Causality in Complex Dynamic Systems: A Challenge in Earth...

ABSTRACT

The understanding of the mechanisms underlyingprocesses such as self-organization, adaptation,emergence, which are characteristics of complexsystems, is of paramount importance when teaching andlearning science. Preliminary research on studentunderstanding of complexity indicates that studentstend to conceptualize dynamic systems in staticdisjointed terms, utilizing a linear-mono-causalapproach which impedes a conceptual understanding ofcomplex causal relations. Hypothesizing that studentunderstanding of the principles of causality plays afundamental role in the understanding of complexity,undergraduate science majors have been interviewed toexplore their approaches to complex natural phenomenaand document changes that occur in reasoning when amodified Aristotelian framework of causality principlesis introduced. Results indicate that the understanding ofemergence, downward causation, and self-organizationare better conceptualized when students utilize themodified Aristotelian framework of causality principles.

INTRODUCTION

Analyzing and teaching natural phenomena meansasking the fundamental questions in science: "Whathappened" "How did that happen?" "Why did thathappen?" Starting from these questions we scientists aswell as our students embark on the fascinating journey of science looking for explanations and trying to establishcausal determinants for observed phenomena of interest. In our discipline we are confronted with non-linearity,self-organization and evolving systems at different levels of complexity, from the formation of a crystal to theunderstanding of how plate tectonics arises asself-organizing system from the lithosphere-mantleinteractions (Bercovici, 1998, 2000, 2003; Tackley, 1998;Anderson, 2002) to global warming. As discussed inmore detail below, processes such as emergence andself-organization are regulated by causal principles andcausal couplings that are not describable by a linearchain of causes and effects and not defined in thedeterministic framework (Drummond, 2001).

Students and teachers have difficulties in describingand explaining phenomena in terms of emergence,self-organization, and stochastic processes (Feltovich, etal., 1989; Resnick,1994, 1996; Wilensky and Resnick, 1999, Penner 2000) and may use different ontologies than theones used by experts when constructing solutions andexplanation to complex systems problems (Jacobson,2001; Chi, 2005, Libarkin et al., 2005). Specifically for thegeosciences, Libarkin et al. (2005) and Libarkin andKurdziel (2006) document the difficulties that students in entry level geosciences courses have in conceptualizingprocesses necessary to achieve an Earth Systems Scienceperspective. Many students tend to have profounddifficulties in explaining mechanisms underlying

transformations necessary for the Earth systems toevolve, remaining in a "proto-process" ontological stage:"wherein the student mentions an understanding that aprocess must exist to cause the transformation, but nofurther explanation of a specific mechanism is given.This includes mention of a process-related word, such asevolution, but without a clear explanation of whatevolution actually is" (Libarkin et al., 2005). Whenstudents try to make sense of complex naturalphenomena, often their explanations assumedeterministic causality (Resnick and Wilensky, 1993;Wilensky and Resnick, 1999; Perkins and Grotzer, 2000;Raia, 2005; Jacobson and Wilensky, 2006). Specifically,students consider phenomena such as emergence andself-organization as being mechanistically caused by aunique cause that completely explains observed patternor by a linear chain of causes and effects (Resnick 1994,1996; Resnick, and Wilensky, 1997; Raia, 2005;Gonzalez-Rubio et al. 2005). For example, a V-shapepattern often observed when geese fly as an organizedgroup arises by a process of self-organization. Inparticular, individual birds have no sense of the overallflock pattern. The V-shape - an emergent property of thesystem - originates from a spontaneous collectivebehavior, that is, from each bird simply reacting to themovement of other birds in the flock (Vicsek, et al. 1995Czirok and Vicsek 2001; Schechter, 1998 for generalscience review). The emergent property has an important control effect on the birds' interactions by defining theboundary conditions that influence birds behavior. Theemergent V-shape, for example, constrains the positionof birds, probably making the flying more advantageousfor individual birds to stay within the V-pattern in termsof air resistance, visibility, etc. Students explain aV-shape pattern as either caused by a leader goosecoordinating the other geese or caused by a preexisting"flying gene" that "forces" each goose to fly in such apattern (Wilensky, 1993, 1995; Resnick, 1994; Raia, 2005).Similarly, students explain the emergence of NorthernHemisphere glaciations as caused by a drastic change inthe average atmospheric temperature, which in turn wascaused by a variation of the energy received by the sun,which in turn was caused by a meteorite impacting theEarth's orbit (Raia, 2005). In a previous study (Raia 2005)on college students' approach to natural phenomena, this way of thinking was associated with a linearmono-causal thinking approach (LMC-A) to complexdynamic systems characterized by a tendency to: 1)conceptualize dynamic systems in static disjointed termsrather than considering the complex interactions amongthe system, its components and, the environment; 2)focus on the isolated behavior of the constituentcomponents, rather than considering also their evolvinginteractions and, 3) identify a single causal force, orlinear chain of unique causal events to explain complexnatural phenomena, rather than recognizing processessuch as emergence and self-organization. Understanding how students approach complexity is important toidentify the general framework in which they learn (Raia,

Raia - Causality in Complex Dynamic Systems 81

Causality in Complex Dynamic Systems: A Challenge in EarthSystems Science EducationFederica Raia Departments of Earth and Atmospheric Sciences, and Secondary Education,

Room MR106, City College of New York, 138th and Convent Avenue, New York,NY 10031, [email protected]

2005). In this framework we need to understand the rolethat various concepts of causality play in understandingsystems' evolution, and if and how an approach that canimpede a deeper understanding of natural phenomena is modifiable when a richer repertoire of causalityprinciples is utilized.

Study Hypothesis - In this paper, based on theframework previously proposed (Raia, 2005), Ihypothesize that natural phenomena can be bestconceptualized by students if they understand andutilize various concepts of causality.

In three steps toward testing the hypothesis 1) Idefine the principles of causality in the context ofcomplex dynamic systems; 2) I subsequently apply themto students' interpretations of Earth systems phenomenato establish the relations among the above principles andthe major categories identified by Raia (2005) and; 3) Idescribe a possible intervention that can supportstudents in developing a richer repertoire of complexcausal models.

DEFINING THE PRINCIPLES OFCAUSALITY

Evaluating Efficient Causality - The philosophicalfoundation of concepts of causality is attributed toAristotle -350 BC, who distinguished formal, material,efficient, and teleological causes. Following Galileo theconcept of causality has slowly narrowed to the uniquemeaning of a mechanistic cause-effect relationship -theAristotelian efficient causality. It is important to notethat, as described in more detail below, the concept ofefficient causality, by definition, is characterized by theassumption that an earlier phenomenon A has a causaleffect on the development of a phenomenon B. Since thisconcept also assumes unidirectional time, B cannot havean effect on A (Bunge, 1979).

The mechanistic concept of causality, neglectingother concepts of causality less able to produce tangibleresults in the applied sciences, was sustained by theundeniable scientific advancement following thescientific revolution of the seventeenth century (Cohen1985; Shapin, 1996). The mechanistic concept of causalitysupports an approach that reduces the explanations tomechanistic explanations, suggesting that a system isfully determined by earlier stages in that process. Thisimplies the reduction of a complex phenomenon tosimply a set of initial conditions that are, according tolaws of nature, jointly sufficient for its occurrence. In themechanistic framework, material processes aredeterministic, time is reversible and processes obey alinear causal (cause-effect) chain (Nagel, 1961). Themechanistic approach, mostly utilized in the teaching ofphysical sciences (Salmon 1990, Emmeche et al. 1997),reduces the teaching and learning of Earth SystemsScience to an adjunct to physical-mathematical sciences(Narasimhan, 2006). This approach strongly contrastswith recommendations and expectation set forth byIreton et al. (1997) of a systems view and understandingof natural phenomena.

A linear causal structure is often observed inlearners' reasoning in science (Gutierrez and Ogborn,1992; Andersson, 1986; Viennot, 1998; Perkins andGotzer, 2000; Raia, 2005). Studies on students'understanding of the forming of atoms and molecules(Nicoll, 2001; Taber, 2001) for example, have shown thatstudents view the process as only related to forces

attracting or repelling constituents' components.Students begin attending our Earth Systems Sciencecourses with the reinforced view that molecules are theminerals' building blocks that, attracting/repelling eachother will form higher level structures. They hypothesize that the attracting/repelling forces mechanistically causethe building blocks to create the crystal, reducing aself-organizing phenomenon to a deterministic productof a set of initial conditions fully determined by earlierstages in that process.

