An ecological theory of learning transfer in human activity

Abstract

All theoretical approaches to learning transfer assume some form of similarity. Behavioral science has, however, conceptualised similarity in superficial terms. Furthermore, no transfer theory has been developed to account for the full range of skills deployed in operational or intellectual activities. Dynamical systems theory is, at its core, a similarity theory. We leverage from a dynamical systems account of human activity to outline a theory of transfer that views repeatable patterns of behavior as macroscale properties that emerge from interactions between microscale processes of perception, cognition, and action. Dynamic coordination’s constitute solutions to goal directed activity and as such, must be tuned to the affordance structure of the situation and to the capabilities of the agent. Learning transfer, defined as improved performance on a criterion activity from prior experience on another activity, is contingent on improved detection and use of crucial affordances because of that prior experience. We bring together arguments relating to similarity, behavioral dynamics, affordances, learning, and analysis at both macroscales and microscales to identify potentially transferable elements of authentic, multifaceted activities that demand an appreciable level of skill.

Keywords:

• Transfer
• cognitive theory
• dynamical systems theory
• ecological science

1. Introduction

Despite its centrality to a coherent understanding of how we adapt to the challenges and opportunities presented by a complex world, the conceptual understanding of learning transfer is fragmented and inconsistent with the range of experimental results now available. The only construct that has gained widespread traction is that of identical elements as proposed by Thorndike (1903). However, despite a substantial body of literature in which Thorndike’s theory of identical elements is noted, the nature of an identical element remains largely unspecified.

Learning transfer is the effect of experience with one goal-directed activity on performance of a different goal-directed activity. Transfer is positive if experience on the first activity results in better performance on the second activity, but negative if that experience results in poorer performance on the second activity. Transfer is zero when performance is neither enhanced nor degraded as a result of experience on the first activity.

We set our definition in contrast to that offered by Singley and Anderson (1989, 1) who commit to the nature of what is transferred: The study of transfer is the study of how knowledge acquired in one situation applies (or fails to apply) in other situations. We also set our definition in contrast to that implied within cognitive training research (see Gobet and Sala (2023) for brief summary) where, instead of something being transferred, a hypothesised capacity is strengthened (e.g. working memory, fluid intelligence). Our definition is consistent with that of Detterman (1993, 4), who makes no such prior commitment (Transfer is the degree to which behavior will be repeated in a new situation). Here we view transfer as an observable and measurable phenomenon.

Transfer is often discussed as it is relevant to knowledge transfer in education (Gorman and Goldstone 2022). Within that context, there is a question as to whether transfer exists (Detterman 1993), how extensive it is (Singley and Anderson 1989), or whether it is of sufficient prevalence and strength to be a worthy target of research (Barnett and Ceci 2002). If transfer is rare or minimal, then practicing an activity within the context it is to be deployed remains the most effective and possibly the only way to improve performance on any activity. Although this conclusion may appear both trivial and compelling, it contrasts with common belief and practice in education and workplace training.

Given the endless variation and complexity of normal human environments, it seems inconceivable that transfer does not exist in some form. The alternative is that we would be constantly challenged throughout our waking hours to learn and adapt to subtle variations in our circumstances (Thompson and Opfer 2012). Transfer involves both learning and performance and its understanding is fundamental to a coherent understanding of all comprehensive theories of human cognition (Sala, Tatlidil, and Gobet 2018; Singley and Anderson 1989). To that end, there is a crucial need for a robust theory of transfer that encompasses a full range of human learned activity.

In developing our theory of transfer, we will take note of principles and insights derived from laboratory research, much of which focuses on stylised cognitive tasks that minimise the roles of perception and action. We will, however, outline an account that is relevant to authentic, multifaceted tasks that demand an appreciable level of skill in one or more of perception, cognition, and action and their coordination. In their most comprehensive form, authentic, multifaceted tasks involve control via feedback loops, and adjustments to disturbances and variability in dynamic activity together with calibration of perception, cognition, and action parameters (e.g. as Mole et al. (2019) describe for driving).

2. Synopsis: towards a theory of learning transfer

In this paper, we forward six central claims (Figure 1).

Figure 1. Synopsis of the argument for an ecological theory of learning transfer.

• No current theory of learning transfer accounts for a comprehensive range of normal human activity. Theoretical efforts have been misdirected in that they focus on feature similarity and on constrained tasks that fail to account for crucial, often implicit elements of human activity. Furthermore, they fail to identify the challenging skill components that, if learned adequately during a training exercise, will induce transfer.

• In contrast to a focus on feature similarity, mathematics, physical science and biological science focus on relational similarity. They employ the constructs of symmetry and transformation, where a symmetry is a form that is preserved from one instance to another. A transformation can be specified that preserves the properties of the symmetry across instances as it allows other properties to change.

• Dynamical systems theory is a similarity theory in that it examines symmetries and transformations in dynamical systems.

• When applied to behavioral science, the symmetry specified under a relational similarity is a functional equivalence.

• The ecological approach pioneered by James Gibson forwards an affordance as a functional construct. Human activity systems as dynamical systems are constrained by affordances; that is, by environmental opportunities that match individual capabilities. Subsequently, effective action requires attunement of human activity systems to affordances.

• Dynamical systems analysis of goal-directed human activity will reveal the constraints of the environment, of the actor, and of the task that shape and guide the activity. That analysis should identify the actor-related activity elements that pose a significant challenge to the actor; those for which satisfactory performance requires new learning. Specification of those challenging elements should suggest appropriate training strategies. Once an actor learns those challenging elements, there will be a boost in that actor’s performance, which will be revealed in an appropriate assessment as positive transfer.

In the remaining sections of this paper, we elaborate on these claims to build a comprehensive theory of learning transfer.

3. Confounding issues

Three issues central to a coherent understanding of transfer have confounded discussion; a failure to appreciate that transfer is necessarily a result of appreciable learning, a failure to distinguish between functional and non-functional properties within a training-transfer scenario, and a failure to appreciate that on first contact with a challenging activity, those to be trained are already competent with many of its complex components.

3.1. Learning for transfer

At least some of the uncertainty as to whether transfer exists is due to the attention paid to transfer of analogical reasoning where the experimental protocol limits the pre-transfer experience to a single problem-solving trial (e.g. Gick and Holyoak 1980; Reed, Ernst, and Banerji 1974). Experimental participants are asked to solve a problem that has an embedded principle as the key to the solution. Transfer is said to occur if participants use that principle to help them solve a second problem. In the two cited studies, Reed, Ernst, and Banerji (1974) observed no transfer while Gick and Holyoak (1980) observed it only after advising the experimental participants of the principle. However, rather than being a test of transfer, this strategy of testing transfer after a single pre-transfer trial is better characterised as a test of generalisation.

These two studies are treated as foundational in discussions of transfer. This confusion of generalisation with transfer has served to divert discussion in unprofitable directions. Here, we view learning transfer as distinct from single-trial generalisation. Our goal is to understand transfer as a consequence of learning or experience. Notably, Chi, Feltovich, and Glaser (1981) showed that experts could generalise abstract principles to solve different physics problems, but novices could not. This result suggests that the experiments by Reed, Ernst, and Banerji (1974) and Gick and Holyoak (1980) might have demonstrated worthwhile transfer if their experimental participants had been given some experience with the tested principle. More recent research has demonstrated that transfer can be achieved by use of more extended instruction of principles (Goldstone, Landy, and Son 2010; Kellman, Massey, and Son 2010; Kellman et al. 2008; Son and Goldstone 2009). An experimental test of transfer should, at a minimum, induce some worthwhile degree of learning in the pre-transfer phase of the experiment.

3.2. Transfer is not a fidelity issue

A second, related issue is that there has been a misconception about the nature of similarity as it applies to transfer. The most pervasive idea is that of identical elements as introduced by Thorndike (1903):

a change in one function alters any other only in so far as the two functions have as factors identical elements. The change in the second function is in amount that due to the change in the elements common to it and the first. [page 80]

Thorndike’s theory is generally interpreted in quantitative and featural terms. For example, Sala et al. (2019, 3) read it as proposing that transfer is directly related to the degree to which the source domain and the target domain share common features. This interpretation can be seen as representing a fidelity view: the greater the fidelity, the better the transfer. Transfer will be 100% when the pre-transfer experience is identical to the transfer experience; that is, there are no missing or superfluous features (elements) in the source domain in relation to the target domain.

