Reconsidering Conceptual Change: Issues in Theory and Practice
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Does it deserve the same appellation, "concept"?
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If it does, how much does the category tell us about J Difficulty in mastering a concept does not necessarily depend on knowledge-structural characteristics ofthe concept. It might be, for example, that the natural environment is simply impoverished in support for learning it. However, even in that case, difficulties in learning diffirent concepts may certainly be systematic, even if they are in relation to existing or possible learning environments rather than intrinsic to the nature ofthe concept.
J The fact that bluare is a simple combination ofalready existing concepts probably explains its ease of learning. Wouldn't it seem important to know which already-known elements contribute to learning new scientific concepts? Surely learning most concepts can't be tabula rasa, and a profile of contributing elements is more than plausible as an important part of understanding a knowledge systems view of a "new" concept. Yet, conceptual change literature, for the most part, treats the issue at the coarsest possible grain size; as in Figure I, the expert concepts ofheat and temperature, orforce, etc.
S Of course, since bluare is an extreme example, few would study its learning as related to scientific concepts. Yet, how do we know there is nOt a complex continuum of scientific concepts, with importantly -different qualitative properties, as illustrated by dog, bluare, and to come force?
I mean to refer to the operational concept in somewhat the Piagetian sense , enfolding the operational properties of cardinality, such as invariance on rearranging a set of objects, or invariance in the case of no additions or removals. This is much sparser knowledge territory than animal types. There simply aren't any similar categories until one gets to the rarified air of group and field theory.
So, I argue, the learning of the concept number is very likely to be quite different from learning dog. Similarly, there is no plausible prototype for "number. All cardinalities have exactly the same operational characteristics. Finally, consider the central concept in most of. Quite plausibly and a significant literature backs this up; e. And yet, it is clear from extended learning difficulties that the professional con. This is quite a particular regime of learning: Substantial prior resources exist perhaps somewhat like bluare , and yet a deep gulf exists between naive and expert concept.
The nature of the gulf is as yet much in debate, which, once again, highlights the need for a refined ability to describe a learning trajectory bit-by-bit in order to understand and catalog such gulfs. With respect to multiplicity, my program of research has attempted to identifY many different types of mental entities diSessa, For simplicity, however, I will discuss only two particular types that make evident a huge range of kinds of mental entities that may be implicated in a more refined view of conceptual change than we currently have.
Fortuitously, the pair of types I discuss are both a among the most theoretically developed and also b are dramatically different in their properties. So exposition concerning these two types can do double duty in this chapter. That may be obvious, but a theoretical accounting for ease of learning is complementary and may be part and parcel of an accounting for learning difficulties.
Why do some people learn certain concepts almost effortlessly while others clo. All in all, I claim there is a huge diversity in conceptual learning phenomena that is not remotely accounted for in current accounts of conceptual change. Different sorts of concepts are evidently different, one from another, and may need individual accounts of relevant processes of change.
Even if concepts are all the same in some deep structural sense, or differ. In order to deal with apparent empirical diversity in knowledge types, my preferred method is straightforward-to begin developing a larger and more i, II accountable list of types of mental entities.
It may be II, , that dozens or more such elements lie behind the construction of a single professional concept, in which case the class of stories about conceptual change illustrated in Figure 1 is patently hopelessly inadequate. In addition to a diversity of types multiplicity and a proliferation in numbers of knowledge elements grain size , several other trends seem strongly implicated in the above discussion.
Reduction in grain size and therefore an increase in the I , I difficulty of even listing all the cognitive elements that go into conceptual change j entails a systems approach. If many elements go into the construction of a concept, i how are they coordinated and combined to produce "a scientific concept"? Furthermore, if multiple elements are involved, then we must describe much more carefully when they work contextuality. A greater accountability to contextuality also means we may have a much better chance to describe particular configurations that cause problems or lead to productive new accomplishments along an extended learning trajectory.
It all seems a mushy soup where what counts as a theoretical perspective can never come to brass tacks in allowing a comparison of its relative effectiveness to that of another view. Vague ideas are extremely hard to hold accountable. Instead, they are mere motivators of experiments and broad interpretive frames for results. Investigators paint data with "word pictures" invoking their favorite terms without ruling out alternative interpretations, and without any strong tests for the cogency and adequacy of the terms they apply.
Concomitant to weak theory, empirical studies don't attend to details. Researchers do not attempt detailed accounts of particular applications of concepts-or descriptions of what has transpired in a segment of learning protocol-for the simple reason that there are no specific, "mechanistic" stories in the offing.
