theory of symbolic representation in problem solving

HYPOTHESIS AND THEORY article

A perceptual account of symbolic reasoning.

• 1 Psychological and Brain Science/Cognitive Science, Indiana University, Bloomington, IN, USA
• 2 History and Philosophy of Science/Cognitive Science, Indiana University, Bloomington, IN, USA
• 3 Institute of Cognitive Science, University of Osnabrück, Osnabrück, Germany

People can be taught to manipulate symbols according to formal mathematical and logical rules. Cognitive scientists have traditionally viewed this capacity—the capacity for symbolic reasoning —as grounded in the ability to internally represent numbers, logical relationships, and mathematical rules in an abstract, amodal fashion. We present an alternative view, portraying symbolic reasoning as a special kind of embodied reasoning in which arithmetic and logical formulae, externally represented as notations, serve as targets for powerful perceptual and sensorimotor systems. Although symbolic reasoning often conforms to abstract mathematical principles, it is typically implemented by perceptual and sensorimotor engagement with concrete environmental structures.

Introduction

How do people reason arithmetically, algebraically, and logically? One well-known answer to this question holds that the human mind trades in inner symbols that amodally represent abstract arithmetic, algebraic, and logical propositions, and manipulates these symbols according to internally represented mathematical and logical rules. On this traditional view, the “inner” takes precedence over the “outer”: notations on paper, computer screens, and classroom blackboards are involved in mathematical problem-solving only insofar as they are “translated” into corresponding mental structures and processes.

Suppose you hold such a traditional view, but then learn that stray marks and subtle changes in spacing can lead otherwise competent students of algebra to “forget” a basic rule such as operator precedence. Several recent experiments have demonstrated just this sort of influence of visual structure on algebraic performance. One example comes from Landy and Goldstone (2007a) , who gave college undergraduates simple algebraic forms, such as “ a + b ∗ c + d = c + d ∗ a + b ,” and asked them to decide whether or not the given symbols described a valid equation (see Figure 1 ). Because the expressions contained both additions and multiplications, determining their validity required respecting the order of operations, which stipulates that multiplications precede additions. By creating artificial visual groups (e.g., by manipulating the physical spacing of equations, or by introducing shapes into the surrounding context as depicted in Figure 1 ), participants' performance could be predictably manipulated: validity-judgments were more likely to be correct if visual groupings were in line with valid operator precedence. Nor is this pattern restricted to algebraic validity. Related research has indicated that spatial layout impacts application of the order of operations rules when calculating ( Kirshner, 1989 ; Landy and Goldstone, 2010 ), when creating story problems ( Jiang et al., in press ), and when working in programming languages such as Python ( Hansen et al., unpublished manuscript ).

Figure 1. Some of the formats employed by Landy and Goldstone (2007a) . Visual cues such as added spacing, lines, and circles influence the application of perceptual grouping mechanisms, influencing the capacity for symbolic reasoning.

How might you interpret this sort of behavioral pattern? You could chalk failure to respect operator precedence, for example, up to performance error, and remain committed to the thesis that the underlying mathematical competence is largely independent of the way notational structures are perceived and physically manipulated. Alternatively, you could wonder whether competence with operator precedence depends non-trivially on the perceptual and sensorimotor mechanisms that target those external notations. To what extent might these mechanisms be responsible not just for our mathematical mistakes, but also for our successes?

The ability to follow operator-precedence rules is just one manifestation of the capacity for symbolic reasoning : the capacity to manipulate arbitrary symbolic tokens according to abstract mathematical and logical rules. In what follows, we propose an account of symbolic reasoning according to which perception, manipulation, and perceptual imagination lie at the heart of mathematical and logical competence. Rather than rely on amodally represented rules, symbolic reasoners make their mathematical judgments using perceptual processes that have no obvious link to the following of formal mathematical rules. Instead, we identify the capacity for symbolic reasoning with the ability to perceptually group, detect symmetry in, and otherwise perceptually organize symbolic notations as they are experienced in the environment. On this view, the kinds of behavioral patterns described above are typical: not only does written format impact the legibility of symbols, it also impacts the application of well-known rules. When notational expressions afford active manipulation, symbolic reasoning is often accomplished by physically interacting with those notations. In contrast, when notations do not afford physical manipulation or perceptual processing, symbolic reasoning may involve processes of visual, aural, and even tactile imagination. Although symbolic reasoning can therefore become “internalized,” it remains rooted in mechanisms close to the sensorimotor periphery.

Although we will emphasize the kinds of algebra, arithmetic, and logic that are typically learned in high school, our view also potentially explains the activities of advanced mathematicians—especially those that involve representational structures like graphs and diagrams. Our major goal, therefore, is to provide a novel and unified account of both successful and unsuccessful episodes of symbolic reasoning, with an eye toward providing an account of mathematical reasoning in general. Before turning to our own account, however, we begin with a brief outline of some more traditional views.

Extant Accounts of Symbolic Reasoning

Computationalism and semantic processing: translational accounts of symbolic reasoning.

Two prominent accounts of symbolic reasoning can be introduced via an analogy from the classroom. Consider the different ways in which students might be taught to think about the following syllogism:

All dogs are mammals;

All mammals are animals;

Therefore, all dogs are animals.

On one hand, students can think about such problems syntactically , as a specific instance of the more general logical form “All X s are Y s; All Y s are Z s; Therefore, all X s are Z s.” On the other hand, they might think about them semantically —as relations between subsets, for example. In an analogous fashion, two prominent scientific attempts to explain how students are able to solve symbolic reasoning problems can be distinguished according to their emphasis on syntactic or semantic properties.

