Students’ Conceptions as Dynamically Emergent Structures

Abstract

There is wide consensus that learning in science must be considered a process of conceptual change rather than simply information accrual. There are three perspectives on students’ conceptions and conceptual change in science that have significant presence in the science education literature: students’ ideas as misconceptions, as coherent systems of conceptual elements, and as fragmented knowledge elements. If misconceptions, systems of elements, or fragments are viewed implicitly as “regular things”, these perspectives are in opposition. However, from a complex dynamic systems perspective, in which students’ conceptions are viewed as dynamically emergent structures, the oppositions are lessened, and the integrated view has significant implications for theory and practice.

Introduction

Rusanen and Pöyhönen (2012) usefully distinguish three fields in which the term “conceptual change” has had prominence: science education, developmental cognitive psychology, and history and philosophy of science. As a science educator, my focus is on the issue as it impinges on students’ learning of science, and that focus will be the central concern of this paper, although the ideas discussed may have implications for the other areas. In science education research, issues of conceptual change have been a prominent focus of research for several decades, and there is wide agreement that student learning in science involves issues of conceptual change rather than simply accumulation of information.

To help ground the issue of conceptual change in science education, consider two different instructional statements from a teacher or textbook. The first statement is: “The atomic symbol for gold is Au”. Students would likely react to such a statement in the following way: “I didn’t know that. Now I know that”. With appropriate study the student will commit this bit of information to memory and will be able to correctly answer questions asking for the atomic symbol for gold. This statement and student response illustrate what might be called an “absorption” view of knowledge and learning–knowledge consists of information that is learned through an information source such as a teacher, a textbook, the internet, etc., and is then committed to memory by the student. This is arguably the dominant view of knowledge and learning in schools today (Linn and Eylon 2011). While this view may be adequate when applied to the learning of such facts, there are other kinds of instructional statements in science that draw very different types of student responses.

An example of this second kind of statement is the following: “When a book is placed on a table, the table exerts an upward force on the book”. Brown (1992) explored the effectiveness of different discussions of this idea. One text discussion of this idea presented several examples of Newton’s third law and then authoritatively stated that this is another example of the third law: the book exerts a force on the table because of its weight, and so by Newton’s third law the table exerts an equal and opposite force back on the book. Even though the approximately one page discussion provided numerous examples of the third law and explicitly stated that a force from the table was the correct answer, less than 30 % of the students reading the explanation accepted this statement. In a particularly forceful rejection similar to the rejections of this idea by other students, one student said:

They’re trying to tell me that for every force there’s an opposite force that happens against it. But they still haven’t told me where it comes from or why, and I have no intention of accepting it until they do. (Brown 1992, pp. 27–28)

This is a rather clear example of resistance to scientific ideas because of the student’s own prior ideas. As another example of a different kind of resistance, consider research by Vosniadou and Brewer (1992) who asked children about their views of the shape of the earth. A number of the children articulated a “fish bowl” model of the Earth. The Earth is ball-shaped, but we live on a flat part inside the spherical Earth. Vosniadou and Brewer call this a “synthetic model”, a combination of taught ideas (the Earth is a ball) and the student’s own ideas (the ground is flat, and there is a definite down direction). In this case the children did not flatly reject the statement that the Earth is a ball, but their existing ideas led to a misconceived notion of where people live on Earth.

These are only two examples of the difficulties students have with many ideas in science. Because of their existing ideas, it is difficult for students to accept or make sense of presented ideas in science, or they make sense of the ideas, but the sense they make is significantly different than the canonical ideas in science, such as the fishbowl model of the Earth. While the dominant view of student learning in schools is still largely that of absorbing information (Linn and Eylon 2011), research in recent decades has shown that student learning of many ideas in science is much better represented by the later examples than by the first example of the atomic symbol for gold.

Duit (2009) has compiled a bibliography with over 8,000 references focused on such student conceptions and sense-making. It seems clear from the large amount of research that student learning in science must take into account students’ pre-existing ideas. Learning in science cannot be fruitfully considered as simply committing information to memory–the information will often be rejected or severely re-interpreted. Since students have existing ideas or conceptions, these ideas must be engaged and modified, they cannot be ignored as is traditionally done. Learning in science must be considered a process of conceptual change, not simply a process of information accrual.

But there is another side to the research on students’ conceptions. While it is certainly true that in a particular context students seem to draw on existing ideas in rejecting or modifying taught ideas, at times in closely related contexts they seem to draw on different ideas. For example, consider the question “what are the forces acting on a stone as it is tossed straight up into the air?” On the stone’s way up, students often seem strongly committed to the idea that there is a “force of the throw” that causes the upward motion and that diminishes to zero as the stone slows down toward the top of the throw. However, if asked what forces are acting on the stone at the moment it reaches the top of the throw, students often seem committed to the idea that there is a force of the throw that balances the downward force of gravity on the stone (diSessa 1993). Asked one way, the force of the throw approaches zero at the top. Asked a different way, the force of the throw balances the downward force of gravity at the top. This is just one example of many studies that find such contextuality in students’ responses to questions under slightly varying conditions.Footnote 1

In this paper I explore three ways of understanding students’ ideas that each have a prominent place in science education: as misconceptions, as systems of ideas, and as fragmented intuitive elements. If misconceptions, systems of ideas, or elements are viewed implicitly as “regular things”, these perspectives are in opposition. However, from a complex dynamic systems perspective, in which students’ conceptions are viewed as dynamically emergent structures, the oppositions are lessened, and the integrated view has significant implications for theory and practice.

Regular Things Versus Emergent Structures

Focusing on the second, conceptual kind of idea about the book on the table or the shape of the earth, it seems clear that there is “something” in the student’s mind that resists or severely re-interprets taught ideas. There is some “conceptual structure” that is resistant to change and that influences student acceptance and/or understanding of these ideas. This is a strong result in many studies across a range of areas in science (Duit 2009). Any theoretical perspective must account for these robust results.

So it seems that there is something (some thing) in students’ minds that resists or distorts taught ideas. In this paper I argue that an implicit assumption is often that this thing is a “regular thing”, behaving in ways similar to other regular things, such as a rock or a baseball or a chair. Following are some of the characteristics of regular things:

  • Static structure Regular things are identifiable, static structures (e.g., a chair). Left by itself it will remain what it is.

  • Predictable Changes to a regular thing are predictable based on influences on it. For example, if you double the net force on a rock, its acceleration will double.

  • Separable If you remove a piece from a regular thing (e.g., remove the leg of a chair), the piece and the whole are not changed (except by being separated from each other). It is possible to separate such static systems into components. Regular things can be taken apart and put back together.

We have grown up in a world of regular things and have developed embodied intuitions about regular things as well as conceptual metaphors about abstract ideas that are based on how regular things behave. As an example, consider the “conduit metaphor”, an implicit metaphor structuring discourse about abstract ideas of communication based on regular containers filled with regular contents (Reddy 1979). In this seminal paper, Reddy presented an analysis of English phrases consistent with this metaphor, providing impetus for the further development of ideas of conceptual metaphor (Lakoff 1993), of “metaphors we live by” (Lakoff and Johnson 1980). For example, consider the following typical English sentences. I have started each with an English sentence relating to communication and followed it with an italicized sentence in a corresponding concrete context of regular containers carrying regular contents.

  • If you say it this way you’ll get your point across more effectively. If you use these containers you’ll lose less in transit.

  • Let me give you an idea of what I’m thinking about. Let me give you a taste of this drink.

  • See if you can put your thoughts into fewer words. See if you can pack your things into fewer suitcases.

Reddy (1979) argues, drawing on many more examples of such sentences, that discourse about communication in English (and likely in many other languages) is framed by implicit grounding in a concrete context of transferring contents (meaning) by means of containers (words).

