Multiple forms of dynamic representation

The terms dynamic representation and animation are often used as if they are synonymous, but in this paper we argue that there are multiple ways to represent phenomena that change over time. Timepersistent representations show a range of values over time. Time-implicit representations also show a range of values but not the specific times when the values occur. Time-singular representations show only a single point of time. In this paper, we examine the use of dynamic representations in instructional simulations. We argue that the three types of dynamic representations have distinct advantages compared to static representations. We also suggest there are specific cognitive tasks associated with their use. Furthermore, dynamic representations of different form are often displayed simultaneously. We conclude that to understand learning with multiple dynamic representations, it is crucial to consider the way in which time is displayed. Multiple Representations of Time Dynamic representations display processes that change with respect to time. For example, they may show blood pumping around the body, the flux of high and low pressure areas in a weather map, the developing results of a computer program running (algorithm animation) or the movements in physical systems such as series of pulleys. Animation is normally considered the prototypical dynamic representation and is defined as a “series of frames so each frame appears as an alternation of the previous one” (e.g. Bétrancourt & Tversky, 2000). Typically, each frame exists only transiently to be replaced by subsequent frames, i.e. the dimension used to represent time in the representation is time. Stenning (1998) refers to this aspect of animation (and other representations such as video and speech) as evanescence, in contrast to still, persistent media such as static pictures or text. The research on the effectiveness of animation for increasing learners’ motivation normally reports positive effects (e.g. Rieber, 1991). However, research addressing whether animation aids learners’ understanding of dynamic phenomena has produced positive results (Kaiser, Profit, Whelan & Hecht, 1992; Rieber, 1991), negative results (Rieber, 1990; Schnotz, Böckheler & Grzondzeil, 1999) or neutral results (Price 2002; Pane, Corrbet & John, 1996). This is not surprising as a single type of representation is rarely maximally effective for all purposes, but rather particular representations facilitate performance on certain tasks (Gilmore & Green, 1984). Nevertheless, there are a number of reasons why research on animation effectiveness has produced such mixed results. A wide range of factors such as outcome measures, individual differences in participants and research environment have been varied, making consistent results less likely (Price, 2002). Nor has only a single type of animation been investigated. Lowe (2003) identifies three types of change events used in animations: transformations, in which the properties of objects such as size, shape and colour alter; translation, in which objects move from one location to another; and transitions, in which objects disappear or appear. Learners may focus on more obvious perceptual events rather than on those that are of most conceptual interest – for example, Lowe (1999) found that novices extracting information from a dynamic weather map focused on less important translations rather than the more important but perceptually subtle transformations. Multiple Dynamic Representations 2 There are a number of reasons why animations may place increased demands on learners. Stenning (1998) analyses animations (as simple as a guide to constructing ‘flat-pack’ furniture) from a perspective that emphasises the semantics and processing requirements of making inferences from representations (see Stenning & Oberlander, 1995 for details of the approach). Firstly, he argues that as the information in animations is presented transiently, relevant previous states must be held in memory if they are to be integrated with new knowledge. Secondly, animations cannot be ambiguous with respect to time and, as a consequence, they force activities to be shown in a particular sequence. Consequently, when what is represented is not fully determined with respect to time, animations may employ tricks (such as showing activities happening in parallel like nails being hammered into a table top simultaneously) or place activities in a particular order where in fact order is irrelevant (and in text could easily be expressed as “now hammer in all four nails”). Thirdly, unlike a static diagram, animations that are not user-controllable do not permit learners to re-access previous states or vary the speed at which information is presented. However, not all work identifies transiently presented information as a necessary aspect of animation. Brown (1988) proposes that persistence is, in fact, a dimension of animation (i.e. representations can range from those that only define the current state of the information to those that contain a history of each change in information). Hence, some of the difficulties associated with processing animations should not apply to dynamic representations that are persistent. In particular, these representations should not lead to the memory loads associated with integrating transient forms of representations. Additionally, learners can inspect previous states at will in persistent representations. However, persistence may cause representations to be very complex if all prior states have to be explicitly represented. In this paper we shall examine how persistence influences both the informational and computational properties of dynamic representation. Furthermore, dynamic representations are almost never presented in isolation but are usually combined with textual description of the situations, pictures or other forms of representation. Hence, we focus on the impact on learners of combining representations with different dynamic form. We will illustrate this argument with a type of learning environment that almost invariably employs multiple dynamic representations – instructional simulation. We begin by describing the properties of simulations and provide an example to use as a case study throughout the rest of the paper. Instructional Simulations Instructional simulations such as SimQuest (de Jong & van Joolingen, 1998) or Stella (Steed, 1992) are domain independent environments that contain an executable model of a system whose results are presented to learners. They allow learners to construct their own knowledge by interacting with an environment, conducting experiments and by observing the effects of these experiments. As a consequence, it is hoped that learners acquire deep, flexible, and transferable knowledge. Simulations overcome one of the limitations of natural systems by allowing representation of processes and quantities that are