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Putting the variability–stability–flexibility pattern to use: Adapting instruction to how children develop
New Ideas in Psychology 55 (2019) 18–23
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New Ideas in Psychology journal homepage: www.elsevier.com/locate/newideapsych
Putting the variability–stability–flexibility pattern to use: Adapting instruction to how children develop
T
Thea Ionescu∗ Babeş-Bolyai University, Department of Psychology, Faculty of Psychology and Sciences of Education, Babeş-Bolyai University, Cluj-Napoca, Romania
ARTICLE INFO
ABSTRACT
Keywords: Variability Stability Flexibility Instruction Zone of proximal development
Through learning, children solve problems by both using known solutions and going beyond those solutions. It has been shown that humans develop by passing through a recursive pattern of variability, stability, and flexibility states. In this paper, I argue that analyzing how the cognitive system behaves in each state when a child tries to solve a problem can provide insight into how to teach and evaluate the system during learning. Ways to teach from this perspective are presented, specifically how to use context, as well as the challenges and implications of this approach. This approach might help integrate some of the essential ideas in education, such as the need to address the zone of proximal development of children and to identify the kind of guidance that works best for efficient learning.
Natural selection prefers high complexity systems as they can reconfigure themselves into a multitude of different states. L. F. Barrett (2017, p. 3, emphasis added). 1. Introduction There seems to be little disagreement about what the role of learning is: On the one hand, it is to stabilize knowledge and abilities (i.e., knowing what and how) and on the other, to encourage the flexible use of knowledge and abilities (i.e., changing what and how, to adapt to challenging situations) (Samarapungavan, Patrick, & Manzicopoulos, 2011). This double role can be found both in learning for development in general and in learning in a particular domain. Some consider flexibility to be one of the defining aspects of human cognition (Goldstone & Theiner, 2017) and learning as a means to achieving it—in other words, to becoming innovative. I argue that better learning can be achieved by borrowing the variability–stability–flexibility (VSF) approach from developmental research to inform instructional approaches. As “high complexity systems” (Barrett, 2017, p. 3), humans develop by passing through a recursive pattern of variability, stability, and flexibility states (VSF states; Ionescu, 2017a). For example, consider language development: When children use a known name such as “excavator” for all kinds of trucks, they are showing variability; when later they use the proper name for each kind of truck, such as “excavator,” “crane,” or “dump truck,” they are in a state of stability; and ∗
finally, when they give one type of truck multiple names, such as “excavator,” “construction truck,” and “vehicle,” they have entered the flexibility state (Ionescu, 2017a; Siegler, DeLoache, & Eisenberg, 2003). A similar process occurs in the development of theory of mind. Initially children do not correctly use “mine” and “yours,” thus showing variability when expressing their own perspective; then they become fixed in their own perspective, showing stability; and finally they become able to grasp multiple perspectives, proving flexibility (Apperly, Samson, & Humphreys, 2009; Ionescu, 2017a; Wellman, Cross, & Watson, 2001). In one domain after another, when one analyzes the development of various processes, this progression shows up: First, children do not know the appropriate way to solve a problem, so they try out different ways, showing variability; then they learn the appropriate answer and show stability; and finally they can change the answer to respond to new demands, exhibiting flexibility (see Fig. 1 in Ionescu, 2017a). In the VSF approach, variability, stability, and flexibility are considered emergent properties of the cognitive system (Ionescu, 2012; 2017a), rather than specific abilities, as in other approaches (e.g., cognitive flexibility as set shifting; Diamond, 2006; Garon, Bryson, & Smith, 2008). There is growing support for the view that flexibility is a property and not a singular process (Müller & Kerns, 2015). In an investigation of cultural influences on cognitive flexibility, Legare, Dale, Kim, and Deák (2018) showed that there is no one expression of cognitive flexibility but that it is influenced by different kinds of educational experiences (e.g., U.S. and South African preschool education experiences influenced rule-switching flexibility but not word-learning
Corresponding author. E-mail address: [email protected].
https://doi.org/10.1016/j.newideapsych.2019.04.003 Received 12 January 2019; Received in revised form 21 April 2019; Accepted 21 April 2019 Available online 07 May 2019 0732-118X/ © 2019 Elsevier Ltd. All rights reserved.
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flexibility). Similarly, Ionescu (2017b) showed that when instructions are specific (or attribute based), preschool children can categorize flexibly, but when instructions are more general (or dimension based), they cannot at the same age. Pope, Fagot, Meguerditchian, Washburn, and Hopkins (2019) found that seminomadic Himba people are more cognitively flexible than Westerners and explained their findings based on differences in environmental uncertainty and educational background: Higher uncertainty and less educational stress on rule use lead to more flexible strategy-use. More and more studies are thus showing that flexibility is not one mechanism or ability that is developing but rather the result of an interaction between internal mechanisms and context such that the cognitive system as a whole becomes able to behave flexibly in different domains. The three terms used - variability, stability, and flexibility - are based on the analysis of the development of various processes as they express the functioning of those processes (Ionescu, 2017a). Here I go one step further and analyze all three states in the context of learning new content in a domain. The reconfiguration mentioned in the epigraph can be thought of as pointing to the aim of learning: Sometimes one needs to reach stability to be able to successfully solve a problem; sometimes one needs to reach flexibility for the same end. One important question in the literature on learning that is as yet unanswered is precisely how the human cognitive system learns to do this, that is, to adapt to changing demands (Day & Goldstone, 2012). Furthermore, the literature sometimes uses the term variability to denote flexibility too (Komar, Seifert, & Thouvarecq, 2015). My goal is to show that compared to previous approaches, this three-state approach better captures and then fosters children's learning and development. The paper proceeds as follows: I first describe learning specific content as passing through the VSF states. I then consider ways to teach specific content from this perspective. Finally, I discuss the challenges and implications of this approach. This approach might help integrate some of the essential ideas in education, such as the need to address the zone of proximal development of children (Vygotsky, 1978) or to identify the kind of guidance that works best for efficient learning (Kirschner, Sweller, & Clark, 2006). These goals, too, are discussed throughout the paper.
literature does not offer consensus about flexibility, for instance, how can programs be developed to foster it (Clement, 2006; Ionescu, 2012)? The present work aims to address this gap. Consider language learning as an example. When a child does not know much about a domain and is faced with solving a problem in that domain, the child will try out possible answers without knowing which one is correct. For example, before learning about clauses, children will use any association of two words as a sentence when trying to communicate, such as “mummy, water.” But note in this phase they are variable: Sometimes they will produce correct clauses, such as “mummy give me water” (i.e., with a predicate) and sometimes not (i.e., “mummy, water”). After learning to speak in sentences, children become stable and will use correct clauses more and more often (i.e., “mummy give me water”). After more practice with using correct clauses, especially after some years of schooling in which stability is constantly reinforced and in fact required for academic performance (i.e., answering in correct linguistic forms), children become flexible: They again may use incomplete clauses in specific contexts, such as in poetry or fiction. In this example, the difference between variability and flexibility becomes clear: When variable, children use incomplete clauses incorrectly, but sometimes they achieve their goal without intending to use a specific sentence form; when flexible, children use incomplete clauses on purpose, employing, for instance, poetic license. In other words, variability means having only the goal of solving the problem by any means possible (a species-specific goal) while flexibility means having the extra goal of going beyond what is already known in order to solve the problem (an individual-specific goal). As such, flexibility implies going beyond stability, whereas variability leads to stability. Taking another domain, consider mathematics for instance. If we refer to addition, children will oftentimes guess the result before understanding the principles of addition, that is they are variable. After learning the principles of addition and some strategies to solve it (e.g., counting the fingers, counting from the smaller number, Siegler, 1999) they become stable and solve additions correctly but usually only if presented in one known order (e.g., 3 + 4 = ? and not ? = 3 + 4). It is only after another practice time that they understand that the important element is the plus sign and the order of each side is irrelevant or that addition has the property of commutativity; that is they become flexible. In the case of learning in a particular domain, there is a linear progression from not knowing to knowing and then to changing known ways for a particular case of problem solving, even if development itself is not linear (see Fig. 1 in Ionescu, 2017a; Smith & Thelen, 2003). On this linear passage particular behaviors can be identified in each state, which can then be used by educators to act during instruction in a way that optimizes children's development.
