook drawings, written explanations or teacher drawn examples may seek to provide a visual representation, yet expect the student to imagine the related actions. Multiple issues arise from this expectation: some students cannot mentally create the moving imagery, there is no way to assess the accuracy of each student’s visualization and the student’s personal assumptions color their mental video. Take for example the traffic jam. Even if the instructor explains the mathematics and explicitly states that the traffic jam will move backward (which of course takes the lesson out of constructionism and into instructionism), it is highly likely given Wilensky et al.’s evidence, that the student will imagine cars being added from behind but the object of the traffic jam moving forward.
• Possibility for student directed input variation – When modeling a situation or system there exist varying factors that influence the outcome of the situation or the behavior of the system. I cannot think of a situation in which all of the factors remain stable in all contexts. For example, gravity might be constant, but the object’s relation to gravity can change. In the collision model, the carts are governed by specific rules of physics, how those rules affect each collision changes based on the mass, velocity, and direction of the carts. By allowing students to change the input values or object states they can explore various cases of a single content idea. The examples given throughout the articles add an important component to this; the students construct each case as it becomes important to them. Choice gives the student agency over their learning, and affords them the opportunity to discover personal questions and inaccuracies in thinking, e.g. the traffic jam, forest fire movement, sheep survival, etc.
• Convincing accuracy through personal construction – Due to the difficulty of understanding the effect of micro and macro actions on a system, as noted in Wilensky & Resnick, scientific results, often through mathematics, can contradict our “common sense.” This can lead to student’s saying “okay, I’ll just believe you” when confronted with a counterintuitive concept.  The student gains no true understanding and possibly thinks it’s not actually, really true because they cannot make sense of it. In these models, there is no “man behind the curtain,” the student either programs the model or they can inspect the existing programming. There is a cyclical process of understanding: disbelieving the results, then checking the code, then trying another case, until they are convinced the model is correct and thus the results must be real. Their learning lives up to their own need for rigor, and is furthered by the time spent figuring out why the code produces the counterintuitive results.

            When thinking about helping the USN students model systems, these elements should be reproduced. Whether or not we create the structure of the program, it’s important that we not limit the scope to our own understandings. I am also reminded that while systems seem complicated in action, the rules governing those actions are very simple. Therefore programming a system is rather easy; it’s interpreting the results that provides challenge. On a personal note, I greatly enjoy the surprising twist that results from this simple-complex dichotomy. It immediately produces questions that are virtually impossible to ignore.