usually invisible in nature (e.g. energy, vectors, equilibrium states, etc.). They almost always provide multiple external representations of the simulated model. For example, a simulation of a harmonic oscillator (e.g. White, 1984) can present the motion of the system by a basic animation of a body’s movement and also by graphically representing this motion in time-series graphs or as phase-plots (for definitions see below). Moreover, both graphs and animation can be presented simultaneously, allowing observation of the interrelation between the two representations. In this paper, we will draw all examples from a simulation of population dynamics (see Van Labeke & Ainsworth, 2002). Population dynamics is the branch of biology that attempts to discover the rules that govern how populations of living organisms grow, decline or oscillate. It describes such features as a species birth/death rate, the maximum number of individuals that can be supported in a population, the rate that predators capture prey and how availability of prey influences the number of predators that can be supported. The relationship between these features is given by fairly complex mathematical expressions. For example, a simplified statement of the relationship between number of predators and prey is given by Lotka-Volterra equations such as dN/dt = r N(1-N/K) – alpha N P, (where r = prey fertility, N = population density of prey, P = population density of predators, K = Multiple Dynamic Representations 3 carrying capacity of the environment and alpha = the number of prey killed by a predator per unit time). However, as may be immediately apparent to the reader, this is a dense expression which learners can find difficult to interpret. To help learners understand such complex relationships, textbooks typically provide a number of forms of representations such as time-series graphs (e.g. the population density of number of prey and predators on the Y axis with time of the X axis), Ln(X) graphs (e.g. the YAxis represents the natural log of population density with time on the X axis), phase-plots (e.g. the number of prey on the X-Axis and number of predators on the Y-Axis), tables of values, histograms, piecharts, text that provides definitions of terms and pictures of the animals described. The advent of instructional simulations expands this representational repertoire in two ways: firstly, by changing static representations into their dynamic equivalents (e.g. a time-series graph can incrementally adjust as the simulation runs or as learners interact with it) and secondly, by allowing new forms of representation such as video or animation. Dynamic Representations in Instructional Simulations There are many ways of classifying representations. Commonly representations are discussed in terms of features such as their modality (text or graphics), abstraction (e.g. iconic or symbolic), sensory channel (auditory or visual), dimensionality (i.e. 2 d or 3d) or dynamism (static or dynamic). In this paper, we argue that to classify representations merely as either static or dynamic is to categorise at the wrong level of granularity. Instead, we propose that in addition to static representations, there are three types of dynamic representation. We contend that each has distinct informational and computational properties. Time-persistent representations The first type of dynamic representation is one we call a time-persistent (T-P) representation. It expresses the relation between at least one variable and time by displaying both (i) the current value and (ii) any other ones that have been computed. Typical examples in this domain include a graph of the population density of predators and prey against time (time-series graph) or a table where each row contains the number of prey killed (e.g. Figure 1). In many ways, this type of representation is very similar to its static equivalent. Often the only difference between this representation when presented in a textbook or in a simulation is that the dynamic representation displays data incrementally rather than presenting the whole data set from the start. Taking a timeseries graph and making it dynamic does not add any new information, although it may make certain features of that information more salient. This is not the case for the other forms of dynamic representation discussed later. For example, if the learner stops the simulation running, it is still possible to determine how fast populations are growing or declining by examining the scale of the representation and previous values of the variables. Therefore, for any dimension of information that a T-P representation displays, it provides the learner with the most amount of information. The finer the granularity of the representation of time the greater this information (e.g. contrast the categorical table with values presented only once every 5 steps of the simulation (Figure 1a) versus a continuous time-series graph (Figure 1b)). Time-implicit representations The second type of representation is time-implicit (T-I), which show a range of values but not the time when these values occurred (once static). The most common example in population dynamics is a phase-plot (or phase space graph) where the X-axis encodes the number of prey and the Y-axis the Multiple Dynamic Representations 4 number of predators, and time is the parameterising variable along the plot line (see Figure 2, 2a is generated from the same information as Figure 1). Like T-P representations, T-I representations show the relation between variables over a period of time. Unlike the T-P representations, however, the time-scale of this information is only perceivable when presented dynamically. For example, Figure 2a, shows that when the number of prey was 41, the numbers of predators was 7, but although we know this happens in the past, there is no way to determine what point in time this occurred. The rate of change of the values being graphed is only visible when the simulation is running and the representation dynamically adjusting. Consequently, when a simulation is stopped learners must invoke internal representations to compare current values to a particular previous state to answer questions about the timescale of growth. Thus, this representation has different information when presented dynamically than when presented statically. For example, in static Figure 2a, there is now no way of determining how long it took for prey numbers to increase from 20 to 40. Similarly, Figure 2b shows a limit cycle and so it is impossible to know how many times this cycle has occurred when presented statically, whereas this information would be obvious in a time-series graph. As a result, these representations contain less information that T-P, i.e. it is possible to derive a T-I representation from a T-P representation but not vice versa. Figure 1 Time Persistent Representations: Predator Prey Population Density (a) Table, (b) Time-