Causal Relations between System Levels - Theemergence of crystal symmetry in a cooling fluid can beunderstood more properly in the context of complex selforganizing systems (Nicolis, 1989; Heylighen, 1995; Pina, 2002; Raia 2005). Complex dynamic systems have ahierarchical nature characterized by multiple interactinglevels (Salthe 1985; 1989; Wilensky and Resnick, 1999;Raia, 2005). The nature of these interactions is not-linear(Campbell, 1974; von Bertalanffy, 1978; Salthe 1985; Kim,1992; Holland, 1998). The symmetry of the crystal(emergent-level) emerges from a number of moleculesfollowing specific rules of interactions (defined byphysical-chemical properties) -lower level. The crystalshape that emerges on the higher system level, definesthe boundary conditions that constrain lower level systemcomponents' behavior, according to the crystalline shape itself. The emergent crystalline structure, which is neitherreducible to the density of the molecules within the fluidsnor to the interactions among them, constrains thebehavior of the parts and the growth of the crystal. Theemergent structure presents new properties that areneither present among the lower level constituents nordeducible from the sum of the properties of themolecules. In this context, a system as a whole emergesfrom the rules of interactions established among thesituated components which also continuously evolve.The variations in the interactions are controlled by theemergent phenomenon, which, as in the example above,continuously defines new boundary conditions. Theemergent phenomenon therefore influences thecomponents' behaviors on the lower system level fromwhich it simultaneously emerges. This process can bealso envisioned as a positive feedback: the components'interactions give rise to the emergent phenomenon(upward causation) and, simultaneously are modified by it (downward causation) (Campbell, 1974; Kim, 1992). So, if as described above the emergence phenomenon isdescribed by boundary conditions, we have a systemwhose boundary conditions continuously change. In theexample above it is necessary to note that thedistributions of the molecule and their properties areconceived as causal determinants because they influenceand control the evolution of the system. The emergentboundary conditions are controlling the systemevolution as well and, therefore, they are also conceivedas causal determinants. These causal determinants andtheir relations control and influence each other givingrise to complex couplings. Basca and Grotzer (2001) have shown that a simple linear model of causality thatestablishes a one-to-one correspondence between causeand effect is instead often utilized by students. They alsofound that students do not consider that a cause canemerge from an evolving system. In the example above,the emergent boundary conditions, and the variedinteractions of components could be ignored by studentsas causal determinants, impeding a deeper

82 Journal of Geoscience Education, v. 56, n. 1, January, 2008, p. 81-94

understanding of the system' behavior as a whole(Perkins and Grotzer, 2000, Raia, 2005).

It is also of fundamental importance to note that theupward (emergence) and downward causations are nottemporally distinct; in fact, the lower level does not stopcreating the upper level while the downward causation“causes back" its effect. The molecules are parts of thecrystal: they constitute it, and participate in the emergent boundary conditions. In this sense, the causal relationsbetween the entities (molecules) of the lower-level andthe level of emergent property (crystal shape) are not of acause-effect nature (efficient cause according toAristotle). Although simultaneity of causal interactions-where causes are at the same time effects- are found inmany aspects of our life including human relations,students seem to have great difficulties inconceptualizing them and tend to construct a one-waylinear chain to explain them (Green, 1997; Perkins andGrotzer, 2000; Chi, 2005; Raia, 2005).

Open Systems: Causal Relations Between Systemand Environment - The coupling of system level withthe environment in which the system is situated is not ofcause-effect nature either. The process can beconceptualized as a feedback loop. A fluctuation in thesystem is amplified until all the components of thesystem are affected and a new configuration emerges.This positive feedback phase can emerge from thecouplings among the components based on theirintrinsic characteristics, their spatial distribution and therules of interaction among them. Negative feedbackssuppress any components' behavior that tends to deviate from the homeostatic configuration (Varela, 1992). Theemergent configuration can be considered as anequilibrium state, when the system has reached aminimum in its energy function or it can be considered adissipative structure when the system, far fromequilibrium exchanges energy and matter and/orentropy with the environment in which is situated (e.g.Bénard cells). The ongoing transformations andrecursive adaptations regulated by the coupling of lowerlevel and emergent level and the coupling of theemergent level and the environment in which the systemis situated, can be considered as processes ofself-organization and therefore are not of cause-effectnature either. Rather, they have the function ofmaintaining the system coherence within its dynamicbehavior, that is, within an integrated processual wholeto regulate the survival of the system over time. Thesecomplex couplings are characterized by causalinteractions. According to Perkins and Gotzer (2000)students' conception of causality can be so simplistic thatit will not allow them to recognize these interactions ascontinually evolving causal control on system' evolutionand behavior. The unfortunate consequences of lack of

recognition span from a general difficulty inunderstanding scientific concepts to a superficialknowledge and understandings of natural phenomena,which cannot satisfy college level scientific preparation.

Modified Aristotelian Concepts of Causality - Withinthis framework it is clear that reducing explanation ofphenomena to a mere search or emphasis of a cause, or"joint" causes in the Galilean and Newtonian sense,restricts the meaning of causality to but one of the fourways of answering the question "Why" proposed byAristotle. Indeed, the paradigmatic transition toward asystem approach benefits from reviewing theAristotelian concepts of causality, which constitute theformal basis for a - non-reductionist - system theoreticalparadigm.

As the Greek philosopher proposed, there are manyways in which because may answer the question why. InPhysics and more extensively in Metaphysics, Aristotleargues that changes as well as emergence requirecomplex relations among four causality principles:efficient, material, formal and teleological. These concepts ofcausality can best be defined using Aristotle' originalexample of the making of a statue of Apollo reported inTable 1. Aristotle argues that although not all four causesare always necessary to explain phenomena or patterns,as for example no efficient cause is always necessary toexplain geometrical patterns, the interplay of the four are necessary to explain complexity, for example life.

As discussed above, in the context of complexsystems such as the one dealt within Earth SystemsScience, a broader framework is required for causalcoupling a) among system' components (lower level), b)between systems' levels (lower and emergent level) and;c) between system and the environment in which thesystem is situated (global level), to understand thesystems evolution.

By utilizing and reinterpreting the four Aristotelianprinciples of causality it is possible to distinguish thefollowing types of controls in our context of EarthSystems Science:

Efficient Causality - It is the standard sense in whichphysical science conceptualizes causality (Bunge, 1979).It can be envisioned as a force, an agent that acts on anobject entailing a temporal cause-effect relation. It results in a temporal sequence of states or phenomena beingcausally interrelated. Efficient causality implicates aninteractional exchange of energy pertaining to the entities of a given level as the molecules interactions leveldescribed in the example of crystal formation.

Material Causality - It refers to the role that thecharacteristic material properties of a given level play inthe evolution of a system. These may include potential


EFFICIENT CAUSE Represents the agent responsible for shaping the bronze into its form of Apollo, i.e., the sculptor.

MATERIAL CAUSE Refers to the material out of which the statue is made (bronze) exerting a control on the kind ofshape the statue will take, in light of the intrinsic properties of the material itself.

FORMAL CAUSERelates to the structure or the form which the organized matter takes becoming somethingdeterminate identifiable as a statue of Apollo and by its own shape constraining any other further transformation

FINAL CAUSE (telos) Defines the purpose to shape the compound of form and matter, e.g. the statue was created forthe purpose of honoring Apollo.

Table 1.Example of Aristotle’ four causality principles applied to the making of a statue.

energy, specific energy of state (Emmeche et al. 2000), the type of molecules or their density distribution in a givenfluid in the example of the crystal formation. In complexsystems such as our evolving planet this causality plays a fundamental role that must be recognized: the presenceof small amounts of dissolved water in theasthenosphere for example seems to greatly influence the Earth-like plate tectonics (Hirth, 2001; Regenauer-Lieb etal., 2001; Solomatov, 2004). In fact, the ocean presencecould modify the strength of lithosphere controlling thevery existence of plate tectonics (Solomatov, 2001). Consequently, this causal control establishes relationsamong different system' levels.

Formal Causality - As described by Aristotle, it is thepattern by which something is organized, or how it isstructured. In the example of the crystal formation itcould be the crystalline structure emerging from theinteractions defining boundary conditions andconstraining the behavior of the parts and theconcomitant crystal growth. This causal relation alsorelates entities of different levels that in the case of theforming crystal can be recognized as the lower level(interacting molecules) and the emergent level (thecrystal structure). In plate tectonics, the changing ofsurface boundary condition -the migration of continents,ridges and trenches - can exert formal control on mantledynamics (Anderson, 2002; Stein and Hansen, 2001).

Functional Causality - This type, referring to teleological or final cause, is NOT considered in the sciencecommunity as operating on natural phenomena when itis referred to an external purpose as in intention, plan (asin Intelligent Design). But it enters the scientificdiscourse when we need to describe regulating functionof maintaining the system coherence within its dynamicbehavior, or "the purpose of a behavior seen from theperspective of a system's chance of remaining stable (or'surviving') over time" (Nagel, 1961; Salmon, 1990;Emmeche et al., 2000). Varela (1992) pointed out that thecapacity of a system to survive is a function of thecoupling between the system emerging properties andthe inputs and solicitations provided by theenvironments in which the system is situated. Theircoupling/interactions are at the core of complex systembehavior. While positive feedbacks for example couldemerge by the interaction of a formal cause (structure)and an efficient cause (forces), these couplings can enteras functional causality at the global system levelcontrolling the evolution of the system through negativefeedback. Adaptation and self-organization can bedescribed by this principle of causality. If we consider the system lithosphere-asthenosphere and assume that thelithosphere is a dissipative structure, (defined as asystem that, far from thermodynamic equilibrium, tendsto self-organize by exporting entropy) the minimizationof dissipation in the lithosphere, may be the organizingrule for global reorganization (Anderson 2002). Thisorganizing rule is of functional causality nature. In astudy conducted on a difference in expert and novicerepresentations of an aquatic system Hmelo-Silver andPfeffer (2004) found that understanding the functions ofa system correlated only with the experts' more elaborate network of concepts and principles to representphenomena and their interrelationships. Similarly,Libarkin and Kurdziel (2006) found that students tend tomention words that describe this organizing rule, butthey do not understand fully its meaning.