My basic contention is that we have said nothing falsifiable when we say force is a concept, or that impetus ideas constitute a theory McCloskey, , until we have said much more about what each of these knowledge terms entails. Stunningly little process data is taken into account in conceptual change research. By and large, the paradigm has employed before and after snapshots. Right and wrong answers-or similar behaviors, all distanced from cogent theoretical accounts of the elements and processes of change-are counted.
Protocol segments are glossed as suggestive reflections of, for example, an "underlying theory," without argument that all the elements of a theory are evident, and without competitive argument that other explanatory constructs are less adequate than "theory. There is a huge ontological gulf between, on the one hand, protocol coding categories and, on the other hand, knowledge element types or system configurations. Yet, our research techniques have yet to clearly distinguish these. To sum up, I advocate a richer empirical accountability, parallel to one for theory.
Such intervie al. They allow nuanced setting of th context to investigate contextuality. They show subjects' levels of commitmen: such as certainty and ambivalence. In a clinical interview, we have many opportunities to look at small moves in learning that contribute, overall, to conceptual change. I've set out a big agenda for the rest of this chapter. I want to illustrate: I. What more accountable theoretical terms might look like.
What different exemplars of such terms are plausible and plausibly play an important part in conceptual change. How different from each other knowledge types might be, and how different types can account for different aspects of reasoning and conceptual change. What sort of details of subjects' behavior can be accounted for with sharpened theoretical terms. For example, what are typical easy and difficult accomplishments along the path to conceptual competence?
I don't intend to prove or demonstrate here, but can only illustrate and suggest. Adequate empirical and theoretical accountability, given the general state of the art, doesn't fit easily into a half-chapter of a book. There is simply too much theoretical groundwork to do, and too much detail in adequate empirical argument. P-prims The first knowledge type I discuss has had an extensive history, and it has been rather thoroughly explained in other places.
See, for example, diSessa , ; ]; What stands here is a review. The nature ofp-prims P-prims, I claim, constitute the bulk but not the totality of intuitive physics, the precursor knowledge that gets reconstructed into schooled competence with Newtonian physics. The name, p-prim stands for "phenomenological primitive.
However, consider the characteristics described below. P-prims have the following properties.
Reconsidering Conceptual Change: Issues in Theory and Practice
They are atomic in the sense that they are essentially always evoked as a whole iii 'contrasno scientific concepts, which I believe can be accounted for only with a systems analysis. The full collection of p-prims exhibits some mild degrees of systematicity, but p-prims are loosely coupled. They do not exhibit deductive relations or any other systematicity typically expected of, for example, theories.
If you see something pushed, you are not surprised-in fact you expect-that it moves in the direction of the push. There is no "covering theory" or articulate reasoning on tap that explains them.
In these cases, subjects might have an intuition about what might happen but then lose it as their attention shifts. In some instances, several conflicting p-prims might apply, and there is unlikely to be any way to resolve such conflicts. Describing p-prims in words is difficult or impossible for subjects, as opposed to theorists. They are frequently fairly simple abstractions of familiar event, such as the fact that a pushed object moves parallel to the push.
However, p-prims' properties especially attachment to particular circumstances are t t determined typically by a long process of development. Instead, many p-prims find useful places in the complex system that is an effective scientific concept. A p-prim might come to be known as an effective special case of a scientific principle, and it will be used in place of the principle in apt circumstances. However, p-prims will no longer function as explanatorily primitive.
Physics explanations need articulate accountability that p-prims can't provide. The changing function of p-prims in learning and t indeed, the natural evolution of the collection of p-prims may be t described as "shifting priorities," degrees of attachment to particular contexts of use. These properties of p-prims are not an ad hoc collection. They are mutually dependent and mutually suggestive in many ways.
For example, the fact that the elements are small suggests large numbers. Large number are reinforced by the fact that p-rims are relatively easy to generate. A single mechanism of learning shifting priorities accounts for naturalistic learning of p-prims and what happens in school. Lack of articulateness goes hand-in-hand with data fluidity. All of them will be used in empirical analyses later in the chapter. Ohm's p-prim entails the following expectations: More efTort begets more result; more resistance begets less result; and so on.
For example, a person pushing against another increases his effort and moves the other back.. Water levels itself in a pan. For example, a box in a wagon moves with the wagon. Process data concerning p-prims. The following example illustrates several of the characteristic properties of p- prims. It shows data fluidity in that J at first feeJs she sees how a situatiQn will Her lack of anything to say illustrates the problematic connections between p-prims and language inarriC1llareness , The insligating interview probe was to ask what happens when a small weight is added to a pulley setup in which two large and equal weights are "balanced," See Figure 3.