Thorndike’s view on this matter (Thorndike 1903, 1922; Thorndike and Woodworth 1901) remains unclear. He does, however, allow that elements can be differentially weighted in their impact on transfer (Thorndike 1922) thereby allowing an interpretation that maximum transfer can be achieved in the absence of identity (full fidelity) between learning and transfer. Nevertheless, there is no possibility that pre-training on a somewhat different activity could result in better performance on a criterion activity than equivalent pre-training on the criterion activity itself. In Thorndike’s words, any disturbance whatsoever in the concrete particulars reasoned about will interfere with reasoning, making it less correct or slower or both (Thorndike 1922, 33). For transfer in general, this conclusion is false. Some manipulations of a training activity that make it less like the transfer activity can induce better transfer (e.g. Cheung et al. 2021; Lintern 1991).

Beyond the empirical evidence, there is a conceptual problem with a fidelity interpretation of Thorndike’s identical elements view. Common elements are not distinguished on the basis of functionality, thereby allowing both functional and non-functional elements to support transfer. Those who have discussed transfer in conceptual or theoretical terms have generally erred in failing to stress the functional nature of elements that support transfer (although, see Norman, Dore, and Grierson 2012).

The associated learning that is the basis for transfer is in the recognition of and the activity in use of a crucial function. For example, a light aircraft has functional features with respect to flight control (e.g. aerodynamic response) and nonfunctional features with respect to flight control (e.g. color of fuselage). The flight student who is learning to land that aircraft must learn to cope with the aerodynamic response but is not concerned with color of fuselage. Similarly, in healthcare, a wound suturing simulation should represent tissue resistance at high fidelity but not necessarily tissue color or shape (Norman, Dore, and Grierson 2012).

3.3. Current competency

Another concern in discussions of transfer is the general failure to distinguish between functionally related activity that must be learned versus functionally related activity that, although complex, is already well learned. For most human adults, a complex task will include a mix of elements that pose different learning challenges. Even a task that demands intensive learning to achieve competency will generally include a subset of elements that require little or no learning. It is improved competency with the more challenging elements, many of which are implicit and cannot easily be described, that will induce a measurable transfer effect. Pretraining directed at helping students learn to recognise and calibrate those elements should benefit transfer. More generally, discussions of transfer need to focus attention on those functional elements of an activity that pose a learning challenge for the student at that time.

3.4. Summary; confounding issues

In summary, any theory of transfer must, at a minimum, focus on functional properties. Furthermore, any experimental paradigm employed to demonstrate transfer must allow sufficient practice or experience with those specific functional elements of the activity that are responsible for any less-than-capable performance.

4. Similarity: psychological science

It seems indisputable that, at its core, transfer is based on some concept of similarity. Different cognitive science programs have sought explanations of transfer in diverse hypothetical constructs. Motor-programs (Schmidt and Young 1987), rules (Gick and Holyoak 1987), instances (Gonzalez, Lerch, and Lebiere 2003; Gorman and Goldstone 2022; Logan 1988), chunks (Simon and Chase 1973), and stimulus-response mappings (Madhavan and Gonzalez 2010) have all seen service. In addition, several different types of cognitive capacities are promoted in cognitive training research (e.g. see Gobet and Sala (2023) or Lintern and Boot (2021) for brief review). Although Thorndike (1903) offered examples of transferable elements, it is hard to abstract a common theme from those examples in terms of the concepts of contemporary psychological science. There is no persuasive evidence that any of these constructs can support a general theory of transfer.

Singley and Anderson (1989) sought to resolve this issue by proposing that the transferable elements are productions as defined in ACT* theory (Anderson 1987), where ACT initialises the phrase, Adaptive Control of Thought, and * signifies a development of an earlier version of the theory (Anderson 1982). ACT* theory treats cognition as a system that interprets facts about a domain of activity as propositions which, after being compiled into productions, become more skillful, more autonomous, and more selective in their range of application. Taatgen (2013) follows a similar approach but argues for a more fine-grained analysis in which productions are decomposed into primitive information processing elements.

Production system theory assumes competence with existing percepts, concepts, and coordinations. Because those elements must be developed in a learning process that offers substantive challenges, they are likely to contribute to transfer. ACT* theory does not account for that learning. The detailed exposition of ACT* theory offered by Anderson (1987) clarifies its limited scope. In the first stage of skill acquisition, the declarative stage of ACT* theory, the learner encodes information about a skill as a set of facts, which are then interpreted to generate behavior. The declarative stage of ACT* theory is an interpretation of a cognitive phase of skill learning as described by Fitts and Posner (1967, 11):

Whether left to his own device, or tutored by an experienced instructor, the beginner in most adult skill-learning situations tries to ‘understand’ the task and what it demands. A good instructor will call his attention to important perceptual cues and response characteristics and give diagnostic knowledge of results. He may also shape behavior by calling ‘good’ any sequence of acts that at all resembles the correct one.

In that this process starts with information that can be recognised and interpreted and also involves the sequencing of known action units, ACT* theory does not account for development of new concepts or new perceptual discriminations. Nor does it account for development of action patterns that are beyond verbal description.

ACT* theory does not, for example, account for the perceptual learning that enables a student pilot to develop the discriminatory power to identify and calibrate the information that can be used to guide a light aircraft along the desired descent path towards the runway aim point. Notably, Fitts and Posner (1967) set their description of the cognitive phase of skill learning within the context of flight instruction. However not all flight instructors can explicitly specify the information that is used to guide a light aircraft along a glideslope and even if a student’s attention is drawn to that information, that student must progress through an arduous learning process before being able to discriminate the values that specify high versus low on the glideslope (Langewiesche 1944). Similarly, ACT* theory does not account for the perceptual discriminations developed in educating the palate for wine tasting or the pattern recognition skills developed in radiology. On the action side, it does not account for the establishment of the coordination pattern that enables a well-controlled and powerful backhand stroke in tennis, the development of juggling competencies, or the development of manipulative skills for laparoscopic surgery.

5. An information theory of transfer

In a break from transfer theories that focus on cognitive operations, Lintern (1991) argued that the transfer effects observed in the manual control literature arise from enhanced sensitivity to perceptual invariants as defined by Gibson (1979). A perceptual invariant is an information property that points to a critical relationship in the activity environment. Such a relationship has a specific value that remains invariant if an activity proceeds as desired but changes value when the activity drifts off target. More generally, events are perceived as similar if they have a common property with a value that remains constant between them. Events will be perceived as dissimilar if the value of that property changes. Thus, an invariant is a property of an event that remains unchanged as other properties change; that which specifies the persistent character of the event (Gibson 1979).

The phenomenon of biological motion perception illustrates the power of invariants. Biological motion perception refers to the ability to apprehend the nature of organised activity from the dynamic relationships between approximately ten points of light attached to the major joints of the body of a person. Johansson (1973) has demonstrated that observers can recognise the activities of walking, running, and dancing from just the relative motions of this sort of point light display, and Mather and Murdoch (1994) have demonstrated that observers can recognise gender of the actor from similar displays. The information that supports these judgements is found in the relative motions of the lights; a stationary display carries no meaning and is not recognised as related to a human body. These dynamic relative motions establish a similarity (a characteristic pattern) that is meaningful to a human observer.

The information theory of transfer (Lintern 1991) proposes that skill learning involves developing the ability to recognise and calibrate those perceptual invariants that are unfamiliar to the learner. In landing a light aircraft, for example, the pilot is guided along the planned descent path to the runway by the angle subtended at the pilot’s eyes between line of gaze to the horizon and the line of gaze to the runway aim point (Lintern and Liu 1991). This angle remains invariant as a pilot follows the correct descent path but changes value when they drift high or low. Initial inability to track the glideslope is thought to be the primary reason that beginning flight students have considerable difficulty in learning to land (Langewiesche 1944). More generally, transfer results from improved facility with perceptual invariants that are crucial for competent performance.

6. From information to function

Although worthwhile transfer can result from developing skill with information patterns (Lintern 1991), information used skillfully in performance of one goal-directed activity is not necessarily available for skillful use in a different goal-directed activity. For example, Infants who will not reach over a risky gap when in a familiar sitting posture will reach over that same risky gap when in a less familiar crawling posture (Adolph 2019). Adults, whose potential capability (i.e. reach, passing through an aperture) is modified by use of a stick, are more accurate at reporting the new capability than they are at reporting the length of the stick (Thomas and Riley 2014). From this we conclude that a focus on information in a scenario with limited dynamic interaction involving cognition or action does not provide an adequate test of transfer for theory development. Furthermore, the research described by Adolph (2000, 2019) and by Thomas and Riley (2014) suggests that the general strategy for satisfying a goal with available resources is to assemble a functional configuration of activity.