The distinction among the above types of causality in analyzing complex phenomena is not clear-cut andmutually exclusive since their identification is stronglydependent on the level of description and analysis(Salthe, 1985, 1989). There is no absolute lower or higherlevel, since they are defined according to the chosen level of observation. For instance, in the example crystalforming from a fluid, what can be interpreted as formalcausality (the space distribution of particles) could beinterpreted at a higher level as a property of the matter ofthe entire mixture (e.g. viscosity) influencing andcontrolling the lower level interactions among molecules (modifying for example the velocity of the diffusingparticles). In this framework, a varied interpretation ofcausality principles can be expected and it is intrinsic tothe approach and analysis of complex dynamic systems(Salthe, 1985). However, from the above discussion itfollows that causal relationships in Earth SystemsScience cannot be restricted to mechanistic causality. The complementary use of different types of causality,derived from the modified Aristotelian framework, is atthe core of complex system behavior.

STUDENTS' USE OF CAUSALITYPRINCIPLES

Method and Design - To explore if there is any relationbetween students' understanding and use of thecausality principles and approach to complex naturalphenomena I analyzed their discourse in approachingnon-linear system dynamics according to the fourprinciples of causality defined above.

Participants - Participants to the interviews are tenupper level undergraduate science students majoring inBiology, Chemistry, Earth Science and Physics from apublic university in New York City which reflects theethnic diversity of the City itself. Here I present a casestudy based on two students' interviews. With the goal to outline a coding methodology based on a newframework of conceptualizing causality principles in thecontext of complexity, the documented two interviews,based on previous study (Raia, 2005), exemplify theendpoint approaches to complexity: Linear-mono-causal (LMC-A) vs. complex dynamic systems approach(CDS-A). As discussed in the introduction,understanding that students approach complexity witheither a linear-mono-causal or systems approach isimportant to identify the general framework in whichthey learn. We also need to understand if theseapproaches relate to the understanding and utilization of various concepts of causality to further understand whatsteps can be taken to support students learning aboutcomplexity.

The names of the students reported here arepseudonyms.

Interviews - The role of the interview is to understandstudents' thinking and reasoning about a specificproblem. Students are asked the questions in a one-toone interview setting that allowed for follow upquestions by the part of the interviewer and areencouraged to describe their own reasoning. Theinterview sections were taped. They are forty-fiveminutes long and divided in two parts. The goal of thefirst part is not to help students come up with the"correct" answer, but to determine the "state space" -therange of most common real difficulties students


encounter when confronted with a problem (Redish, andSteinberg, 1999). The second part of the interview teststhe effect of an explicit intervention on studentsreasoning and it is described in details in third section ofthis paper: Intervention Effort. Students' responses arealso recorded and analyzed applying the same coding ofcausality principles.

Questions - Three questions, based on the results onprevious studies on students understanding of complexdynamic systems (Raia, 2005; Wilensky and Resnick,1999) were developed to elicit student approaches tonon-linear dynamic systems and the understanding ofcausality. They are reported in Table 2. They addressprocesses of non-linear interactions, emergence,adaptation, and self-organization.

Analysis of Students' Responses - The recordedinterviews were transcribed and coded according to thefour principles of causality defined above utilizing thecontent analysis method to categorize and analyzequalitative data developed by Mayring (2002). The codeswere given on a scale of 0 to 3 on the base of thecontextual meaning of the sentence. A complete absenceof any form of recognition of causality was given score 0.If for example, a student identifies properties of materialor describes patterns but does not identify them ascausalities, that is, the student does not relate them to theexplanation, the score was given a 1. If the causalities areidentified then the score is equal to 2. If more then onecausality principles is coupled the score is 3. Table 3reports the font code used to highlight the differentcausality principles identified with a score of 2 instudents' discourse. A proto-state of recognition coded as


Table 2. The three questions, reported here together, are presented separately to students. For question 2only a sample of the snowflakes shown to students is reported here. The entire collection of real snow crystals captured by Kenneth G. Libbrecht is shown during the interview Please refer to the published material forviewing the entire collection (Libbrecht, 1999)able 2. Questions asked.

1 and a higher sophistication in recognition of causalemergence (emerging causes) coded as 3, are describedin detail in the following section. They are nothighlighted by a font code as done for code 2 in Table 3.The reason for excluding the codes 1 and 3 from fontcoding in the students' responses is to avoid an overloadof symbols and to stress the intention of this project toreveal if students tend to consider as causal controls morethen one causality principles in the development andevolution of a natural phenomenon.

Inter-rater Variability - Two experienced raters wereblinded to the rating of the other rater'sassessment-rating of the answers to the three questionsfor both students Linda and Kate. In a second step, theraters compared their assessment/coding results. If theresults were non-consistent, a discussion with the goal ofresolving the discrepancy followed. Below I provideexamples where discrepancies were found and how theywere resolved.

There was full agreement on the recognition ofefficient causality, while there was some disagreementspecifically on the identification of formal and materialcausality as code 1 or 2. For example in the responses toquestion 2 (Table 2) a student, reasoning on how thecrystal forms explains:

Kate: " I think chemistry, THEY HAVE SOMEKIND OF BONDS, IN CERTAIN WAYSTHEY FIT TOGETHER BASED ONATTRACTION …SOMEHOW THEELECTRONS OF THESE OTHER ONES(points at the sides of the crystals)…AREATTRACTED."

Interviewer: which electrons? Kate: "you see, the molecules of the water are

polar, so they connect O is negative and H ispositive so they attract."

There was complete agreement in recognizing thecausality principle identified in the capital bold font(Table 3) as efficient causality. On the other hand, whenKate refers to the polarity of the water molecules, one ofthe raters score it as Formal = 1 (student describes apattern but does not identify it as a causality principle inthe explanation of the phenomena observed). Kate doesnot relate the shape of the molecules as a control factor inemergence of the crystal shape, but only to justify thepolarity character of the water molecule. When this point was discussed the other rater envisioned a possibleunderstanding of an efficient causality emerging fromthe structure of the molecule. After the discussionsection, this tentative interpretation was then appliedseparately by both raters to Kate's following discourse:

Kate: "…I don't know why they would do that"

Kate: " when you see ice on the floor it isn't .. itdoesn't look like flakes… I guess it does have acrystal structure, so if you have a microscopeyou can see it …there is a difference, but I reallydon't know why.

Both raters coded Kate' reasoning as a formalcausality=1, indicating a "proto state" of recognition offormal causality. In effect Kate never uses it to explain the pattern observed and reiterates "but I really don't knowwhy". Both raters independently coded both parts of herdiscourse as formal =1. Full agreement was reached.

The possible recognition of material causality in thestatement regarding the polarity of water was coded bythe rater also as efficient causality -electrons respond toan attracting force. An understanding of materialcausality would have implied recognition of theattraction (efficient causality) as emergent from closeinteraction of atoms.

It is interesting to note that during a discussionsession the raters have both pointed out that theinterpretation of causality as either formal or materialcan depend on the level description and analysis. Asdescribed in the introduction, causal complex relationscontinuously evolve among three levels: a lower level(among system' components interactions) emergent level and global level (the environment in which the system issituated). I report below an example of student'sdiscourse on how the crystal forms "from seeds crystals,"coded in full agreement when considering the same levelof focus by raters: the one composed by interacting"seeds"

Linda: " [….]I also think that in a sample thatmight be not just on single seed crystal. Theymight be more 5 or 6, whatever number. Howthe little crystal seeds are forming influencesthe others (material causality). For instance howmuch space is there among them, like, one istoo close to another crystals,[…] (formalcausality).

The interpretation of the two statements as materialand formal causality is not necessarily mutuallyexclusive. As discussed in the section 1, theiridentification is strongly dependent on the level ofdescription and analysis. What was interpreted as formal causality (the space distribution of "seeds" at the locallevel where the "seeds" interact) could be interpreted at ahigher level as a property of the matter of the entiremixture (e.g. viscosity) influencing and controlling thelower level processes (modifying for example thevelocity of the diffusing particles). Within the context ofthe questions posed to students, this problem did notarise, because the questions were explicitly designed tofocus the students' attention on a specific system's levelof analysis leaving no room for ambiguousinterpretation. It is important to note though, that thediscussion prompted by this example allowed the ratersto notice that any possible discordance in theinterpretation if different level of focus were chosen wasonly related to formal and material causality principles.These two causality principles as defined above canrelate entities of different levels and allow simultaneityand reciprocal influence of "cause" and "effect." Simultaneity and two way relations between "cause'and" effect" are not in agreement with a conception ofprocesses that obey a linear causal chain.