Analogous to the syntactic approach above, computationalism holds that the capacity for symbolic reasoning is carried out by mental processes of syntactic rule-based symbol-manipulation. In its canonical form, these processes take place in a general-purpose “central reasoning system” that is functionally encapsulated from dedicated and modality-specific sensorimotor “modules” ( Fodor, 1983 ; Sloman, 1996 ; Pylyshyn, 1999 ; Anderson, 2007 ). Although other versions of computationalism do not posit a strict distinction between central and sensorimotor processing, they do generally assume that sensorimotor processing can be safely “abstracted away” (e.g., Kemp et al., 2008 ; Perfors et al., 2011 ). On all computationalist accounts, when an individual is confronted with a symbolic reasoning task such as a natural-language “word problem” or a formal reasoning problem expressed in the notational formalisms of algebra, calculus, and logic, the perception of notations in the environment causes a tokening of equivalent symbols and expressions of “Mentalese” ( Fodor, 1975 ). These mental symbols and expressions are then operated on by syntactic rules that instantiate mathematical and logical principles, and that are typically assumed to take the form of productions, laws, or probabilistic causal structures ( Newell and Simon, 1976 ; Sloman, 1996 ; Anderson, 2007 ). Once a solution is computed, it is converted back into a publicly observable (i.e., written or spoken) linguistic or notational formalism.

An influential alternative to computationalism is analogous to the semantic approach to the syllogism above: the heterogeneous family of semantic processing accounts, according to which symbolic reasoning is carried out by systems that interpret and represent meaningful mathematical and logical relations. Accounts of this type differ according to the particular representational formats they posit, ranging from amodal or generically spatial “mental models” ( Johnson-Laird et al., 1992 ), to rich perceptual and sensorimotor “simulations” of specific objects and scenes ( Barsalou, 1999 ), and even to indirect “conceptual metaphors” that drive people's intuitions and conclusions about a specific mathematical problem ( Lakoff and Nuñez, 2000 ). What distinguishes these accounts from computationalism is the idea that symbolic reasoning occurs not on the basis of syntactic rules, but on the basis of meaningful interpretations of a particular mathematical or logical task domain. For example, Lakoff and Nuñez argue that real-number concepts are derived from experiences with physical lengths, and that the capacity for simple arithmetic arises from an innate ability to estimate and compare such lengths. On Johnson-Laird's “mental models” account, symbolic reasoning problems are solved by “inspecting” a mental model of the problem: the validity of “ a & b ∴ b ” can be determined by recognizing that “ b ” is a component of the model for “ a & b .” In much the same way, Barsalou's “perceptual symbol systems” account suggests that logical expressions are interpreted by mentally simulating concrete scenarios to which the expression applies: a scene that includes both an apple and an orange includes an orange.

Despite their differences, computationalist, and semantic processing accounts share the assumption that processes of perception and action play a relatively limited role in the process of symbolic reasoning. Although both accounts acknowledge that the perception of notations is important for the construction of internal representations, they also assume that once such representations have been constructed, the physical notations that express the original mathematical or logical problem may be ignored or altogether discarded until a solution is communicated. Notably, this even applies to accounts which, like Barsalou's, posit a special role for sensorimotor representations in general, yet attribute a curiously limited role to sensorimotor representations of the notations that are actually perceived while a symbolic reasoning task is being performed. In general, computationalist and sematic processing accounts are alike in being essentially translational : they suppose that processes of perception and action do little other than mediate between notational structures in the external environment and the internal structures and processes in which symbolic reasoning really occurs.

It is worth elaborating on this translational aspect. The capacity for symbolic reasoning is expressed behaviorally by converting an input representation of a mathematics or logic problem into an output representation of a corresponding solution. Initially, the problem is represented in a public language, either as a natural-language “word problem”, or in the special notational systems designed for algebra, calculus, and logic. Eventually, this problem representation is converted into a written or spoken solution. But exactly how does this conversion occur? Like many other kinds of problem solving, the process of symbolic reasoning can be seen as a chain of transformations that links input and output representations, each of which changes its format and/or semantic structure. Some transformations, such “ a and b ” to “ a & b ,” involve a change in format without a change in semantic structure. In contrast, transformations such as “~(~ a ∨ ~ b ) ∴ b ” to “ a & b ∴ b ” involve changes in format and semantic structure: the resulting representation is a simplification of the original problem.

Computationalist and semantic processing accounts of symbolic reasoning are equally translational because they both assume that problem representations are passed from a perceptual apparatus to an internal processing system in a form that is no simpler than the external (notational or linguistic) problem representation. That is, they assume that all transformations that involve changes in semantic structure take place “internally,” over Mentalese expressions, mental models, metaphors or simulations, and that sensorimotor interactions with physical notations involve (at most) a change in representational format. On these accounts, when a subject is asked to evaluate a formal expression such as “~(~ a ∨ ~ b ) ∴ b ,” a mental representation of that expression must be constructed before it can be simplified to “ a & b ∴ b .” Similarly, notational variants of one-and-the-same proposition—e.g., “ All Fs are Gs ,” “( x )( Fx → Gx ),” and “∀ x [ Fx ⊃ Gx ]” will be converted into one-and-the-same Mentalese expression, mental model, metaphor or simulation. In general, therefore, computationalist and semantic processing accounts of symbolic reasoning rely equally on the assumption that the principal role of sensorimotor processes—the processes that govern the perception of and physical interaction with public symbols and expressions—is simply to provide inputs to and carry outputs from those internal structures and processes that are ultimately responsible for performing all substantial steps in a mathematical or logical problem solving chain.