2. The VSF pattern applied to learning specific content Learning specific content in a domain means being able to know after learning has occurred how to solve problems in that domain, that is, to apply the acquired knowledge. In the first phase, when the child does not know that domain, variability occurs. In other words, this is a phase in which the child tries to solve problems in the domain by whatever means he/she can find. After gaining knowledge in that domain, what is both interesting and important is that solving problems requires the child sometimes to “stay” with a known solution but other times to “go beyond” that solution. Staying with known solutions provides cognitive coherence and is a sign of learning from the past (Smith, 2009); this is stability, in other words, the phase in which the cognitive system applies procedures known to be successful in solving the problem at hand. Stability is also considered a key property that allows the organism to maintain meaningful connections to the external world (Schöner, 2009). Going beyond known solutions, that is, flexibility, offers the child the chance to adapt to new demands and use what she or he has learned to solve new problems. Included in this category are transfer of knowledge (Clerc & Clément, 2016; Goldstone & Day, 2012; Lobato, 2012) and innovation (Carr, Kendall, & Flynn, 2016). These learning outcomes are still poorly predicted by current educational systems and it is questionable if school itself is efficient in producing these outcomes in most students (Robinson & Aronica, 2009). This may be because schools are concerned more with transmitting knowledge (thus with stability), but it could also be because studies on child development still offer few general principles to help education in practice: When the
3. Instruction and the VSF pattern Whereas flexibility involves identifying and adopting a different perspective and then changing one's response (Ionescu, 2017a), variability can be seen as the attempt to identify and adopt a potential perspective to solve a problem, and stability as the identification and adoption of known or practiced perspectives. While the literature acknowledges constant transitions from instability to stability of behavior when the system learns new things (Chow, Davids, Hristovski, Araujo, & Passos, 2011; Lickliter, 2017; Piaget, 1952; Wellman et al., 2001), a finer distinction between variability and flexibility as two distinct forms of instability seems to step out when one looks at human development (see examples above and in Ionescu, 2017a). What I attempt with this new approach is to show that the states before and after stability are not the same. As outlined above, when characterized by variability, the child does not have enough knowledge in a domain. To go back to the example of word learning, a child who just learns the word “excavator” uses it 19
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inappropriately in this state, that is, for all kinds of trucks in all contexts. Thus the child should be allowed to explore the new content, i.e., the new word, in typical contexts. During exploration the system will tune its attention to perceive the relevant details and thus slowly approach a “good” answer—in the example above, learning other new words appropriate for different kinds of trucks. In each domain the system can rarely discover the “good” solutions by itself, so it needs help: For example, children need an adult to name the objects because they cannot figure out proper names solely by themselves (Schaffer, 2004). The system needs guidance and instruction to arrive at stability (Kirschner et al., 2006; Mayer, 2004). In this second phase of acquiring the content of a domain, the desired behaviors will include knowing the word meaning and using it appropriately in typical contexts. For that, an important phase is that of practicing the content and exercising the tuned mechanisms (see a list of candidate mechanisms in Fig. 1, Ionescu, 2012) in typical contexts. This practice gives the system both the knowledge and the occasions to use all the necessary mechanisms for handling that knowledge in those contexts. For example, selective attention becomes more and more efficient in singling out the relevant details to be observed when solving problems with the known procedures. As such, this phase may be very important for allowing the system to know the content in depth (Ionescu, 2017c; Ionescu et al., 2017; Smith & Slone, 2017). During learning of truck names, for instance, this means learning the new words and using them in the construction setting so that their meanings are fully grasped. From the point of view of statistical learning, it may also be important for allowing the system to thoroughly observe statistical regularities so that it can pass to the next phase, their combination (see Smith & Yu, 2008; for statistical learning in word learning). The combination of known procedures leads to the next phase, flexibility. When a cognitive system is flexible it can go beyond the known ways to solve a problem in a domain when new demands require it. In the word-learning example above, the child can go beyond the construction site context and understand that an “excavator” is also a “vehicle.” To prepare the system to achieve flexibility, instruction should focus on putting the now known content into different contexts or perspectives so that the system can further tune attention to new relevant aspects of the known procedures. This can be thought of as “playing with knowledge.” Because context is so relevant for information processing (Braem & Egner, 2018; Mayr, Smuc, & Risku, 2011; Perry, 2015; Shafto, Coley, & Baldwin, 2007; Thomas, Purser, & Mareschal, 2012) teaching context sensitivity may be one of the most important ways to foster flexibility. In sum, during variability, exploration should be encouraged in typical contexts for the domain; for stability, practice should involve typical and close-to-typical contexts; and finally, for achieving flexibility, the content should be put in new contexts. In this way, the cognitive system will develop all the needed mechanisms and will tune them to context so that in the end it can adapt the content it knows to new demands (new contexts). (see Table 1)
The dependence of cognition on context is a well-known idea (see the embodied cognition approach, Barsalou, 2008; Glenberg, 2008; Gomila & Calvo, 2008; Wilson, 2002; see also Chow, Davids, Hristovski, Araujo, & Passos, 2011). The VSF approach can help educators understand how to use context for learning and development: Manipulating context during instruction as outlined above could facilitate children's transition from novice to experts in particular domains (see also the idea of context manipulation for insight, Kounios, Fleck, Green, Payne, Stevenson, Bowden, & Jung-Beeman, 2008). It is interesting that the literature on instruction suggests pure discovery and programs with minimal guidance do not really work (Fyfe, McNeil, Son, & Goldstone, 2014; Kirschner et al., 2006; Mayer, 2004). While pure discovery has been thought to help children arrive at the relevant knowledge by themselves and so to promote better storage in long-term memory, surprisingly, guided instruction and direct instruction were found to work best (Kirschner et al., 2006; Stockard, Wood, Coughlin, & Rasplica Khoury, 2018). In other words, children need structured guidance to learn the content of a domain well (guidance that includes scaffolding in various ways; Hmelo-Silver, Duncan, & Chinn, 2007; Samarapungavan, Patrick, & Mantzicopoulos, 2011). Hmelo-Silver et al. (2007) pointed out two other interesting facts: (1) Just-in-time direct instruction is indeed needed from time to time in problem-based and inquiry learning; and (2) students learn more from a lecture after an initial exploratory problem-solving phase. On the one hand, the VSF approach can help clarify the idea of “just-in-time” (Hmelo-Silver et al., 2007) for certain methods in education (Kirschner et al., 2006). The differential need for guidance (i.e., different amounts at different moments of teaching (Hmelo-Silver et al., 2007) can be linked to the child's current VSF state and the passage from one state to another: A lot of guidance is needed when the child is variable, less and less guidance when stable, and only some hints when flexible. This may be why the current literature offers contradictory results: Children may have been in different states, states that were not evaluated in the respective studies. Knowing a child state or whether he or she is at transition from one state to another is helpful because intervention seems most effective at transition points (Thelen, 1995): Just in time can become a known moment in time for when to provide direct instruction, for example when passing from variability to stability. On the other hand, the initial exploration (Hmelo-Silver et al., 2007) helps motivation and attention tuning, but then direct guidance is needed so that the system acquires the relevant knowledge of a domain. After a child reaches stability, guidance can become more and more subtle; and when the child is flexible, the cognitive system can search with less help for new solutions. The role of instruction-by-exploration is to foster curiosity about the domain, similar to a young child's curiosity about learning the names of objects or how toys work. This curiosity then leads the child to keep learning the content of that domain, more than when educators begin directly with targeted teaching; and this may be why learners benefit more from a lecture after initial exploration. We can speculate then that variability is also important for