The surprising thing is that, whether we like it or not, the English language does follow this viewpoint. It provides, in the form of a wealth of metaphorical expressions, [a view that is] perfectly coherent with the assumption that human communication achieves the physical transfer of thoughts and feelings. (p. 287)

Stated baldly in this way, the conduit metaphor seems rather simplistic. Reddy’s point is not that we cannot think about communication differently, but rather that the conduit metaphor provides a kind of implicit default view of communication that privileges the conduit view, and that it requires effort to view communication differently.

To begin with, it must be made clear that no speaker of English, not even your author, has discarded the conduit metaphor. Thinking in terms of the toolmakers paradigm [a parable portraying communication as constructing meaning rather than transferring meaning] briefly may, perhaps, have made us aware of the conduit metaphor. But none of us will discard it until we succeed in bringing about an entire series of linked changes in the English language”. (p. 297)

Similar to Reddy, I am not arguing that no one has ever thought of students’ conceptions as other than regular things. There have been many treatments of students’ conceptions, conceptual growth, and conceptual change from perspectives similar to what I call here an emergent or dynamic view. What I am arguing is that our embodied intuitions and discourse forms privilege a “regular thing” view of abstract ideas, and that a “regular thing” view of students’ conceptions can obscure important implications for science education theory and practice.

In what follows I first discuss three perspectives on students’ conceptions widely employed in research in science education on students’ conceptions: as misconceptions, as coherent systems of intuitive ideas, and as intuitive fragments, indicating how each perspective might be seen from an implicit regular thing view. From an implicit regular thing view, these perspectives are in significant opposition. I then discuss complex dynamic systems and dynamically emergent structures and how this integrative perspective can apply to students’ conceptions. From an emergent structure view, oppositions among the perspectives decrease dramatically, and each perspective can be seen as a somewhat different take on emergent conceptual structures.

Students’ Conceptions Viewed as Regular Things or Collections of Regular Things

Misconceptions

Initially one of the most salient aspects of such student conceptions was their affect on presented science ideas. For example, Brown (1989) discussed questions focused on Newton’s third law. One of the questions asked was about a sixteen pound bowling ball striking a four pound bowling pin. Before instruction, only 1 % of students answered correctly that the forces they exert on each other would be equal. After a full year of instruction in physics, in answer to this question (which is a “simple” application of the explicitly taught idea of Newton’s third law), only 5 % answered correctly that they would exert equal forces on each other. Ninety-nine percent of the incorrect answers indicated that the bowling ball exerted the greater force. The students seemed to have a misconception that the bowling ball “has” more force than the pin because of its motion and/or greater weight.

The Private Universe Project, a well-known project examining such student ideas in science (Schneps and Crouse 2002), has called these “misconceptions that block learning”. As a science instructor, information about such misconceptions can be extremely helpful. Rather than thinking that students are unintelligent or inattentive when they answer simple questions incorrectly, I now have a better explanation–they have a misconception. Further, the large amount of research identifying various student misconceptions can be very helpful to me in identifying ideas with which I would expect my students to have difficulty. This is a significant upside of research in this tradition. But there is a downside if these misconceptions are implicitly viewed as regular things.

Considered as regular things, misconceptions are unitary entities in the mind. For example, many authors discuss “the misconception that ____”, where the blank could be filled in with something like “mass is not conserved during burning”, “molecules expand when heated”, “a force is required to make things move”, “plants eat with their roots”, etc. Considered in this way, these are “chunks of conceptual knowledge” that are simply wrong. They need to be removed and replaced with canonical scientific conceptual knowledge.

This view of students’ conceptions as chunks of wrong conceptual knowledge is strongly critiqued from each of the other two perspectives. It is critiqued most strongly from the perspective that seems most antithetical—students’ conceptions as intuitive fragments.

The educational implications of the view of intuitive physics as theoretical include that misconceptions can and should be confronted, overcome, and replaced by valid principles. For this conclusion to be viable, misconceptions need to be relatively isolable and few in number, they need to be false or at least unproductive so that replacement is in order, and they need to be amenable to “attack” with data and argument. This monograph questions all of these assumptions. Instead, I approach intuitive physics as an expression of an underlying sense of mechanism that occasionally exhibits relatively uniform results but on the whole lacks important systematicities of theoretical science. As such, it does not need to be replaced so much as developed and refined. (diSessa 1993, p. 109)

While the remaining two views are often at odds with each other, they are in agreement in denouncing a view of students’ conceptions as unitary misconceptions. For example, while Vosniadou and colleagues are often seen as providing support for such a view in the face of challenges by elemental proponents, Vosniadou herself strongly opposes such a characterization of her position in agreeing with the criticisms of diSessa (1993) and Smith et al. (1993) about the misconceptions perspective:

…we are not describing unitary, faulty conceptions but a complex knowledge system consisting of presuppositions, beliefs, and mental models organized in theory-like structures that provide explanation and prediction. (Vosniadou et al. 2008, p. 22)

Both of the remaining perspectives view students’ conceptions not as unitary incorrect chunks of conceptual knowledge, but rather as collections of conceptual elements. The point of contention is whether these conceptual elements are assembled or disassembled.

Systems of Knowledge Elements

A number of theorists espouse a view of students’ conceptions arising out of a complex system of knowledge elements organized into coherent structures. One of the critiques of a misconceptions perspective is that in some cases students’ ideas seem to be strongly resistant to change while in other instances students more easily accept alternative views. To simply say that some misconceptions are entrenched while others are less entrenched is not very explanatory. Another critique is that in many cases when students express their ideas, there is evidence of unstated implicit assumptions or conceptions underlying more conscious models. For example, in the shape of the Earth question discussed above, children articulating the fishbowl model of the Earth seem to be basing this model on the implicit assumptions that the Earth is flat (at least the part we live on) and that there is an absolute down direction (Vosniadou and Brewer 1992).

In order to deal with these flaws of a unitary misconceptions perspective, a number of theorists discuss students’ conceptions as systems of conceptual elements.Footnote 2 These conceptual elements are connected together and consist of both implicit or subconceptual assumptions or presuppositions as well as more conscious conceptual elements. Because of the interconnections of conceptual elements, these systems of ideas behave in many ways as do scientists’ theories, albeit without the level of sophistication nor the scientific cultural context of scientific theories. From this “theory–theory” view of students’ conceptions, disrupting some of students’ alternative ideas will involve many changes to this systemic structure and so will be more strongly resisted than changes involving fewer interconnected elements.

From an implicit regular thing perspective, the coherent structures would be conceptualized as similar to a collection of static objects connected together in some way, such as a Tinkertoy® structure (wooden circles with holes in them connected together by wooden rods). While this view provides an explanation of entrenchment (taking apart a larger Tinkertoy® structure will be more difficult), it has a more difficult time dealing with the contextuality of students’ ideas, a central focus of the third perspective.

Intuitive Fragments

Another group of theorists, while also arguing that students’ conceptions arise out of a collection of knowledge elements, propose that these knowledge elements are not organized into coherent structures. Instead the knowledge elements are “quasi-independent” (Clark and Linn 2013). Focusing strongly on the contextuality of students’ responses, these theorists describe students’ conceptions as more of a loose assemblage of knowledge elements cobbled together for each context rather than a previously assembled system of elements that applies broadly.