Toward a Constitutive Account: The Cyborg View

Translational accounts of symbolic reasoning can be distinguished from constitutive accounts, in which sensorimotor mechanisms are not merely part of the causal chain that links external notations to internal representations, but are crucially involved in transforming the problem representation into one that has a simplified semantic structure. Recall that on the translationist view, mental resources can be divided into those that “translate” the outer situation into a generally isomorphic inner representation, and those that act on that representation to solve the problem. On a constitutive account, sensorimotor mechanisms not only translate the problem, they are involved in the transformations that substantively solve it. One prominent view that can be associated with such a constitutive approach might, to borrow Andy Clark's terminology, be called the cyborg view of symbolic reasoning ( Clark, 2003 ). Grounded on recent work in the area of “situated cognition,” the cyborg view holds that notations constitute external technological artifacts that “scaffold” the biological processes involved in symbolic reasoning ( Clark, 1997 , 1998 , 2006 ; Menary, 2007 ; Sutton, 2010 ). This “scaffolding” is typically achieved by notations that permit the extraneural storing, inspection, deletion and manipulation of information in a way that facilitates the execution of symbolic reasoning tasks, and has positive effects on the speed and accuracy with which these tasks can be performed as well as their potential complexity. To cite a well-known example, “carrying” a digit during a complex multiplication task by writing it on a piece of paper, adding it to the result and then crossing it out obviates the need to store and manipulate that digit in biological memory, thereby freeing up valuable cognitive resources, minimizing possible error from misremembering, and permitting the multiplication of extremely large values. One way of explaining the cognitive benefit of such “scaffolding” is to view notations as constitutive parts of integrated, boundary-crossing symbolic reasoning systems: When computing “123 × 89”, “carrying” the tens digit of the temporary product “3 × 9” and adding it to the units digit of “2 × 9” transforms the original complex multiplication problem into a series of simpler multiplication and addition problems that can easily be done in the head. Thus, the active manipulation of physical notations plays the role of “guiding” the human biological machinery through an abstract mathematical problem space—one that may far exceed the space of otherwise solvable problems.

While emphasizing the ways in which notations are acted upon, however, proponents of the cyborg view rarely consider how such notations are perceived. Sometimes, this neglect is intentional, as when the utility of cognitive artifacts is explained by stating that they become assimilated into a “body schema” in which “sensorimotor capacities function without… the necessity of perceptual monitoring” ( Gallagher, 2005 , p. 25). At other times, this neglect seems to be unintended, however, and subject to corrective elaboration. For example, although Andy Clark (1998 , p. 168) argues that the human ability to deploy and manipulate notations in symbolic reasoning tasks “involves the use of the same old (essentially pattern-completing) resources to model the special kinds of behavior observed in the public [notational] world,” it remains unclear exactly which pattern-completing resources are in play, and what kinds of patterns they complete. In general, therefore, although cyborg theorists have shown quite successfully that notations can be constitutively involved in symbolic reasoning, and have made great strides in cataloguing the kinds of bodily interactions that lead to cognitive success, few specific details have emerged regarding the relevant perceptual processes that facilitate these interactions, as well as the physical characteristics that determine when and why a particular notation is cognitively beneficial.

Consider how such details might explain the influence of visual structure on algorithmic reasoning discussed earlier. Order of operations behavior need not be implemented in a set of high-level productions or in a collection of explicit memorized rules, but also need not be determined by active manipulations of physical notations. Instead, such behavior might largely depend on visual processes that segment the scene into parts, wholes, and groups. One possibility is that because the algebraic system tends to align spatial structure and precedence rules, perceptual grouping processes acquire biases compatible with those rules ( Kirshner and Awtry, 2004 ); another is that because proofs tend to maintain tightly bound structures, leading to increased statistical regularity in high precedence operations, experience with algebraic derivations modifies perceptual organization. Other regular cultural cues have long been known to impact grouping ( Wertheimer, 1923/1938 ). By extending the cyborg view's emphasis on environmental interaction with a detailed understanding of perceptual processing, a theoretical framework might be developed that accounts for the effect of aligning visual grouping and syntactic binding discussed earlier (see Figure 1 ), but that may also explain many other episodes of formally correct and incorrect symbolic reasoning.

In what follows, we articulate a constitutive account of symbolic reasoning, Perceptual Manipulations Theory , that seeks to elaborate on the cyborg view in exactly this way. While accommodating the cyborg view's emphasis on the active manipulation of physical notations, Perceptual Manipulations Theory additionally emphasizes the perceptual processes that facilitate and govern such manipulations, as well as the physical characteristics of particularly successful (and unsuccessful) notational formalisms. On our view, the way in which physical notations are perceived is at least as important as the way in which they are actively manipulated.

Perceptual Manipulations Theory

Perceptual Manipulations Theory (PMT) goes further than the cyborg account in emphasizing the perceptual nature of symbolic reasoning. External symbolic notations need not be translated into internal representational structures, but neither does all mathematical reasoning occur by manipulating perceived notations on paper. Rather, complex visual and auditory processes such as affordance learning, perceptual pattern-matching and perceptual grouping of notational structures produce simplified representations of the mathematical problem, simplifying the task faced by the rest of the symbolic reasoning system. Perceptual processes exploit the typically well-designed features of physical notations to automatically reduce and simplify difficult, routine formal chores, and so are themselves constitutively involved in the capacity for symbolic reasoning. Moreover, if a particular symbolic reasoning problem cannot be solved by perceptual processing and active manipulation of physical notations alone, subjects often invoke detail-rich sensorimotor representations that closely resemble the physical notations in which that problem was originally encountered. On our view, therefore, much of the capacity for symbolic reasoning is implemented as the perception, manipulation and modal and cross-modal representation of externally perceived notations.