Table 1 Children's states, instruction and its effect on passing from one state to another. Children's state
Instruction Effect of instruction
Variability
Stability
Flexibility
(not knowing a domain; not well-functioning parameters yet; not tuned to context)
(knowing the domain; well functioning parameters tuned to typical contexts)
(going beyond known paths in a domain; well functioning parameters sensitive to contextual changes)
Free exploration/Guided instruction in typical contexts Motivation Potential discovery of the solution
Guided instruction in typical, close-totypical contexts and new contexts Solid knowledge base Apply known solution to new, close to typical contexts ⇒Pass to the flexibility state
Exploration in new contexts guided by previous knowledge
• • known ways of solving the • Acquire problem
• •
⇒ Pass to the stability state
20
•
Find new ways for solving the problem ⇒ Transform this state into a new stability state or enter a new variability state for new knowledge in the domain
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fostering motivation for a domain. In sum, each state is equally important, and in education each state needs to be addressed differently to promote optimal learning. This idea is supported by new studies in brain research: On the one hand, the conceptual distinctions employed in psychological studies might not represent the mechanisms the brain uses when processing information (Eldar, Cohen, & Niv, 2013; Miller & Fusi, 2013; Spencer & Buss, 2015; Stokes et al., 2013). As a consequence, researchers should focus on the dynamics of processing and not on fixed processes. On the other hand, it seems that the brain functions optimally near a critical point (see the criticality hypothesis; Beggs, 2008; Pfeffer et al., 2018) that separates variability from stability in neural network activity. As such, to adapt education to how the brain learns, it might be necessary to change from models of information processing as distinct and separate mechanisms back to a model of the whole organism during learning (Gibson, 1994) and the states it is in while learning. Criticality is also a central issue in dynamic systems accounts (Chow, Davids, Hristovski, Araújo, & Passos, 2011) as a phase in which the system is more apt to change to new behaviors. By differentiating variability and flexibility based on developmental arguments one could better understand change during learning: Change is triggered by different instructional methods in the states before and after stability and this might have important consequences for teaching.
is already present in nonlinear pedagogy (Chow, 2013; Chow et al., 2011) especially in motor learning, but again there it is based on two states, instability and stability. Inserting flexibility brings further clarifications. For example, Chow et al. (2011, p. 25) stated that “more options need to be created for advanced learners and fewer options for novice learners.” “More options” are easy to handle after a phase of stability, akin to using new contexts for the system to pass to flexibility; “fewer options” are good in the variability state and it is similar to the idea of instructing children in the typical context until they acquire knowledge in a domain. Thus taking a three-state view helps explain the seemingly contradictory results in the literature: that sometimes new contexts help but sometimes not (Chow, 2013). One prediction that follows is that learning needs different constraints in the variability and flexibility states even if both states can be described as unstable states (i.e., in which the search for solutions is high) and both then take the system to a stability state (i.e., after flexibility, if the new way of solving a problem becomes a regular strategy the system can be considered to have entered a new stability state). Second, this approach may be of help in the application of the concept of the zone of proximal development (ZPD) in education. The ZPD refers to the gap between what a child can do by him- or herself and what the child can do only with help from a more knowledgeable person (Schaffer, 2004; Vygotsky, 1978). It has been suggested that teaching children in this gap helps them progress better than when the focus is on what they know (assignments that are too easy) or well beyond what they know (assignments that are too difficult; Schaffer, 2004). This kind of teaching is so far just an ideal in education, because it is truly difficult to work individually with each child in a classroom of 30 children and to address their learning potential individually. The VSF perspective can help educators get closer to the ideal of ZPD: If one groups children according to the three VSF states, then teaching focused on three groups is easier than teaching each child individually. Call it three-state ZPD. When using the VSF approach to evaluate the threestate ZPD, one can appreciate the level of the child and tailor the instruction to the child's needs so that he or she can pass to the next proximal state; the result of using this approach is a classroom divided into three groups, which is much easier to handle than addressing each child individually (see also Winner, 2012, pp. 75–81). This approach can then help teachers avoid unproductive situations in which the instruction does not fit the child's current state, such as offering interesting new contexts for particular content to a child in the variable state who is not yet ready to learn new ways to solve problems. A third insight that follows from the previous ones is that the VSF approach may in fact help integrate ideas from two main traditional theories, namely, those of Piaget and Vygotsky. Oftentimes, these two theories are treated as, if not opposite, at least separate theories in developmental studies and in education (Poole, Warren, & Nunez, 2007; Schaffer, 2004). For example, the Piagetian child is oftentimes considered as learning by him- or herself and constructing his or her own development by actively manipulating information, while the Vygotskian child is embedded in culture. More importantly for the current topic is that Piaget talked about recurrent passages from disequilibrium to equilibrium in the development of intelligence and Vygotsky stressed the idea of individualization by coining the notion of ZPD. However, when taking a VSF perspective one can easily integrate these latter ideas: One can reach a deeper understanding of the passage from disequilibrium to equilibrium, because disequilibrium before and after equilibrium are not the same. At the same time, the VSF approach stresses individualization according to the three described states. As such, this approach stresses both regularity—the recurrent passage through the VSF states—and interindividual differences. This can help educators address differences between children more easily, by addressing differences between three main groups as change in learning a domain occurs. One must also consider the challenges of the VSF approach. The first challenge is to understand what level of variability is optimal for good
4. The promises and challenges of the VSF approach applied to instruction Using the VSF approach to inform teaching is both promising and challenging. In terms of promise, there are several insights that differ from those derived from previous theories. First, a main idea is that not all instability is the same. This is important because different teaching strategies are needed for different kinds of instability to facilitate the passage from one state to another. In the literature on flexibility, some authors have argued that flexibility can happen without previous knowledge and even that previous knowledge can hinder flexibility (Defeyter & German, 2003; German & Defeyter, 2000; Gopnik et al., 2017; Yonge, 1966); others have argued that “true” flexibility emerges after one has a solid knowledge base in a domain (Bilalic, McLeod, & Gobet, 2008; Ionescu, 2017c). It is interesting to note that studies on experts have shown that up to a point, the knowledge base can indeed hinder the process of finding new ways to solve a problem, but after that point, it helps. Bilalic et al. (2008) found that “ordinary” chess experts had difficulties finding an unfamiliar and easier way to win a game, but “super” experts did this with ease. The authors argued that real expertise helps flexibility. One way to address this issue is to differentiate between the states before and after stability, namely, variability and flexibility. As a simple linguistic analysis can show, variability refers more to producing multiple ways to approach a problem, whereas flexibility refers more to bending or modifying a known way (Ionescu, 2017a). As such, those who argue that previous knowledge can interfere with problem solving may in fact be talking about the passage from variability to stability, whereas those who argue for the importance of knowledge may in fact be talking about the passage from stability to flexibility. Equally important it is to understand the nature of stability too: if a system just entered this state it might behave differently then after some time spent in this state (in other words if it is closer to variability or to flexibility). A corollary follows to further clarify the nature of flexibility: An important difference between variability and flexibility is the search for new perspectives with the purpose of going beyond stability. Specifically, whereas during variability the system just looks for a perspective in order to solve the problem, flexibility implies the knowledge of appropriate perspectives (i.e., the system is already stable) and the intention to change/adapt these so that new ways of problem solving can emerge. As shown in the previous section, context can then be used differently to help the system while learning. This idea 21
