Simple is not always easy: Young children’s encounters with complexity Sharona T. Levy*, David Chen Tel-Aviv University, School of Education, Ramat-Aviv, 69978, ISRAEL * [email protected]

ABSTRACT The wider question with which we engage involves the relationship between people and complex systems. The main issues we approach are the relationship between task complexity and learning, and the processes through which reasoning becomes more complex. In this study, we explore kindergarten children’s learning of water dynamics while constructing water-pipe systems. The role of task complexity in learning was investigated, revealing a curious finding. In many cases, the children expressed new and better rules first in more complex tasks, when a familiar relation is co-varied with an unfamiliar one. This took place before their unveiling in simpler tasks. The facilitating nature of more complex settings, based on relationships that partially reinforce previous notions, provokes questioning of the sequence ‘from simple to complex’ in planned learning environments. Processes through which reasoning increases complexity in service of a higher coherence with system behavior were examined. It was found that learning of complex phenomena progressed through increasing consistency by ignoring information previously attended to, before releasing this consistency in order to explore additional dimensions, and finally integrating the various dimensions into a single framework.

INTRODUCTION The wider question with which we engage involves the relationship between people and complex technological systems. The main issues we approach are the relationship between task complexity and learning, and the processes through which reasoning becomes more complex. In Latin complexus means “entwined” or “twisted together”. In order to have a complex you need to have two or more components that are joined in some way that is difficult to separate. The amount of information in an array, as well as the relationship between the observer and the target system are two completing dimensions of some definitions for complexity (Heylingen, 1996). Research into the way young children approach complexity points to their inability to reason with more than one causal relationship. For example, Robert Siegler has conducted much research (e.g. Siegler, 1978) regarding children’s reasoning about different physical devices and phenomena, such as the balance scale. He found that until the age of 4 there is no consistent use of rules. From there, children advance to reasoning with one dominant dimension. 8-year olds can form a rule for a sub-ordinate dimension if the other dimension is not varied. Only at the age of 12, can they coordinate two dimensions.

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Different scientists have described conceptual change. Some of the prominent features of such transitions include encoding – paying attention to relevant dimensions (Siegler, 1978), integration and differentiation of prior knowledge (Carey, 1985), restructuring through enculturation where spontaneous and formal concepts find a common ground (Vygotsky, 1986), enrichment and revision of framework theories (Vosniadou 1994), increasing metaconceptual awareness of the relationship between theory and data (Kuhn, 1989), increasing consistency between islands of knowledge (diSessa, 1993), and unsteady response patterns that fluctuate between older and newer understandings (Alibali & GoldinMeadow, 1993). In this study, we explore the way young children’s reasoning changes when involved in the goal-oriented activity of building concrete and complex water systems. We propose that in such settings, the easy provision of visual and tactile feedback together with the interest invested into making operating objects work together in enhancing young children’s abilities to reason more complex-ly and correctly about such systems. Our main aims were (a) to examine the interaction between task complexity and young children’s learning, and (b) to uncover processes that take place during the shift from lower to higher dimensionality in reasoning. METHOD The sample included 29 children aged 5’2”-6’3”, 15 in an experimental group and 14 in a control group. They were selected randomly out of 80 children in a public school in the Israeli city of Rishon-LeZion. Randomness was reduced due to partial parents’ authorization. Instruments Three sets of instruments have been developed. A construction kit for building large water-flow systems was developed. It is modular and transparent and its components enable the creation of a large variety of systems (see Figure 1). One can control the water flow using diverse components (pipes, faucets, vessels, connectors and qualitative speed measuring devices) to determine the relationship between the streams’ features and the following variables: height, exit-hole cross-section, resistance, hierarchical structure of the system and the system’s water flow control. The children create the topography with metal-net cubes and then connect the water system onto it.