Causality FontEFFICIENT Capital letters & BoldFORMAL Capital letters & Underline

MATERIAL Capital letters & Italicfunctional Lowercase & bold

Table 3. Font code utilized to mark identifiedcausality principles in students’ discourse

Functional Causality Principle Versus TeleologicalCausality - The following example of student' reasoningabout crystal formation (question 2) and in particular, the reasoning on "why ice does not look like snow flakes"provided some discordance in the coding of the tworaters:

Kate: " for example, this is very basic, tomorrow Ihave to present on quantum physics I feel that it is not important unless there is a cause that youcan use it for …underlying motivation"

The sentence "there is a cause that you can use it for…underlying motivation" is teleological in nature (anexternal purpose as in intention and plan) and posedquite a problem because, although Kate apparently is not using it to explain her understanding of a scientificconcept, she uses it as an analogy to explain that "there isa reason why ice doesn't look like (snow) flakes."

One of the raters (A) coded it as a functional causality = 1. The other rater (B) recognizing only a teleologicalcausality not utilized in science scored it = 0.The subsequent students' discourse (passage 2) followedafter the interviewer asked how that concept wouldapply in the example of crystal formation:

Kate: "there is reason for behaving this way, forexample bonds here. If you drop something…the reason that something falls down isbecause of gravity ...there is a pattern and is due to gravity …and here (points at the flakes) is thesame, there is a pattern so there is a reason thatleads to this structure

Rater A originally coded the sentences "there isreason for behaving this way" as well as "there is a reason that leads to this structure" as functional causality = 1,recognizing into it a teleological nature. Rater B, in lightof a previous description by the same student on bondscreated by attraction forces and the example of objectfalling because of " gravity" scored this passage asEfficient causality = 2.

The discussion that followed when the coding wasdiscussed did not lead to full agreement on bothpassages. Rater A agreed that the second passage couldbe coded as efficient causality = 2 but a disagreementremained on the first passage. Both raters felt that apossible interpretation of the discordance could have

risen from the difficulty the student had in explaining acomplex phenomenon of self-organization utilizing onlyefficient causality principles. Libarkin et al. (2005)reported that often students remain in a "proto-process"ontological state of understanding that a causal controlmust exist to explain a phenomenon. If Kate is trying toexplain any processes utilizing efficient causalityprinciple then, is possible that this causality is envisioned as the "ultimate reason," giving it a teleological character.

Results - Students' Discourse - In this section I reportand contrast two of the student interviews as theyexemplify, in Raia' framework (2005), linear-mono-causal vs. system approach to complexity andtheir use of causality. It is important to reiterate here thatthis work proposes a method to identify causalityprinciples in describing causal relations in complexityand does not claim to generalize the results on specificcausal model schema or approaches to complex systemstudents hold.

Question 1

Kate: "it is related to why they stay alive. If youtake that away, they become extinct. Forexample, if you cut the food supply, the specieswill not be able to live or if you cut off theirenvironment they need, they will die. If youlook how they strive in an environment...thenyou make what was positive for them negative,then they die".

Kate's reasoning seems consistent with a linearapproach: when in a series of experiments, a certainefficient cause Ca has shown to have an effect Ea, and Cbhas an effect Eb, the causes can be added to give the sumof the effects, or conversely a cause can be subdivided incomponents and the effect will be consequently dividedin effects (Ea, Eb …En). In the context of Raia's categories(Table 4) to describe a Linear-mono-causal (LMC-A) vs.complex dynamic system (CDS-A) Approach, Kate'sreasoning seems to fall in category 3 (Identifies a singlecause) and 4 (Recognizes causality as unidirectional) ofLMC-A.

In contrast, let us consider the following examplewhere causality principles are highlighted according tothe font code reported in Table 3:


LINEAR-MONO-CAUSAL APPROACH (LMC-A) COMPLEX DYNAMIC SYSTEM APPROACH (CDS-A)Categories

1 Skips levels Recognizes contiguous levels2 Consider isolated behavior of constituent components Considers components and their interactions

3 Identifies a single cause/ linear chains of uniquecauses

Establishes complex relations between levels of differentproperties

4 Recognizes causality as unidirectional -upward ordownward Considers emergent property and Downward Causation

5 Landmark view - Conceptualize dynamic systems instatic disjointed terms

Dynamic view -Considers complex interaction with theenvironment in which the system is situated

Table 4. Five categories characteristics of two approaches to complex dynamic systems are modified fromRaia (2005). The categories are divided into two main groups according to the specific approach identified:Complex System Approach (CDS-A) vs. Linear Mono-Causal Approach (LMC-A). The categories thatcharacterize LMC-A are in the dark gray column on the left. The categories that characterize CDS-A are in thelight gray column on the right.

Linda: […] I am thinking about dinosaurs …people are not sure if there was a meteorite thathit the Earth or a volcano that blew up, like asuper volcano … a very large one. I think thereis one more thing ...I cannot recall what that is… but at least those two are thought to havechanged the climate of the whole entire Earth.…Let's say that there is a change in the climateof the whole Earth. Such a change in theclimate, can be looked at in terms of … it couldhave effected the growing season, and also the temperature. So, if you think that for exampleDINOSAURS WERE COLD BLOODED theymight not be able to adjust too well to theTEMPERATE CHANGE, maybe too cold for

them, their metabolism could not change. THE CHANGE IN CLIMATE COULD EFFECTTHE AIR, so the ATMOSPHERE HAD TOOMUCH OF CHEMICALS (LIKE SULFUR,CARBON DIOXIDE) THAT THERE WERENOT CONDUCIVE TO LIFE and these larger


KATE: " they are snowflakes"Interviewer: "how do you know?"Kate: " I don't know, I just know" (Silence no other words) Question againKate: " I saw pictures of them and some of them look like

this"Interviewer: "Like this how?"Kate: " Like this"[…]Kate: " I don't know they look alike".[…]Kate: " I think chemistry, THEY HAVE SOME KIND OF

BONDS, IN CERTAIN WAYS THEY FIT TOGETHERBASED ON ATTRACTION …SOMEHOW THEELECTRONS OF THESE OTHER ONES (points at thesides of the crystals)…ARE ATTRACTED."

Interviewer: which electrons? Kate: "you see the one the molecules of the water is polar, so

they connect O is negative and H is positive so theyattract…I don't know why they would do that

Interviewer: "What do you mean?"Kate: " when you see ice on the floor it isn't .. it doesn't look

like flakes….mmm I guess it does have a crystalstructure, so if you have a microscope you can see it…there is a difference between snow and ice …there is no structured ice. IT IS LIKE THE GEESE THERE IS AREASON WHY THEY DO IT ….. BUT I DON'T KNOW WHY, WHY THEY DO IT, THERE MUST BE AREASON, BUT I REALLY DON'T KNOW WHY"

Kate: "YOU SEE THERE IS A PATTERN AND THEREMUST BE A REASON WHY"

Interviewer: "I am not clear on what do you mean by"reason", can you explain to me?"

Kate: " for example, this is very basic, tomorrow I have topresent on quantum physics I feel that it is not importantunless there is a cause that you can use it for…underlying motivation"

Interviewer: "mmm ok I understand this for a humanbehavior, in terms of our crystals what does it mean, canyou give me some examples?

Kate: " there is reason for behaving for example bonds here. If you drop something …the reason that that somethingfalls down is because of gravity ...there is a pattern and isdue to gravity …and here (points at the flakes) is thesame, THERE IS A PATTERN SO THERE IS AREASON THAT LEADS TO THIS STRUCTURE"

Table 5a. Excerpts from Kate’s response to Question 2 during the first part of the interview. The font codecorresponding to the causality principles is reportedin Table 3.

LINDA: "they are probably some kind of crystal, probablywater crystal, snow flake , or some other crystal fromsome other material….just my own personal experienceTHEY KIND LOOK THEY ARE THE SAME, THEYHAVE THE SAME DIFFERENT TYPES OF SHADING, LIKE ALL FOR EXAMPLE THEY SEEM TO HAVEKIND OF A LITTLE BIT LIGHTER SIDES, A LITTLEBIT DARKER, AND SEEMS TO BE THAT PATTERNTHROUGH OUT, LIKE FOR EXAMPLE YOU HAVETHIS LIGHTER SIDE AND THEN DARKER SIDE, ANDTHE COLOR RANGE SEEMS TO BE ABOUT THESAME, but the pattern (compares the general macroscopicshape of all the crystals) seems to be quite different, somaybe they are not the same structures, the sameelements building it, it maybe that is either someimpurity in it … just from personal experience we seesnow flakes all sorts of shapes just even in regular life noteven in a scientific ..so …I think they are snow flakes, butthey can be crystals of other material. I think to know youneed to look at the chemical composition just to provethat are snowflakes.