A move from information to function offers a distinctively different conception of the nature of similarity and of transfer. The distinction is consistent with the more encompassing distinction between ontology and epistemology; a concern with the structure of our surround versus a concern with how we abstract meaning from it (Figure 2). Most generally, in relations between anatomy and physiology, syntax and semantics, structure and function, and information and affordance, ontological distinctions are based on features while epistemological distinctions are based on function. Transfer theories to this point have been constructed at the ontological level of explanation. Here we propose an epistemological theory of transfer that takes account of the functional significance of information in the execution of authentic, multifaceted activities that involve perception, cognition, and action in varying combinations.

Figure 2. Ontology versus epistemology offer distinctively different perspectives on the nature of similarity.

In building our argument, we will work through conceptions of similarity as used in scientific endeavors outside of behavioral and social sciences. We will then converge on an appeal to the roles of affordances (Gibson 1979) and behavioral dynamics (Warren 2006) in development of a functional approach to learning transfer.

7. Similarity: beyond psychological science

Rosen (1988) has argued that similarity is a universal scientific concept, providing diverse and insightful interpretations in relation to organisation in formal and natural systems. Ifenthaler (2012), in a brief review of similarity for learning, summarised distance, feature, and probabilistic similarity where distance similarity applies to continuous dimensions (e.g. colors, loudness of tones), feature similarity applies to objects with many distinctive features (e.g. faces, countries), and probabilistic similarity accounts for attributes that vary over time (e.g. salience). Although Ifenthaler observed that the concept of similarity is widely used in almost every scientific field, he neglected to consider conceptions of similarity as used in other sciences, continuing to focus on feature similarities that reside at the ontological level of description.

Here we will argue that ideas found in other sciences have implications for a theory of transfer through their significance to coordination dynamics and self-organisation. By way of working into that argument, we will draw lessons from concepts of geometric, allometric, and dynamic similarity and associated concepts of transformation and symmetry. Following Feynman (1967), a symmetry is a repetition whereby a property or group of properties is preserved under a specified temporal or spatial transformation. A symmetry is thereby a pattern or organisational form that repeats even while other elements of the situation change.

7.1. Geometry

Geometry is the branch of mathematics concerned with the properties and relations of points, lines, surfaces, and solids. In a thesis now widely referred to as the Erlangen Program, Klein (1893) expressed the idea that diverse geometries could be distinguished by reference to the types of transformations that maintain some properties as similar while allowing other properties to change. High school students engage with a portion of this approach as they work with the congruent and similar figures of Euclidian geometry. Congruent figures maintain size and shape under rotation or reflection (transformations that result in different orientations), in which case, it is said that size and shape symmetry are preserved under those transformations. Similar figures maintain shape (but not size) under rotation, reflection, or dilation; that is, shape symmetry is preserved under those transformations.

Other geometries not typically encountered in high school can also be classified in terms of symmetry under transformation. Affine geometry, for example, allows preservation of parallelism under a shear transformation whereby, for example, a parallelogram remains a parallelogram while a rectangle converts to a non-rectangular parallelogram. Topology is a geometry in which properties are preserved under stretching, twisting, crumpling, or bending but not under tearing or meshing. As is clear from these examples, geometric transformations do not preserve identity but rather, preserve partial identity under a specified class or group of transformations.

7.2. Allometry

Allometry is the study in physical and biological systems of the relationship between size of parts in relation to size of the whole where, to maintain function, certain scaling relationships are maintained across systems of similar form but of disparate size (Thompson 1917). To illustrate, structural supports of a bridge must be scaled up to maintain overall strength (function) if the form of the bridge is modelled on a smaller exemplar. The same principle applies to biological forms. Thompson (1917) was concerned with recurring patterns across change in biological systems, which he discussed in terms of a Theory of Transformations (see, especially, his chapter XVII).

The allometry of locomotion examines the effect of body size, body mass, and limb structure on the kinematics and dynamics of gait patterns. Alexander (1984) has argued that quadrupeds of different sizes and masses, traveling at a velocity specified by the same Froude number, exhibit similar gait patterns. In this context, the Froude number is a dimensionless ratio that scales speed to the accelerative force of gravity and to selected physical dimensions of the animal under analysis. This relationship constitutes a dynamic, self-organising symmetry; animals of similar form but of different size tend to move in a dynamically similar fashion whenever they move at similar speeds as normalised by the Froude number. Allometric investigations can inform us about the mechanisms responsible for recurring patterns across different biological systems.

7.3. Self-organisation

The science of self-organisation studies the emergence of patterns (sometimes identified as order parameters) at a macroscale in response to dynamic interaction of symmetry-breaking selection mechanisms that act at a microscale. The natural gaits of quadrupeds are illustrative; a gait pattern offers a low-dimensional, macroscale description that finds an explanation via a high-dimensional description of interaction and coordination at a microscale.

Also noteworthy is the transition sequence through gaits of walk, trot, canter, and gallop as the quadruped increases its speed (where speed acts as the control parameter). The gait transition (a non-linear, symmetry-breaking transition) occurs naturally, with the many degrees of freedom at the microscale converging on a new coordination mode that becomes evident at the macroscale. The new mode settles into a stable pattern as a result of the natural dynamics of the system; the mass of the quadruped body and its limbs, the flexibility of its joints, the force exerted by its muscles, the elasticity of its tendons, etc.

The different coordination modes are emergent patterns (Lintern and Kugler 2022) that optimise the relationship between effort and production (i.e. speed) and can thereby be characterised as comfort modes. As consistent with Warren (2006), the term emergent is used here and elsewhere in this paper in the technical sense of an organised pattern of behavior as generated by the dynamic interaction between underlying processes described at the microscale rather than by realisation of a preexisting plan or by reproduction of a preexisting image (Guastello 2017; Kugler and Turvey 1987).

Following Prigogine and Stengers (1984), locomotory gaits can be viewed as dissipative structures; patterns created from the changing balance of forces as induced by flows of energy through the system. Dissipative structures are forms of order that emerge via non-­linear state transitions when energy flows exceed the dissipative capacity of an existing structure (i.e. in this case, current gait). They emerge as a result of the instability produced in existing structures by those higher rates of energy flow. Both the new form of order and its underlying dynamics are dissimilar to the original, but these patterns repeat over instances and between quadrupeds. In this respect, self-organisation can be characterised as a theory of similarity (Rosen 1988).

7.4. Behavioral dynamics

This interpretation of self-organisation motivates a search for the dynamical laws that determine stability or instability of patterns that represent a similarity. Warren (2006) has undertaken such a search on the way to developing a theoretical framework he identifies as behavioral dynamics. His framework integrates an information-based approach to perception with a dynamical systems approach to action. An agent and an environment are treated as a pair of dynamical systems, coupled forcefully and informationally. In a later section of this paper, we will elaborate on how this theory of behavioral dynamics provides a foundation for a theory of transfer.

8. Similarity: interim summary

Our cursory introduction to similarity has revealed a number of ways in which it is treated differently in many other sciences in contrast to how it is generally treated in psychological science.

8.1. Similarity is relational

The similarities generally discussed in psychological science reference localised entities; either quantitative dimensions or patterns found in real objects or hypothetical constructs conceptualised in the image of real objects (e.g. Ifenthaler 2012; Medin, Goldstone, and Gentner 1993; Simon and Chase 1973; Tversky 1977). Similarity may be conceptualised more generally as psychological similarity but operationalised by reference to properties such as distance (Gorman and Goldstone 2022). In contrast, the similarities found in geometry, allometry, and dynamical systems theory are globally emergent of relational interactions between underlying constraints; they do not exist as individual properties. Their existence is non-local, having a field-like character, and are transient, existing only when the forceful and the informational constraints are active.

8.2. Similarity as described at a macroscale is non-Representational

The standard psychological science approach instantiates similarities as plans, models, images, patterns, chunks, or features. Transfer is enhanced to the extent these can be established and strengthened in pre-transfer to then be transported across the ­learning-transfer divide. Identical elements (Thorndike 1903) or productions (Singley and Anderson 1989) for example, are the entities that might be transported from learning to transfer.