From an implicit regular thing perspective, these pieces would be conceptualized as disconnected regular things, such as Tinkertoy® circles that are not yet connected by wooden rods. A strong critique of this view, seen in this way, is that it is difficult to see how such a collection of disconnected pieces could provide the kinds of resistance to taught ideas we saw above in response to the book on the table or the shape of the earth questions. The data seem to be saying that there is something substantial in students’ minds resisting instructional ideas, while the elemental theorists seem to be saying “no there’s not, there’s just a lot of disconnected fragments”. For example, Panagiotaki et al. (2006) appear to interpret the elemental perspective in this way:

Instead, it is suggested that children’s emerging knowledge of the earth is fragmented and incoherent, and that children’s ideas about the earth are culturally communicated; claims that in some aspects echo diSessa (1988). Before children acquire scientific knowledge of the earth, they are ‘theory free’: they simply do not know, and have no strongly held views, about the earth. (pp. 354–355)

By contrast, elemental theorists are at pains to point out that dynamic structures (“systematicities”—diSessa 1993) can be emergent from the pieces. Responding to the critique that elemental perspectives portray students’ ideas as disconnected, fragile, and random, and cannot account for the robustness of students’ ideas, diSessa replies:

Fragile’ and ‘random’ are prejudiced descriptors that do not capture much of my view of knowledge in pieces. Elements of intuitive knowledge are contextual in that there are many of them, and they each have quite specific contextual boundaries. The region of applicability of an element might, however, be quite broad. For example, the idea that ‘increased effort’ begets ‘greater results’ applies across the physics/psychology boundary, which professional physical ideas like ‘force’ do not cross. (diSessa 2013, p. 39)

While diSessa would balk at calling the instantiation of something like Ohm’s p-prim along with other related and relevant p-prims a “theory-like structure”, it is far from the “fragile” and “random” instantiation of unrelated knowledge fragments, and it possesses a kind of dynamic structure that in certain contexts would be surprisingly robust. In the following section I will explore more general ideas of dynamically emergent structures and then return to the application of this idea in the context of students’ conceptions and conceptual change.

Dynamically Emergent Structures

Science in general sees systems of interconnected elements, such as economies or ecologies, as stable entities…It is also useful, however, to see complex systems as constantly changing their internal structure and external environment through self-organization… (Manson 2001, p. 411)

In order to articulate an emergent structure view, and how it differs from a regular thing view, I will draw on an example of emergent structure using the Netlogo software (Wilensky 2010). In the Netlogo simulation for slime mold cells, several hundred small triangles (called “turtles” in Netlogo) appear on the screen. When the simulation begins, the triangles start moving and clumping together into dynamically emergent groups. Here is the information provided with the simulation:

This project is inspired by the aggregation behavior of slime-mold cells. It shows how creatures can aggregate into clusters without the control of a “leader”. In this example, each turtle [moving triangle] drops a chemical pheromone (shown in green). The turtles also “sniff” ahead, trying to follow the gradient of other turtles’ chemicals. Meanwhile, the patches diffuse and evaporate the pheromone. Following these simple, decentralized rules, the turtles aggregate into clusters.

A brief video of this simulation is available at http://youtu.be/cnKAUDgRn30. I would strongly urge readers to view this video, as the dynamics are difficult to describe verbally or in a still picture. In this dynamic metaphor, the clusters that emerge because of the dynamics of the system show an idea that is central to this discussion–emergent structure. Because of the natural dynamics of the system, structures emerge from otherwise independent elements that are formed and maintained dynamically. As can be seen in the video, some of these emergent structures are robust, maintaining their identity over significant periods of time. Other emergent structures are more ephemeral, “evaporating” after a period of time. This dynamic metaphor is not meant to serve as any kind of a cognitive model. Rather it is meant to serve as an example of the central idea of emergent structure.

If one were to take a snapshot of these structures, it would look like Fig. 1. The clusters look like regular things–like balls with clusters of triangles at their centers. Or, thinking more systemically, they might be seen as clumps that have been put together and that stay together because of some kind of static interconnections among the triangles. If someone were to come along and say that we should focus on the triangles as independent pieces, another focused on the clusters of triangles might point out that the elements are clumped together into structures, and so they are not independent. However, from a dynamic perspective, these positions are not antithetical. The turtles are independent in the sense that they are not statically connected to other turtles. But they also clump into structures that are dynamically formed and maintained.

Fig. 1
figure1

A snapshot of the emergent structures

Such emergent structures have several characteristics that distinguish them rather sharply from regular things. In what follows I discuss three important distinctions between regular things and emergent structures—static versus emergent structure, predictability or linearity versus non-linearity, and separability versus interdependence or embeddedness.

Dynamic Emergence and Evolution of Structures or States

A regular thing has an identifiable, static structure. Left by itself it will remain what it is. By contrast a dynamically emergent structure (e.g., a living organism) naturally changes over time. Referring to the snapshot above and comparing it to the video example, both have structures. However, in the snapshot, the structures can be interpreted as static structures–if you put them on the shelf and come back to them a year later they will look the same, just as a rock will look the same a year later. By contrast, consider the dynamic structures in the video. Over time these structures will continue to evolve and change. For some of the structures there will be substantial stability over time while some structures will evaporate or merge with other dynamic clusters.

Non-linearity

Changes to a regular thing are predictable based on influences on it. If you double the net force on a rock, its acceleration will double. If you sit on a chair that is not strong enough, it will break. If you throw a baseball at a window with enough speed, it will break the window. With dynamically emergent structures or states, at times strong influences can lead to little change (strong stabilities or “attractors” develop that are affected little by external influences), and at times weak influences can lead to substantial, often unpredictable changes (the “butterfly effect”).

As an example of a dynamic attractor, consider a simple ecosystem of rabbits and grass. Running another Netlogo simulation shows the counterintuitive nature of such dynamic states. If the rabbits get enough grass to eat they will have the energy to live and to reproduce. However, if the rabbits don’t have enough to eat, they will start to die of starvation. The following scenario illustrates a kind of dynamic equilibrium that is similar to homeostasis in the body. If the population of rabbits gets too high, they will eat too much grass. This will decrease the population of grass to the point where the rabbits won’t have enough to eat. Many rabbits will die of starvation. Enough rabbits may die that the grass can grow almost without check, greatly increasing the population of grass. In this environment of plenty, the remaining rabbits will flourish, increasing the rabbit population, returning us to another surplus of rabbits that will eat too much grass….

In Fig. 2, from a Netlogo simulation, the population of rabbits starts off at about 100, and the population of grass starts off at about 300 units. The rabbits stabilize at about 150, and the grass stabilizes at about 250 units after some oscillations. So we can see that the population of rabbits is dependent on the population of grass and vice versa. This interdependence will keep the populations oscillating around relatively stable values. Because of the setup of the system (the system boundaries and the interacting elements and their characteristics), the system seems attracted to this state of affairs. In fact, in dynamic systems terminology this is called an “attractor.” There is no central control making the system “settle” into this state of affairs, yet the system seems uncannily guided to its dynamic equilibrium state, just as the slime mold cells seem uncannily guided to clump together.

Fig. 2
figure2

Starting with 100 rabbits

But what would happen if we added a large number of rabbits to the system? Thinking in “regular thing” terms, if you have a pile of marbles and add a lot more marbles, you would expect to end up with a lot more marbles. In this simulation, rather than starting off with 100 rabbits, in Fig. 3 we start off with 900 rabbits. By this thinking we should end up with far more rabbits than when we started off with 100. What we find is that to a large extent, no matter how many rabbits we start with, the system “settles” to a dynamic steady state of about 150 rabbits. The system seems “attracted” to this state, and in dynamic systems terms this would be called an “attractor”.

Fig. 3
figure3

Starting with 900 rabbits. Source This figure has been published previously as figure 6.3 on p. 138 of the International Handbook of Research on Conceptual Change (2008, Stella Vosniadou editor, Routledge)

Embeddedness

If you remove a piece from a regular thing (e.g., take a leg off of a chair), the piece and the whole are not changed (except by being separated from each other). It is possible to separate such static systems into components. You can take apart a chair and put it back together. However, dynamically emergent structures are typically not so analyzable. If you remove a piece from a dynamically emergent structure (e.g., remove a heart from a person), both the piece and the whole may be substantially changed. In the example of the heart and the body, the body dynamics embed the heart dynamics, and the heart dynamics are embedded in the body dynamics.