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stability afterward, and similarly how much stability an individual needs to reach flexibility. This understanding can be achieved only via experimental studies that change instruction little by little and follow children's progress. Linked directly to this, devising methods to investigate the passage from one state to another may prove difficult. My colleagues and I are currently working in the lab on designing some microgenetic studies to pinpoint these passages. An interesting question for future research is if there are knowledge thresholds that could make the transition of the system from one state to another more likely to happen. Another challenge will be to develop specific methods for teaching every domain in school according to the three-state ZPD: There may be specific difficulties particular to each domain. Finally, encouraging differences between children also means that because not all children will pass at the same pace through the VSF states when learning in a domain, they should be allowed to remain in a certain state in a specific domain. A second question thus follows: How does one know if a child cannot progress to the next state? In closing this section, I would like to emphasize the following idea: The type of context (typical vs. new) and the type of exploration (free vs. guided) should be adapted to the state the child is in. Several programs focused on improving creativity in children in schools have recommended free exploration as a means for achieving this. Yet so far, schools have not succeeded in optimizing children's creativity (Robinson & Aronica, 2009), which I believe is because focusing on free exploration keeps the child in the state of variability, whereas for flexibility a phase of stability is also needed, and this is based on more direct guidance. Variable children do not access the relevant knowledge of a field, or at least not by themselves in most cases. This is why guidance is needed. I would stress that in the state of stability, thorough understanding and repetition of content is needed for the cognitive system to acquire a solid knowledge base. It is from this knowledge base (i.e., a stable knowledge of a domain) that the system will be able to change, combine, and innovate, in other words, to become flexible and able to play with solutions (Prince, 2004). And this is more likely to happen if during instruction, knowledge is put explicitly in new contexts but only after it was well practiced in typical contexts. Future directions should thus aim at explaining exactly how the cognitive system passes from one state to another. If flexibility means that the system has the right parameters well tuned to context, then stability should represent a system with good parameters not yet well tuned to context, and variability a system without well-functioning parameters. This can be studied by following children's learning in a domain from t zero (i.e., baseline) to t flexible (i.e., flexibility) and charting the changes that occur on this path as a consequence of manipulating context. Furthermore evaluation instruments need to be devised so that teachers can easily assess the state of a particular child. Understanding the passage through VSF linked to sensitivity to context could ultimately take educators closer to being able to help children develop as whole systems connected to the environment (Sheya & Smith, 2018) and not as a puzzle of specific abilities or processes. In sum, I argue for the use of the VSF approach in education because it can guide educators to design appropriate constraints for children in these three states. In other words, identifying the state a child is in can help the teacher to design differential teaching but not for each child in a classroom but for three larger groups. The way a teacher can use context and also exploration and guidance would thus change according to the targeted state: The options a child is given may thus better be used by the child because he/she will be in the state-specific zone of proximal development for specifically that instructional method.
how flexibility develops, and second how it relies on stability. In this essay I have proposed a general framework that can then be adapted to learning in a domain, to help education promote the reconfiguration of the cognitive system into different states, so that children reach their full potential. Flexibility is the end state of a pattern of three states (VSF) and to foster it we need to understand the passage through all of them. And for this we need new theoretical approaches and new tools. Some authors have argued that there is a need for a new scientific language to understand the complexity of development (Oudeyer, 2016; Spencer, Blumberg, & Shenk, 2016); this may also be true for learning and instruction: Education researchers may need to look for new models that frame education in a way that more closely follows the dynamics of children's development. On the one hand, a new language means new ways of thinking that can then change instructional approaches. On the other hand, more than just a new language, the approach proposed here offers a viable middle ground between nonindividualized instruction (as is found in most schools today) and individualized instruction (which is so hard to achieve in general education; usually it is reserved for children with special needs, both negative and positive). More specifically, the VSF approach can help educators address differences according to the three VSF states—a good compromise between not addressing them at all and working individually. In addition, changes in context can be systematically used to help children move from variability to stability and to flexibility. Until now, most often teaching addressed variability (via exploration) and stability (via practicing known ways of problem solving). By not addressing the transit from stability to flexibility and by not acknowledging the difference between variability and flexibility educators cannot foster creativity and innovation. These two highly praised outcomes of learning can be reached only if all three states are considered—as they represent a natural passage during development—and then addressed differently. In some ways, this new approach might lead to a fractal-like view (Mandelbrot, 1983) of development and learning: The recursive reoccurrence of the VSF states might be a key to understanding the nature of learning and development. And what is more for education, this key can help teachers better address each child's potential. Acknowledgments The author wishes to thank Anita Todd for editing the manuscript; Bogdan Bucur for insightful discussions about patterns and their analysis; and three anonymous reviewers for very helpful comments. References Apperly, I. A., Samson, D., & Humphreys, G. W. (2009). Studies of adults can inform accounts of theory of mind development. Developmental Psychology, 45(1), 190. Barrett, L. F. (2017). The theory of constructed emotion: An active inference account of interoception and categorization. Social Cognitive and Affective Neuroscience, 12(1), 1–23. Barsalou, L. W. (2008). Grounded cognition. Annual Review of Psychology, 59, 617–645. Beggs, J. M. (2008). The criticality hypothesis: How local cortical networks might optimize information processing. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 366(1864), 329–343. Bilalić, M., McLeod, P., & Gobet, F. (2008). Inflexibility of experts—reality or myth? Quantifying the einstellung effect in chess masters. Cognitive Psychology, 56(2), 73–102. Braem, S., & Egner, T. (2018). Getting a grip on cognitive flexibility. Current Directions in Psychological Science, 27, 470–476. Carr, K., Kendal, R. L., & Flynn, E. G. (2016). Eureka!: What is innovation, how does it develop, and who does it? Child Development, 87(5), 1505–1519. Chow, J. Y. (2013). Nonlinear learning underpinning pedagogy: Evidence, challenges, and implications. Quest, 65(4), 469–484. Chow, J. Y., Davids, K., Hristovski, R., Araújo, D., & Passos, P. (2011). Nonlinear pedagogy: Learning design for self-organizing neurobiological systems. New Ideas in Psychology, 29(2), 189–200. https://doi.org/10.1016/j.newideapsych.2010.10.001. Clement, E. (2006). Approche de la flexibilite cognitive dans la problematique de la resolution de probleme. L'Année Psychologique, 106, 415–434. Clerc, J., & Clément, É. (2016). Metacognition and cognitive flexibility in transfer of learning. Metacognition: Theory, performance and current research (pp. 17–42). .