Within the science of self-organisation, similarity is conceptualised in terms of the action of the dynamical laws that determine stability or transitional instability (Rosen 1988). For a transfer theory based in behavioral dynamics, the desired form of behavior is re-created within each event. What is transferred is not a representation or image but rather, a competency that is constituted by the tuning of the underlying dynamics that generate the desired behavioral pattern. As with the establishment of gaits of quadrupeds, the microscale processes responsible for pattern emergence in a dynamical system do not contain anything like a representation of the functional pattern either in isolation or as a constellation.

The lesson for transfer theory is that, although we are concerned with the organised activity that emerges from the action of dynamical laws, we need to attend at the microscale to how those dynamical laws are instantiated in both the learning and transfer phases of our research and in our training programs. For instructional purposes, we need to identify at the microscale what we can strengthen or change that will establish and stabilise the desired macroscale form (the symmetry) of the intended activity.

8.3. Symmetry under transformation; force and information

The Erlangen Program is held in such high repute partly because, in formulating it, Klein (1893) introduced the concept of transformations that would preserve the symmetry of selected geometric properties as other properties changed. Thompson (1917) emphasised forces that preserve symmetry in the face of change, distinguishing them from symmetry-­breaking forces responsible for distinctive features of physical systems. Note, however, the different roles for force and information in the different disciplines. Geometry is a formal system and as such, force and extrinsic information play no role. Thompson’s theory emphasised the role of extrinsic forces. A theory of transfer as informed by Warren’s (2006) theory of behavioral dynamics will explore the roles of both force and information as they are responsible for symmetries as emergent behavioral patterns.

9. Similarity as functional invariance

Our argument in this paper rests on a claim of similarity as functional invariance. We turn to an example of a chess endgame, adapted from Jim’s Chess Channel (2013, Feb 20), to clarify the distinction between functional and non-functional similarity.

Figure 3 shows four variations on an endgame in which White retains a pawn with king while Black is reduced to king only. White has advanced their remaining pawn from rank 2 to rank 4 and will continue, in successive moves, to advance it to rank 8 with the goal of promoting it to a queen and then deploying that into general play. White will win if successful. For Black, a draw is the best possible outcome. Black has the next move and will pursue the white pawn with intent of capture before White can deploy their new queen. For example, the configuration shown in Figure 3c allows the black king to proceed along a diagonal to reach c7 immediately following the move of the white pawn to b7. Although White can now advance their pawn to b8 and promote it to a queen, Black will capture that queen in the next move. In contrast, the configuration shown in Figure 3b allows White to advance their pawn to b8, promote it, and then deploy it before Black can capture it.

Figure 3. Variations on an end game in which White retains a pawn with king while Black is reduced to king only, also showing a virtual window of vulnerability for the white pawn in relation to the black king.

Figure 3 also shows a virtual window of vulnerability for the white pawn in relation to the black king. This window of vulnerability, currently anchored by the white pawn at b4, is a square with size defined by the move-distance to rank eight for the white pawn. This square will shrink accordingly with every advance of the white pawn. Unless the black king can step into this virtual window of vulnerability, it will be unable to capture the new white queen. By reference to this virtual window, both players should be able to foresee the outcome of the game at a glance.

The virtual window of vulnerability identifies a functional invariance. Such an interpretation pairs panels c and d as similar (both allow capture of the new white queen) and also pairs panels a and b as similar (neither allows capture of the new white queen). In contrast, chunking theory (Simon and Chase 1973) would likely classify the four configurations shown in Figure 3 as distinctive while a feature theory (e.g. Tversky 1977) would likely classify panels b and c as similar and panels c and d as dissimilar. Perceptually, the black king might seem to offer the greatest threat to the white pawn in panel a, but functionally, it offers no threat. The reverse is true for panel d.

10. Affordances and information

For the purposes of transfer theory, a function is an opportunity to achieve a desired outcome with activity of a certain type or, in ecological terms, an affordance (Adolph 2019; Gibson 1979; Reed 1996; Thomas and Riley 2014; Wagman et al. 2013). As an opportunity to pursue a goal, an affordance constitutes a relation between agent and environment. It is a reciprocal relationship in that information about an affordance guides activity while activity generates information about an affordance. Transfer rests on an improved ability to identify and use affordances to satisfy a goal.

If an affordance is to be useful, the agent must establish a relationship with it (Reed 1996). To allow that, an affordance must provide information that announces its availability and reveals how it can be used to satisfy a functional goal. Use of an affordance constitutes a solution to a goal-directed activity. Information invariants guide the agent to a stable solution, help the agent refine and sustain a solution, guide the agent through transitions to a new solution for new circumstances, and guide the agent back to a solution that has worked in the past for functionally similar problems. Prospective, occurrent, and retrospective information combine in various, nuanced ways to assist the agent in finding, tuning, and sustaining a solution and in re-invoking it within a future event (Reed 1996).

Some resources offer multiple affordances. A sidewalk, as a surface of support, offers opportunities for standing, walking, and running. However, generalisation to other similar resources will not always be complete. As a surface of support, a frozen lake surface offers opportunities for standing, walking, and skating but, because of its low surface friction, not for running. Resources must, of course, be scaled to the properties and capabilities of the agent if they are to serve as affordances. A thin, brittle sheet of ice on a lake will not bear the weight of an adult person and thereby does not provide any support-based affordances. Furthermore, while prospective information will generally guide an agent to an affordance, that is not always the case. For example, it may be possible to confirm the efficacy of a frozen lake surface as a load-bearing surface only by way of occurrent information and at some risk.

An affordance does not require a process of associatively linking recognition and action (Adolph 2019); all that is required is a motivated agent who can recognise the situation and who has the capability to use it to advantage. For example, the virtual square of vulnerability is not learned as an independent pattern which then has a move sequence attached to it to form a production (a condition-action pair) as described by Simon and Chase (1973) for chunking. The virtual square of vulnerability is a relational property. It exists in the form shown in Figure 3 only because the white pawn is threatened by the black king. A threat from any other piece would create a vulnerability of a different form. A player learns to recognise the pawn-king virtual square of vulnerability as presenting a functional ­perception-cognition-action opportunity when exposed repeatedly to game situations that present such opportunities.

Affordances are both functionally flexible and functionally specific (Reed 1996). They are not drawn from a library of fixed solutions (Adolph 2019) as are chunks, for example. Although an affordance does not constrain a solution to a single, tightly specified trajectory, it does limit what is possible. Reflecting on the vulnerability affordance depicted in Figure 3, flexibility is shown by the fact that Black can capture the new white queen from any position that allows their king to step into the white pawn’s square of vulnerability. Specificity is shown by the fact that that Black cannot capture the new white queen from any of the many other positions on the board. Furthermore, that flexibility and specificity can generalise between situations. This vulnerability affordance, for example, can take on different dimensions, be situated in different locations, and support different tactics depending on available pieces and their configuration (e.g. see The Chess Website 2022).

Specificity and flexibility develop from an agent’s familiarity with the functional nature of materials and opportunities as has been gained by extensive, routine engagement with diverse situations. Ultimately, the agent is seeking to assemble a functionally specific activity that is attuned to the specific demands of the situation. Subsequently, we should anticipate that transfer resulting from learning to recognise and use an affordance can be both functionally flexible and functionally specific.

To enhance transfer in a training program, we need to identify affordances that are crucial to the task but not yet under full control of the trainee. We then need to focus instruction and learning on those affordances.

11. Behavioral dynamics

The theory of behavioral dynamics, as developed by Warren (2006), addresses how the many degrees of freedom within the behavioral system can assemble temporarily into an ordered, functional pattern as shaped by physical forces, information, and task constraints associated with goals. Stable behavioral solutions (symmetries) emerge from the interaction of an agent with affordances; those opportunities that constitute a match between essential resources and an agent’s perception-cognition-action capabilities (Reed 1996). The symmetries (the stable solutions) offer a macroscale description of activity while the invariants of perception, cognition, and action offer a microscale description of that activity. Within dynamical systems theory, these stable solutions are identified as attractors (Abraham and Shaw 1983). In psychological science, they might be termed comfort modes (Kugler and Turvey 1987) or settling modes.