Summary

So we can see that there are two very different ways of thinking of “things”: as regular things with static structure that react predictably to influences and that can be taken apart and put back together, or as dynamic entities with emergent structure that react often unpredictably to influences and that are more organic, unable to be easily assembled, disassembled, and reassembled. In what follows I discuss the three current perspectives on students’ conceptions as different takes on emergent structures and argue that this is an integrative view that can help make sense of aspects of each of the perspectives.

Students’ Conceptions as Emergent Structures

Strike and Posner (1992), who recommended more emphasis on the conceptual ecology in their critique of earlier conceptual change views (Posner et al. 1982), proposed a more dynamic view of students’ conceptions:

Our view of conceptual change must therefore be more dynamic and developmental, emphasizing the shifting patterns of mutual influence between the various components of an evolving conceptual ecology. (p. 163)

diSessa discusses a view of students’ conceptions as a complex dynamic system, using as an example the emergence of the V shape of geese flying as an example of the emergence of structure.

Within the complex knowledge system perspective, thinking or ‘concept use’ is the phenomenological presentation of a complex system in operation. The system, itself, much less its pieces, looks nothing like its appearance. A familiar example is that birds flock in such a way as to give the appearance of having a leader. However, there is nothing like the concept of ‘leader’ in the simple rules that each bird follows. The fact of a leader might emerge from a rule like (anthropomorphism aside) ‘all things equal, it’s convivial to fly slightly behind and to the side of a colleague. (diSessa 2008, p. 52)

In this view, students’ conceptions are considered dynamic not simply because they evolve dynamically (which they do), but because they form dynamically–they are dynamically emergent from the interactions of conceptual resources (Brown 2010; Brown and Hammer 2013). Because of this emergent nature of students’ conceptions, “conceptual systems” and “conceptual fragments” views are not qualitatively distinct. The pieces in fragmented or elemental views interact dynamically to form emergent structures, which in some cases might be robust enough to be considered as coherent ideas across a particular domain.

Knowledge in pieces can treat large-scale conceptual structure as configurations of pieces, and that is in fact an important part of the knowledge in pieces program. Empirical work of exactly this sort has been done. I claim it provides a more powerful theory of “big chunks” by understanding their properties as stemming from their constituents, and also by providing hints as to how the chunks might have been constructed. (diSessa 2008, p. 56)

Clark (2006), coming from an elemental perspective, looked closely at the learning of eighth grade students in thermodynamics and found both coherence and contextuality. He asked how large a “domain” must be in order for students to be considered coherent in their reasoning:

Across how large a domain must a student be ontologically and causally consistent for a researcher to rate the student’s understanding as being theory-like? At one narrow extreme, all of the case-study students demonstrated consistency in their understanding across some narrow domain for some idea. At the other extreme, not even scientists are fully coherent and consistent in their understanding across the entire overarching domain of science. Unfortunately, “big enough” is hard to define in an objective manner for reliable application by multiple researchers. (p. 548)

Similarly, the coherent conceptual structures of the systems theorists are considered also as emergent dynamic structures (rather than pre-set static structures, such as a Tinkertoy® structure). The two camps would still differ in their predictions of coherence, with pieces advocates predicting less robust dynamically emergent structures and coherence advocates predicting more robust dynamically emergent structures,Footnote 3 but in this view these are quantitative rather than qualitative differences.

In this view misconceptions would be seen as misconceived responses to conceptual questions generated by these emergent conceptual structures. Strike and Posner (1992), two of the authors on one of the seminal papers launching the conceptual change research program in science education (Posner et al. 1982), in their revisionist take on conceptual change take this perspective:

… it may be that misconceptions do not exist in any form of representation as alternative formulations to preferred conceptions. Instead, misconceptions may exist as various factors in a conceptual ecology that function to select for or prefer some representation of a misconception when the opportunity to do so exists. (pp. 156–157)

For example, consider the misconception that an object thrown upward has a force that causes it to move up. This is sometimes called the “motion implies a force” misconception (Clement 1982), but diSessa (1988) proposes a more dynamic origin in which intuitions of causality and agency generate the idea of an upward force. Or consider the misconception that we live in the middle of a ball shaped earth. Vosniadou and Brewer (1992) view this as generated from intuitive presuppositions of a flat Earth and an absolute down direction combined with taught ideas of a ball-shaped Earth.

If misconceptions, systems of elements, or fragments are viewed implicitly as “regular things”, these perspectives are in opposition. Students’ conceptions are chunks of wrong conceptual knowledge, OR they are coherent systems of interrelated conceptual elements with static structure, OR they are independent intuitive fragments. However, from a complex dynamic systems perspective, in which students’ conceptions are viewed as dynamically emergent structures, the oppositions are lessened, and the integrated view has significant implications for theory and practice.

Implications of Viewing Students’ Conceptions as Emergent Structures

This is a discussion of the implications of a general view of students’ conceptions as dynamically emergent structures. While I argue that there are significant implications of this general view, it is important to point out that there are many more specific implications that this general view cannot make. It cannot say which instructional orientation will be most effective in a particular context, it cannot say how particular conceptual structures evolve, nor can it predict particular conceptual difficulties. For these kinds of questions, more focused investigations are needed exploring the details of specific conceptual dynamics and their evolution.

For example, Vosniadou and Brewer (1992) explored children’s conceptual dynamics concerning the shape of the Earth and drew implications about students’ intuitive dynamics as well as students’ generation of conscious models. Clark (2006) considered in detail conceptual changes in four eighth grade students’ ideas in thermodynamics, finding both local coherences as well as contextualities in their evolving conceptions. And Cheng and Brown (2012) explored students’ conceptual dynamics in the topic of magnetism and found that scaffolding students to use particular modeling criteria had important benefits for the coherence and sophistication of the models that students generated. Each of these studies has interesting and important contributions to make that a general view of students’ conceptions as dynamically emergent cannot make.

There are also theoretical models consistent with a dynamic perspective that make more specific claims. Vosniadou (2013) discusses ideas of intuitive presuppositions and more conscious specific models. diSessa (1993, 2013) discusses the elemental view as well as a number of specific intuitive elements. Brown (1993) and Cheng and Brown (2010) discuss conceptual resources such as verbal symbolic knowledge, conscious models, implicit models, and core intuitions. And Bereiter and Scardamalia (2013), in discussing a similar emergent view, propose symbolic connectionist networks (e.g., Thagard 2000; Koponen and Pehkonen 2010) as most likely to provide insights about specific emergent structures.

But even though there are a number of more specific implications that a general dynamic view is unable to provide, there are still important implications that come from a general view of students’ conceptions as emergent structures rather than regular things with static structure. Here I look at the three characteristics of emergent structures and discuss what implications these have for science education theory and practice.

Dynamic Emergence and Evolution of Structures or States

One of the main benefits is that adopting an emergent view allows us to see work from the various perspectives as complementary rather than oppositional. Work done taking an elemental view of students’ conceptions can now be seen to be compatible with, rather than at necessary odds with, work viewing students’ conceptions as thing-like or system-like. Rather than saying students’ conceptions are thing-like OR system-like OR piece-like, we can say “they exhibit characteristics of each of these, as does any emergent structure”. We are free to draw on insights from each of the perspectives not simply out of eclecticism, but because each of the perspectives becomes part of a coherent viewpoint of emergent dynamic structure. Dynamic conceptual elements form emergent structures that give rise to misconceived responses.

This is not to say that an emergent view eliminates all debate. From a dynamic view, we would expect the intuitive elements to be forming emergent structures, dynamic alliances of intuitive elements. From this perspective, Vosniadou agrees that a system view acknowledges the elemental view but sees the elements as forming into more robust dynamic structures than elemental advocates anticipate.

