DiSessa, 1983
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SUMMARY OF THE SUMMARY
Andrea diSessa claimed that, based on our experience of everyday physical phenomena, we all have collections of common-sense, intuitive ideas that seek to explain the phenomena. These naive concepts or general principles are called “phenomenogical primitives” or p-prims, and usually operate below the level of consciousness. For the novice student, the process of learning consists in “cutting apart” some p-prims into ideas that more accurately reflect reality, and in abandoning others that are false or no longer useful. This results in a re-ordering of the priority of these p-prims so that they do not constitute a barrier to an expert understanding of physics concepts. (An example of this might be the demotion of the “rigidity” p-prim so that the “squishiness” and “springiness” p-prims can guide the student’s thinking more accurately about certain physical processes.)
Recognizing which p-prim to apply to the phenomenon under study is an important skill that the expert develops on her way to a true explanation of the phenomenon. P-prims can still help the expert in two ways. They can serve as a short-hand model of a physical phenomenon that, while not exhaustively telling the whole story with maximal explanatory accuracy, conveniently organize related concepts, and so save time and effort in the analysis of the phenomenon. Also, accurate p-prims can control the reasoning pathways of the physicist, by intuitively alerting her to which concepts are appropriate to apply in certain circumstances (the “cuing-priority”) and which concepts need to be reordered in their priority or abandoned (the “reliabilty-priority”).
DiSessa’s thesis is that learning physics depends not so much on the quantity or quality of science information presented to the student, but on the process (sometimes intuitive, sometimes intentional) of the novice prioritizing previously-held naive p-prims, until the p-prims are replaced with more accurate and fundamental explanations, resulting in an expert understanding of physical phenomena.
Ch. 2 Phenomenology and the Evolution of Intuition by Andrea diSessa, 1983
INTRODUCTION
In math, a primitive, foundational, axiomatic level of understanding is accepted as necessary; in science, many agree that this level exists as well. It also seems to be true about cognition: “Because of this character we shall naturally find such primitives, like axioms, at the root of many explanations and justificiations.” In this chapter, the “evolution and function of primitives in physics understanding, from naive to novice to expert.”
Goethe referred to “primordial phenomenon,” high level ideas that were purely abstract but still phenomenolgical (empirical rather than purely rational). Given the existence of these ideas, direct experience can play a role in understanding abstract concepts. DiSessal prefers the term “phenomenological primitives” or p-prims, to describe ideas that are accepted, usually unconsciously, as axiomatic, based on our common life experiences.
The naive physics student begins with a rich but unorganized collection of phenomnea on which to base his understanding of physics. Further study and further experience on the part of the student sorts the p-prims by their usefulness, until some are “cut apart” or abandoned as useless. This evolution of cognition is not always purposeful, explicit and intentional; indeed, it is sometimes a covert process. Along with this at the level of cognitive modeling is the activity of recognition. “The process of recognition of phenomena is central” (p. 17).
In this chapter, DiSessa cites the interviews done with four MIT undergrads taking freshman physics. However, perhaps most of this comes from his own thinking and observations on learning because there is no data, as such, other than the summarized results of the interviews. “The interpretations we offer motivate and explain the ideas we propose; they are not offered as proof” (p.17).
SPRINGINESS
The first student, M. is given the example of a falling and rebounding ball to explain. The question: as the ball falls, it gains KE, but when it collides with the floor, it is motionless (KE = 0). Where does the energy go? M. had difficulty indentifying the storage of the energy in the mechanical distortion of the ball and the floor, as energy can be stored in a spring. She gave an almost animistic explanation of the more massive Earth rejecting the energy that disturbed her but could offer nothing better. Even when “squishiness” was offered as an explanation, she rejected it for things that in her experience did not squish, e.g., ping pong balls. Later, after studying kinetic theory, M., still incorrectly, offered that some of the KE could be stored as internal energy (heat). Because she did have a naive “rigidity” p-prim, but did not have a “springiness” p-prim, she did not “see” springiness in the various rebounding balls considered by her interviewer. DiSessa believes that “within her intuitive frame,” i.e., with these p-prims in place, it makes no sense to ask her why some materials (steel, glass) are rigid, because this concept was held uncritically, as a p-prim (p.18).
Expert physicists, on the other hand, make rigidity a low-priority explanatory concept, choosing instead higher-priority concepts that explain and subsume it, like forces. “A physicist views rigidity as irrelevant to any deep explanation of how things happen” (p.19). Something like springiness, however is (1) a more powerful explanatory concept, and (2) provides a “convenient organizing conception,” a “macro-model” which summarizes the detailed causality of an elastic collision. But since perfectly elastic collisions are ideal rather than real, the expert physicist is comfortable with numerical results that approach but do not attain ideality, and is ready to turn to a “more elaborate special model,” if a deeper, more fundamental explanation is necessary.