The word balance is nol used; instead, the idea is provoked by a symmetrical picture, What J says initially is consistent with generalized springiness, The weight simply perturbs the system by some amount. However, a different intuition soon takes over, one that happens to be correct-thc unbalanced system continues to move away ITom "equilibrium.
Had she not evidently lost track of her initial conceptualization, her lack of showing proportionality of excursion from equilibrium with perturbing strength would have contradicted the proposed descriplion of generalized springiness. Thus, matching process data provides many opportunities to contradict theoretical assumptions or prior empirical resulls such as the nature of generalized springiness , See lhe "principle of in variance," discussed later.
Figure 3. A "balanced"' pulley situarion is "diseqlllibrmed" by a smallll'eighl on olle o[two larger alles. J: I mtan if mal'S a tiny, tiny weight, if II probably go down, and then. If lhal weight is:. It wouldn'l stop. It would keep going slow, slow, slow all the I way down. II would not stop. I: So you changed your mind. I: Can you say what made you change your mind? I: Cause it didn't make any sense?
J: No. I don't know why I said that. I don't know. I don't know if I didn't think about it or I just sat there thinking in my mind, but I wasil I mean, I know that that wouldn't happen. It uses a previously documented p-prim generalized springiness to explain a counter-factual prediction; it explains momentary sensemaking; it explains "losing track" as a general phenomenon involving p-prims data fluidity ; it explains inability to articulate.
I have personally documented scores of p-prims that are at once plausibly "naturalistic" learnable with experience in the natural world and explain surprising non-physics predictions and explanations given by students e,g. I like concepts, theories, and ontologies provide no explanation whatsoever for. I commonplace cognitive phenomena. I, I want to make brief reference to one ofthe most significant successes of p-prims I i in accounting for important phenomena in conceptual change. It is described in , ; detail in diSessa , and illustrates how process data can bear on issues of!
I conceptual change. In another session, J was asked to describe what happens when a i ball is tossed into the air. Initially, J provided a proper physics explanation, involving only one force, the force of gravity. However, J was then prompted to consider the peak of the toss. The point of this probe was to test the salience to J of dynamic balance and overcoming p-prims.
Consistent with data fluidity and in accordance with previously documented p-prims, J began to reformulate her explanation in terms of two competing forces, where one overcame the other. After an extended bout of reasoning in which J tried alternative candidates for the force competing with gravity, J reached a stable explanation of the toss involving at least four p-prims in a natural configuration: J used force as mover, dynamic balance, overcoming, and dying away, One thing that is particularly notable is that the explanation she produced had been documented in the literature and touted as exemplifying a deeply held intuitive theory of motion McCloskey, Thus, we see a student's description emerge on the basis of well-documented intuitive 9 Of course.
Similarly, she might have been able to explain andjustify. None ofthese alternative explanations are consistent with the broad corpus of data from J, but we cannot enter into details here. If the description constitutes a theory, we have seen in this analysis how that theory can arise, at least in one case. Ifthe description does not implicate a theory, we still see how it came about and probably know more about its properties due to this process data analysis than is contributed by calling it a theory.
P-prims show penetration into the details of process data that are exceptional in the conceptual change literature. Coordination Classes In this section I describe another kno. Because this type of mental entity is newer and less researched than p-prims, I make a more extended exposition of its properties. Coordination classes are large, complex systems, rather than atomic elements.
P- prims are extremely likely to constitute fragments of coordination classes. For simplicity, parametric differences among coordination classes will be almost completely suppressed in the remainder of the chapter. Unlike p-prims, which playa role in both expert and naIve thought, coordination classes may well not exist at least with similar parameters of behavior in naIve thinking.
In any case, whether and which naiVe coordination classes exist is an open empirical question. In contrast, coordination classes provide a very different functionality. They provide the means for gening a certain class of information from the world. The fundamental assumption behind the idea of coordination classes is that information is not transparently available in the world.
Indeed, in different circumstances, we may need to use very different means to determine the same kind of information. In general, people must be creative in using any information that may be easily available in a situation, and then inferring the specific information they need from that. The structure ofcoordination classes While p-prims are nearly atomic, although embedded in a recognttlOn system, coordination classes have a lot of internal structure.
A great deal of this structure depends on specifics related to particular coordination classes. However, some large-scale partitioning of its internal parts can be made. In particular, [ distinguish the set of methods by which any relevant infonnation is gleaned from the world, which I call read Jut strategies, from the collection ofpos. The latter set of inferences I call the causal net. The causal net encompasses inferences that may seem more mathematical or a priori in addition to some we would instinctively describe as causal. Let me exemplify with one of my favorite hypothetical examples of a possible coordination class.