Interviewer: "so let's assume they are snowflakes, how wouldyou think they form"?

Linda : "From what I know you must have some kind ofseed crystal, part of material that forms the little bit of itand just kind of build on to that as the temperature andthe pressure change throughout the material, mmm ITHINK THAT IT FORMS ACCORDING TO HOW THEPATTERN WAS ORIGINALLY TO START WITH, IMEAN THESE ARE THREE DIMENSIONAL SHAPES,EVEN THOUGH IT IS VERY MINUTE IT HAS SOMECHARACTERISTICS AND BECAUSE BUILDS LAYERUPON LAYER IT TAKES WHATEVER THE ORIGINALSHAPE … there are I guess some variation from theoriginal little seed crystal. My first inclination would beto look and see if there are SOME KIND OF IMPURITY,AND SEE IF THAT IMPURITY WOULD EFFECT THEWAY THAT THE CRYSTAL BUILD ON THE LITTLESEED CRYSTAL OR see also if they might have formedunder different temperatures and different pressures,and i will investigate how seeds crystals to start fromgrew under different temperatures and pressures andimpurities.….. I would try to see if I could see thatmoment when the little crystal, that little seed startsforming and see if you can look at the shape.… and I alsothink that well in a sample THAT MIGHT BE NOT JUSTON SINGLE SEED CRYSTAL BUT MAYBE BE LIKE 5OR 6 , WHAT EVER NUMBER, AND HOW THE LITTLECRYSTAL SEED FORMING INFLUENCE THEOTHERS, FOR INSTANCE HOW MUCH SPACETHERE AMONG THEM, LIKE ONE IS TOO CLOSE TOANOTHER CRYSTALS, then this kind of crystals willform (indicates the snow flack with rigged ends), becausethe other one crystal is forming on the little arm of theother through a little hole (space), AND IF DOES NOTHAVE ANY CONSTRAINS LIKE THIS KIND of crystal(indicates the figure with a full snowflake) where youdon't really see any branching or holes between branches[…]

Table 5. Excerpts from Linda’s responses to Question2 during the first part of the interview. The font codecorresponding to the causality principles is reportedin Table 3.

animals would have felt these effects andwere not be able to … their respiration wouldnot be so efficient having these chemicals inthe air, although it didn't kill themimmediately. So, I think there all these factorstogether from the environment and theirresponse to it […..].

Interviewer: "what about other species, besidedinosaurs?"

Linda: "I like to say that I think sometimesspecies get too specialized, FOR EXAMPLEFOR THE LOCATION WHERE THEY LIVEAND THEN A GLOBAL THING, OR NOTNECESSARILY GLOBAL, BUT JUS LIKESOMETHING CHANGES, let's say anearthquake would happen (Linda mimics a faultdislocating a terrain) and now, the place wherethey were living is under water, let's say theonly place the they could live was a little rockcliff -crustaceans for example they cannot live100% of the time underwater - and now, theirenvironment is underwater. If they only livedin that little area and were successful, and nowthat area does not exist anymore -that is theenvironment changed- and they cannot change with it, then they disappear.

Contrary to Kate, Linda stresses the capacity ofspecies to survive as a function of the coupling betweenthe inputs and solicitations provided by theenvironments in which the species are situated and thepossibility of new emerging properties that would allowthe species to survive in a new environment. In terms ofcausality principles, Linda's response seems to considermore then one causality principle, in striking contrastwith Kate's sole use of efficient causality. Linda utilizesthe efficient causality principle when she refers to themodification in the atmosphere caused by interactionthat happened in the same level of description - forexample the eruption of a volcano that emit particles thatenters the atmosphere modifying its characteristics.Other causality principles are also used by Linda to linkthe different levels of the system under consideration.The modification of the environment in which thespecies are living for example, exerts a formal control onthe evolution of the systems constraining the initial andboundary conditions under which the species have torespond to change. Linda recognizes contiguous levelsof the system (environment level, species level, organlevel) and recognizes the links that exist among them aswell as the formal control that each can have on the other. This is described by Raia (2005) as belonging to category1 (recognizes contiguous levels), 3 (establishes relationsbetween levels of different properties) and 4 (considersemergent property and downward causation) of CDS-A.Linda describes how the constraints imposed by thelower level, as in the example of cold blooded animals,can control the emergence of a new behavior or property- ascribed to category 3 (establishes relations betweenlevels of different properties) in CDS-A. Her dynamicview as an evolving system is described by category 6 ofCDS-A (considers complex interaction with theenvironment in which the system is situated).

Question 2

The use of causality in answering question 2,reported in Table 5, by Kate (Table 5a) and Linda (Table

5b) have been discussed in detail in the previous section.It is consistent with the results from answers given inquestion 1. Kate utilizes only the concept of efficientcausality and does not consider properties of materialand its organization as causal determinants of systemsbehavior. A very interesting pattern becomes evident inKate's approach. She never describes the patternobserved. In fact, her response to the interviewersolicitation to elaborate on how she recognizes thepattern as snowflakes is striking:

Kate: " they are snowflakes"Interviewer: "how do you know?"Kate: " I don't know, I just know" (Silence no other words) Question is posed againKate: " I saw pictures of them and some of them

look like this"Interviewer: "Like this how?"Kate: " Like this"[…]Kate: " I don't know they look alike"

Kate' reasoning seems to be consistent with a linearmono-causal approach to complexity (Raia, 2005). Herunderstanding that similar but not identical patterns arecaused by one and only one specific cause, does not allow her to consider how differences and similarities in thepattern can emerge. The non-linearity of causalcouplings is responsible for the unpredictability ofmicro-details. This approach is consistent with theLMC-A categories 1 (skips levels), 3 (identifies a singlecause/ linear chains of unique causes) and 4 (recognizesonly unidirectional causality -upward or downward)(Raia, 2005).

Conversely Linda extensively describes the patternsshe observed, considering them as an important factor inthe understanding of how crystals form. She utilizesthree causality principles: material, formal andfunctional, establishing causal relation among system'levels and considering the system -environmentinteractions This approach is consistent with the CDS-A:categories 1 (recognizes contiguous levels), 3 (establishes relations between levels of different properties), 4(considers emergence and downward causation) and, 5(considers complex interaction with the environment inwhich the system is situated-dynamic view) (Raia, 2005). It is interesting to note that in her discourse efficientcausality doesn't appear, possibly not allowing her tounderstand some relations among components of thesame level.

Question 3

In her response to Question 3 B Linda recognizes that the water has to travel first through one medium beforepassing through the second with possible modificationof the "properties" of the water before reaching the gravel (Table 6), Kate, not recognizing the non-linearity of theinteraction, the form and the distribution of the material,adds the times the water took to pass through thematerials:

Kate: "I think that it will take longer, the sand willhold on to the water it will be released later butthe one that is not, passes in …you know likeplants some goes through and the rest isreleased later. if we consider that, then you


need to add the times: the first part is 6 seconds(5 sec for sand +1 sec for gravel) and the secondpart, if the sand released water in 3 moreseconds then you add 4 (3 +1) seconds for therest of the water to come out."

In general, Kate's linear approach also correspondsto the understanding of a monistic (one and only)causality: efficient. Conversely Linda utilizes acombination of causality principles. Kate also envisionsthat all the water and only the water will pass throughwith no modification but the time of local andmomentarily retention.

INTERVENTION EFFORT

In a previous study (Raia, 2005) it was found thatLMC-Approach correlates with students use of efficientcausality principle and an absence of description ofpatterns in student discourse. Students, given a patternand asked how it had emerged: 1) identified an efficientcause to justify a natural phenomena and the emergenceof a pattern 2) in the explanation of how the patternformed or maintained its shape, they never include adescription of the pattern itself, in effects precluding thepossibility to raise one of the fundamental questions inscience, posed at the beginning of this paper - what hashappened. Similar attitudes have been also reported byEngel Clough and Driver (1985) in their study of highschool students' explanation of drinking from a straw.Rather then considering a pressure differentialestablished between the pressure inside and outside thestraw ( a distribution in space and time -formalcausality), students explained the phenomenon in termsof sucking or pulling (efficient causality). Similarrelations among the use of efficient causality, linearunidirectional causality and failing to search for othercontrols have also been observed by Perkins and Grotzer(2000).