5. Concluding remarks Flexibility is highly praised in contemporary society together with creativity and innovation (Carr, Kendal, & Flynn, 2016). In order to be able to educate people to become as such, we need to understand first 22
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New Ideas in Psychology journal homepage: www.elsevier.com/locate/newideapsych
Putting the variability–stability–flexibility pattern to use: Adapting instruction to how children develop
T
Thea Ionescu∗ Babeş-Bolyai University, Department of Psychology, Faculty of Psychology and Sciences of Education, Babeş-Bolyai University, Cluj-Napoca, Romania
ARTICLE INFO
ABSTRACT
Keywords: Variability Stability Flexibility Instruction Zone of proximal development
Through learning, children solve problems by both using known solutions and going beyond those solutions. It has been shown that humans develop by passing through a recursive pattern of variability, stability, and flexibility states. In this paper, I argue that analyzing how the cognitive system behaves in each state when a child tries to solve a problem can provide insight into how to teach and evaluate the system during learning. Ways to teach from this perspective are presented, specifically how to use context, as well as the challenges and implications of this approach. This approach might help integrate some of the essential ideas in education, such as the need to address the zone of proximal development of children and to identify the kind of guidance that works best for efficient learning.
Natural selection prefers high complexity systems as they can reconfigure themselves into a multitude of different states. L. F. Barrett (2017, p. 3, emphasis added). 1. Introduction There seems to be little disagreement about what the role of learning is: On the one hand, it is to stabilize knowledge and abilities (i.e., knowing what and how) and on the other, to encourage the flexible use of knowledge and abilities (i.e., changing what and how, to adapt to challenging situations) (Samarapungavan, Patrick, & Manzicopoulos, 2011). This double role can be found both in learning for development in general and in learning in a particular domain. Some consider flexibility to be one of the defining aspects of human cognition (Goldstone & Theiner, 2017) and learning as a means to achieving it—in other words, to becoming innovative. I argue that better learning can be achieved by borrowing the variability–stability–flexibility (VSF) approach from developmental research to inform instructional approaches. As “high complexity systems” (Barrett, 2017, p. 3), humans develop by passing through a recursive pattern of variability, stability, and flexibility states (VSF states; Ionescu, 2017a). For example, consider language development: When children use a known name such as “excavator” for all kinds of trucks, they are showing variability; when later they use the proper name for each kind of truck, such as “excavator,” “crane,” or “dump truck,” they are in a state of stability; and ∗
finally, when they give one type of truck multiple names, such as “excavator,” “construction truck,” and “vehicle,” they have entered the flexibility state (Ionescu, 2017a; Siegler, DeLoache, & Eisenberg, 2003). A similar process occurs in the development of theory of mind. Initially children do not correctly use “mine” and “yours,” thus showing variability when expressing their own perspective; then they become fixed in their own perspective, showing stability; and finally they become able to grasp multiple perspectives, proving flexibility (Apperly, Samson, & Humphreys, 2009; Ionescu, 2017a; Wellman, Cross, & Watson, 2001). In one domain after another, when one analyzes the development of various processes, this progression shows up: First, children do not know the appropriate way to solve a problem, so they try out different ways, showing variability; then they learn the appropriate answer and show stability; and finally they can change the answer to respond to new demands, exhibiting flexibility (see Fig. 1 in Ionescu, 2017a). In the VSF approach, variability, stability, and flexibility are considered emergent properties of the cognitive system (Ionescu, 2012; 2017a), rather than specific abilities, as in other approaches (e.g., cognitive flexibility as set shifting; Diamond, 2006; Garon, Bryson, & Smith, 2008). There is growing support for the view that flexibility is a property and not a singular process (Müller & Kerns, 2015). In an investigation of cultural influences on cognitive flexibility, Legare, Dale, Kim, and Deák (2018) showed that there is no one expression of cognitive flexibility but that it is influenced by different kinds of educational experiences (e.g., U.S. and South African preschool education experiences influenced rule-switching flexibility but not word-learning
Corresponding author. E-mail address: [email protected].
https://doi.org/10.1016/j.newideapsych.2019.04.003 Received 12 January 2019; Received in revised form 21 April 2019; Accepted 21 April 2019 Available online 07 May 2019 0732-118X/ © 2019 Elsevier Ltd. All rights reserved.
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flexibility). Similarly, Ionescu (2017b) showed that when instructions are specific (or attribute based), preschool children can categorize flexibly, but when instructions are more general (or dimension based), they cannot at the same age. Pope, Fagot, Meguerditchian, Washburn, and Hopkins (2019) found that seminomadic Himba people are more cognitively flexible than Westerners and explained their findings based on differences in environmental uncertainty and educational background: Higher uncertainty and less educational stress on rule use lead to more flexible strategy-use. More and more studies are thus showing that flexibility is not one mechanism or ability that is developing but rather the result of an interaction between internal mechanisms and context such that the cognitive system as a whole becomes able to behave flexibly in different domains. The three terms used - variability, stability, and flexibility - are based on the analysis of the development of various processes as they express the functioning of those processes (Ionescu, 2017a). Here I go one step further and analyze all three states in the context of learning new content in a domain. The reconfiguration mentioned in the epigraph can be thought of as pointing to the aim of learning: Sometimes one needs to reach stability to be able to successfully solve a problem; sometimes one needs to reach flexibility for the same end. One important question in the literature on learning that is as yet unanswered is precisely how the human cognitive system learns to do this, that is, to adapt to changing demands (Day & Goldstone, 2012). Furthermore, the literature sometimes uses the term variability to denote flexibility too (Komar, Seifert, & Thouvarecq, 2015). My goal is to show that compared to previous approaches, this three-state approach better captures and then fosters children's learning and development. The paper proceeds as follows: I first describe learning specific content as passing through the VSF states. I then consider ways to teach specific content from this perspective. Finally, I discuss the challenges and implications of this approach. This approach might help integrate some of the essential ideas in education, such as the need to address the zone of proximal development of children (Vygotsky, 1978) or to identify the kind of guidance that works best for efficient learning (Kirschner, Sweller, & Clark, 2006). These goals, too, are discussed throughout the paper.
literature does not offer consensus about flexibility, for instance, how can programs be developed to foster it (Clement, 2006; Ionescu, 2012)? The present work aims to address this gap. Consider language learning as an example. When a child does not know much about a domain and is faced with solving a problem in that domain, the child will try out possible answers without knowing which one is correct. For example, before learning about clauses, children will use any association of two words as a sentence when trying to communicate, such as “mummy, water.” But note in this phase they are variable: Sometimes they will produce correct clauses, such as “mummy give me water” (i.e., with a predicate) and sometimes not (i.e., “mummy, water”). After learning to speak in sentences, children become stable and will use correct clauses more and more often (i.e., “mummy give me water”). After more practice with using correct clauses, especially after some years of schooling in which stability is constantly reinforced and in fact required for academic performance (i.e., answering in correct linguistic forms), children become flexible: They again may use incomplete clauses in specific contexts, such as in poetry or fiction. In this example, the difference between variability and flexibility becomes clear: When variable, children use incomplete clauses incorrectly, but sometimes they achieve their goal without intending to use a specific sentence form; when flexible, children use incomplete clauses on purpose, employing, for instance, poetic license. In other words, variability means having only the goal of solving the problem by any means possible (a species-specific goal) while flexibility means having the extra goal of going beyond what is already known in order to solve the problem (an individual-specific goal). As such, flexibility implies going beyond stability, whereas variability leads to stability. Taking another domain, consider mathematics for instance. If we refer to addition, children will oftentimes guess the result before understanding the principles of addition, that is they are variable. After learning the principles of addition and some strategies to solve it (e.g., counting the fingers, counting from the smaller number, Siegler, 1999) they become stable and solve additions correctly but usually only if presented in one known order (e.g., 3 + 4 = ? and not ? = 3 + 4). It is only after another practice time that they understand that the important element is the plus sign and the order of each side is irrelevant or that addition has the property of commutativity; that is they become flexible. In the case of learning in a particular domain, there is a linear progression from not knowing to knowing and then to changing known ways for a particular case of problem solving, even if development itself is not linear (see Fig. 1 in Ionescu, 2017a; Smith & Thelen, 2003). On this linear passage particular behaviors can be identified in each state, which can then be used by educators to act during instruction in a way that optimizes children's development.