The neural processes that PMT takes to be involved in symbolic reasoning almost never have as their primary function the implementation of amodally represented rules or models. Instead, they include sensorimotor systems for visual grouping and perceptual organization, object recognition, object tracking and symmetry detection, among others. Although skills such as object-recognition may appear quintessentially “cognitive” to some, we treat them as sensorimotor capacities to highlight the fact that, rather than apply to abstract mathematical or logical entities, they apply directly to the physical properties of notations in the environment such as shape, relative spacing and position. Indeed, insofar as most mathematical and logical notations are well-designed, these properties are frequently suggestive of how they ought to be manipulated, thus promoting formally valid “symbol-pushing”. For example, the fact that the multiplicands in “ xy + z ” are closer to one another than to the additive term can be understood as a manifestation of the order-of-operations rule that multiplication is to be performed before addition—a manifestation that is immediately recognized by mechanisms of perceptual grouping (see section Evidence for Perceptual Manipulations Theory). Notably, such sensorimotor competences are often more robust than the formal systems to which they are applied: while a formula such as “(((P→((Q&R)” would be rejected by a machine following strict well-formedness rules, even beginning logic students interpret it as a conditional, and must be explicitly trained by pedagogues with ulterior motives to focus on a narrower set of structural elements. As we discuss in greater detail below, a wide range of (correct and incorrect) mathematical behavior can be attributed to the way the perceived details of formal notations “interlock” with domain-general sensorimotor capacities.

Perceptual Manipulations Theory suggests that most symbolic reasoning emerges from the ways in which notational formalisms are perceived and manipulated. Nevertheless, direct sensorimotor processing of physical stimuli is augmented by the capacity to imagine and manipulate mental representations of notational markings. Faculties of spatial reasoning, mental transformation, referential symbolism and a rich set of capacities for acquiring and imagining physical behaviors such as walking, pointing, writing, and erasing can all be used to internally reproduce the actual perceived details of physical notations and to mentally manipulate them in ways that resemble physical actions. Insofar as our account emphasizes perceptual representations of formal notations and imagined notation-manipulations, it can be contrasted with Barsalou's perceptual symbol systems account, in which “people often construct non-formal simulations to solve formal problems” ( Barsalou, 1999 , 606). Moreover, our emphasis differs from standard “conceptual metaphor” accounts, which suggest that formal reasoners rely on a “semantic backdrop” of embodied experiences and sensorimotor capacities to interpret abstract mathematical concepts. Our account is probably closest to one articulated by Dörfler (2002) , who like us emphasizes the importance of treating elements of notational systems as physical objects rather than as meaning-carrying symbols.

Although there are clear differences between PMT and other accounts of symbolic reasoning, our view incorporates elements from many of them—albeit with a greater emphasis on perception. For illustration, consider a student already competent in logic now learning set theory. The perceivable physical similarities of ∩ and ∪ to ∧ and ∨, including the up-down symmetry between each pair, serve as a perceptual , rather than conceptual, metaphor. To see how this metaphor may be applied, consider the duality principle that

which bears a striking visual similarity to De Morgan's law,

This visual similarity is partially a result of common symbology, including the use of capital letters for elements, the use of horizontal lines for equality, the use of bars for negation, and the above-mentioned use of similar shapes for basic operations. Partially, though, the similarity results from the arrangement of these parts—if one is written in prefix notation, for instance, the similarity is markedly decreased (it is beyond the scope of this work to attempt a general definition of similarity; for a review, see Goldstone and Son, 2005 ). For a student learning a new formal system, these notational similarities ground the transformations typical to set theory by mapping them onto the more familiar domain of logic, facilitating the application of similar principles and ideas, and licensing particular manipulations, sometimes even prior to obtaining a rich understanding of the conceptual issues involved. To the degree that these inferences are licensed, learning may be facilitated. Although the relevant perceptual and sensorimotor processes are modality-specific, when mathematical notations are well-designed, human mathematical competence can be incredibly flexible: radically different mathematical and logical propositions can be treated in similar formal ways because of similarities in the way in which they are physically manifested as notations. Of course, it is not always or often the case that capturing visual and semantic regularities across domains is the explicit goal of mathematicians introducing notation (though see Smaill, 2012 , for one apparent case). We predict, however, that when there are significant visual similarities in notations used across domains, people will tend to import assumptions from a well-understood domain into a novel one.

Perceptual Manipulations Theory also posits a novel psychological role for much-discussed magnitude- and quantity-detection systems. Visual quantity (e.g., the number of blocks, dots, or sheep presented in a drawing or on a computer screen) is often thought to be directly represented by an evolved “number system” dedicated to amodal magnitude representation ( Gelman and Gallistel, 1978 ; Barth et al., 2003 ; Dehaene et al., 2004 ; Machery, 2007 ). It has been argued that such quantity-sensitive mechanisms provide the basic representational vehicles over which formal mathematical reasoning occurs ( Gallistel et al., 2005 ; Spelke, 2005 ; Carey, 2009 ), but PMT holds a more textured view. Quantity-sensitive mechanisms certainly sometimes represent numbers. In symbolic reasoning tasks, however, a primary function of magnitude and quantity-detection systems is to enable reasoners to track magnitude and quantity properties of notational formalisms. For example, when dealing with large numbers such as “ 3,000,000,” magnitude-detection plays a role in keeping track of the number of digits ( Hinrichs et al., 1982 ). Similarly, when teaching a rule such as the product rule captured by “ a 5 a 3 = a 8 ,” a teacher may write something like “ ( aaaaa ) × ( aaa ) = ( aaaaaaaa )” and let magnitude-detection (and explicit counting) systems do the rest. Thus, a significant portion of the verification process may be implemented by perceptual and sensorimotor skills and quantity-detection systems that process the notational formalism itself, without necessarily interpreting the notation's meaning.