Based on these studies, the intervention wasdesigned to make student aware of other concepts ofcausality. This was done by two steps. a) During thesecond part of the interview, students are introduced tothe modified Aristotelian framework of causalityprinciples. The interviewer introduces the definitions, explicitly asks the students to describe the pattern of theflock of birds reported in Table 7 and helps themapplying the definitions utilizing the same examplereported in Table 7. b) Students are solicited to take afirst step toward the identification of formal causalityprinciple. They are asked to describe the pattern in aproblem they have addressed in the first part of theinterview and to a new problem. Their responses arerecorded and analyzed applying the same coding ofcausality principles reported above. Making students aware of hidden causes can enhancetheir knowledge of the existence of more complexrelation among causalities, but it does not mean thatstudents will not apply a linear causality in theirexplanation. The reason for conducting the second partof the interview protocol is to test the effect of an explicitintervention on students reasoning and to try todifferentiate a linear-mono-causal thinking approach tocomplexity from a tendency of thinking about thingspotentially induced by instruction and thereforepotentially modifiable.

Second Part of Interview - Based on the recognition that students shun from describing patterns (Raia, 2005) andtend to disregard their influence in the evolution ofsystem behavior (Raia, 2005; Basca and Grotzer, 2001),Kate was asked to describe the distribution of material in


LINDA:[...] so individually in the gravel would take let's say 1minute, while in the sand 2 minutes, but for the this(indicate the container with both) it will take more than 3minutes, because when you have two types of thingstogether, the water has to travel first through the sandbefore getting there, so I think it will take a little more time,just because it's going through different kind of mediabefore you collected so SINCE YOU HAVE THE SANDAND THE GRAVEL, THE SAND AND THE GRAVELTOGETHER …IT JUST SEEMS THAT THE WATERWOULD, ONCE IT GOES THROUGH THE SAND ITMIGHT HAVE OTHER PROPERTIES, like MIGHT HAVEATTRACTED SOME CHARGE OR SOME LITTLESAND, might have mix with it too, and it need to settle outfirst before it gets to the gravel and when it gets to the gravel is not just water, but is water with a little bit of sand and gets stack inside the mmm IN THE GRAVELS THERE ARELITTLE HOLES AND SO THE WATER CAN SETTLEDOWN WITH THE SAND …is now TRAPPED IN ALITTLE CREVASSES IN THE GRAVEL and so the newwater (indicates the one above flowing down) has to wait tothe other water to get out first or maybe it will never getsthere because now the sand is blocking

Table 6. Linda response to question 3B. The font codecorresponding to the causality principles is reportedin Table 3.

APPLICATION OF CASUALITY PRICIPLES

The V-shape (macro-level) emerges from a number of birdsfollowing specific rules of interactions at the birds' systemlevel. For example, when another birds is too close, a birdmoves away (EFFICIENT causality) The shape thatemerges on the higher system level, V-shape, defines theboundary conditions that constrain (FORMAL causality) theposition of birds, the agents on a lower system level,according to the V-shape itself. The emergent structure,which is neither reducible to the density distribution andnumber (MATERIAL causality) of the birds nor to theinteractions among them (possibly EFFICIENT causality),constrains the behavior of the parts and the growth of theV-shape. The birds are parts of the flock: they constitute it,and participate (MATERIAL causality) in the emergentboundary conditions (FORMAL causality). Considering the environment in which flock is situated: The couplingbetween the system emerging properties and the inputs and solicitations provided by the environments has alsoregulating function, which is of maintaining the systemcoherence within its dynamic behavior (functionalcausality) over time.

Table 7.- Different studies (Vicsek, et al. 1995 Czirokand Vicsek 2001; Schechter, 1998 for general sciencereview) have shown that the flock moves as anorganized group, in a V-shape ordered pattern, andseems to behave as a single integrated whole (like asingle large animal). This behavior does not resultfrom the commands of a leader, nor from the action of a “V-flying” gene controlling bird behavior. Moreover,individual birds seem to have no sense of the overallflock pattern. The font code corresponding to thecausality principles is reported in Table 3.

the container in details (question 3) during the secondpart of the interview. Her response includes 3 causalityprinciples highlighted here according to the font codereported in Table 3.

Kate: "well, we have 3 things: sand, gravel andwater. SAND IS SMALLER THAN GRAVELand is PACKED THIS WAY (Kate draws for thefirst time), MORE COMPACTED BECAUSE,SEE, GRAVEL, YES LEAVES MORE SPACEAND WHEN WATER GOES ...mmm what I am thinking now …see the sand can interact toowith the gravel …see the sand CAN BEMOVED A BIT BY THE WATER and CANMOVE AMONG THE GRAVEL AND CLOGTHE VOIDS …mmm this will account for adelay …see yes, ah, I cannot really add thetimes, something else can happen between thesand the water and the gravel"

During the first part of the interview, it was noticedthat Linda does not explicitly and easily utilize efficientcausality in her explanations. Efficient causality, aspreviously described, is one of the fundamental causality principles necessary to consider causal interactionsestablished among components of the same level. On theother hand her focus, while building explanations, seems to be concentrated on the relations between levels, partlyignoring the one established among components of thesame level. The intervention, explicitly utilizing formalcausality, is designed to bring her attention to therelation among components of the same level.Specifically she was asked to draw the seed crystal she

mentioned as part of the material necessary for theformation of crystals in question 2.

Linda draws and describes a hypothetical moleculeconfiguration where the atoms are aligned in a straightline.

"So, from THIS KIND OF SHAPE, .. these two(molecules), can be next to each other (randomlydraws others similar molecules near the first) ….it branches out …. IF THIS ARE MADE OF WATER …actually ITWOULD HAVE A DIFFERENT SHAPE (drawsthe water molecule). … I don't think that themolecule just pack closely, somehow they like tobe apart from one another … mmm.. probably ITIS ABOUT THE CHARGES ASSOCIATED WITHTHEM and I so if THERE IS SOME REPULSION AMONG THE OXIGEN ATOMS THEYCANNOT REALLY GET ANY CLOSER(Linda draws water molecules connected to each other)"It looks like a dendrite …is branching out andkeeps doing itI am thinking that maybe this branching will have to change, this is the real world, so maybe thecrystal is not that happy to have one branch solong and other short … so it tends to arrange themolecules in a more "stable way"

Linda now uses all four causalities principles. When,as asked, she focuses her attention to the moleculesinteractions level, she is able to describe the possiblecausal interactions she recognizes as important controlfactors in the emergence of the crystal. At he same time,


LINDA: this is very interesting …. veryThis has been different, (referring to interview) from science classes…because in music we always are taught to think about all

the different options and in science on a test or in a class I always feel they want one answer, but I can think about eight, andthink which one do they want and I try to guess which one do they want ...I can come up with lets' say eight differentanswers and some kind of proof for each one, but I am never sure which one they want …

Interviewer: interesting, so you also study music, can you tell me how music is different for you?Linda: yes, let's say you are in a class and you learning a piece of music. There are notations on the page and there are hints on

what they would like you to present, but there is not technical right and wrong answer, for example you need to play thispassage loud, how loud do you play it? (Note that students in music classrooms are asked to define the boundary conditionsthemselves).

Well that depends how loud you started (formal causality control), how loud you want to get to, you have to think whereyou want to go to at the end, and also depends on which instrument you play (material causality control), are you play thistype of instrument then that loud cannot be too loud or if you play with another person you might say well I know they play little softer all the time, so I back off or they play really loud so I might as well bang it out (consideration of complex componentsinteractions)…. or like , let' say you are writing a piece of music. Composition lessons for example, the professor will say:these are your rules, you have to write a 20th century piece.

And there are these things called cells, so rather than writing with the regular do re me fa sol la si do scales you have topick 3 tones out of that scale and you gonna use different types of mathematics to develop what kind of rhythm you wantand you need to put the notes together according to the cell you design. Which 3 notes I am going to use? It does not matter,the 3 notes I think are best, I can also being given the instruments let' say piano and clarinets, so I have to think what rangethe clarinet is going to sounds the best ..so you need to think about all this different parts but he (the teachers) only gave metwo directions -3 notes cell and piano and clarinet- and you need to think about what is the most interesting thing and youare paid off also in terms of grades by coming up with as many options you can think of because when you then put ittogether you read out what you don't need or don't want, options that do not work with that sound.

Interviewer: so during the process you actually say, I don't need this or that …Linda: you actually think all the options you can and pick the one that sounds best, you decide things to do but you are also

controlled by other things, other players, the combination of sounds, that not necessarily take you where you plan to goinitially…. , you cannot be really sure about the end

Interviewer: so how about the building of crystalsLinda: very similar, some they work out and other do not and the one that work are kept, the others not, and you do not start

with one or two things and start to build the right thing […]

Table 8. Linda reflections - after been introduced to the modified Aristotelian causality principles - on howshe perceives science to be taught and her understanding and difficulty with this approach of teaching.

she never disregard the importance of causal interactions between levels and the system and its environment.

It is important to recall that both interventions efforts where done utilizing the principle of formal causality.The recognition that a pattern by which something isorganized/ structured, the explicit consideration ofboundary conditions as a causal controls for the behavior of a system seem to play a fundamental role in thecapacity to explore other form of causal explanations.