An activity environment may present an actively engaged agent with a complex affordance structure that supports multiple stable solutions and presents multiple obstacles. Such an activity environment can be represented as a layout of attractors and repellers (Guastello 2017; Warren 2006). Gradient fields represent the force of attraction or repulsion as a relaxation rate (Warren 2006). The behavior resulting from a decision point, where an agent may choose one of multiple available attractors, can be understood as a bifurcation (Warren 2006). The decision point may be represented as a saddlepoint (Guastello 2017) with mutually orthogonal attractor and repeller forces.

Information as provided by perception of invariants is critical for the agent to discover, select, and tune a stable solution and to then establish that solution for reuse in functionally compatible situations. In early encounters with a problem, an agent may be guided into the proximity of a stable solution (the region of the attractor field) by meaningful appraisal of the opportunities presented by the affordance structure. That appraisal may be informed by prior functional experience, or by guidance from a coach. The agent may test likely possibilities and then tune the dynamical properties of their own activity system to the selected opportunity.

In physical theory, a self-organising dynamical system can be nudged out of its stable mode by a force perturbation. In behavioral theory, information perturbations dominate. An agent can be induced to transition out of a stable mode and into the search for a different solution by their general dissatisfaction with the progress of events as triggered by ongoing feedback. A transition might also be precipitated by a change in the affordance structure that results in some opportunities and resources becoming unavailable or other more desirable opportunities and resources becoming available and evident.

In dynamical systems theory, transitions between dynamical modes (e.g. modes of quadruped locomotion) are precipitated by symmetry-breaking instabilities (Prigogine and Stengers 1984). For goal-directed human action, a sequential activity can be viewed similarly. It can be characterised as a sequence of demands whereby the agent must proceed through a series of solution states (e.g. execution of aircraft cockpit procedures as guided by a checklist). Each successive solution state satisfies the demands at that point with transitions between steps being induced by transitions in immediate goals accompanied by symmetry-­breaking perturbations in the information field as one constellation of demands and affordances gives way to another.

Although cognitive theories focus on the role of information in shaping behavior, a dynamical systems approach demands proportionate attention to the role of physical forces. To illustrate, time-to-contact (an information invariant) is said to be an important control parameter for collision avoidance, but whether or not time-to-contact specifies a functional property in a situation depends on the dynamic response of the control system (Stanard et al. 2012). Time-to-contact is an influential control parameter in many natural systems because those systems, when in motion, obey the laws of inertial dynamics. However, virtual systems need not obey those same laws. More generally, a similarity theory for transfer inspired by dynamical systems theory must take account of both the information and the forces (as described at the microscale) that preserve functional symmetry under a training-­transfer transformation. In many cases, an actor will have to become attuned (via learning) to the essential information and forces. That improving attunement will reveal itself as enhanced transfer in an appropriate assessment.

12. Affordances, behavioral dynamics, and transfer

Four constructs play a central role in this theory of transfer:

• An affordance, as a relationship between agent and environment, presents an opportunity to satisfy a goal.

• Most generally, a symmetry is a form or function that repeats across situations. For a theory of transfer, a symmetry is a solution (a functional pattern of activity) that can be assembled and reassembled as a functional equivalence for use in diverse but relevant situations. A symmetry is assembled in use of one or more affordances.

• In natural language, a transformation is said to generate radical change. In geometry and science, a transformation preserves the invariance of a specified relationship (i.e. a symmetry) while allowing change in other properties. The relationship held invariant defines the transformation.

• A dynamic system is one that changes as a result of rate-dependent processes. Some cognitive operations can be viewed as rate independent (e.g. the solution to an arithmetic problem is not influenced by the speed of the calculation) but here we take rate independence as a limiting case within an otherwise largely rate-dependent system.

The theory of behavioral dynamics has agents interacting with their environment by establishing and re-invoking coordinated, dynamical patterns as stable solutions. These stable solutions constitute the symmetries that may be learned and refined and then transferred to other relevant situations. The virtual window of vulnerability for chess, as shown in Figure 3, offers an evocative illustration of how transfer can work. This window of vulnerability is not necessarily obvious to a novice chess player. Familiarity to it will likely develop during normal chess play, but also could be developed by focused or specialised training. Once established, skill with the window of vulnerability constitutes a stable solution (a symmetry) that can, by way of the appropriate transformation, be deployed in diverse but relevant situations. That transformation is specific to the relationship that defines the symmetry. It can be applied to a variety of chess board configurations but must preserve the defining relationships of the symmetry.

Stable solutions (symmetries) can only be established and re-invoked given enabling affordances. Subsequently, if there is to be positive transfer from one situation to another, the affordances must match in at least some critical respects. For the chess solution as described for Figure 3, only panels c and d have the required affordance. This solution does not work for panels a and b.

As in the case of the virtual window of vulnerability, recognition of a resource as an affordance will require learning or discovery by exploration or both. Additionally, the agent must be capable of interacting with that resource to satisfy a goal. Unlike the chess situation, development of essential action capabilities may also require learning or discovery by exploration or both. Where learning is required for recognition and use of a resource as an affordance, the newly learned skills will transfer to other situations that may differ in many respects but otherwise encompass compatible affordances. The transfer of skills learned in a personal computer aviation training device to piloting an aircraft (Taylor et al. 1999) offers an example. Most critically, empirical demonstrations of transfer will rely on there being new learning in pre-transfer to recognise or use at least some of the crucial affordances involved in the transfer activity.

Much of the transfer literature notes that transfer is disconcertingly specific (Detterman 1993). Gobet and Sala (2023), observing that empirical data do not support the common expectation of transfer between loosely related domains, argue there can be no transfer from a domain such as algebra to one such as a foreign language. Domain is widely forwarded as a crucial construct for understanding transfer. It does not, however, establish reliable boundaries for strength of transfer effects (Sala and Gobet 2020) and remains an intuitive, unspecified construct. We think an appeal to domain is an irrelevant distraction, much in the sense that an appeal to fidelity is an irrelevant distraction. The theory of affordances offers a grounded view; the likelihood of transfer depends on whether situations have a common subset of affordances that pose significant learning challenges.

Many affordances are not bound by contextual specifics. As noted above, for example, both a sidewalk and a frozen lake may be surfaces of support that offer opportunities for standing and walking, although walking on a low-friction versus a high-friction surface requires constrained postures, constrained patterns of movement, and possibly even specialised footwear. Nevertheless, adapting the arguments of Adolph (2019), while there is little likelihood of transfer from one activity to another in use of a resource (e.g. between walking and skating on low-friction surfaces), there is likely to be transfer for an activity type between resources with partially matched affordances (e.g. transfer of walking from a high-friction to a low-friction surface). In our current discourse, because skating and walking are different symmetries (different dynamically stable solutions), we anticipate no transfer between them. In contrast, because high- and low-friction surfaces share a subset of affordances, there should be transfer between them for a common activity.

Furthermore, affordances can apply across superficially different but dynamically similar situations. For example, narratives of critical incidents from cognitive engineering reveal how diverse functional knowledge, acquired through extensive prior experience, can be applied to unique, high-demand situations (Klein 1998). Such effects cannot be explained by the inflexible specificity inherent in associative linking. Rather, they demand explanation in terms consistent with the functional flexibility and functional specificity described by Reed (1996) for affordances.

Functional flexibility in concert with functional specificity is suggestive of abstract principles as a basis for generalisation. Affordance theory, by that reading, has some commonality with the deep structure theory of Chi, Feltovich, and Glaser (1981). However, the generalisability of an affordance and its potential to support transfer is tied to its function. As revealed by an example from Chi and VanLehn (2012), the principles described in deep structure theory are detached from function. The example from Chi and VanLehn (2012) is of an ambulatory bridge and a dental bridge being similar (analogously) by a common principle of connection, which is a featural similarity (Figure 1). The affordances (at the level of functional similarity) are different; an ambulatory bridge affords crossing of an otherwise uncrossable gap while a dental bridge restores appearance and structural stability.

In summary, transfer is likely only where crucial affordances are common to both the pre-transfer and transfer situations and where there is some significant learning associated with the relevant perceptual and conceptual patterns or relevant action coordinations in pre-transfer. There is a common expectation of transfer from action video games and dynamic computer-based exercises to manual control tasks such as driving and flying (as noted by Wightman and Lintern 1985), which remains without conclusive support despite considerable research (Lintern and Boot 2021). An affordance perspective suggests that such transfer is unlikely because the dynamic coordinations (the symmetries) of action video games and dynamic computer-based exercises differ from those of driving and flying. Similarly, transfer of skill based on the affordance of field-of-safe-travel (Gibson and Crooks 1938) is unlikely between diverse locomotory modes such as walking, cycling, driving, and flying because the dynamic control coordinations are so different.