The emphasis that PMT places on domain-general systems for perceptual processing and bodily interaction with physical systems of notations underscores the importance of the historical development of a common set of well-designed mathematical notations. Although historically the development of visual commonalities across notations may have been largely accidental, this development has served mathematics well, providing visual cues that allow the human perceptual and motor systems to effectively operate over them. One prediction of PMT is that when notations align perceptual and structural similarities, learning will be facilitated. Of course, when they misalign, as they sometimes do, learning is predicted to be impaired ( Marquis, 1988 discusses several such cases). Still, better notation systems could yet be constructed in all branches of formal reasoning to take full advantage of visual cues that automatically “steer” the reasoner in the direction of formally valid solutions. In this way, the human capacity for symbolic reasoning winds up being ordinary, bodily situatedness in novel, artifactual sensorimotor space: the space of (well-designed!) notations.

Evidence for Perceptual Manipulations Theory

Most of the existing literature on symbolic reasoning has been developed using an implicitly or explicitly translational perspective. Although we do not believe that the current evidence is enough to completely dislodge this perspective, it does show that sensorimotor processing influences the capacity for symbolic reasoning in a number of interesting and surprising ways. The translational view easily accounts for cases in which individual symbols are more readily perceived based on external format. For example, blurring symbols will make them harder to perceive. Perceptual Manipulations Theory also predicts this sort of impact, but further predicts that perceived structures will affect the application of rules—since rules are presumed to be implemented via systems involved in perceiving that structure. In this section, we will review several empirical sources of evidence for the impact of visual structure on the implementation of formal rules. Although translational accounts may eventually be elaborated to accommodate this evidence, it is far more easily and naturally accommodated by accounts which, like PMT, attribute a constitutive role to perceptual processing.

Perceptual Manipulations Theory holds that skill with symbol systems is implemented in alignments between elements of external notations and perceptual and motor systems. Therefore, it predicts that the physical appearance of notations should strongly influence formal behavior. For example, it should be difficult to differentially respond to two similar-looking notational forms even if they are conceptually dissimilar. Substantial evidence suggests that this prediction holds. For example, Kirshner and Awtry (2004) show that the common mistake of confusing the valid rule regarding multiplication of two like terms by adding their exponents ( a n ∗ a m = a n + m ) with the visually similar but invalid rule regarding added terms ( a n + a m = a n + m ) can be avoided by teaching students a linguistic notation in which these equations no longer resemble one another. In the same way, common mistakes such as

can be prevented just by changing the notational format in which they are learned (see Marquis, 1988 for several examples of visual patterns in algebra). The frequency of these mistakes—as well as the fact that they can be prevented by switching notational formats—are hard to explain from a translational perspective in which perceived problems are converted into inner propositions or models, and in which formal dissimilarity ought to trump visual similarity. In contrast, they are quite easily explained from a perspective that attributes a constitutive role to perceptual processing. What appears to be happening is that students apply a very general maxim of perceptual pattern learning: if two things look similar, similar things can probably be done with them, and if they look different, they require different actions. Although this is not a formally valid way of reasoning over symbol systems (and indeed, often leads to the mistakes reported above), this general strategy may lead to correct solutions whenever visual similarity does mirror formal similarity (see also Cohen Kadosh, 2009 ). Indeed, such mirroring is widespread, and appears to be regularly exploited by reasoners. Consider the way algebraic notation aligns formal structure with perceptual grouping in the expression

Here, formal structure is mirrored in the visual grouping structure created both by the spacing ( b and c are multiplied, then added to a ) and by the physical demarcation of the horizontal line. Instead of applying abstract mathematical rules to process such expressions, Landy and Goldstone (2007a , b see also Kirshner, 1989 ) propose that reasoners leverage visual grouping strategies to directly segment such equations into multi-symbol visual chunks. To test this hypothesis, they investigated the way manipulations of visual groups affect participants' application of operator precedence rules. Maruyama et al. (2012) argue on the basis of fMRI and MEG evidence that mathematical expressions like these are parsed quickly by visual cortex, using mechanisms that are shared with non-mathematical spatial perception tasks.

Interestingly, perceptual processes play a role not only in the way notations are perceived, but also in the way they are created. By studying beginning logic students' physical arrangement of logical formulae in an online natural deduction tutoring system ( Allen and Menzel, 2007 ), Landy and Goldstone (2007b) found statistically significant patterns of space-insertion consistent with the hypothesis that spaces are used to aid visual grouping within logical formulae. That is, reasoners not only exploit visual groups that are already present in the physical representation of a symbolic reasoning task, but also actively and endogenously reproduce such groups when they make it easier to find a solution. But why do reasoners insert such formally irrelevant features to their written notational formalisms? From a translational perspective, this question is difficult to answer: once a solution to a symbolic reasoning problem is computed, it merely needs to be translated into a public language, one in which the observed space-insertion patterns are formally irrelevant. From the perspective of PMT, however, it seems likely that such patterns either derive from the possibility that mathematical and logical equations are internally encoded in a perceptually-rich format in which details about spacing is retained, or from the utility of such patterns in computing intermediate solutions on paper by applying the same visual object-segmentation systems that were initially used to interpret the problem. Supporting the possibility that spatial structure plays a crucial role in the process of interpretation of equations, Jiang et al. (in press) report that subjects inventing story problems match the physical structure of provided equations.

The visual system is well-known to be particularly responsive to dynamic stimuli such as motion. This is reflected in the apparent relevance of motion and transformation in algebraic understanding of proofs. Nogueira de Lima and Tall (2007) documented that schoolchildren learning algebra often treat transformations such as

not as the repeated application of formal Euclidean axioms, but as “magic motion,” in which a term moves to the other side of the equation and “flips” sign. Landy and Goldstone (2009) suggest that this reference to motion is no mere metaphor. Subjects with significant training in calculus found it easier to solve problems of this form when an irrelevant field of background dots moved in the same direction as the variables, than when the dots moved in the contrary direction.