When Linda was introduced to the modifiedAristotelian causality principles, she elaborated on thegeneral idea of approaching natural phenomena, theway she perceives science to be taught and herunderstanding and difficulty with this approach ofteaching. I report here her entire reflection because itgives important insights in her way of approachingnatural phenomena when free to think without beingpushed to come up with the "right" answer and theimportance of explicitly considering coupling ofdifferent controls in understanding emergentphenomena of any nature. Her reflections are reported in Table 8 with some comments inserted (in parenthesis) inthe first part highlighting the active role students musthave in defining and considering important constrainsand controls in non-science classrooms.

CONCLUSIONS - APPROACH TOCOMPLEXITY AND THE USE OFCAUSALITY

As the goal of scientific research is establishing causaldeterminants of phenomena, in this paper, I showed thatin the context of complex dynamic systems, the rule ofinteraction among system's components, system's levelsand the system and the environment in which the systemis situated are governed by different causality principles.The understanding of these different kinds of controls aswell as their interactions in the evolution of naturalphenomena can give important insight in unfolding howwe approach complexity.

There seems to be a relation between a complexdynamic systems approach (CDS-A) (Raia, 2005) and theutilization of the 4 types of causality in an integratedmanner as shown by Linda' reasoning. On the contrary,Kate' tendency to identify only one causality - favoringexplanations that assume deterministic causality - toexplain natural phenomena seem to be associated with alinear mono-causal approach (LMC-A). This relationdoes not imply that students hold a certain causalschema, but it is indicative of the kinds of obstacles theyface when approaching complex natural phenomena. Asrecognized by other research (Feltovich, et al., 1989;Resnick and Wilensky, 1993; Resnick,1994, 1996;Wilensky and Resnick,1999; Hmelo-Silver and Pfeffer,2004, Raia, 2005; Gonzalez-Rubio, 2005; Chi, 2005;Libarkin and Kurdziel, 2006; Jacobson and Wilensky,2006), students have great difficulties in understandingcomplex processes of emergence, self-organization andadaptation. These processes are characterized bycomplex causal interactions that are not reducible tolinear sequences of causes and effects.

Recognizing contiguous levels, and the complexrelations between levels of different properties such asemergent phenomenon and also its control on the levelsfrom which it emerges (category 1 , 3 and 4 of CDS-approach), would require the recognition that the

causality relations among levels are of formal, and/ormaterial nature. Higher level properties emerging fromlower level causal interactions function as constraints,boundary conditions and selection criteria for the lowerlevel emergent processes. This understanding contrastswith the use of efficient causality among levels that seesthe levels as completely independent entities,temporarily distinct and, therefore impeded frominfluencing each other simultaneously. As discussed inthe context of the role of continually changing boundaryconditions and negative and positive feedbacksprocesses, simultaneity of causal controls over theevolution of a system is of fundamental importance.Conceptualizing the upward or downward causation asbeing of efficient causality nature, forces us to considerlevel A as the cause of the properties and processes of theother level B. In this case, considering level B to be theeffect of A the level means that level B, is considered to be completely ineffective in the evolution of a system and oflevel A because level B is temporarily distinct from thecause from which it has originated. This use of causalrelations can be recognized in category 1 (skips levels), 3(identifies a single cause/ linear chains of uniquecauses), and 4 (recognizes only unidirectional causality-upward or downward) of LMC-A. It supports the ideaof one level directly influencing lower or higher levels ina temporal sequence where there is a sharp distinctionbetween cause and effect. By contrast, self-organizationand adaptation are processes that must be understood asfunction of the coupling between the system emergingproperties and the inputs and solicitations provided bythe environments in which the system is situated. Theseare emergent causal relations that control the capacity ofa system to survive.

The Importance of Formal Causality - A veryinteresting and important result was found in therelation between LMC-Approach -with the explicit use of only an efficient causality- and the absence of description of patterns in student discourse. Similar results havebeen also described in a previous study (Raia, 2005):students, given a pattern and asked how it has emergedrush to identify an efficient cause to justify the observedphenomena while never describing the pattern as anessential part and condition to proceed in theirexplanation of the shape formation or maintenance. Bydoing so, students preclude the possibility to raise one ofthe fundamental questions in science, posed at thebeginning of this paper - what has happened. Similarattitudes have been also reported in physics andchemistry students' reasoning (Rozier and Viennot, 1991; Viennot, 1998; Nicoll 2001; Taber, 2001).

In this paper I showed the very important roleplayed by the recognition and utilization of formalcausality in supporting students develop and utilizericher and more adequate repertoire of causal models forthe analysis of natural phenomena. Consequently,important interventions can be taken in the context of the classroom. In the teaching of physical science the initialand boundary conditions are most often provided tostudents as a given and the students are very rarelyasked to identify and describe them or considering howthe same boundary conditions can change and modifysystems' behavior. Students are also rarely asked todescribe patterns and variables distributions in spaceand time as important controls on the system behavior.


These represent, as discussed in this paper, other types of causality that are necessary to integrate in the description and analysis of natural complex phenomena. Studentsshould be explicitly asked to describe them, and takethem into account as important constrains of systemevolution. As shown, it is possible that when students are helped to utilize other kinds of causality principles, theycould move toward a more in-depth understanding ofcomplexity.

The intervention on students reasoning aboutnatural phenomena indicates that to help them use agreater repertoire of causality principles it is notnecessary to point out the specific causality principle that should have been utilized in their discourse. It ispossible to support students considering other causalityprinciples - as seen with Linda's responses - by makingan explicit request to consider formal causality control.In the classroom students should be explicitly asked todescribe patterns, distribution of data, and build fromtheir observations possible lines of explanations andinvestigation.

ACKNOWLEDGMENTS

I would like to thank Richard Steinberg of the ScienceEducation Group at City College of New York and MarioDeng at Columbia University for the valuable review ofinterviews and the coding assigned. I thank them also for the numerous discussions on general system theory andits applications and significance in science education aswell as medical and biological systems. I gratefullyacknowledge the careful and thorough reviews on anearlier version of this manuscript by the reviewers,specifically Julia Libarkin, as well as the perceptivecriticism by Associate Editor Dexter Perkins. For theinsightful and constructive comments that greatlyimproved the manuscript, I would like to thank CarlDrummond, Editor-In-Chief of the Journal of Geoscience Education. This work was supported (in part) by a grantfrom The City University of New York PSC-CUNYResearch Award Program (Award# 68636-00 37).

REFERENCES

Anderson, D. L., 2002, plate tectonics as a far- from-equilibrium self-organized system, In: Stein, S., andFreymuller, J. editors, AGU Monograph: PlateBoundary Zone, Geodynamics Series 30, p. 411-425.

Andersson, B., 1986, The experimental gestalt ofcausation: a common core to pupils preconceptionsin science, European Journal of Science Education,v.8, p.155-171.

Basca, B.B. and Grotzer, T.A., 2001, Focusing on thenature of causality in a unit on pressure: How does itaffect students understanding? Paper presented atthe annual conference of the American EducationalResearch Association, Seattle, WA, April.

Bercovici, D., 1998, Generation of plate tectonics fromlithosphere-mantle flow and void-volatile self-lubrication, Earth Planetary Science Letters, v.154,p.139- 151.

Bercovici, D., Ricard, Y., and Richards, M.A., 2000, Therelation between mantle dynamics and platetectonics: a primer. In: Richards, M., Gordon, R. andvan der Hilst, R., editors, The History and Dynamicsof Global Plate Motions, Geophysical Monograph121, American Geophysical Union, p.5-46.

Bercovici, D., 2003, The generation of plate tectonics from mantle convection, Earth and Planetary ScienceLetters v. 205, p.107-121.

Bunge, M. A., 1979, Causality and Modern Science, (3rd)edition, Dover, New York, 394p.

Campbell, D.T., 1974, Downward causation inhierarchically organized biological systems, In:Ayala, F.J. and Dobzhansky, T., editors, Studies inthe Philosophy of Biology, Berkeley, University ofCalifornia Press, p.179-186.

Chi, M. T. H., 2005, Commonsense conceptions ofemergent processes: Why some misconceptions arerobust, Journal of the Learning Sciences, v.14,p.161-199.

Cohen, I. B., 1985, The revolution in science, Cambridge,Mass: Belknap Press of Harvard University Press,711 p.

Drummond, C.N., 2001, Immanence and Configuration -The Quest for Cause, Journal of GeoscienceEducation, v. 49, p. 329.

Emmeche, C, Koppe, S., and Stjernfelt, F., 1997,Explaining emergence -toward an ontology of levels, Journal of General Philosophy of Science, v.28,p.83-119.

Emmeche, C., Køppe, S, and Stjernfelt F., 2000, Levels,emergence, and three versions of downwardcausation, In: Andersen, P.B., Emmeche, C.,Finnemann, N.O., and Christiansen, P.V., editors,Downward Causation. Minds, Bodies and Matter,Århus, Aarhus University Press, p. 13-34.