In contrast, affordance theory accounts for the positive transfer of landing skills to flight from training in a basic flight simulator with a closed-loop visual display (Lintern 1980) where the action coordinations and perceptual properties crucial to landing an aircraft are represented in the simulator. Transfer will occur if the transformation between simulator and aircraft preserves the essential relationships of a critical symmetry that was developed by practice in the simulator.

Whether or not situations encompass the necessary affordances and demand the requisite coordinations and learning for support of transfer can only be established by comprehensive analysis. More generally, affordance theory suggests an empirical strategy for exploring whether functional equivalence of an affordance common to different situations can support transfer across those situations.

13. Learning

Dynamical systems theory as developed by Warren (2006) is based on a modeling paradigm invoked for exploration of self-organising systems; a class of systems that are open thermodynamically where the forms that constitute the dissipative structures emerge from transitions induced by flows of energy and matter. In addition to being thermodynamically open, human activity systems are semantically open in the sense that, via interaction with their environment, they generate new semantic properties. This results in accumulation of new and meaningful perceptual, conceptual, and action capabilities that are not imported from an external source (they are emergent). Semantic openness is a property not commonly found in the self-organising systems that have been associated with thermodynamic openness and it is one not typically addressed in the transfer literature. Here, we address that issue via a discussion of processes that support learning.

The organisation of biological wholes is built up by differentiation of an original whole that segregates into parts with different functions (von Bertalanffy 1950). Gibson (1969) has applied this fundamental concept of biological design to perceptual learning whereby differentiation of perceptual properties results in progressive refinement of discriminations in the perception of existing structure within the perceptual environment. Gibson (1991) contrasts differentiation to any form of add-on or enrichment. Wine tasting offers a classic example of how agents progressively develop finer and more concrete distinctions. It is a discriminative, selective process of discovery as opposed to a constructive process of assembly. The flavors of wines exist as potentially discriminable properties even if the agent cannot discriminate them. In learning to appreciate a wine, an agent learns to identify a flavor and distinguish it from other flavors.

We propose progressive differentiation as the fundamental learning process that enables agents to refine solutions by tuning their activity system to demands. Once discovered, a solution is progressively refined through continued engagement. At the microscale of description, previously unnoticed perceptual properties and cognitive concepts become evident, and related distinctions are refined. Postures and coordinated patterns of action that may seem unnatural at first are brought into approximate configuration and then progressively tuned to demands.

Our claim is not that other forms of learning, such as associative and causal learning (Anderson et al. 2021; Holyoak and Cheng 2011) cannot contribute to transfer, but that progressive differentiation provides a strong and unique contribution to learning and to transfer. Associative and causal learning connect existing percepts, concepts, and action patterns whereas progressive differentiation generates new ones.

14. Towards a theory of transfer

Psychological science largely treats transfer as a product of either perception, or cognition, or action. A relational-dynamical theory demands an integration; it demands an approach that finds transfer within the perception-cognition-action system. There is a mutual shaping of the whole system by engagement with the world. Diverse patterns of functional behavior are emergent to the extent they develop through coordinated action of underlying processes rather than being predetermined by the design intent of an agent external to the system (Lintern and Kugler 2022). We are likely to find useful concepts for microscale descriptions in current psychological explanations of perception, cognition, and action, but when reflecting on how perception, cognition, and action function at the macroscale in relation to engagement with the world, they must be treated as a unified system.

Within a transfer paradigm as informed by a theory of behavioral dynamics, a challenging activity, described at the macroscale, becomes established as a reliable and repeatable pattern (a symmetry) as a consequence of some nontrivial amount of learning or experience. That activity is enabled by coordination between processes described at the microscale. To satisfy the transfer demand, it is necessary after learning to be able to reproduce that activity (as described at the macroscale) reliably and repeatedly in the transfer context. The agent thereby preserves a performance symmetry under the transformation from the learning phase to the transfer phase.

The challenge for an explanation of transfer is to identify at the microscale the processes and their coordination that are involved in the execution of the more difficult aspects of the activity; those that pose challenges in perceiving the affordances of a situation or in using them. As the natural gait of a quadruped might be disrupted by an injury that would be described at the microscale (e.g. a strained muscle or tendon), the performance of the targeted activity might be less capable because of limited competency with some of the microscale elements associated with perceiving and using relevant affordances. A training regime that focuses attention on those limits to competency is likely to enhance transfer.

The search at this level of description is for elements that pose significant performance challenges early in exposure to the activity. These challenges will be associated with recognition, discrimination and calibration of perceptual invariants, with interpretation, judgment and comprehension of meaning related to affordances, and with configuration and execution of action patterns. Some microscale processes will not pose any substantive learning challenge, but it is those that do that will carry the weight of detectable transfer effects. They may acquire this status as learning challenges by being unfamiliar and obscure or possibly by constituting awkward, seemingly unnatural patterns of coordination.

The goal is to preserve symmetry across the learning-transfer divide. Adapting Klein (1983), the constellation of microscale processes that support performance both in learning and in transfer constitutes a transformation group. Operationally, to achieve worthwhile transfer, we need to ensure that those processes and their coordination (as described at the microscale) that pose a substantive learning challenge are present in the learning context. In explicit departure from a fidelity or whole-similarity assumption, those microscale processes with which the learner is already competent do not need to be present in the learning context.

The theory of progressive differentiation implies that instructional strategies that focus on crucial performance-related perceptual properties and concepts and that guide coordinated patterns into their desired configuration will enhance learning. Strategies that compare and contrast crucial informational and conceptual properties or draw attention to them or that model effective coordination patterns or reveal coordination relationships are likely to induce good transfer. Such transfer can be tested empirically by examining how well learners transfer new skills to whole activities after specialised training on the elements that analysis has revealed as being performed poorly by those with limited experience on the targeted activity yet are crucial to its performance.

15. Instructional strategies

While our ecological theory of transfer focuses on the nature of transfer, a complementary body of research focuses on how to improve learning and transfer with more effective methods and strategies of practice and instruction. Part training, adaptive training, desirable difficulty, revealing the imperceptible, and deliberate practice are among the many ideas that have motivated research into diverse instructional strategies.

15.1. Part training

Part training research has a mixed record of achievement. Wightman and Lintern (1985), in a review of part training for manual control, found little by way of positive effects. They argued that researchers had typically used an overly simplistic strategy for decomposing the task to be learned, with the result that the training had separated interdependent elements that needed to be practiced as a unit while focusing on task parts that required little learning. Post that review, the learning strategies program that led to development of the space fortress research activity (Donchin 1989) was unusually successful in demonstrating the efficacy of part-training largely because of an early emphasis on understanding the structure of the activity (Lintern 1989; Mané and Donchin 1989). That early analysis of structure had identified the components of the space fortress task that would benefit from intensive, isolated practice.

15.2. Adaptive training

Adaptive training is based on the intuitively appealing assumption that a demanding task can be learned more efficiently if presented throughout training at a level of difficulty that is optimally matched to each individual’s current ability (Kelley 1969). Early research showed little advantage from adaptive training possibly because of uncritical selection of the manipulated training variable (Lintern and Gopher 1978). Control order became a popular adaptive variable, with practice for a second-order system progressing from easy to difficult through zero- to first- to second-order control (sometimes designated as displacement, velocity, and acceleration respectively). Prior experiments had shown, however, that transfer from zero- to first- and first- to second-order control was poor (Briggs, Fitts, and Bahrick 1958; Lincoln 1953). The lesson to be drawn from this is that the specific nature of the training manipulation is important whereas an appeal to a general variable such as task difficulty that can be manipulated in diverse ways has limited value. This is a lesson that apparently remains unheeded even decades later (e.g. Marraffino et al. 2021).

15.3. Desirable difficulty

In contrast to the adaptive training assumption that reduction in difficulty during training facilitates learning, Schmidt and Bjork (1992) argued that certain manipulations that increase difficulty during learning induce better transfer. Such manipulations, which Bjork and Bjork (2020) refer to as desirable difficulties, result in a performance reversal from learning to transfer (Soderstrom and Bjork 2015). Instructional manipulations such as summary feedback after multiple trials instead of immediately after each trial, alternating task variations rather than presenting them in blocks, and varying the training task on a selected dimension for transfer to a novel variation have all been effective.