From the framework theory point of view, to the extent that knowledge elements such as p-prims could be postulated to operate in our conceptual system, they become organized in conceptual structures much earlier than it is claimed by the knowledge in pieces approach. (Vosniadou 2013, p. 22)

This then becomes an empirically testable question, and the question has been explored in several studies,Footnote 4 with differing results. But a dynamic view changes the nature of these results from deciding which of two fundamentally opposed views is supported empirically to exploring the extent of the robustness of the dynamically emergent conceptual structures.

If we accept that students’ conceptions are dynamically emergent structures, with some level of coherence and some level of contextuality in dynamic interplay, this has higher-level implications for how we view conceptual change. From a general dynamic view, conceptual change is seen as the evolution of dynamic conceptual structures under various “evolutionary pressures”, which could be “external”, (such as a student’s interpretation of a phenomenon or social interchange), or “internal”, (such as a different dynamic conceptual structure that is also instantiated). There are several important implications of this view of dynamic conceptual evolution:

  1. 1.

    Such dynamic evolution is often nonlinear

  2. 2.

    The dynamic conceptual structures are embedded in other dynamics

  3. 3.

    These dynamic conceptual structures settle to our interpretation of a phenomenon or idea. If evolutionary pressures challenge this “take”, there will necessarily be periods of perceived disequilibrium.

  4. 4.

    New dynamic conceptual structures evolve from existing dynamic structures, they are not “taken in” from outside.

I discuss each of the first two points in separate sections below, but I discuss further here points three and four. The third point, that as these conceptual structures evolve, there will necessarily be periods of perceived disequilibrium, indicates the importance of such disequilibration or cognitive conflict in learning. The fourth point, that new dynamic conceptual structures evolve from existing dynamic structures, indicates the centrality of analogical and metaphorical reasoning.

Existing Dynamic Structures often Give Rise to Conceptual Perturbations

There are many questions to which large numbers of students give misconceived responses, often clustering into a small number of very popular kinds of responses. In many cases they are quite committed to their views. But rather than viewing these responses as representing a unitary, static misconception, we can view these as the settling of dynamic conceptual structures to interpretations that make sense to the students. With Piaget (whose biological view of conceptual schemes is resonant with the emergent view discussed here), someone coming from a dynamic view would see puzzlement and disequilibrium as a necessary part of an evolution toward a new conceptual equilibrium. As such we should not shy away from supporting students as they work through such puzzlements, and a teacher may at times engineer discrepant events if they have evidence of particularly robust but inappropriate emergent structures. While elemental views are often perceived as opposing such confrontation, this is not necessarily the case:

The p-prims perspective does not rule out confrontation. From this perspective, students need to build from their productive resources, but if they have become complacent, confrontation may be an effective device to prompt them into a process of inquiry and construction. One may also think of confronting a robust but inappropriate pattern of p-prim activation. (Hammer 1996, p. 121)

However, the discrepant event would not be viewed as destroying the misconception but rather as providing some impetus to “fold back” (Pirie and Kieren 1994) to firmer conceptual ground in order to evolve more sophisticated emergent structures that are still rooted intuitively. Such “cognitive perturbations” (Li et al. 2006; Dega et al. 2013) are then necessarily a part of ongoing efforts at sense-making rather than one-off events to eliminate unitary misconceptions. This sense-making will necessarily involve the evolution of new dynamic structures from existing dynamic structures.

New Dynamic Structures Evolve from Existing Dynamic Structures

Many of Piaget’s ideas have been strongly critiqued, particularly his idea of domain independent stages, but one of his central ideas has continued and grown in stature with recent work on modeling cognition as complex dynamic systems (Thelen and Smith 1994; Thelen and Bates 2003), work on embodied cognition (Varela et al. 1991; Wilson 2002), and work on conceptual metaphor (Lakoff and Johnson 1980; Lakoff 1993). This central idea is that dynamic conceptual structures (Piaget called these “schemes”) evolve from earlier schemes. As such, some aspects of earlier schemes will tend to persist as the dynamic structures evolve.

For example, a fundamental tenet of embodied cognition is that understandings of basic ideas such as space, motion, and force, as well as more abstract ideas grounded in these intuitive ideas, arise because of sensorimotor, bodily interactions with one’s surroundings.Footnote 5 Pushing and pulling on things leads to the construction of intuitive understandings of the effects of varying levels of effort and resistance. Moving around, attempting to put things inside of, under, or on top of other things, and generally exploring the constraints and affordances of objects in three-dimensional space leads to the construction of ideas of space. Moving oneself and making other things move leads to the construction of ideas of motion. In other words, bodily interactions with one’s environment are intimately intertwined with fundamental intuitive understandings. Gallese and Lakoff (2005) provide evidence that similar neural pathways are employed in actual bodily interactions as in more abstract conceptualizations of space, motion, and force.

An important implication for science education is that we need to take very seriously this grounding of more abstract ideas in these embodied intuitions (Niebert et al. 2012; Cheng and Brown 2010; Amin 2009; Klein 2006). Clement (2008) provides evidence that such grounding is fundamental in even expert’s thinking about problems on their “personal frontier”, that is, problems for which they do not have pre-existing solution methods. Brown (1993) argues that if students can be helped to “re-focus their core intuitions” through extension of intuitive conceptual anchors, this can be very helpful in making sense of previously counterintuitive ideas. Brown (1992), Brown and Clement (1989), Clement and Brown (2008) provide evidence that extension of intuitive conceptual anchors helps students make sense of counterintuitive ideas such as an upward force from a table, a frictional force from a floor, and equal forces between objects colliding.

Involving students in modeling and analogical reasoning (e.g., Brown and Clement 1989; Brown 1993; Gutwill et al. 1999; Dagher 1998; Gilbert and Boulter 2000; Clement and Steinberg 2002; Clement 2008; Khine and Saleh 2011) can provide explicit scaffolding for the evolution of their intuitive dynamic structures into dynamic structures that support more canonical views of scientific phenomena and ideas. From an emergent perspective, multiple dynamic conceptual structures will be brought to bear on considerations of phenomena and ideas, and aspects of these dynamic structures will persist as more integrated dynamic structures evolve. Engaging students in analogical reasoning and modeling is then seen as an intentional scaffolding of analogical and metaphorical reasoning, processes that conceptual metaphor theorists (Lakoff and Johnson 1980; Lakoff 1993) view as fundamental rather than peripheral or ornamental and that one influential cognitive scientist (Hofstadter 2001) calls “the core of cognition”. Since instruction cannot import new structures into students’ minds, and new dynamic conceptual structures therefore must evolve out of existing dynamic conceptual structures, such analogical and metaphorical reasoning is fundamental to conceptual evolution.

Non-linear Conceptual Growth

From a regular thing perspective, “conceptual change” carries with it the implication of exchanging something old and bad for something new and good. For example, a view of misconceptions as unitary static entities might characterize conceptual change as “flipping” from the completely wrong misconceived view to the correct view (diSessa 1993; Smith et al. 1993). But a dynamic view sees conceptual change and growth as an evolution over time of the dynamic conceptual system. This means that instruction aimed at genuine conceptual change and growth will encourage the operation of these dynamics over extended periods of time rather than viewing a “constructivist lesson” as a quick fix.

Both systems and fragmented perspectives see the pace of change as slow and gradual. From an emergent view, students will need time for their dynamic structures to evolve to new stabilities that support more sophisticated and canonical views. Systems theorists have tended to view this extended time as due to the need for students to work through changes in their more coherent conceptual structures. Elemental theorists have tended to view this extended time as due to the need for students to evolve more coherent structures from initially quasi-independent elements. An emergent view sees both occurring and both requiring time. As students grapple with new ideas and puzzling phenomena, they will need time both to challenge existing stabilities and to evolve new stabilities.

