New-Media Literacies in Visual Studio .NET

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Figure 9.2. A template for the rocket ship program.
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Figure 9.3. Left, A normative programming model, equivalent to F = ma (suppressing the role of m). Right, The relevant part of the spaceship program, developed by students.
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1 The power of abstract, well-adapted representations: We trace much of the success of this activity to the fact that we framed the task in terms of programming. In particular, students had learned about vectors, which therefore constituted a ready language in which to express problems of motion. Vectors are precisely the right level of abstraction for expressing Newton s laws, although traditionally algebra and calculus are used in 231
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Andrea A. diSessa place of programming constructs. In this activity, students spontaneously introduced vectors into the program, although they named them whimsically (e.g., George as the name of the velocity vector). An important remark is that learning vectors and some relations to motion was remarkably easy. Students had seen simple programs that moved objects with a vector velocity. The meaning of vector velocity became intuitively clear in dragging the tip of the velocity vector around, showing that the object moved always in the direction of the vector, with a speed proportional to its length. Vectors, in fact, were also easily learned in this way (according to principle 4, of dynamic representations) by much younger (sixth grade) students. They became very popular as user interface controls in game programs. While another prerequisite to this task, vector addition, might be deemed an abstract principle in traditional instruction, its meaning was easily visible and important in manipulating motion in the context of such games. A productive level of abstractness is one hint that a representation can provide. Programming representations have another advantage, mathematical precision, which we saw working to students advantage. For example, in a preliminary activity a few days before, students discussed the effect of a hit (an impulse) on a moving object. In that natural language context, students accepted as adequate a simple statement that the hit combined with previous motion. In the context of formulating a program, however, the idea of combination was just the start of an extended inquiry into exactly how impulse and velocity should combine and be situated in the overall program. An absolutely critical point in all of these examples is whether the students understand their accomplishment, or whether the representational (and other support) they are given led them on an un-illuminating garden path, however correct we might view the result. In this case, I report, too briefly, that students struggled substantially with the main conceptual element here, how thrust combines with existing velocity. Several proposals were tried and eventually rejected. Even after the idea of vector addition was introduced as a possibility, how it should be used in this case was unclear. Finally, one student tentatively proposed that thrust combined by adding with existing velocity (George) to create the new, self-perpetuating velocity. Several students immediately reacted with enthusiasm at the proposed solution, and this generated the final form of the program. Consult Sherin, diSessa, and Hammer (1994) and diSessa (1995) for details. 2 Representational task tuning; conceptual/representational pump-priming: It should be clear that we prepared the way for students work by intro232
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New-Media Literacies ducing vectors as a way to describe motion, and also by introducing them to vector addition. In fact, they had used and experimented with vector addition as a way to represent combined, simultaneously present motions, such as the motion of a boat in the current of a river. Students introduced the idea of vector addition in the spaceship context by explicitly invoking the boat-and-river-current model. But they still had more work to do to adapt it to this problem. In particular, they had to understand how the transient thrust becomes permanently incorporated into motion (via vector addition). The template we provided, Figure 9.3, scaffolded focus on the key conceptual parts. The tick procedure represents Newton s first law. The kick procedure is the locus of Newton s second law. As the group seemed just at the limit of its competence in accomplishing this task, we feel the activity would likely have failed without this simple but effective partitioning of concerns. 3 Dynamic representations: I have already mentioned the effectiveness that we felt dynamic representation had in conveying an understanding of vectors in simple programs that controlled the real-time motion of objects. In developing their version of Newton s laws, the students often ran the program in their imagination to evaluate hypotheses for filling in slots in the template. In addition, once the program was complete, students played with it to solidify its meaning and to develop an intuitive fluency with its implications. 4 Support for social collaboration: As a full-class exercise, managing student student and student teacher collaboration is a critical need. In this case, a single, hour-long episode that targeted a particular result depended in important measure on how the members of the class coordinated their efforts. Here, I mention a few examples of the types of coordination that we listed under the general topic of collaboration. a Reading student ideas The evident currency for the discussion was programming code. While perhaps as ambiguous as words at first mention, code fragments can be disambiguated by imagining or actually running the program. While nuances of student intuition were not necessarily captured directly in code, it constituted a public, stable, and precise backdrop on which the more subtle job of physical reasoning and judgment could be played out. In this activity students seemed to participate with a feeling that code fragments could stand for their ideas. For example, students pointed to code when referring to my idea or to the ideas of colleagues. b Goal and hypothesis clarity How does one know when one has a 233
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Andrea A. diSessa theory of motion On the other hand, the concrete goal of this exercise was to produce a complete, working, and sensible program. Although sensible may be an important topic for debate, the completeness of the program for accomplishing the given task, and the fact of its working, are easily observed by the whole community. In managing the discussion, the teacher often asked for clarification concerning what students meant in terms of code. He asked, what does that mean for our program What does that say about what s in kick c Summary representation The end-state of this design was a simple, memorable program, similar in function to mnemonic recitation of equations like F = ma. We know students could easily reproduce these little templates; for example, the river-and-boat code fragment that introduced vector addition into this problem came in as an easily re-produced code fragment. Of course, mnemonic symbol sequences are not the same as understanding. But they are a part of it. Scientists sometimes think by drawing in equations when appropriate and manipulating them. Student understanding of Newton s laws works, in some measure, as a person-plus-symbol-system interaction, which is, as mentioned, my prototype for the very meaning of literacy. d A focus for intervention Conducting this discussion was a challenging task, even for the talented (graduate student) instructor involved in designing Newton s laws. In our analysis, we saw him using focus on the representational form of the problem to bring students together, and to move the discussion forward. He often asked students to focus on a particular place in the program, or how their ideas related to particular expressions and places. He sometimes intervened in suggesting more mnemonic terms for elements in the program. Thrust, for example, emerged from a negotiation with students. (George would be renamed in later work, following this activity.) As a last resort, teachers can suggest particular expressions, which can then be examined for their meaning and sensibility. In this case, the instructor did not provide any substantial suggestions about what should be in the program. In general, teachers competence at these skillful interventions would be an important part of their new literacy. With respect to non-representational principles, the success of this case seemed to us most sensitive to the framing of the task (principle 7). We believe the semi-concrete but also non-earthly context provided enough remove from familiar contexts to allow consideration of some of the non-intuitive aspects of Newton s law for example, the idea that motion would continue forever without a thrust. At the same time, students evaluated the resulting motion in terms of pro234
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New-Media Literacies ductive earthly intuitions (principle 6). See Sherin, diSessa, and Hammer (1993) for details.
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