As one explanation for these effects, Bjork (2018) invoked the concept of transfer-appropriate processing whereby the training regimen exercises the cognitive processes that support performance in transfer. Transfer-appropriate processing has been invoked as an explanation for positive transfer effects that might otherwise be explained by an appeal to depth of cognitive processing (Morris, Bransford, and Franks 1977). In the research described by Bjork (2018), manipulations that encourage transfer-appropriate processing are contrasted to manipulations that seemingly allow the task to be reproduced largely by remembering it.

An appeal to transfer-appropriate processing aligns with the transfer theory we have described. However, discussions of transfer-appropriate processing have not described the processes on which transfer is based in sufficient detail to guide general development of instruction.

15.4. Revealing the imperceptible

An appeal to revealing the imperceptible as an instructional strategy can be motivated by reflection on the discussion by Poulton (1974, 14–16) of asymmetric transfer in manual control. Some scenarios reveal crucially informative properties while others conceal them. Strong transfer can be anticipated where the training scenario reveals crucially informative properties that are largely concealed in the transfer scenario (Lintern 1991).

To execute a lumbar puncture (insertion of a needle into the space between two lumbar bones to remove a sample of cerebrospinal fluid), a healthcare practitioner must mentally visualise the spinal anatomy as they position and insert the needle. By use of transparent simulated tissues in a training simulation, Cheung et al. revealed to students how to position and angle the needle in relation to normally concealed structures. Those trained under this method showed an advantage in conceptual understanding over those trained on a control condition in which the simulated tissues were not transparent.

Under the assumption that the major challenge for a flight student in learning to land a light aircraft is to identify and calibrate visual glideslope-tracking information, Lintern (1980) provided adaptive visual guidance in simulator training trials in advance of a transfer test with no augmented guidance. The adaptive algorithm activated the additional guidance only when the student broke an error envelope, thereby emphasising for the student what the scene looked like while they were on glideslope in contrast to when they were off glideslope. The adaptive feature of the algorithm ensured that the student did not come to rely on that guidance to stay on glideslope. On the transfer test, students trained on the adaptive guidance outperformed students trained with no additional guidance or with guidance that was non-adaptive.

15.5. Deliberate practice

Deliberate practice as outlined by Ericsson (2008) emphasises repeated practice by a focused, motivated learner of an activity with a well-defined goal. A deliberate practice regime encourages learners to focus on a challenging aspect of a well-defined task. Improvement ensues if learners repeatedly practice the same or similar tasks and receive detailed immediate feedback on their performance (Ericsson 2004).

15.6. Summary; instructional strategies

This brief review of instructional strategies has revealed diverse streams of thought. Early research on adaptive training and part training was poorly conceptualised and failed to attend to known transfer relationships. The idea of desirable difficulties as outlined by Bjork and Bjork (2020) offers a salutary reminder that the result of instruction as measured by a test of transfer does not always align with performance trends observed in training. The lesson that we cannot rely on performance in training to assess training effectiveness has not been fully assimilated even today (e.g. Klein and Borders 2016). Furthermore, there are some glaring divergences; deliberate practice as described by Ericsson (2004) stresses the value of practicing a fixed task and of receiving precise, immediate feedback while the desirable difficulties work as described by Bjork and Bjork (2020) shows an advantage for variation in the learning task and use of delayed summary feedback.

It is possible that some of these empirical observations are not sufficiently robust or generalisable to be taken seriously but more likely, the seemingly divergent trends reflect diverse contextual and situational effects. The theoretical constructs we have forwarded in our ecological theory of transfer have the potential to guide research into instructional strategies and to inform explanations of seemingly incommensurable empirical results. For example, as we note above, the concept of progressive differentiation implies that a focus on crucial performance-related perceptual properties within an instructional strategy will enhance learning. In some situations, that focus might be strengthened by intensive and unvarying attention to important perceptual properties as encouraged by deliberate practice. In other situations, it might be accomplished by task variations consistent with a desirable difficulty schedule that reveal a critical property by maintaining its invariance as other properties change.

16. Requirements for analysis at the microscale

In light of our preceding arguments, it should be evident that successful demonstrations of transfer and successful realisation of these ideas in operational training programs depend crucially on identification at the microscale of those elements of the activity that are challenging to novice performers. In that respect, the effort of Boot et al. (2016) in seeking to generate insights into strategies, errors, mental representations, and shifting priorities in performance of a dynamic computer activity was well motivated. This effort was, however, limited by its exclusive focus on standard cognitive constructs and by its failure to search for competency components that are difficult to articulate such as, for example, the ability of experienced radiologists to judge at better than a chance level, with a single, brief glance, that a radiographic image reveals a clinically relevant lesion (Evans et al. 2013).

While we can expect to learn about many competency components through interviews with experts and through observations of expert performances, many elements of expertise remain hidden from educated observers and even from the explicit awareness of the experts themselves. Special strategies of analysis are needed to uncover these more obscure competency elements. Structural analysis of the optic array, as outlined by Gibson (1979), offers one way forward. That strategy has been used to identify the visual information used in control of steering, braking, and intercepting (Fajen 2007). Lintern and Liu (1991) followed that strategy in first identifying the horizon-aimpoint angle as a potential perceptual invariant for descent-path control in landing a light aircraft and then establishing experimentally that it had the predicted effect on performance. The cognitive analysis methods employed by Staszewski (2004) in uncovering powerful but largely unknown strategies for landmine detection, and by Klein (1998) in uncovering a hidden source of information in a missile defense activity, also suggest possibilities while the strategy described by Ericsson (2004) of identifying benchmark tasks that capture differences in performance between practitioners with varying levels of experience is promising. The dynamical analyses outlined by Guastello (2017) and Warren (2006) offer a powerful complement to these behavioral analyses by revealing the global layout of the activity, thereby directing attention more systematically to the micro-elements that support that global layout.

17. Analysis for learning design

In this paper, we did not wish to focus on an intriguing but constrained problem but rather to develop an account of transfer that could encompass a comprehensive range of challenging human activities. To that end, the activities we have analyzed, although not common or ubiquitous in human experience, represent routine challenges for individuals with appropriate training and expertise. Furthermore, as a set, they cover the full range of those activity components traditionally parsed in terms of perception, cognition, and action. We bring together the preceding arguments relating to similarity, behavioral dynamics, affordances, learning, and analysis at both macroscales and microscales to identify the potentially transferable elements of four activities:

• Execution of a backhand stroke in tennis (an activity largely composed of coordinated action),

• Endgame tactics for chess (a predominantly planning, reasoning, and thinking activity),

• Landing a light aircraft from final approach to touchdown (a manual control activity involving a sequence of coordinated actions), and

• Insertion of a peripheral intravenous cannula for direct delivery of fluids, medications, or nutrients into a healthcare patient (a procedural sequence that relies heavily on fine action coordination as guided by subtle, vaguely specified information).

The goal for this type of analysis is to identify at the microscale the activity elements that pose the more substantive impediments to competent performance as assessed at the macroscale. The analysis then identifies the type of instructional interventions that can be expected to improve competency with those more challenging activity elements. Here we offer a brief and selective summary of the results of analyses undertaken on these four activities. A full account of these analyses is available in Lintern, Kugler, and Motavalli (2024).

17.1. Tennis backhand

The beginning tennis player typically finds that the backhand stroke demands an awkward, unnatural trunk–limb coordination. It thereby becomes a limiting factor in the player’s ability to perform well on the court. A coach may use modeling or guidance to help the beginning player establish an approximate configuration. The student may then engage in deliberate practice, focusing on the performance limiting elements of the stroke, with coaching advice focusing on correcting sub-optimum postures and on coordination. Transfer would be assessed as positive if performance in competitive games improves, especially in relation to use of the backhand stroke.

17.2. Endgame tactics for chess

Skillful flexibility in the endgame is essential for a chess player who wants to be rewarded with a win for superior play during the opening and middle games. A player who enters the endgame with a marginal strategic advantage will more readily checkmate their opponent in an expeditious manner if they are skilled in endgame tactical maneuvers (e.g. rule-of-the-square, opposition and outflanking, triangulation). Intensive learning might follow a schedule of deliberate practice on a wide range of situations designed to exercise each tactic, with each tactic exercised in tactic blocks to a high level of competence, followed by extensive experience with a series of problems that mix the desirable tactics. Training should cover a comprehensive range of endgame tactics and fully embed in the student the ability to differentiate situations of use for the different tactics and to employ tactical variations in response to countermoves by the opponent. Transfer would be assessed as positive if end game performance in competitive games improves especially in relation to use of the instructed tactics.

