Representational principles in VS .NET

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2 The power of abstract, well-adapted representations: Much of modern science relies, near its core, on representations such as algebra, calculus (which is both a conceptual and representational accomplishment), differential equations, etc. A particular representation can pick the right level of abstraction, and thus constrain the search for valid and comprehensible laws and models. Certain (mainly) representational entities, such as vectors, are perspicuously adequate to encode exactly what the history of science has found out about certain domains, notably many aspects of physics. Thus, providing a representational form can also provide important hints and constraints in re-inventing basic science. Of course it is critical that students understand those representations enough to use them creatively. This is precisely a key advance of new 222
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New-Media Literacies media, extending traditional scientific representations with ones that are as expressively powerful but much easier to learn. A big and perhaps surprising lesson here is that writing simple programs turns out to be much easier than writing, for example, algebraic expressions for important science, and it is arguably as or more expressive of the important underlying ideas (see the discussion in diSessa, 2000, and Sherin, 2001). 3 Representational task tuning; conceptual/representational pump-priming: Many of our re-invention tasks are framed in representationally partially formed terms. For example, we often provided a template that gives a hint or starting place for inquiry, helping students by putting the focus on a key conceptual point, or by providing an organization of the task. A related strategy, pump-priming, involves prior exploration or instruction in related tasks, or in a task that is a sub-task of the full re-invention task. This can take the form of an inquiry that results in a model that is related to or part of the target re-invention. Considerations in formulating a starting template or in designing a prior exploration can tune tasks to an appropriate level of difficulty.3 4 Dynamic representations: Paper and pencil, algebraic, and similar representations lack a pair of characteristics that are an important part of the story for new media: dynamics and interactivity. These have implications both for expressiveness and for learning. With respect to expressiveness, laws of nature expressed as simple programs can be run, and students can see the effects of the laws, for example in actual motion of objects. In developing their own versions of laws, students can see, consider, and react to their symbolic hypotheses. This is more than supporting feedback loops; it also invokes intuitive and perceptual knowledge that might otherwise be locked out of student work.4 5 Support for social collaboration: External, perceptually shared representations support good collaboration. Of course, the representation needs to be properly expressive of the ideas at issue. Thus adaptation to both science s best ideas (item 2 above), and to student ideas (in item 4 above) is important. A positive evaluation of a representational form depends on how the medium meets these requirements. Support for collaboration has at least the following aspects: a Reading student ideas Words are notoriously vague, and in many cases new-media and computational representations provide a better expressive language for students to display, and teachers to read, student ideas. b Goal and hypothesis clarity Creating computational representations 223
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Andrea A. diSessa has an evident end-state in many cases: A program runs and shows adequate behavior. Contrast this to producing a theory or even creating an equation, which has uncertain implications. At earlier stages, students can express hypotheses often in terms of particular, unambiguous expressions. c Summary representation Like famous equations that litter the history of science, from Newton s F = ma to Einstein s E = mc2, computational representations can provide compact and precise summaries of key ideas. This compactness and precision are often in sharp contrast to natural language or pictures. Many who extol the virtues of new media completely ignore the fundamental and transformative power of symbolic formulations. e A focus for teacher intervention We have seen teachers use external computational representations in many ways to help students along productive intellectual pathways (conceptual support) and, more broadly, to provide practical and discussion/organizational guidance (pragmatic support). For example, a teacher can focus attention on a particular part of a program, or, more strongly, suggest a possible direction of pursuit (either a known-to-be-productive direction, or one chosen for interesting contrast) in concrete, representational terms.
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