This example is taken' from Piagetian studies of children's concepts of time Piaget, Consider the following situation, illustrated in Figure 4. A blue train and a red train leave a station at the same time, A. The blue train is' slower than the red train. The red train stops at a time, B, before the blue train stops, at time C. Because the red train travels much faster than the blue train, the blue train doesn't manage catch up to the red train's stop position by time it, itself, stops. A red train and blue train leave the station simultaneously.
The slow blue train continues to move after the red train stops. There is a lot of variability in what children say in response to such a setup. However, some respond as follows. When asked which train went on for a longer time, they say that the red train did. While this may seem to entail a simple confusion of meaning of "long," that possibility can be ruled out be rephrasing the question.
For example, children may be asked, "If the red train stopped at lunch time, what time did the blue train stop? For example. When queried whether the blue train was running! In terms of coordination class theory, children have quite adequate readout strategies. If a blue process started at the same time as a red process, and the blue process continued when the red one stopped, adults instantly conclude that the blue process went on for a longer time than the red process. They also know that no infonnation about position e.
In tenns of coordination class theory, adults have a causal net that contains the appropriate inference on the basis of observations about whether one process continued when the other stopped. It is not true that children have no causal net at all. They have a different one. They infer sensibly enough that if a moving object gets farther away, it has been running longer. The problem is that they don't know the applicability conditions for that inference, that it only applies to a single object or to multiple objects moving at the same speed.
The causal net is not a homogeneous subsystem. We shall ilhJ! The development ofcoordination classes The development of a coordination class is an extended and complex affair. The descriptor "coordination" implies that a lot of pieces must be put in place to achieve an effective coordination class. Given what we have said, above, however, we can describe different phases and different kinds of difficulties faced in this construction. In order to read out the particular form of information of interest, one must accumulate both I readout strategies and also 2 inferences in the causal net that are sufficient to cover all contexts in which the information is needed.
We call this achieving appropriate span. In each context of interest, it may be that particular readout strategies and inferences need to be combined. In the data that follow, we will see, in particular, dramatic al ures of alignment due to contextuality of pieces of the coordination class.
How does one "look closely" to detect whether something is a yof force or not? This implicates probably a very important class of meta-knowledge. Jing the ious It in t in :7 It 'e a Figure 6. Do you seeflveness? The element in Figure 6 illustrates a failure of alignment. Your coordination class knowledge sees an arc connected to a right angle and concludes that this is a five. It is a mirror-image five. Alignment can be restored by adding strategies that detect the! Process data concerning coordination classes egy 1 1 "Coordination class" is intended to be a theoretically well-elaborated candidate for a model of scientific concepts.
In particular, we hypothesize that the properties of t in conceptual development of the physics concept of force are explainable as lith consequences of its being a coordination class. Jto Force as a "concept" has many properties that suggest it is a good candidate for a arc coordination class. First, crude data about the difficulty of learning force suggest it ese may have many pieces and parts-that is, it might well be a system in the range of the complexity of a coordination class.
It seems very likely that students will need to coordinate 1 many readout strategies and causal net inferences to properly see forces and their ny. We expect to see! You can feel them. Physicists expect to be able to feel forces in most This is a. Generally researchers equate learning physics with learning formal aspects of it. Two other methods of coordinating force are important to mention. These are :. First, physicists know the principle of "action and reaction": that when a force is applied to any object, the object applying the force always feels on itself an equal force in the opposite direction.
This provides a simple inference. Any time there is a force on one object, you know there is another force present, and you can infer its direction and magnitude, "equal and opposite. Most particularly, we know I claim that intuitive ideas about physics come mainly in the form of p-prims. Furthermore, p-prims evidently allow inferences that might be part of a causal net. For example, force as a mover implies that the direction of a force can be determined from the direction of motion.
The amount of a force is in some measure determinable by Ohm's p-prim: If the "effort" in question is a force, it must be greater in situations where there is a greater outcome. All in all, p-prims are excellent candidates for early elements in a learner's causal net. P-prims' theoretical properties lend detail to expectations about learning force. At the broadest level, knowing that intuitive ideas in physics are rich and numerous, we expect a high degree of context sensitivity.
Achieving alignment across a wide range of circumstances may be very difficult.
More particularly, learners start with a lot of p-prims that are evoked in circumstances that have nothing much to do with learned physics. Thus, there are many opportunities for context dependence that is directly attributable to the context dependence of p-prims. To the extent that we have documented particular p-prims, we can predict or explain behaviors in coordinating force by the use of particular p-prims in circumstances where we know those p-prims are likely to apply.