Engel Clough, E. and Driver, R. 1985, What do studentsunderstand about pressure in fluids? Research inScience and Technological Education, v.3, p.133-144.

Feltovich, P. J., Spiro, R. J., and Coulson, R. L.,1989, Thenature of conceptual understanding in biomedicine:The deep structure of complex ideas and thedevelopment of misconceptions, In D. Evans and V.Patel, editors, The cognitive sciences in medicineCambridge, MA, MIT Press, p. 113-172.

Gonzalez-Rubio, R., .Raia, F., and, Steinberg, R.N.,Exploring Student Understanding of Newtown'sThird Law, Einstein in the City conferenceProceeding CCNY 11-12 April, 2005.

Green, D.W., 1997, Explaining and envisaging anecological phenomenon, British Journal ofPsychology, v. 88, p.199-217.

Gutiérrez, R., and Ogborn, J., 1992, A causal frameworkfor analyzing alternative conceptions, InternationalJournal of Science Education, v.14, p.201-220.

Heylighen F., 1989, Self-Organization, emergence andthe architecture of complexity, In Proceedings of the1st European Conference on System Science, AFCET, Paris, p. 23-32.

Heylighen, F., 1995, Downward Causation, In Heylighen F., Joslyn, C., and Turchin V. editors, Principia Cybernetica Web, Principia Cybernetica,Brussels, http://pespmc1.vub.ac.be/DOWNCAUS.html.

Hirth, G., 2001, Are oceans required for earth-like platetectonics?, Eos Transactions AGU, v. 82, Fall Meeting Supplement, Abstract.

Hmelo-Silver, C. E., and Pfeffer, M.G., 2004, Comparingexpert and novice understanding of a complexsystem from the perspective of structures, behaviors, and functions, Cognitive Science, v. 28, p. 127-138.

Holland, J. H., 1998 Emergence: From chaos to order,Cambridge, Massachusetts, Perseus Books, 258 p.


Ireton, M.F.W., Manduca, C.A., and Mogk, D.W., 1997,Shaping the future of undergraduate earth scienceeducation-innovation and change using an earthsystem approach, Report of workshop convened bythe American Geophysical Union, Washington, D.C.http://www.agu.org/sci_soc/spheres/

Jacobson, M. J., 2001, Problem solving, cognition, andcomplex systems: Differences between experts andnovices, Complexity, v.6, p. 41-49.

Jacobson, M.J., and Wilensky, U., 2006, Complex Systems in Education: Scientific and Educational Importanceand Implications for the Learning Sciences, Journalof the Learning Sciences, v.15, p.11-34.

Kim, J., 1992, Downward causation, in emergentism andnon-reductive physicalism, In Beckermann, A.,Flohr, H., and Kim, J., editors, Emergence orreduction? Essay on the prospects of nonreductivephysicalism, Berlin, de Gruyeter, p.119-38.

Libarkin, J.C., Anderson, S., Dahl, J., Beilfuss, M., Boone,W., and Kurdziel, J., 2005, College students' ideasabout geologic time, Earth's interior, and Earth'scrust, Journal of Geoscience Education, v. 53, p.17-26.

Libarkin, J.C., and Kurdziel, J., 2006, Ontology and theteaching of Earth system science, Journal ofGeoscience Education, v.54, p. 408-413.

Libbtrech K. G.., 1999, SnowCrystals.com,http://www.its.caltech.edu/~atomic/snowcrystals/ (December, 2005).

Mayring, P., 2000, Qualitative Content Analysis. ForumQualitative Sozialforschung/Forum: QualitativeSocial Research, v.1, http://www.qualitative-research.net/fqs-texte/2-00/2-00mayring-e.htm.

Nagel, E., 1961, The structure of science, problems in thelogic of scientific explanation, Harcourt, Brace andWorld, Inc. 618p.

Narasimhan,T., 2006, On Earth Sciences and Publicschools' EOS v. 87, n 47, p. 529.

Nicoll, G., 2001 A report of undergraduates' bondingmisconceptions, International Journal of ScienceEducation, v.23, 7, p.707- 730.

Nicolis, G., 1989, Physics of far-from-equilibriumsystems and self-organisation, in: The New Physics,P. Davies, editor, Chap 11. p. 316

Penner, D., 2000, Explaining Systems: InvestigatingMiddle School Students' Understanding ofEmergent Phenomena, Journal of Research ScienceTeaching, v.37, p.784-806.

Perkins, D. N. and Grotzer, T. A., 2000, Models andmoves: Focusing on dimensions of causalcomplexity to achieve deeper scientificunderstanding, Paper presented at the Presented atthe Annual Meeting of the American EducationalResearch Association, New Orleans LA.

Pina, C. M., 2002, On the surface processes of crystalgrowth at low temperatures Mcfa Annals Volume I,August, http://mariecurie.org/annals/

Raia, F., 2005, Students' understanding of complexdynamic systems, Journal of Geoscience Education,v. 53, p. 297-308.

Redish, E.F., and Steinberg, R.N., Teaching physics:Figuring out what works, Physics Today, 1999, v.52,p.24-30.

Regenauer-Lieb, K., Yuen, D. A., and Branlund, J., 2001,The initiation of subduction: Criticality by additionof water?, Science, v. 294, p.578- 580.

Resnick, M., 1994, Turtles, termites, and traffic jams:Explorations in massively parallel microworlds, MIT Press, Cambridge, MA, p.184.

Resnick, M., 1996, Beyond the centralized mindset,Journal of the Learning Sciences, v.5, p.1- 22.

Resnick, M., and Wilensky, U., 1997, Diving intocomplexity: developing probabilistic decentralizedthinking through role-playing activities, Journal ofthe Learning Sciences, v.7, p.153-172.

Resnick, M., and Wilensky, U., 1993, Beyond theDeterministic, Centralized Mindsets: a new thinkingfor new science, Paper presented at the annualmeeting of the American Educational ResearchAssociation, Atlanta, GA.

Rozier S., and Viennot, L., 1991, Students' reasoning inthermodynamics, International Journal of ScienceEducation, v.13, p.159-170.

Salmon W.C., 1990, Four decades of scientificexplanations, Minneapolis, University of MinnesotaPress, 234 p.

Salthe, S., 1985, Evolving Hierarchical Systems, NewYork, Columbia University Press p.136-143.

Salthe, S.N., 1989. Self-organization of /in hierarchicallystructured systems, Systems Research,, v.6,p.199-208.

Shapin, S., 1996, The scientific revolution, Chicago, IL :University of Chicago Press, 218p.

Solomatov, V. S., 2001, The role of liquid water inmaintaining plate tectonics and the regulation ofsurface temperature, Eos Transactions AGU, v. 82,Fall Meeting. Supplement., Abstract # U03A-09.

Solomov, S.V., 2004, Initiation of subduction bysmall-scale convection, Journal of GeophysicalResearch, v. 109, B01412, p.1-16.

Stein, C and Hansen, U., 2001, Formation of plates innumerical mantle convection models, EosTransactions AGU, v. 82, Fall Meeting Supplement.

Swope, R. J. and Giere,R., 2004 A strategy for teaching aneffective undergraduate mineralogy course, Journalof Geoscience Education, v.52, p.15-22.

Taber, K. S., 2001, Shifting sands: a case study ofconceptual development as competition betweenalternative conceptions, International Journal ofScience Education, v.23, 731-753.

Tackley, P.J., 1998, Self-consistent generation of tectonicplates in three-dimensional mantle convection, Earth Planetary Science Letters, v. 157, p.9-22.

Varela, F. Un Know-how Per l'Etica, The Italian Lectures3, Editrice La Terza, Bari, 1992, 138p. (Englishversion, 1999, Ethical Know-How, StanfordUniversity Press).

Vaughan, J., Nemchin, A., Davidson L., and Quinton S.,2004,Teaching process mineralogy in Australia,Journal of Geoscience Education, v.52, p.45-51.

Velbel, M., 2004, Laboratory and homework exercises inthe geochemical kinetics of mineral-water reaction:rate law, Arrhenius activation energy, and therate-determining step in the dissolution of halite,Journal of Geoscience Education v. 52, p.52-59.

Viennot, L., 1998, Experimental facts and ways ofreasoning in thermodynamics: learners' commonapproach. In: Connecting Research in PhysicsEducation with Teacher Education, Tiberghien, A.,Jossem, E.L and Barojas J., editors InternationalCommission on Physics Education 1997,1998http://www.physics.ohio-state.edu/~jossem/ICPE/TOC.html (14 December, 2005).

von Bertalanffy, L., 1978, General System Theory:foundations, development, applications. G, BrazilerInc. New York, 297 p.

Wilensky, U., and Resnick, M., 1999, Thinking in levels:A dynamic systems perspective to making sense ofthe world. Journal of Science Education andTechnology, v. 8, p. 3-19.


Causality in Complex Dynamic Systems: A Challenge in Earth...

Documents

Transcript of Causality in Complex Dynamic Systems: A Challenge in Earth...