The difference between the expert and the novice is “control of reasoning.” When an expert sees the phenomenon take place in a real situation, recognition of the relevant concept occurs, and application of a ready-made macro-model happens. This “cuing mechanism” which is part of the expert’s reasoning arsenal saves the expert time and increases his accuracy in explaining a phenomenon. However, this almost instinctive level of problem solving may not always yield the most accurate explanation; the expert physicist may have to slow down and appeal to a more accurate model consisting of higher-priority concepts. DiSessa’s point in all of this is to examine how these concepts are organized and accessed, how they are “prioritized” by the naive, the novice and the expert. His thesis: “Our proposal, in brief, is that explanatory knowledge of a certain type has a particular place in a priority hierarchy” (p. 19, footnote 2).
DiSessa identifies two types of prioritzing that are concerned with the “flow of control” to and away from an explanatory concept. “Cuing priority” lets the expert know that a concept may have some explanantory usefulness; “reliability priority” warns the expert of potentially higher priority knowledge, that would result in a more accurate or fundamental explanation (p.22). As pointed out already, DiSessa believes that all this occurs quickly and unconsciously, and rather than being high-level reasoning, constitutes a “low-level control of reasoning mechanisms” (p. 20, footnote 3).
Next, DiSessa points out that choosing between priorities is highly context dependent. If a student has little prior knowledge about a phenomenon (e.g., the “springiness” of steel) there will be too small an incentive to choose the best explanation over an incomplete one. To become more like the expert, the novice must enlarge “the set of contexts which cue the idea” (p.20). So, the reliability priority of fundamental explanations are of high reliability only in a context where that explanation is applicable. But even if a concept is applicable in a particular context, a still higher priority explanation (e.g., “conservation of energy” v. “springiness”) can trump it (p.20).
Finally, DiSessa suggests that there are pathways of control among the different priorities of explanatory concepts, where a context in which a more naive idea exists (e.g., the p-prim “bounciness”) cues and then defers to a higher-priority idea (the p-prim “springiness”). Although an expert probably would not appeal to such a low-priority idea at all, for the naive or novice, it can function as a pathway to more fundamental, higher-priority explanations.
If all the above is true, DiSessa doesn’t hold out much hope for changing the novice’s mind by simply telling them which explanatory concepts are the correct ones. “Reorganization and change of function of knowledge structures seems less obviously amenable to external manipulation then ‘giving students new knowledge’” (p.21). Instead, she thought that such a shift in learning might have to be an extended process “in which the coherence and success of the evolving new control system gradually compels reorganization of priorities” (p.21).
To illustrate this, DiSessa returns to the hapless M., who is actually doing a good job of appealing to various contexts in which she has witnessed springiness, notes an apparent family resemblance among them (“squishiness” and “rebound decreases with softness”) but still defends the wrong conclusions concerning the phenomenon, conflating modulus of elasticity and hysteresis (two unrelated properties of matter). Then DiSessa discusses an interview with T., where the property of stable balancing is illustrated with a pencil balancing on a finger. After trying to explain the phenomenon conventionally (torques, etc.), he noted that when he did work on the pencil, it seemed to store that energy and recover it to rebalance the pencil. T. noted that the pencil was acting like a spring, but being a novice, was unable to analyze it further; he could only claim the analogy as an attempted explanation, showing at least that he could abstract springiness as a model, unlike M.
DiSessa has described the development of the p-prim of springiness from an everyday phenomenon easily observed but not so easily explained (naive), to an abstraction (novice) of one of the properties of matter (squishiness) that makes things bounce. Finally, it becomes an archetypal model or “schema” that serves the expert as an explanation. It is broadened (all bouncy things) or narrowed (no things that stay squished) as necessary. It serves as an explanation, yes, but is readily abandoned for a higher-priority one, if needed.
OHM'S P-PRIM
Some phenomena (like the example given, of a vacuum cleaner motor changing its pitch when the airflow is restricted) take a form very much like Ohm’s Law: an impetus (analogous to voltage), a resistance (electrical resistance), and a result (current). In the case of the vacuum cleaner motor, this p-prim can cause a “conceptual illusion,” mistakenly recognizing an interference when there is none. Or it can result in an anthropomorphism, postulating that the motor must work harder to overcome the perceived interference. DiSessa points out that as students move from naive to novice, they recognize the lower-priority nature of this explanation, often to the point of rationalizing data to account for it.