2. The VSF pattern applied to learning specific content Learning specific content in a domain means being able to know after learning has occurred how to solve problems in that domain, that is, to apply the acquired knowledge. In the first phase, when the child does not know that domain, variability occurs. In other words, this is a phase in which the child tries to solve problems in the domain by whatever means he/she can find. After gaining knowledge in that domain, what is both interesting and important is that solving problems requires the child sometimes to “stay” with a known solution but other times to “go beyond” that solution. Staying with known solutions provides cognitive coherence and is a sign of learning from the past (Smith, 2009); this is stability, in other words, the phase in which the cognitive system applies procedures known to be successful in solving the problem at hand. Stability is also considered a key property that allows the organism to maintain meaningful connections to the external world (Schöner, 2009). Going beyond known solutions, that is, flexibility, offers the child the chance to adapt to new demands and use what she or he has learned to solve new problems. Included in this category are transfer of knowledge (Clerc & Clément, 2016; Goldstone & Day, 2012; Lobato, 2012) and innovation (Carr, Kendall, & Flynn, 2016). These learning outcomes are still poorly predicted by current educational systems and it is questionable if school itself is efficient in producing these outcomes in most students (Robinson & Aronica, 2009). This may be because schools are concerned more with transmitting knowledge (thus with stability), but it could also be because studies on child development still offer few general principles to help education in practice: When the
3. Instruction and the VSF pattern Whereas flexibility involves identifying and adopting a different perspective and then changing one's response (Ionescu, 2017a), variability can be seen as the attempt to identify and adopt a potential perspective to solve a problem, and stability as the identification and adoption of known or practiced perspectives. While the literature acknowledges constant transitions from instability to stability of behavior when the system learns new things (Chow, Davids, Hristovski, Araujo, & Passos, 2011; Lickliter, 2017; Piaget, 1952; Wellman et al., 2001), a finer distinction between variability and flexibility as two distinct forms of instability seems to step out when one looks at human development (see examples above and in Ionescu, 2017a). What I attempt with this new approach is to show that the states before and after stability are not the same. As outlined above, when characterized by variability, the child does not have enough knowledge in a domain. To go back to the example of word learning, a child who just learns the word “excavator” uses it 19
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inappropriately in this state, that is, for all kinds of trucks in all contexts. Thus the child should be allowed to explore the new content, i.e., the new word, in typical contexts. During exploration the system will tune its attention to perceive the relevant details and thus slowly approach a “good” answer—in the example above, learning other new words appropriate for different kinds of trucks. In each domain the system can rarely discover the “good” solutions by itself, so it needs help: For example, children need an adult to name the objects because they cannot figure out proper names solely by themselves (Schaffer, 2004). The system needs guidance and instruction to arrive at stability (Kirschner et al., 2006; Mayer, 2004). In this second phase of acquiring the content of a domain, the desired behaviors will include knowing the word meaning and using it appropriately in typical contexts. For that, an important phase is that of practicing the content and exercising the tuned mechanisms (see a list of candidate mechanisms in Fig. 1, Ionescu, 2012) in typical contexts. This practice gives the system both the knowledge and the occasions to use all the necessary mechanisms for handling that knowledge in those contexts. For example, selective attention becomes more and more efficient in singling out the relevant details to be observed when solving problems with the known procedures. As such, this phase may be very important for allowing the system to know the content in depth (Ionescu, 2017c; Ionescu et al., 2017; Smith & Slone, 2017). During learning of truck names, for instance, this means learning the new words and using them in the construction setting so that their meanings are fully grasped. From the point of view of statistical learning, it may also be important for allowing the system to thoroughly observe statistical regularities so that it can pass to the next phase, their combination (see Smith & Yu, 2008; for statistical learning in word learning). The combination of known procedures leads to the next phase, flexibility. When a cognitive system is flexible it can go beyond the known ways to solve a problem in a domain when new demands require it. In the word-learning example above, the child can go beyond the construction site context and understand that an “excavator” is also a “vehicle.” To prepare the system to achieve flexibility, instruction should focus on putting the now known content into different contexts or perspectives so that the system can further tune attention to new relevant aspects of the known procedures. This can be thought of as “playing with knowledge.” Because context is so relevant for information processing (Braem & Egner, 2018; Mayr, Smuc, & Risku, 2011; Perry, 2015; Shafto, Coley, & Baldwin, 2007; Thomas, Purser, & Mareschal, 2012) teaching context sensitivity may be one of the most important ways to foster flexibility. In sum, during variability, exploration should be encouraged in typical contexts for the domain; for stability, practice should involve typical and close-to-typical contexts; and finally, for achieving flexibility, the content should be put in new contexts. In this way, the cognitive system will develop all the needed mechanisms and will tune them to context so that in the end it can adapt the content it knows to new demands (new contexts). (see Table 1)
The dependence of cognition on context is a well-known idea (see the embodied cognition approach, Barsalou, 2008; Glenberg, 2008; Gomila & Calvo, 2008; Wilson, 2002; see also Chow, Davids, Hristovski, Araujo, & Passos, 2011). The VSF approach can help educators understand how to use context for learning and development: Manipulating context during instruction as outlined above could facilitate children's transition from novice to experts in particular domains (see also the idea of context manipulation for insight, Kounios, Fleck, Green, Payne, Stevenson, Bowden, & Jung-Beeman, 2008). It is interesting that the literature on instruction suggests pure discovery and programs with minimal guidance do not really work (Fyfe, McNeil, Son, & Goldstone, 2014; Kirschner et al., 2006; Mayer, 2004). While pure discovery has been thought to help children arrive at the relevant knowledge by themselves and so to promote better storage in long-term memory, surprisingly, guided instruction and direct instruction were found to work best (Kirschner et al., 2006; Stockard, Wood, Coughlin, & Rasplica Khoury, 2018). In other words, children need structured guidance to learn the content of a domain well (guidance that includes scaffolding in various ways; Hmelo-Silver, Duncan, & Chinn, 2007; Samarapungavan, Patrick, & Mantzicopoulos, 2011). Hmelo-Silver et al. (2007) pointed out two other interesting facts: (1) Just-in-time direct instruction is indeed needed from time to time in problem-based and inquiry learning; and (2) students learn more from a lecture after an initial exploratory problem-solving phase. On the one hand, the VSF approach can help clarify the idea of “just-in-time” (Hmelo-Silver et al., 2007) for certain methods in education (Kirschner et al., 2006). The differential need for guidance (i.e., different amounts at different moments of teaching (Hmelo-Silver et al., 2007) can be linked to the child's current VSF state and the passage from one state to another: A lot of guidance is needed when the child is variable, less and less guidance when stable, and only some hints when flexible. This may be why the current literature offers contradictory results: Children may have been in different states, states that were not evaluated in the respective studies. Knowing a child state or whether he or she is at transition from one state to another is helpful because intervention seems most effective at transition points (Thelen, 1995): Just in time can become a known moment in time for when to provide direct instruction, for example when passing from variability to stability. On the other hand, the initial exploration (Hmelo-Silver et al., 2007) helps motivation and attention tuning, but then direct guidance is needed so that the system acquires the relevant knowledge of a domain. After a child reaches stability, guidance can become more and more subtle; and when the child is flexible, the cognitive system can search with less help for new solutions. The role of instruction-by-exploration is to foster curiosity about the domain, similar to a young child's curiosity about learning the names of objects or how toys work. This curiosity then leads the child to keep learning the content of that domain, more than when educators begin directly with targeted teaching; and this may be why learners benefit more from a lecture after initial exploration. We can speculate then that variability is also important for