Below, we will, indeed, attribute particular learning difficulties in particular circumstances to the use of particular p-prims. In the following, we again turn to process data from the subject J. In general, we see a very high degree of context sensitivity that undermines a coherent aligned coordination class for force.
More particularly, we will observe the following: I. J does not expect to be able to directly feel a force. She does not use that expert coordinating strategy. While she is consciously aware that "action and reaction" is a good way to "a "see" forces that is, she knows it is a good element of a proper causal net for force , she does not always use it.
J exhibits commitment to the general principle that motion implies the existence II of a force, However, in a situation where a particular p-prim is salient and '. If I I can feel that ii'S being pulled harder.
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So e 1'I whal would you say to thai? J: Well, first I'd say, "how can you tell it's being pulled harder?
I guess I'd say, "well, you can feel it in your hand. Gravity's uniform. So gravity won'l pull any harder on something Ihat's in 1 of I Ihe same place as it will on something else J: You're feeling the weight oflhe object. So that's different from the force. Instead, we see that principles can serve as elements in the II causal net, as well as p-prims. J implicates "action and reaction" by referring to the force of the e table on the book as "equal and opposite.
J: Right. And it's the same as like equal and opposite forces. I mean, this chair right s now is pushing up on me and the chair is pushing up on you. And Ihe ground is e pushing up on your feet. And that's something that's hard to think about. A short time later, J explains this is something she learned that would not be evident to "the man in the street. This chair's pushing up on me. I think thai'S somelhing that, once you've taken physics, lhat's lotally normal. The interviewer provides an opportunity for J to use "action and. However, directly following he provides the same opportunity to use "action and reaction" to conclude that, since the table via friction is pushing backward on the book, the book must be pushing forward on the table.
J declines this opportunity. Book Figure 7. The table pushes backwards on the book as it slides. What about the force that the book is exerting on my finger'? J: Umm. It's the same as the force you're exening on the book. I: Alright, what about the force of the book on the table as I'm pushing this thing along?
Is there a sideways force? So friction is pushing on the book that way against the motion. The book is not pushing on the table either way. The reason for this failure to use the same principle in almost the same context a failure of alignment due to context sensitivity in the causal net is not evident in the available process data here. However, in other parts of the set of interviews, J shows that she thinks friction is simply a different kind of force, and, perhaps, she therefore believes it is not susceptible to the use of "action and reaction.
Below, the interviewer tries to make the reaction force of the table salient by invoking another principle. In many contexts J exhibited articulate, reflective and deep commitment to the principle that if there is motion, there is a force. The interviewer puts a paper under the book and shows that it moves when you push the book hence implicating a force on it. J declines the use of her own principle here. If contact is creating motion, then there is no need for a force. So, suppose I said that I have to hold it because the book is exerting a force on the paper. J: I think it's just sliding, and I think it's just bringing the paper with it.
I mean, it's a really simple situation I would just say that it's [the book is] sliding against the table and bringing the paper with it. To sum up, we ohserve in this process data an expectable fragmentation in context dependencies. In two cases, explicit principles that function as causal net inferences are applied in some contexts, but not others. In one case, the reason for this context dependence seems clearly the salience of a particular p-prim in a particular context. Because contact can convey motion, the principle that motion requires a force doesn't apply to this case.
A BRIEF REVIEW In order to make the connection between my original critique of conceptual change research and what I have displayed concerning "conceptual ecology" more clear, I will undertake a brief review in terms of the program I set out for the chapter, following the critique. Both p-prims and coordination classes are much more specific than dictionary definitions and typical invocations of, for example, "concepts" or "theories" in conceptual change research.
We have discussed the nature of elements, their origins, what happens during development, the function of the knowledge types, typical patterns of use, and the level and kinds of systematicity between elements and across contexts. More on the laner appears in the next section. Table I reviews some of the main points. Empirical investigations are necessary to venfy that any hypothetical p-prim or coordination class has the necessary properties. P-prims, for example, account for intuitive predictIons and judgments of plausibility. Coordination classes provide a specific model of a type of full-blown concept, which entails a lot about the difficult and easy parts of conceptual change.
Following our discussion, summarized in Table I, p-prims and coordination classes contrast in many ways with each other. Theoretically, there is no way to mistake one for the other. More broadly, rfully expect that we will need many other knowledge types to fully explain the transition from naTve student to conceptually-competent physicist.
Starting from the last question, establishing appropriate span and alignment is difficult, and we should expect continued examples of failures of this sort in the trajectory toward competence. Not only did we document failures of these types in a subject's process data,. That p-prim contact conveys motion "explained" a situation a paper moving under a pushed book and thus aborted the use of an articulate principle for this subject , that motion requires the existence of a force.