The amount of time necessary for supporting conceptual change and growth is a genuine concern given the amount of content coverage expected in many science classes. However, the almost unquestioned assumption in most instruction is that if we want students to learn more, we need to teach more at a faster uniform pace. If we need to build a brick wall faster, we need to put the bricks on top of each other at a faster uniform pace. However, if students’ conceptions are dynamically emergent, we might expect progress in the system to be non-linear–we might think of an analogy to population growth rather than to adding bricks in the wall. Instructionally, this would mean expecting a period of slow growth at the outset with more rapid progress later, as dynamic structures develop in sophistication and integration. Trying to speed up the necessary initial conceptual groping could prove counterproductive in the long run as students would not evolve the necessary dynamic conceptual structures that will support further evolution of more sophisticated dynamic structures.

When learning is at the most fundamental level, as it is here, with all the abstractions of Newtonian mechanics just around the corner, don’t rush! When the mind is evolving the abstractions which will lead to physical comprehension, all of us must cross the line between ignorance and insight many times before we truly understand. (Hawkins 1962, p. 40)

Allowing for the necessary growth will at first be slow but may eventually outstrip linear instructional approaches when students “truly understand” and are then able to move forward more quickly with related ideas.

Embedded Dynamics

There are many interrelated dynamics in instructional contexts. For example, Leander and Brown (1999) point out several interrelated dynamics in the context of a discussion in a physics class. From a dynamic perspective, such interrelated, embedded dynamics are to be expected. Both systems and elemental theorists discuss conscious ideas as interdependent with intuitive ideas (presuppositions or primitives). However, as with the intuitive fragments versus conceptual systems debate, different views are often contrasted as oppositional rather than complementary. As one example, consider the debate about cognition as social versus individual.

Piaget’s ideas are often contrasted with those of Vygotsky, with Piaget portrayed as saying cognition develops in a bottom-up fashion from sensori-motor schemes through the reflective abstraction of the individual to grow into operational schemes. Vygotsky is portrayed as saying that by contrast, cognition is top-down. Social structures become mental structures in the zone of proximal development, and so development moves from the social to the individual. From a regular thing view, Piaget seems to be saying that students cobble together, on their own, Tinkertoy® cognitive structures from more primitive pieces. Vygotsky seems to be saying that these structures are instead imported into students’ minds from social interaction.

But both Piaget and Vygotsky can be seen as advocates of a dynamic view, although the particular dynamic systems they used as framing metaphors were different. Piaget viewed development from a biological metaphor, with cognitive structures seen to develop in ways analogous to biological structures. Vygotsky viewed individual development from a metaphor of the dynamic interactions that lead to cultural development. Vygotsky’s zone of proximal development is typically defined operationally as “the distance between the actual developmental level as determined by independent problem solving, and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers” (Vygotsky 1978, p. 86). However, more theoretically it can be considered as the zone in which social interaction can have a strong effect on the evolution of dynamic cognitive structures: “the dynamic region of sensitivity in which the transition from interpsychological to intrapsychological functioning can be made” (Wertsch 1985, p. 67). In the terms discussed here, the intrapsychological (conceptual) is embedded in the interpsychological (social). In the zone of proximal development, social dynamics can affect the evolution of conceptual dynamics, not through a transfer from the social to the psychological, but through a scaffolding of the development of the dynamic conceptual structures.

Students’ conceptual dynamics, with embedded conscious and intuitive elements, are themselves embedded in affective, social, epistemological, and sociocultural dynamics (Leander and Brown 1999; Hammer 1994). Similar interconnections can be made among these various dynamics as has been discussed here in more detail between individual and social dynamics. Research taking individual, social, sociocultural, epistemological, and affective perspectives can be seen as complementary rather than oppositional.

Teachers can help their classes navigate these interdependent dynamics so that conceptual change and growth is more likely (Brown 2000). However, because of the unpredictability of the interdependent dynamics, teachers need to be armed with flexible, research-based curricula and particularly with awarenesses of the interdependent dynamics and effective ways of navigating these dynamics. Such awarenesses are greatly strengthened through professional interactions among practitioners, and where professional interactions are encouraged and supported through such mechanisms as professional learning communities and lesson study, learning gains are evident (Lewis et al. 2006; DuFour and Eaker 1998).

Conclusions

In a seminal paper promoting ideas of conceptual metaphor, Reddy (1979) discussed what he termed the “conduit metaphor” of communication. While a constructivist alternative to this metaphor (the toolmaker’s paradigm) is intelligible, Reddy argues that the constraints on discourse of the implicit metaphor inhibit widespread adoption of the alternative view. This implicit metaphor supports the absorption view of learning, which remains the dominant view of teaching and learning in schools (Linn and Eylon 2011). In this paper I argue that a related implicit metaphor, the “regular thing” metaphor, privileges consideration of students’ conceptions as regular things with static structure rather than as dynamically emergent structures.

Even the term “structure” is fraught with regular thing implicit overtones. Towers and Davis (2002) discuss two types of structure. The first type is the kind that corresponds to what I call here “regular things” and that Towers and Davis call “architectural” structures. Examples would be building a building, constructing a brick wall, putting Tinkertoys® together, or in general putting regular things with static structure together to build something more complicated but also with static structure. This is the usual meaning of “structure”, and it fits well with an implicit metaphor of regular things.

In viewing students’ conceptions implicitly as regular things, three widespread views of students’ conceptions (as misconceptions, as systems of intuitive ideas, and as collections of intuitive fragments) are in necessary opposition. Misconceptions would be seen as chunks of incorrect conceptual knowledge. Systems of intuitive ideas would be seen as architectural structures with static interconnections among elements. And intuitive elements or fragments would be seen as separated bits of intuitive knowledge, with no structure. Viewed in these ways, each of these views is in necessary opposition to the others. In particular, it is difficult for a view of students’ conceptions as scattered pieces to account for the robustness of many student ideas, and it is difficult to account for the contextuality of students’ ideas if these ideas are viewed as chunks of incorrect conceptual knowledge or as static structures.

But an alternative notion of structure is that of dynamically emergent structure, similar to what Towers and Davis (2002) call a biological view of structure. In this view, structures form dynamically and evolve, change, and grow dynamically. From this perspective, each of the three views can be seen as complementary, each focusing predominantly (although not exclusively) on different aspects of the dynamic structures. Elemental theorists would focus significant attention on the dynamic elements, systems theorists would focus significant attention on the dynamic structures formed, and misconceptions would be viewed as students’ emergent ideas from these dynamic structures. Debates will remain, as systems theorists characterize the dynamically emergent structures as more coherent and robust than those coming from elemental views. But these debates can be seen as important empirical debates within a dynamic framework rather than as clashes of diametrically opposed theoretical frameworks.

Notes

  1. 1.

    Yates et al. (1988), Clark (2006), Clark and Jorde (2004), diSessa et al. (2004), Clark et al. (2011).

  2. 2.

    Wiser and Carey (1983), Carey (1985, 1999, 2000), Gopnik and Schulz (2004), Gopnik and Wellman (1994), Vosniadou (1994, 2002), Vosniadou e al. (2008).

  3. 3.

    Ioannides and Vosniadou (2002), diSessa et al. (2004), Clark et al. (2011).

  4. 4.

    Ioannides and Vosniadou (2002), diSessa et al. (2004), Clark et al. (2011).

  5. 5.

    Piaget (1977), Inhelder and Piaget (1958), Johnson (1987), Varela et al. (1991), Lakoff and Johnson (1999), Gallese and Lakoff (2005), Wilson (2002).

References

  1. Amin, T. G. (2009). Conceptual metaphor meets conceptual change. Human Development, 52(3), 165–197.

    Article  Google Scholar 

  2. Bereiter, C., & Scardamalia, M. (2013). Self-organization in conceptual growth: Practical implications. In S. Vosniadou (Ed.), International handbook of research on conceptual change (2nd ed., pp. 504–519). New York: Routledge.

    Google Scholar 

  3. Brown, D. E. (1989). Students’ concept of force: The importance of understanding Newton’s third law. Physics Education, 24(6), 353–358.