One suggestion of PMT is that mathematical concepts may be encoded using multiple strategies, and that perceptual-motor strategies may emerge over the process of using a symbol system. As an example, Varma and Schwartz (2011) examine the case of negative number acquisition, and in particular the acquisition of processes allowing the comparison of positive and negative numbers. Initially, learners are faster at comparing numbers that are close together when one is positive and the other negative—a reversal of the usual distance effect that holds with positive numbers ( Moyer and Landauer, 1967 )—but one that is consistent with a rule-based strategy involving comparing signs. More expert learners show a typical size effect, so that numbers that are ‘far apart’ are discriminated more quickly. The authors suggest that negative numbers are initially processed by children using rules, but that “symbolic manipulation can transform an existing magnitude representation so that it incorporates additional perceptual-motor structure.”

In summary, PMT suggests that learning how to perceptually and physically engage notations is critical to the capacity for reasoning in accordance with their mathematical meanings. To be successful, learners must discover which aspects of a notation are relevant and meaningfully aligned with mathematical rules and concepts, and must then acquire an appropriately “rigged up” sensorimotor system (see also: Goldstone et al., 2010 ). Although the sensorimotor skillset required for sophisticated symbolic reasoning is likely to be highly developed and available to learners only after some struggle ( Piaget, 1953 ; Bednarz et al., 1996 ), Kellman et al. (2008) have already found that training students to recognize algebraic expressions using standard perceptual learning techniques leads to lasting gains both in equation reading and comprehension, as well as in algebraic problem-solving. Indeed, substantial evidence indicates that notation systems that align with computationally useful processes are relatively easy to acquire across a variety of domains including arithmetic and algebra ( Kirshner and Awtry, 2004 ; Landy and Goldstone, 2007c ), electric circuit design ( Cheng, 1999 ), and sequence and grammar learning ( Pothos et al., 2006 ; Endress et al., 2007 ). Our account expects such results because appropriate alignment between the formal and the perceptual significantly simplifies the search for correct solutions. Although we will not speculate extensively about possible implications for mathematics education, results such as these also suggest that the PMT approach can be a productive way to think about new pedagogical approaches to designing and reasoning with formal notations. In particular, it seems likely that the most effective and easily-learned notations and rule-systems are the ones that have greatest alignment with preexisting or easily learned perceptual and sensorimotor routines. On our view, one principal virtue of well-structured notation systems is that they leverage automatic sensorimotor operations by making their products formally useful, and the better the alignment between the formal and the sensorimotor, the more useful those products will be.

Theoretical Implications

Is there a “fundamental” mathematical reasoning system.

A contribution of PMT is that it provides a novel account of how to bring mathematical and logical reasoning into the fold of embodied cognition more generally. Although PMT accommodates the cyborg view and its emphasis of the environment, it adds a detailed conception of the constitutive role of perceptual processing in symbolic reasoning: perception is at least as important as physical manipulation. One consequence of this view is that mathematical and logical reasoning need not be rooted in single, special-purpose cognitive mechanisms. Although we do not deny the existence of amodal numerosity or magnitude detection systems, our account does not assign those systems a uniquely fundamental role in the development of mathematical reasoning capacities. Instead, on our view symbolic reasoning is carried out by a wide variety of perceptual and motor skills, including fast numerosity and magnitude evaluation; repeatable actions like pointing, counting, and stacking; object segmentation and grouping; motion detection and visualization; writing and reading; and many other sensorimotor skills. Additionally, it seems reasonable to assume that the same sensorimotor skillset may also play a pivotal role in other mathematical domains such as geometry and category theory, the elementary portions of which both of which rely considerably on diagrams and other iconic notations. More controversially perhaps, since all areas of mathematics and symbolic reasoning involve—at some point—the learning of rules and abstract principles via notational systems, it may even be the case that the same perceptual and motor processes that implement the capacity for symbolic reasoning also play different but equally fundamental roles in implementing various kinds of abstract reasoning in mathematics and beyond. Whether this leaves any significant role for amodal systems remains to be seen, but see Dove (in press) for an argument for representational pluralism.

A corollary of the claim that symbolic and other forms of mathematical and logical reasoning are grounded in a wide variety of sensorimotor skills is that symbolic reasoning is likely to be both idiosyncratic and context-specific. For one, different individuals may rely on different embodied strategies, depending on their particular history of experience and engagement with particular notational systems. For another, even a single individual may rely on different strategies in different situations, depending on the particular notations being employed at the time. Some of the relevant strategies may cross modalities, and be applicable in various mathematical domains; others may exist only within a single modality and within a limited formal context. For example, consider the fact that there is significant potential for error when a successful strategy in one domain is exported to another domain—as, for example, when beginning logic students make the mistake of distributing a negation across a conjunction, going from ~( X & Y ) to (~ X & ~ Y ), because they perceive a similarity to the algebraically legal manipulation of −( x + y ) to (− x + y ). Although in this particular case such cross-domain mapping leads to a formal error, it need not always be mistaken—as when understanding that “~~ X ” is equivalent to “ X ,” just as “−− x ” is equal to “ x .” In some contexts, such perceptual strategies lead to mathematical success. In other contexts, however, the same strategies lead to mathematical failure.

If the capacity for symbolic reasoning is in fact idiosyncratic and context-dependent in the way suggested here, what are the implications for scientific psychology? PMT implies that the “deep” facts about human mathematical, algebraic, logical, and other mathematical abilities are unlikely to be facts about inner computations and models, but are instead facts about how humans manage to exploit perceptual and sensorimotor strategies in appropriate, context-specific ways—and about how they fall prey to these strategies when applying them inappropriately. The reason that mathematicians have the intuition that people who are merely “pushing symbols” are failing to grasp fundamental mathematical meanings is that they are indeed failing to do so—though this failure may be more widespread, and indeed more powerful, than mathematicians and psychologists have previously assumed. Being more specific than this, however, seems difficult. Therefore, the key to understanding the human capacity for symbolic reasoning in general will be to characterize typical sensorimotor strategies, and to understand the particular conditions in which those strategies are successful or unsuccessful.