Table 1 Children's states, instruction and its effect on passing from one state to another. Children's state
Instruction Effect of instruction
Variability
Stability
Flexibility
(not knowing a domain; not well-functioning parameters yet; not tuned to context)
(knowing the domain; well functioning parameters tuned to typical contexts)
(going beyond known paths in a domain; well functioning parameters sensitive to contextual changes)
Free exploration/Guided instruction in typical contexts Motivation Potential discovery of the solution
Guided instruction in typical, close-totypical contexts and new contexts Solid knowledge base Apply known solution to new, close to typical contexts ⇒Pass to the flexibility state
Exploration in new contexts guided by previous knowledge
• • known ways of solving the • Acquire problem
• •
⇒ Pass to the stability state
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Find new ways for solving the problem ⇒ Transform this state into a new stability state or enter a new variability state for new knowledge in the domain
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fostering motivation for a domain. In sum, each state is equally important, and in education each state needs to be addressed differently to promote optimal learning. This idea is supported by new studies in brain research: On the one hand, the conceptual distinctions employed in psychological studies might not represent the mechanisms the brain uses when processing information (Eldar, Cohen, & Niv, 2013; Miller & Fusi, 2013; Spencer & Buss, 2015; Stokes et al., 2013). As a consequence, researchers should focus on the dynamics of processing and not on fixed processes. On the other hand, it seems that the brain functions optimally near a critical point (see the criticality hypothesis; Beggs, 2008; Pfeffer et al., 2018) that separates variability from stability in neural network activity. As such, to adapt education to how the brain learns, it might be necessary to change from models of information processing as distinct and separate mechanisms back to a model of the whole organism during learning (Gibson, 1994) and the states it is in while learning. Criticality is also a central issue in dynamic systems accounts (Chow, Davids, Hristovski, Araújo, & Passos, 2011) as a phase in which the system is more apt to change to new behaviors. By differentiating variability and flexibility based on developmental arguments one could better understand change during learning: Change is triggered by different instructional methods in the states before and after stability and this might have important consequences for teaching.
is already present in nonlinear pedagogy (Chow, 2013; Chow et al., 2011) especially in motor learning, but again there it is based on two states, instability and stability. Inserting flexibility brings further clarifications. For example, Chow et al. (2011, p. 25) stated that “more options need to be created for advanced learners and fewer options for novice learners.” “More options” are easy to handle after a phase of stability, akin to using new contexts for the system to pass to flexibility; “fewer options” are good in the variability state and it is similar to the idea of instructing children in the typical context until they acquire knowledge in a domain. Thus taking a three-state view helps explain the seemingly contradictory results in the literature: that sometimes new contexts help but sometimes not (Chow, 2013). One prediction that follows is that learning needs different constraints in the variability and flexibility states even if both states can be described as unstable states (i.e., in which the search for solutions is high) and both then take the system to a stability state (i.e., after flexibility, if the new way of solving a problem becomes a regular strategy the system can be considered to have entered a new stability state). Second, this approach may be of help in the application of the concept of the zone of proximal development (ZPD) in education. The ZPD refers to the gap between what a child can do by him- or herself and what the child can do only with help from a more knowledgeable person (Schaffer, 2004; Vygotsky, 1978). It has been suggested that teaching children in this gap helps them progress better than when the focus is on what they know (assignments that are too easy) or well beyond what they know (assignments that are too difficult; Schaffer, 2004). This kind of teaching is so far just an ideal in education, because it is truly difficult to work individually with each child in a classroom of 30 children and to address their learning potential individually. The VSF perspective can help educators get closer to the ideal of ZPD: If one groups children according to the three VSF states, then teaching focused on three groups is easier than teaching each child individually. Call it three-state ZPD. When using the VSF approach to evaluate the threestate ZPD, one can appreciate the level of the child and tailor the instruction to the child's needs so that he or she can pass to the next proximal state; the result of using this approach is a classroom divided into three groups, which is much easier to handle than addressing each child individually (see also Winner, 2012, pp. 75–81). This approach can then help teachers avoid unproductive situations in which the instruction does not fit the child's current state, such as offering interesting new contexts for particular content to a child in the variable state who is not yet ready to learn new ways to solve problems. A third insight that follows from the previous ones is that the VSF approach may in fact help integrate ideas from two main traditional theories, namely, those of Piaget and Vygotsky. Oftentimes, these two theories are treated as, if not opposite, at least separate theories in developmental studies and in education (Poole, Warren, & Nunez, 2007; Schaffer, 2004). For example, the Piagetian child is oftentimes considered as learning by him- or herself and constructing his or her own development by actively manipulating information, while the Vygotskian child is embedded in culture. More importantly for the current topic is that Piaget talked about recurrent passages from disequilibrium to equilibrium in the development of intelligence and Vygotsky stressed the idea of individualization by coining the notion of ZPD. However, when taking a VSF perspective one can easily integrate these latter ideas: One can reach a deeper understanding of the passage from disequilibrium to equilibrium, because disequilibrium before and after equilibrium are not the same. At the same time, the VSF approach stresses individualization according to the three described states. As such, this approach stresses both regularity—the recurrent passage through the VSF states—and interindividual differences. This can help educators address differences between children more easily, by addressing differences between three main groups as change in learning a domain occurs. One must also consider the challenges of the VSF approach. The first challenge is to understand what level of variability is optimal for good
4. The promises and challenges of the VSF approach applied to instruction Using the VSF approach to inform teaching is both promising and challenging. In terms of promise, there are several insights that differ from those derived from previous theories. First, a main idea is that not all instability is the same. This is important because different teaching strategies are needed for different kinds of instability to facilitate the passage from one state to another. In the literature on flexibility, some authors have argued that flexibility can happen without previous knowledge and even that previous knowledge can hinder flexibility (Defeyter & German, 2003; German & Defeyter, 2000; Gopnik et al., 2017; Yonge, 1966); others have argued that “true” flexibility emerges after one has a solid knowledge base in a domain (Bilalic, McLeod, & Gobet, 2008; Ionescu, 2017c). It is interesting to note that studies on experts have shown that up to a point, the knowledge base can indeed hinder the process of finding new ways to solve a problem, but after that point, it helps. Bilalic et al. (2008) found that “ordinary” chess experts had difficulties finding an unfamiliar and easier way to win a game, but “super” experts did this with ease. The authors argued that real expertise helps flexibility. One way to address this issue is to differentiate between the states before and after stability, namely, variability and flexibility. As a simple linguistic analysis can show, variability refers more to producing multiple ways to approach a problem, whereas flexibility refers more to bending or modifying a known way (Ionescu, 2017a). As such, those who argue that previous knowledge can interfere with problem solving may in fact be talking about the passage from variability to stability, whereas those who argue for the importance of knowledge may in fact be talking about the passage from stability to flexibility. Equally important it is to understand the nature of stability too: if a system just entered this state it might behave differently then after some time spent in this state (in other words if it is closer to variability or to flexibility). A corollary follows to further clarify the nature of flexibility: An important difference between variability and flexibility is the search for new perspectives with the purpose of going beyond stability. Specifically, whereas during variability the system just looks for a perspective in order to solve the problem, flexibility implies the knowledge of appropriate perspectives (i.e., the system is already stable) and the intention to change/adapt these so that new ways of problem solving can emerge. As shown in the previous section, context can then be used differently to help the system while learning. This idea 21