What we might call the “Ohm’s Law” p-prim (an impetus modulated through a resistance yields a result) seems intuitively correct. However, even when explaning the properties of an electrical circuit, it turns out that the way Ohm’s Law is usually taught is an interpretation that lacks the “deep meaning” of a fundamental explanation (p.25). DiSessa does not explain how we really should be understanding Ohm’s Law in a high-priority, fundamental manner. But, if he is correct, then the “Ohm’s Law” p-prim is abused by some physicists to explain Ohm’s Law itself!
ROLLING AND PIVOTING
In another illustration of how p-prims effect our understanding of physical phenomena, DiSessa discusses two coins, one rolling around the circumference of the other. The truth is that the top of the rolling coin must end up touching the bottom of the stationary coin, concluding with both coins having the same orientation. The “false intuition” that DiSessa noted had the marked arrows on the coins pointing in opposite directions for two reasons: (1) a confusion of rolling with an other p-prim, rotation, and (2) a confusion of rolling with yet another p-prim, pivoting. Once the rolling p-prim is further limited to a restricted version of rolling, “rolling on the level,” and pivoting is recognized, the coin problem is easily solved. He noted that “[r]estriction of meaning like this should be expected to be typical of the evolution of p-prims” (p.28). (DiSessa also suggests that for those who still don’t see the coin as pivoting, to imagine the circular coin to instead be a many-sided polygon.) So, a theory that saw all rolling as a special case of pivoting would demote the rolling p-prim to a lower priority. DiSessa points out that in a case like this, where there is a continuity with naive ideas and that cuing is an integral part of expert knowledge, even experts will make good use of their phenomenological knowledge to solve such problems.
A NOTE ON ABSTRACTION
DiSessa defined “abstraction” as the process “through which naive phenomena become changed to serve as expert p-prims” (p.29). As an illustration of this, he postulates a student learning about potential energy by compressing a spring, but allowing his “squishiness” p-prim to dominate his thinking. [I found this confusing (is he now conflating observed phenomena with p-prims, which I take to be explanatory ideas) and disingenuous (he made up this “thought experiment” although in a footnote claims that several students have had this experience.] In explaining how a p-prim is formed, he said that common sense observations of a phenomenon serve as a model for the causality under study, and that the resulting sequence of thoughts “binds together in an appropriate way the elements of previous knowledge which serve as a basis for the interpretation. The structure (does she mean organization of new ideas?) of that comination is the new element for the student,” and the student feels justified in accepting the new ideas because it appears to explain the phenonemon being studied (p.29). Abstraction, then, is when concrete entities (the student, the spring, etc.) become part of the explanatory story, resulting in “the selection of a conventional interpretation of an everyday event.”
PERSISTENT FALSE INTUITIONS
DiSessa began by noting that he has really been discussing the process and role of “intuition” in his chapter. Physics teachers want to develop their students’ sense of “physical intuition,” and some research is now being done on the way in which “preconceptions” (actually, his p-prims, but those with an unwarrentedly high priority that need to be demoted) persistently prevent an expert understanding of physical phenomena (p.30). He mentioned three: (1) “Dying Away” (a natural, simple, unanalyzable principle that causes a misunderstanding of the role of friction, part of the “intuitive knowldege structure” that attempts to explain motion, sound, etc.); (2) “Force as Mover” (the idea that the direction of the force being studied decrees the direction of motion of a body by ignoring the effects of any previous motion, perhaps due to naive p-prims like “carrying” or “moving from a state of rest,” which ignore more expert p-prims like “pivoting” and “deflection” which compete with the more naive p-prims only when they are emphasized or isolated); (3) “Force as Spinner” (an idea that the application of a force that produces a torque somehow drains away the effect of an applied force, well-illustrated by the famous “yo-yo” example, where even experts find “force as spinner” powerfully cued and given a high priority).
SUMMARY AND CONCLUSION
Everyone has a collection of naive abstratctions of simple, everyday phenomena which they observe. These “p-prims” become less primitive, or are abandoned altogether as the student progresses from naive to novice to expert. Or, they can become part of the experts thought structures, either as (1) helpful, short-hand models, or (2) an intuitive cue that directs the expert to pursue more sophisticated explanations. The difference between a naive/novice (common sense) and expert (scientific reasoning) approach does not have so much to do with the content of one’s knowledge, but with the organization and prioritization of these p-prims. Understanding this, along with principles of recognition and remembrance of an interpretation of an even, is important to understanding human cognition. Teachers especially should pay attention to a student’s collection of p-prims, and seek to modify the priorites of those p-prims, not only to make difficult concepts understandable to a naive student, but also to help the student develop an expert understanding of science concepts.
(Mark Pichaj)