    Google Scholar 

  4. Brown, D. E. (1992). Using examples and analogies to remediate misconceptions in physics: Factors influencing conceptual change. Journal of Research in Science Teaching, 29(1), 17–34.

    Google Scholar 

  5. Brown, D. E. (1993). Refocusing core intuitions: A concretizing role for analogy in conceptual change. Journal of Research in Science Teaching, 30(10), 1273–1290.

    Google Scholar 

  6. Brown, D. E. (2000). Merging dynamics: An integrating perspective on learning, conceptual change, and teaching. Paper presented at the annual meeting of the American Educational Research Association, New Orleans.

  7. Brown, D. E. (2010). Students’ conceptions—coherent or fragmented? And what difference does it make? Paper presented at the annual meeting for the National Association for Research in Science Teaching, Philadelphia, PA.

  8. Brown, D. E., & Clement, J. (1989). Overcoming misconceptions via analogical reasoning: Abstract transfer versus explanatory model construction. Instructional Science, 18(4), 237–261.

    Google Scholar 

  9. Brown, D. E., & Hammer, D. (2013). Conceptual change in physics. In S. Vosniadou (Ed.), International Handbook of Research on Conceptual Change, (2nd ed., pp. 121–137). New York: Routledge.

  10. Carey, S. (1985). Conceptual change in childhood. Cambridge, MA: The MIT Press.

    Google Scholar 

  11. Carey, S. (1999). Sources of conceptual change. In E. K. Scholnick, K. Nelson, & P. Miller (Eds.), Conceptual development: Piaget’s Legacy (pp. 293–326). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  12. Carey, S. (2000). Science education as conceptual change. Journal of Applied Developmental Psychology, 21(1), 13–19.

    Article  Google Scholar 

  13. Cheng, M., & Brown, D. E. (2010). Conceptual resources in self-developed explanatory models: The importance of integrating conscious and intuitive knowledge. International Journal of Science Education, 32(17), 2367–2392.

    Google Scholar 

  14. Cheng, M., & Brown, D. E. (2012). The role of metacognition in students’ development of explanatory ideas of magnetism. Paper presented at the annual meeting for the National Association for Research in Science Teaching, Indianapolis, IN.

  15. Clark, D., & Jorde, D. (2004). Helping students revise disruptive experientially supported ideas about thermodynamics: Computer visualizations and tactile models. Journal of Research in Science Teaching, 41(1), 1–23.

    Google Scholar 

  16. Clark, D. B. (2006). Longitudinal conceptual change in students’ understanding of thermal equilibrium: An examination of the process of conceptual restructuring. Cognition and Instruction, 24(4), 467–563.

    Article  Google Scholar 

  17. Clark, D. B., D’Angelo, C. M., & Schleigh, S. P. (2011). Comparison of students’ knowledge structure coherence and understanding of force in the Philippines, Turkey, China, Mexico, and the United States. Journal of the Learning Sciences, 20, 207–261.

    Article  Google Scholar 

  18. Clark, D. B., & Linn, M. C. (2013). The knowledge integration perspective: Connections across research and education. In S. Vosniadou (Ed.), International handbook of research on conceptual change (2nd ed., pp. 520–538). New York: Routledge.

    Google Scholar 

  19. Clement, J. (1982). Students’ preconceptions in introductory mechanics. American Journal of Physics, 50(1), 66–71.

    Article  Google Scholar 

  20. Clement, J. (2008). Creative model construction in scientists and students: The role of imagery, analogy, and mental simulation. Dordrecht: Springer.

    Google Scholar 

  21. Clement, J. J., & Brown, D. E. (2008). Using analogies and models in instruction to deal with students’ preconceptions. In J. J. Clement (Ed.), Creative Model Construction in Scientists and Students: The role of analogy, imagery, and mental simulation (pp. 139–155). New York: Springer.

  22. Clement, J. J., & Steinberg, M. S. (2002). Step-wise evolution of mental models of electric circuits: A “learning-aloud” case study. The Journal of the Learning Sciences, 11(4), 389–452.

    Article  Google Scholar 

  23. Dagher, Z. (1998). The case for analogies in teaching science for understanding. In J. Mintzes, Wandersee, J., Novak, J. (Eds.), Teaching science for understanding (pp. 195–211). San Diego: Academic Press.

  24. Dega, B. G., Kriek, J., & Mogese, T. F. (2013). Students’ conceptual change in electricity and magnetism using simulations: A comparison of cognitive perturbation and cognitive conflict. Journal of Research in Science Teaching, 50(6), 677–698.

    Article  Google Scholar 

  25. diSessa, A. A. (1988). Knowledge in pieces. In G. Forman & P. Pufall (Eds.), Constructivism in the computer age. Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  26. diSessa, A. A. (1993). Toward an epistemology of physics. Cognition and Instruction, 10(2 & 3), 105–225.

    Article  Google Scholar 

  27. diSessa, A. A. (2008). A birds-eye view of the “pieces” vs. “coherence” controversy (from the “pieces” side of the fence). In S. Vosniadou (Ed.), International handbook of research on conceptual change (pp. 35–60). New York: Routledge.

    Google Scholar 

  28. diSessa, A. A. (2013). A birds-eye view of the “pieces” vs. “coherence” controversy (from the “pieces” side of the fence). In S. Vosniadou (Ed.), International handbook of research on conceptual change, (2nd ed., pp. 31–48). New York: Routledge.

  29. diSessa, A. A., Gillespie, N. M., & Esterly, J. B. (2004). Coherence versus fragmentation in the development of the concept of force. Cognitive Science, 28, 843–900.

    Article  Google Scholar 

  30. DuFour, R., & Eaker, R. (1998). Professional learning communities at work. Bloomington, Ind.: National Education Service.

    Google Scholar 

  31. Duit, R. (2009). Bibliography–STCSE. Students’ and teachers’ conceptions and science education (http://www.ipn.uni-kiel.de/aktuell/stcse/download_stcse.html).

  32. Gallese, V., & Lakoff, G. (2005). The brain’s concepts: The role of the sensory-motor system in conceptual knowledge. Cognitive Neuropsychology, 22(3), 455–479.

    Article  Google Scholar 

  33. Gilbert, J. K., & Boulter, C. J. (2000). Developing models in science education. Boston: Kluwer.

    Google Scholar 

  34. Gopnik, A., & Schulz, L. (2004). Mechanisms of theory-formation in young children. Trends in Cognitive Science, 8, 371–377.

    Article  Google Scholar 

  35. Gopnik, A., & Wellman, H. M. (1994). The theory. In L. A. Hirschfeld & S. A. Gelman (Eds.), Mapping the mind: Domain specificity in cognition and culture (pp. 257–293). New York: Cambridge University Press.

    Google Scholar 

  36. Gutwill, J. P., Frederiksen, J. R., & White, B. Y. (1999). Making their own connections: Students’ understanding of multiple models in basic electricity. Cognition and Instruction, 17(3), 249–282.

    Article  Google Scholar 

  37. Hammer, D. (1994). Epistemological beliefs in introductory physics. Cognition and Instruction, 12(2), 151–183.

    Article  Google Scholar 

  38. Hammer, D. (1996). Misconceptions or p-prims: How may alternative perspectives of cognitive structure influence instructional perceptions and intentions? Journal of the Learning Sciences, 5, 97–127.

    Article  Google Scholar 

  39. Hawkins, D. (1962). Messing about in science. Science and Children, 2(5), 39–44.

    Google Scholar 

  40. Hofstadter, D. R. (2001). Analogy as the core of cognition. In D. Gentner, K. J. Holyoak, & B. N. Kokinov (Eds.), The analogical mind: Perspectives from cognitive science (pp. 499–538). Cambridge, MA: The MIT Press.