Figure 1: Factors determining water-flow from pipe; a plumbing system

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Three physical relations determine water-flow from a pipe (see Figure 1). The first involves heights: lower pipe-ends and higher water source levels provide a greater water-flow. The second relation pertains to the width or cross-section area of the pipe-end. The narrower pipe-ends have the same water-flow, with narrower and faster or farther-reaching streams. The third concerns the resistance of the pipe until its end. The longer the pipe, the greater the number of curves, and the smaller the curve’s angle - the smaller the water-flow emanating from the pipe. The second instrument is a sequence of four building tasks, creating a half-open learning environment and designed as a progression of increasing complexity. The first task was to create a watering system for two plants (big and little) from a single water source bag. The plants were to be watered over an extended period with the large plant getting more water. The second task was to construct a plumbing system for a two-story building so that neither neighbor would complain the other was getting more water. The third task was to plan and build a colormixing machine by streaming colored water (blue, red and yellow) into three transparent boxes and then dispensing the liquids in a controlled manner below them. The last task was more open – to plan and build a water garden that could include pools, fountains and other devices. The third instrument is a set of tasks, which were administered during six structured interviews. These were aimed at assessing the children’s understanding of system behavior as it changed throughout the experimental period. Content validity of the interview tasks was assessed by two experts – mechanical engineers well versed in teaching the subject of flow-dynamics in high-school and college. They built with the kit, examined the proposed tasks – removed, changed and added some tasks. Procedure The children constructed four different water systems, based on increasingly complex combinations of the three physical relations and concepts of control. They were tested individually and carried out the tasks with minimal involvement of the researcher. Both groups were interviewed before and after the activities, and the experimental group was interviewed at the end of each of the four building sessions. The control group participated in alternative activities that involved astronomy and Greek mythology, controlling for maturation and the effect of the first interview upon the last one, but especially for the time-with-theinterviewer, an important aspect in studying younger children. Throughout this period, the builders were interviewed 6 times, using 33 prediction tasks. They were asked to predict and compare the streams that would emanate from different water systems, and to describe them. They replied to each task in three forms: describing a real system, drawing streams onto a schematic of the system, and explaining their drawing. The highest-level response among the three was analyzed, and its consistency was coded. The tasks involved variation of one or two dimensions out of three that determine water flow: height of the water-exit (hence ‘height’), hole-width of the water exit (hence ‘hole’), and resistance until the exit (hence ‘resistance’). Not all tasks were administered in all sessions for reasons of brevity. The children’s explanations were coded as ‘if-then’ rules. In the first part we examine these rules and look at the way children discuss the effect of height and of hole-width upon the streams in the different tasks. In the second part, we probe only the ‘if’ part of the rules. The children’s explanations were coded as follows: the number of rules in an explanation, their consistency, the deviation of

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these dimensions from those varied in the tasks. Some special response patterns were investigated more closely in order to detect additional regularities. The reliability of the system features the children attended to and the rules they described was evaluated by three independent judges: the researcher and two colleagues. Inter-judge reliability was 96% for identification of causal features, and 91% for the determination of the children’s rules from the transcripts. RESULTS The results are organized along two themes: (1) interaction between task and learning; (2) on the way from simple to compound reasoning. Interaction between task and learning In what tasks do correct rules make their first appearance? During the experimental period, the children learnt two rules. The resistance rule was understood correctly from the start, e.g. ‘longer pipes slow down the water’ or ‘the curves stop the water from going through’. Prior to building, the children had believed that higher pipes supply stronger streams and that wider holes provide more water. The height rule was learnt first: lower exits ‘make stronger streams’. The ‘hole’ rule was learnt later, towards the end of the experimental period: narrower holes supply faster or farther streams, with a third of the children stating a compensating relationship in which wider holes ‘have fat streams that fall closer - straight down’. Does the change in the way the children understand the causal rules underlying system behavior take place in a consistent manner for all tasks? We examined this question by noting the height rules and the hole rules for each session for each task. In Figure 2, we can see that the first rise to correct rules takes place in the first session, but not in the simpler tasks. In the tasks varying height & resistance, and hole & resistance respectively, the correct rules first appeared. The dip in session 2 for the height rules is a result of a temporary bias towards hole-width rules, which we shall shortly describe. In the height & hole varying tasks, height rules did not even reach a ‘correct’ median and the hole rules followed the singlevariation tasks’ rules. Individual patterns were examined and they replicate the group results. Hole rules in different tasks 4

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Figure 2: Height and hole rules in the various tasks along the experimental timeline. Rule median: 1-no rule, 2-incorrect rule, 3-correct rule.

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On the way from simple to compound reasoning How many rules do the children use when explaining their predictions? The number of rules in response to the double-variation tasks is examined for the experimental group. This will provide us with a general progression, along which we can then place additional types of responses, based upon different properties. Timeline for rules and deviations for double-variation tasks 100

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Figure 3: Rule structures the children used when explaining their predictions of water behavior for the double variation tasks. Chi-square statistic describes deviation from task variations. It is explained in the next section.

The children had predicted water behavior for each task 2-3 times in each session. Their ‘best’ response was coded and its frequency was noted (overall frequency is 69%, with a SD of 24%). The children’s best rules were coded as having the following structures: no rule, a single rule, two different relevant rules provided in different instances of the same task – hence the ‘fluctuating’ rules or two interrelated rules. In the Figure 3, we observe the timeline for these different responses. We can see that in the temporal progression, single rules are dominant throughout, but are gradually and partially displaced, first by 2 single fluctuating rules, and then by double rules, that are used in a quarter of the explanations in the posttest. Each child provided at least one double rule in the posttest. How do the features in the children’s causal models map onto the task variations? The system properties upon which the children base their explanations of water behavior are compared with the actual variations. The frequency of each feature for each session is compared: children’s explanations and task variations for the single- and the double-variation tasks. The difference between the two is termed the ‘deviation from task-variations’. The chi-square test statistic was used to calculate this deviation, and to examine its significance. These statistics are viewed over time:

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Experimental group deviation from task variations as a function of time - single and double variation tasks 60

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Figure 4: Deviation from task variation for the single- and double-variation tasks.