What is Mathematical Rule-Following and Who is the Mathematical Rule-Follower?

Perceptual Manipulations Theory claims that symbolic reasoning is implemented over interactions between perceptual and motor processes with real or imagined notational environments. Since symbolic reasoning involves manipulating symbols and expressions according to mathematical and logical rules, this view implies that the human ability to follow abstract mathematical and logical rules is carried out by sensorimotor processes that apply to concrete —i.e., readily perceivable and physically manipulatable—notations. But how is it that “primitive” sensorimotor processes can give rise to some of the most sophisticated mathematical behaviors? Unlike many traditional accounts, PMT does not presuppose that mathematical and logical rules must be internally represented in order to be followed. Rather, overt rule-following emerges from the fine-tuned interactions between the perceptual and sensorimotor systems with well-designed physical notations—symbolic reasoning is a form of sophisticated “symbol pushing” that happens to adhere to the formal rules of mathematics and logic, due to a lengthy process of cultural adaptation and pedagogical scaffolding.

Like interlocking puzzle pieces that together form a larger image, sensorimotor mechanisms and physical notations “interlock” to produce sophisticated mathematical behaviors. Insofar as mathematical rule-following emerges from active engagement with physical notations, the mathematical rule-follower is a distributed system that spans the boundaries between brain, body, and environment. For this interlocking to promote mathematically appropriate behavior, however, the relevant perceptual and sensorimotor mechanisms must be just as well-trained as the physical notations must be well-designed. Thus, on one hand, the development of symbolic reasoning abilities in an individual subject will depend on the development of a sophisticated sensorimotor skillset in the way outlined above. On the other hand, the development of symbolic reasoning abilities within a society will depend on the availability of notational formalisms that promote formally valid “symbol-pushing.” Indeed, the development of mathematical expertise is often historically cotemporaneous with the development of powerful, efficient, and easily learned systems of formal mathematical and logical notation ( Dantzig, 1954 ; Stedall, 2007 ).

We have described an approach to symbolic reasoning which closely ties it to the perceptual and sensorimotor mechanisms that engage physical notations. We argued for this approach on the basis of empirical evidence that shows algebraic and mathematical knowledge to be surprisingly fragile in the face of minor perceivable differences, and on the basis of evidence that suggests that competent symbolic reasoners typically rely on semantically irrelevant properties of notational formulae in order to quickly and accurately—but also sometimes inaccurately—solve symbolic reasoning problems. With respect to this evidence, PMT compares favorably to traditional “translational” accounts of symbolic reasoning.

Nevertheless, there is probably no uniquely correct answer to the question of how people do mathematics. Indeed, it is important to consider the relative merits of all competing accounts and to incorporate the best elements of each. Just as the particular sensorimotor strategies being invoked are likely to differ across individuals and situations, it is also likely that different episodes of symbolic reasoning require different explanations—be they in terms of comparisons based on conceptual metaphors, situated interactions with notations, or even conscious applications of formal rules. Although we believe that most of our mathematical abilities are rooted in our past experience and engagement with notations, we do not depend on these notations at all times. Moreover, even when we do engage with physical notations, there is a place for semantic metaphors and conscious mathematical rule following. Therefore, although it seems likely that abstract mathematical ability relies heavily on personal histories of active engagement with notational formalisms, this is unlikely to be the story as a whole. It is also why non-human animals, despite in some cases having similar perceptual systems, fail to develop significant mathematical competence even when immersed in a human symbolic environment. Although some animals have been taught to order a small subset of the numerals (less than 10) and carry out simple numerosity tasks within that range, they fail to generalize the patterns required for the indefinite counting that children are capable of mastering, albeit with much time and effort. If we consider the working memory requirements for noticing that the pattern ___-ty one, ___-ty two, ___-ty three, etc. repeats after “twen-,” “thir-,” “for-,” and so on, then it may not seem so unlikely that only a species with a rather large brain could even notice let alone generalize the pattern. And without that basis for understanding the domain and range of symbols to which arithmetical operations can be applied, there is no basis for further development of mathematical competence.

Although we have not accounted for forms of mathematical reasoning beyond symbolic reasoning except in passing, the account of mathematical rule-following suggested here points toward the possibility that processes of perception, visualization, and interaction may play a crucial constitutive role in mathematical and logical reasoning in general. Unlike more established views, many of which acknowledge the utility of mathematical notations as concise representations of abstract mathematical meanings but then go on to downplay their importance for symbolic reasoning proper, PMT suggests that notations and the sensorimotor processes that engage them are often at the very heart of high-level mathematical and logical cognition. In this vein, since many forms of advanced mathematical reasoning rely on graphical representations and geometric principles, it would be surprising to find that perceptual and sensorimotor processes are not involved in a constitutive way. Therefore, by accounting for symbolic reasoning—perhaps the most abstract of all forms of mathematical reasoning—in perceptual and sensorimotor terms, we have attempted to lay the groundwork for an account of mathematical and logical reasoning more generally. The potential for a satisfying unification of the successes and failures of human symbolic and other forms of mathematical reasoning under a common set of mechanisms provides us with the confidence to claim that this is a topic worthy of further investigation, both empirical and philosophical.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Keywords: human reasoning, formal logic, mathematics, embodied cognition, perception

Citation: Landy D, Allen C and Zednik C (2014) A perceptual account of symbolic reasoning. Front. Psychol . 5 :275. doi: 10.3389/fpsyg.2014.00275

Received: 11 December 2013; Accepted: 14 March 2014; Published online: 21 April 2014.