    Google Scholar 

  41. Ioannides, C., & Vosniadou, S. (2002). The changing meanings of force. Cognitive Science Quarterly, 2, 5–61.

    Google Scholar 

  42. Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence; an essay on the construction of formal operational structures. New York: Basic Books.

  43. Johnson, M. (1987). The body in the mind: The bodily basis of meaning, imagination, and reason. Chicago: University of Chicago Press.

    Google Scholar 

  44. Khine, M. S., & Saleh, I. M. (Eds.). (2011). Models and modeling: Cognitive tools for scientific enquiry. New York: Springer.

    Google Scholar 

  45. Klein, P. D. (2006). The challenges of scientific literacy: From the viewpoint of second-generation cognitive science. International Journal of Science Education, 28(2–3), 143–178.

    Google Scholar 

  46. Koponen, I. T., & Pehkonen, M. (2010). Coherent knowledge structures of physics represented as concept networks in teacher education. Science & Education, 19(3), 259–282.

    Article  Google Scholar 

  47. Lakoff, G. (1993). The contemporary theory of metaphor. In A. Ortony (Ed.), Metaphor and thought (2nd ed., pp. 202–251). Cambridge, UK: Cambridge University Press.

    Google Scholar 

  48. Lakoff, G., & Johnson, M. (1980). Metaphors we live by. Chicago: University of Chicago Press.

    Google Scholar 

  49. Lakoff, G., & Johnson, M. (1999). Philosophy in the flesh: The embodied mind and its challenge to Western thought. New York: Basic Books.

    Google Scholar 

  50. Leander, K., & Brown, D. E. (1999). “You understand, but you don't believe it”: Tracing the stabilities and instabilities of interaction in a physics classroom through a multidimensional framework. Cognition and Instruction, 17(1), 93–135.

    Google Scholar 

  51. Lewis, C., Pery, R., Hurd, J., & O’Connell, M. P. (2006). Lesson study comes of age in North America. Phi Delta Kappan, 88(4), 273–281.

    Google Scholar 

  52. Li, S. C., Law, N., & Lui, K. F. A. (2006). Cognitive perturbation through dynamic modelling: A pedagogical approach to conceptual change in science. Journal of Computer Assisted Learning, 22, 405–422.

    Article  Google Scholar 

  53. Linn, M. C., & Eylon, B.-S. (2011). Science learning and instruction: Taking advantage of technology to promote knowledge integration. New York: Routledge.

    Google Scholar 

  54. Manson, S. M. (2001). Simplifying complexity: A review of complexity theory. Geoforum, 32, 405–414.

    Article  Google Scholar 

  55. Niebert, K., Marsch, S., & Treagust, D. F. (2012). Understanding needs embodiment: A theory-guided reanalysis of the role of metaphors and analogies in understanding science. Science Education, 96(5), 849–877.

    Article  Google Scholar 

  56. Panagiotaki, G., Nobes, G., & Banerjee, R. (2006). Children’s representations of the earth: A methodological comparison. British Journal of Developmental Psychology, 24(2), 353–372.

    Article  Google Scholar 

  57. Piaget, J. (1977). The development of thought: Equilibration of cognitive structures. New York: Viking Press.

    Google Scholar 

  58. Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics, 26(2/3), 165–190.

    Article  Google Scholar 

  59. Posner, G. J., Strike, K. A., Hewson, P. W., & Gertzog, W. A. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Science Education, 66, 211–227.

    Article  Google Scholar 

  60. Reddy, M. J. (1979). The conduit metaphor: A case of frame conflict in our language about language. In A. Ortony (Ed.), Metaphor and thought (pp. 284–324). New York: Cambridge University Press.

    Google Scholar 

  61. Rusanen, A.-M., & Pöyhönen, S. (2012). Concepts in change. Science & Education, 22(6), 1389–1403. doi:10.1007/s11191-012-9489-x.

    Article  Google Scholar 

  62. Schneps, M. H., & Crouse, L. (2002). A private universe: Misconceptions that block learning [videorecording]. S. Burlington, Vt.: Annenberg/CPB.

  63. Smith, J., diSessa, A., & Roschelle, J. (1993). Misconceptions reconceived: A constructivist analysis of knowledge in transition. The Journal of the Learning Sciences, 3(2), 115–163.

    Google Scholar 

  64. Strike, K. A., & Posner, G. J. (1992). A revisionist theory of conceptual change. In R. A. Duschl & R. J. Hamilton (Eds.), Philosophy of science, cognitive psychology, and educational theory and practice. Albany: SUNY Press.

    Google Scholar 

  65. Thagard, P. (2000). Coherence in thought and action. Cambridge, MA: MIT Press.

    Google Scholar 

  66. Thelen, E., & Bates, E. (2003). Connectionism and dynamic systems: Are they really different? Developmental Science, 6(4), 378–391.

    Google Scholar 

  67. Thelen, E., & Smith, L. (1994). A dynamic systems approach to the development of cognition and action. Cambridge, MA: MIT Press.

    Google Scholar 

  68. Towers, J., & Davis, B. (2002). Structuring occasions. Educational Studies in Mathematics, 49, 313–340.

    Article  Google Scholar 

  69. Varela, F. J., Thompson, E. T., & Rosch, E. (1991). The embodied mind: Cognitive science and human experience. Cambridge, MA: MIT press.

    Google Scholar 

  70. Vosniadou, S. (1994). Capturing and modeling the process of conceptual change. Learning & Instruction, 4, 45–69.

    Article  Google Scholar 

  71. Vosniadou, S. (2002). On the nature of naïve physics. In M. Limon & L. Mason (Eds.), Reconsidering conceptual change: Issues in theory and practice. The Netherlands: Kluwer.

    Google Scholar 

  72. Vosniadou, S. (2013). Conceptual change in learning and instruction: The framework theory approach. In S. Vosniadou (Ed.), International handbook of research on conceptual change (2nd ed., pp. 11–30). New York: Routledge.

    Google Scholar 

  73. Vosniadou, S., & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24(4), 535–585.

    Article  Google Scholar 

  74. Vosniadou, S., Vamvakoussi, X., & Skopeliti, I. (2008). The framework theory approach to the problem of conceptual change. In S. Vosniadou (Ed.), International handbook of research on conceptual change (pp. 3–34). New York: Routledge.

    Google Scholar 

  75. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge MA: Harvard University Press.

    Google Scholar 

  76. Wertsch, J. V. (1985). Vygotsky and the social formation of mind. Cambridge, MA: Harvard University Press. ch. 1 & 3.

  77. Wilensky, U. (2010). Netlogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University. Evanston, IL. Available at http://ccl.northwestern.edu/netlogo/.

  78. Wilson, M. (2002). Six views of embodied cognition. Psychonomic Bulletin & Review, 9(4), 625–636.

    Article  Google Scholar 

  79. Wiser, M., & Carey, S. (1983). When heat and temperature were one. In D. Gentner & A. Stevens (Eds.), Mental models (pp. 267–298). Hillsdale, NJ: Lawrence Erlbaum Associates Inc.

    Google Scholar 

  80. Yates, J., Bessman, M., Dunne, M., Jertson, D., Sly, K., & Wendelboe, B. (1988). Are conceptions of motion based on a naive theory or on prototypes? Cognition, 29, 251–275.

    Article  Google Scholar 

Download references

Acknowledgments

I want to thank Stella Vosniadou, Andy diSessa, and David Hammer, for their helpful comments on an earlier draft of the manuscript.

Author information

Affiliations

Authors

Corresponding author

Correspondence to David E. Brown.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Brown, D.E. Students’ Conceptions as Dynamically Emergent Structures. Sci & Educ 23, 1463–1483 (2014). https://doi.org/10.1007/s11191-013-9655-9

Download citation

Keywords

  • Conceptual Change
  • Conceptual Metaphor
  • Knowledge Element
  • Conceptual Element
  • Emergent Structure