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stability afterward, and similarly how much stability an individual needs to reach flexibility. This understanding can be achieved only via experimental studies that change instruction little by little and follow children's progress. Linked directly to this, devising methods to investigate the passage from one state to another may prove difficult. My colleagues and I are currently working in the lab on designing some microgenetic studies to pinpoint these passages. An interesting question for future research is if there are knowledge thresholds that could make the transition of the system from one state to another more likely to happen. Another challenge will be to develop specific methods for teaching every domain in school according to the three-state ZPD: There may be specific difficulties particular to each domain. Finally, encouraging differences between children also means that because not all children will pass at the same pace through the VSF states when learning in a domain, they should be allowed to remain in a certain state in a specific domain. A second question thus follows: How does one know if a child cannot progress to the next state? In closing this section, I would like to emphasize the following idea: The type of context (typical vs. new) and the type of exploration (free vs. guided) should be adapted to the state the child is in. Several programs focused on improving creativity in children in schools have recommended free exploration as a means for achieving this. Yet so far, schools have not succeeded in optimizing children's creativity (Robinson & Aronica, 2009), which I believe is because focusing on free exploration keeps the child in the state of variability, whereas for flexibility a phase of stability is also needed, and this is based on more direct guidance. Variable children do not access the relevant knowledge of a field, or at least not by themselves in most cases. This is why guidance is needed. I would stress that in the state of stability, thorough understanding and repetition of content is needed for the cognitive system to acquire a solid knowledge base. It is from this knowledge base (i.e., a stable knowledge of a domain) that the system will be able to change, combine, and innovate, in other words, to become flexible and able to play with solutions (Prince, 2004). And this is more likely to happen if during instruction, knowledge is put explicitly in new contexts but only after it was well practiced in typical contexts. Future directions should thus aim at explaining exactly how the cognitive system passes from one state to another. If flexibility means that the system has the right parameters well tuned to context, then stability should represent a system with good parameters not yet well tuned to context, and variability a system without well-functioning parameters. This can be studied by following children's learning in a domain from t zero (i.e., baseline) to t flexible (i.e., flexibility) and charting the changes that occur on this path as a consequence of manipulating context. Furthermore evaluation instruments need to be devised so that teachers can easily assess the state of a particular child. Understanding the passage through VSF linked to sensitivity to context could ultimately take educators closer to being able to help children develop as whole systems connected to the environment (Sheya & Smith, 2018) and not as a puzzle of specific abilities or processes. In sum, I argue for the use of the VSF approach in education because it can guide educators to design appropriate constraints for children in these three states. In other words, identifying the state a child is in can help the teacher to design differential teaching but not for each child in a classroom but for three larger groups. The way a teacher can use context and also exploration and guidance would thus change according to the targeted state: The options a child is given may thus better be used by the child because he/she will be in the state-specific zone of proximal development for specifically that instructional method.
how flexibility develops, and second how it relies on stability. In this essay I have proposed a general framework that can then be adapted to learning in a domain, to help education promote the reconfiguration of the cognitive system into different states, so that children reach their full potential. Flexibility is the end state of a pattern of three states (VSF) and to foster it we need to understand the passage through all of them. And for this we need new theoretical approaches and new tools. Some authors have argued that there is a need for a new scientific language to understand the complexity of development (Oudeyer, 2016; Spencer, Blumberg, & Shenk, 2016); this may also be true for learning and instruction: Education researchers may need to look for new models that frame education in a way that more closely follows the dynamics of children's development. On the one hand, a new language means new ways of thinking that can then change instructional approaches. On the other hand, more than just a new language, the approach proposed here offers a viable middle ground between nonindividualized instruction (as is found in most schools today) and individualized instruction (which is so hard to achieve in general education; usually it is reserved for children with special needs, both negative and positive). More specifically, the VSF approach can help educators address differences according to the three VSF states—a good compromise between not addressing them at all and working individually. In addition, changes in context can be systematically used to help children move from variability to stability and to flexibility. Until now, most often teaching addressed variability (via exploration) and stability (via practicing known ways of problem solving). By not addressing the transit from stability to flexibility and by not acknowledging the difference between variability and flexibility educators cannot foster creativity and innovation. These two highly praised outcomes of learning can be reached only if all three states are considered—as they represent a natural passage during development—and then addressed differently. In some ways, this new approach might lead to a fractal-like view (Mandelbrot, 1983) of development and learning: The recursive reoccurrence of the VSF states might be a key to understanding the nature of learning and development. And what is more for education, this key can help teachers better address each child's potential. Acknowledgments The author wishes to thank Anita Todd for editing the manuscript; Bogdan Bucur for insightful discussions about patterns and their analysis; and three anonymous reviewers for very helpful comments. References Apperly, I. A., Samson, D., & Humphreys, G. W. (2009). Studies of adults can inform accounts of theory of mind development. Developmental Psychology, 45(1), 190. Barrett, L. F. (2017). The theory of constructed emotion: An active inference account of interoception and categorization. Social Cognitive and Affective Neuroscience, 12(1), 1–23. Barsalou, L. W. (2008). Grounded cognition. Annual Review of Psychology, 59, 617–645. Beggs, J. M. (2008). The criticality hypothesis: How local cortical networks might optimize information processing. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 366(1864), 329–343. Bilalić, M., McLeod, P., & Gobet, F. (2008). Inflexibility of experts—reality or myth? Quantifying the einstellung effect in chess masters. Cognitive Psychology, 56(2), 73–102. Braem, S., & Egner, T. (2018). Getting a grip on cognitive flexibility. Current Directions in Psychological Science, 27, 470–476. Carr, K., Kendal, R. L., & Flynn, E. G. (2016). Eureka!: What is innovation, how does it develop, and who does it? Child Development, 87(5), 1505–1519. Chow, J. Y. (2013). Nonlinear learning underpinning pedagogy: Evidence, challenges, and implications. Quest, 65(4), 469–484. Chow, J. Y., Davids, K., Hristovski, R., Araújo, D., & Passos, P. (2011). Nonlinear pedagogy: Learning design for self-organizing neurobiological systems. New Ideas in Psychology, 29(2), 189–200. https://doi.org/10.1016/j.newideapsych.2010.10.001. Clement, E. (2006). Approche de la flexibilite cognitive dans la problematique de la resolution de probleme. L'Année Psychologique, 106, 415–434. Clerc, J., & Clément, É. (2016). Metacognition and cognitive flexibility in transfer of learning. Metacognition: Theory, performance and current research (pp. 17–42). .
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