We can see that the builders’ fit-to-task in the double-variation tasks increases almost monotonously. However, for the single-variation tasks, a temporary rise and fall in deviation takes place at an intermediate time. Examination of the individual tasks shows that the temporary increase in deviation corresponds with a predominant use of rules based on hole-width, while ignoring dimensions that had previously been attended to. A similar bias was seen among the control group in the posttest. When noting the children’s priorities among the rules, hole-width rules were preferred throughout. Height was preferred to resistance until session 2, when they switched priorities. Intermediate response patterns Three types of intermediate responses were examined more minutely for each child: biased, fluctuating and balancing responses: irrelevant rules precede and accompany relevant rules in a single explanation (e.g. ‘the holes are the same... but the higher pipe brings less water’. It was found that the biased response precedes the fluctuating one and is temporally separated from the balancing responses that are provided in the later sessions. To conclude this section, the ordering of response patterns is the following: single rules  biased rules  fluctuating rules  double rules + balancing rules.

DISCUSSION This study examined young children’s encounters with complexity while building water systems, and the way they adapt to this complexity. The results are discussed regarding two ideas: (a) simple is not always easy. (b) anchoring reasoning processes on the road from simple to compound reasoning. Simple is not always easy What facilitates the learning of complex systems? In education, we find the progression ‘from simple to complex’ in many planned learning sequences. This order assumes that if one is to learn a complex system, its simpler building blocks need to be understood. One of the consistent phenomena discovered in our study is the converse – learning may be facilitated by more complex situations, where some variations are familiar and understood. The children expressed a

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correct height (or hole) rule first in the tasks varying height (or hole) and resistance, and only later in tasks varying only height. They had known the correct rule for resistance from the start. Technological systems that surround us everyday are complex. They contain many parts, are organized in different structures, and utilize a manifold of causal rules - being the fruit of many years of human-effort in accumulating, integrating and generating knowledge. The systems in this experiment behave in a way that cannot always be understood in terms of the separate rules. The interactions are more complex and system behavior results from these interactions. A possible explanation for this lies in the reinforcing character of the correct rules. Model revision doesn’t occur when a cognitive system is confronted with a totally confusing situation, even if it is simple. Rather, in order to facilitate learning, the unfamiliar needs to be paired up and anchored with familiar phenomena, even if this means ‘complicating’ the situation. In a sense, the height rule is ‘piggyback riding’ on the resistance rule on the way to attaining a better mapping with reality. The resistance rule is supported by system behavior and further supports learning of the other rules. It may be that the children’s correct understanding of the effect of resistance upon water flow resonates with reality, inducing a sense of partial mapping. With this reinforcement it may be easier for inconsistencies to be resolved, rather than in complete lack of correspondence between theory and data. Reinforcement of succeeding strategies (using resistance to change water flow) opens the door and supports entry for a coupled variation of a previously non-succeeding rule. A complementing interpretation is based upon Lehrer & Schauble’s (1998) study. There, they found that the 5th graders, who were reasoning over a 40-minute interview about a succession of increasingly complex gear-mechanisms, changed their explanations over time. These explanations became more rule-based and included mechanistic descriptions to a greater extent when the tasks were more complex. This may have resulted from the complex tasks being administered later on in the interview. However, feedback was not provided. It would seem that an increase in task complexity challenges and elicits more sophisticated reasoning. Finally, an additional explanation can be found in the similarity between the building tasks and the interview tasks. The children built functional structures, but could not always explain their choices. These structures were complex, including variations of different features. It is possible that similarity with the rich building situation was greater in the more complex tasks and this elicited the shift from implicit to explicit knowledge. This finding is surprising but consistent. Its lack of precedents demands further corroboration and research in other settings and with different tools. From facilitating factors, we turn now to the process by which mental models shift from simple to compound reasoning. Anchoring reasoning processes on the road from simple to compound reasoning The regularities found in the children’s paths from single-featured rules to doublefeatured rules is described. We have found a phenomenon, which to our best knowledge has not been previously found – the increase in reasoning consistency (anchoring) that follows initial fragmented knowledge, when the individual ignores features previously attended to. An initially preferred feature becomes the only one used in reasoning about such systems. This process is induced by prior questioning regarding many systems made of the same kinds of

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parts. It is not associated with the building process, as it takes place among the control group in the posttest as well. It precedes the loss of consistency reflected in the fluctuating responses (see also Alibali & Goldin-Meadow, 1993) that are necessary to incorporate additional dimensions (encoding, in Siegler’s terms) into the causal model. Finally, when more features are encoded, their combined effect can be seen in reasoning that includes two rules, beyond the typical abilities Siegler (1978) describes in his developmental and learning studies. Thus, learning progresses through the sequential enhancement of three abilities: (a) extending a rule’s applicability or increasing the consistency of its use bridging knowledge-islands by creating a common framework to reason within. (b) encoding more causal properties of the system at hand (Siegler, 1978) while losing consistency. (c) rule integration (Carey, 1985; diSessa, 1993) - entwining the different features into causal structures that are both consistent and complex. The findings of this research have far-reaching implications on technology education in terms of teaching and learning.

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