17.3. Landing a light aircraft

In the landing approach, a beginning flight student typically finds it difficult to judge the angle of descent to the runway aimpoint. The student must learn to perceive and to calibrate the angle between aimpoint and horizon to fix the descent path. Lintern (1980) has shown that this may be facilitated by practice in a flight simulator with a closed loop visual system that employs adaptive visual guidance to show the student the correct descent angle. Transfer was assessed in this experiment by comparing landing performances in the simulator of students trained with adaptive visual guidance versus those trained without it. More generally, transfer can be assessed by evaluation of landing performance in a light aircraft with qualified instructor.

17.4. Insertion of a cannula into a peripheral vein

The healthcare student must become adept at fixing the vein in place (action coordination) and at advancing both the needle and the cannula with appropriate force (perception-action attunement-coordination). Development of the appropriate skills requires precise focus on the challenging elements and sensitive tuning over many trials. Learning may be facilitated by deliberate practice, focusing on the performance limiting elements of the needle insertion activity, with expert feedback focused on helping trainees recognise the correct angles, pressures, and micro-coordinations. Transfer can be assessed by evaluation of performance by an expert as a student works on patients.

17.5. Summary; Analysis for learning design

Most generally, these analyses suggest that learning should focus on those activity elements that pose substantive impediments to competent performance. The impediments will change as the learner progressively develops competence and then expertise with the whole activity. Indeed, we should remain mindful of the possibility of developmental cascades (Adolph 2019) where improved capability with one activity element triggers rapid improvement in other activity elements and even in other activities.

Subsequently, learning environments must be tailored to the challenges faced by the individual learner at the current stage of their competence. Once those elements that pose substantive impediments are identified, it should be possible to develop plausible hypothesis about the types of instructional strategies and instructional systems that will help a learner develop competency with them. Most critically, the analysis should consider the activity as a perception-cognition-action whole or else transfer may fail because the activity elements most challenging to the learner, especially those that constitute interdependencies between perception, cognition, and action, are neglected in the training regime.

18. Summary and conclusion

Transfer theory is said to be a crucial test of cognitive theory (Sala, Tatlidil, and Gobet 2018; Singley and Anderson 1989). From the view of cognition (inclusive of perception and action) as a shaping force for a full range of goal-directed activity, transfer theory has so far failed that test. The ecological theory we outline here was motivated by this challenge.

In forwarding a claim to view our development as a theory, we take a theory to be an interlocking set of principles that explain and predict the crucial phenomena under study (Reber, Reber, and Allen 2009). Subsequently, a theory of transfer should explain the nature of activity, the nature of learning, the nature of transfer, and how to promote and measure transfer. Those explanations must be based on a set of mutually consistent principles related to learning and performance of a broad range of perception-cognition-action activities. We believe we have satisfied that need.

We are mindful of the claim that potential for falsification is an essential criterion for theory. However, we concur with Singham (2020) that theoretical falsification cannot work even in principle and that workability is a more important goal (also see Lintern 2012). To that end, we use our discussion of chess to point to testable distinctions between affordance theory versus other similarity ideas that are common in behavioral science. In addition, our section on Analysis for Learning Design shows how our approach is testable by a sequence of analysis and experimentation. Although the emphasis of that section is on workability, repeated failure to achieve meaningful transfer after applying the method would cast considerable doubt on the theory.

We have been troubled by the penchant within transfer research to employ hypothetical constructs that, as explanatory concepts, allow endless variations to account for unanticipated effects (Lintern 1991). We sought to enhance the stability and construct validity of explanatory concepts by reference to relationships between observable properties rather than by reference to hypothetical constructs. That involved co-opting concepts from ecological psychology and building on constructs that have shown robust explanatory power in other scientific endeavors. We were aided considerably in that regard by widespread use of relational concepts of similarity in other scientific areas.

We wished to maintain contact with standard concepts of mainstream cognitive science but have noted the narrow scope of well-known transfer theories. We were motivated to build a transfer theory for authentic, multifaceted tasks that demand an appreciable level of skill. Essentially, how could we account for transfer effects for challenging authentic activities that rely on perception, cognition, and action in some combination. Behavioral dynamics conceptualises perception, cognition, and action as microscale processes that, through their dynamic coordination, generate emergence of organisation as described at a macroscale. Dynamic coordinations constitute solutions to goal directed activity and as such, must be tuned to the affordances of the situation and to the capabilities of the agent. Transfer to other situations with similar affordances will be enhanced to the extent that detection and use of affordances requires nontrivial learning.

The concept of transformation as forwarded by Klein (1893/1872) and Thompson (1917) is foundational to our ecological theory of transfer. A transformation is defined by a group of operations that preserve symmetry in the face of change, distinguishing them from operations responsible for the distinctive features that result from change. For transfer theory, a transformation can include both force and information processes. The goal for training is to preserve crucial symmetries across the learning-transfer transformation. The challenge for transfer theory and research is to describe the appropriate transformation at the microscale, thereby offering a description at a level of detail that will suggest interventions to strengthen the symmetry as described at the macroscale.

Our ecological theory of transfer replaces the view of knowledge as stored by one of knowing as capability constructed in action (Clancey 1997). In most forms of transfer theory, stable transferable entities are developed through learning or experience to be transported across the learning-transfer divide. From a dynamical systems perspective, the behavioral coordinations do not exist as such within the agent but emerge from relational interactions between microscale processes. The stability is within the repetition: the ability to recreate essential patterns of behavioral coordination as needed for the current situation. Rather than being transported from learning to transfer, the similarity at the macro-scale is regenerated or recreated by interactions of micro-processes within structures.

Frequently cited theories of transfer are limited in scope, invoking concepts of similarity that are either narrowly focused, superficial, or poorly conceptualised. The foundational concepts of identical elements, similarity, and fidelity as typically discussed do not account for much transfer data; for example, those data generated by carefully planned differences between training and transfer scenarios (e.g. Cheung and Kulasegaram 2022; Lintern 1980, 1991; Schmidt and Bjork 1992). Furthermore, a coherent understanding of transfer has been impeded by a general failure to appreciate that measurable transfer can result only from substantial improvement in one or more activity elements that are crucial to overall performance. Nor has there been a general appreciation that those activity elements that do induce transfer are necessarily functional. In accordance with our ecological theory, transfer will result from training that improves competency with those functional activity elements that, when not performed well, significantly limit overall performance.

Transfer theory has failed to generate any widespread interest in areas it should: operational training in diverse work environments, education, and strengthening of everyday life skills. Within healthcare, instruction of the new skills required for laparoscopic surgery (Gallagher and O’Sullivan 2011) and so-called robotic surgery (Catchpole et al. 2022) could benefit appreciably from comprehensive theoretical guidance relating to transfer. Serious Games (Ye et al. 2020), which are computer-based environments that combine learning strategies, knowledge, and game elements to teach specific skills, could also benefit, with attendant benefits to diverse areas of education and training. Absent a more comprehensive conceptual structure that taps the full range of perception, cognition, and action, the design of training systems and of training principles for these areas will continue to flounder. Here, we offer this ecological theory of transfer as one that can provide more consistent and more comprehensive guidance.

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Additional information

Notes on contributors

Gavan Lintern

Gavan Lintern is adjunct at Monash University Accident Research Centre. His PhD is in engineering psychology (University of Illinois). He has served as faculty at the Aviation Research Laboratory of the University of Illinois. His research is in design of ecological information systems and design of flight simulators for transfer.

Peter N. Kugler

Peter N. Kugler is retired. He has taught at Columbia University, University of Connecticut, UCLA, University of Illinois, and Radford University where he held the Dalton Professorship in Computer Science and Eminent Scholar. His published work has focused on problems related to self-organization, emergence through measurement, and semantics.

Al Motavalli

Dr. Al Motavalli is an anaesthesiologist in Melbourne, Australia, holding degrees in medicine, MSc Human Factors & System Safety, Master of Health Professional Education, Master of Arts. His current interests include the safe integration of AI interventions in perioperative environments, cognitive systems engineering in healthcare, and simulation education.