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Copyright © 2014 Landy, Allen and Zednik. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: David Landy, Psychological and Brain Science/Cognitive Science, Indiana University, 107 s Indiana Ave., Bloomington, IN 47405, USA e-mail: [email protected]; Colin Allen, History and Philosophy of Science/Cognitive Science, Indiana University, 107 s Indiana Ave., Bloomington, IN 47405, USA e-mail: [email protected]

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The Origins and Development of a Symbolic Mind: The Case of Pictorial Symbols

• Published: 12 March 2020
• Volume 51 , pages 53–64, ( 2020 )

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Two themes emerge from studies of the development of symbolic understanding; that development proceeds through multiple levels of understanding prior to full and reflective knowledge of the representational function of pictorial symbols, and that development is founded upon individual cognitive and social cognitive proclivities as well as on supports from others in the social group. The classical theoretical antecedents to this contemporary perspective on the development of pictorial symbol understanding are briefly reviewed here and followed by evidence from contemporary research that provides support for these claims in the domain of pictorial symbol understanding and its development.

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Callaghan, T. The Origins and Development of a Symbolic Mind: The Case of Pictorial Symbols. Interchange 51 , 53–64 (2020). https://doi.org/10.1007/s10780-020-09396-z

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Published : 12 March 2020

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DOI : https://doi.org/10.1007/s10780-020-09396-z

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FLEXIBLE USE OF SYMBOLIC TOOLS FOR PROBLEM SOLVING, GENERALIZATION, AND EXPLANATION

We provide evidence that student representations can serve different purposes in the context of classroom problem solving. A strategy used expressly to solve a problem might be represented in one way, and in another way when the problem is generalized or extended, and yet in another way when the solution strategy is explained to peers or a teacher. We discuss the apparent long-term memory implications this has regarding the preferences that students have for their original versus later developed representations, and how these preferences relate to the use of representational flexibility in classroom settings.

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This paper investigates the types of representations used by high-achieving eleven-year-old pupils in their argumentation in the process of mathematical problem solving. The literature review addresses pedagogical and psychological aspects of knowing representations and using them in the process of problem solving. In our empirical study we examine a sample of 109 eleven-year-old pupils who took part in the final round of a national mathematical competition in Serbia. A total of 656 problem solutions was analyzed. The results show that these pupils used and often combined inventive iconic and conventional numerical/symbolical representations in their argumentation. We discuss pupils’ choice of representations which lead to correct solutions and adjusted representations corresponding to the type of problem (algebraic or logical-combinatorial). The aim of the paper is to draw attention to the importance of studying representational approaches pupils take when solving problems.

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Based on Verschaffel et al.’s conceptualisation of flexible strategy choice, this article provides a critical review on the literature concerning flexible representational choice in mathematical learning. We argue that, while flexibility in the selection of a representation to complete a mathematical task has traditionally been understood as choosing the representation(s) that match(es) the characteristics of the to-be-solved task, research evidence suggests that it also includes the ability to take into account the characteristics of the subjects interacting with the representations, as well as the context in which such interaction takes place. The instructional and research implications of acknowledging the subjectivity and contextuality of flexible representational choice are examined.

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Mathematics uses a wide range of representations, but the mathematical symbol is not the only way to code information. Different ways of representing mathematical concepts and relationships are used, especially in the early stages of learning. Generally, the teacher decides on the choice of representational forms to use. But in the process of solving mathematical problems, it is the pupils – not the teacher – who are engaged in the problem-solving, and the coding used should support their cognitive work. This paper analyses how different representations can influence the results of work on an untypical mathematical problem. The task was solved by a group of 7–8 year-old pupils participating in a mathematics club. The examples selected for analysis indicate a strong relationship between the choice of representations and the final result of the pupils' work.

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Reasoning and explanation by students has been of interest to most mathematics and science educators and psychologists like Piaget. Reasons are used to justify propositions and involve the use of language and sym-bols (mathematics or otherwise). Researchers have ex-plored the use of language and symbols (signs and drawings) by students in the process of reasoning (Robotti, 2002; Radford, 2001). Vygotsky has also con-sidered language as a tool for the construction and management of thinking. Traditional mathematics classrooms, which are mostly teacher directed, emphasize writing clear steps, using correct symbols, syntax, etc., and not thinking about these objects, identifying relationships between these objects and operation signs and giving reasons using language or symbols. A number of studies have pointed out students' inability to deal with symbolic expres-sions. Students can neither make sense of the structure of the expression nor consistently use rules to manipu-late them...

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In this communication, we discuss the role of representations in the development of conceptual knowledge of 2nd grade students involved in additive quantitative reasoning through the analysis of the resolutions of two tasks that present transformation problems. Starting to discuss what is meant by additive quantitative reasoning and mathematical representation, we present after some empirical results in the context of a teaching experiment developed in a public school. The results show the difficulties with the inverse reasoning present in both situations proposed to students. Most students preferably use the symbolic representation, using also the written language as a way to express the meaning attributed to its resolution. The iconic representation was used only by a pair of students. Representations have assumed a dual role, that of being the means of understanding the students' thinking, and also supporting the development of their mathematical thinking.

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How do people learn flexible problem-solving knowledge, rather than inert knowledge ,that is not ,applied ,to novel problems? Both the source of the knowledge,– instructed or invented – and a central learning process – engaging,in self- explanation,– may ,influence the development ,of problem- solving flexibility. Seventy-seven third- through fifth-grade students learned about mathematical,equivalence under one of four conditions that

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• < Previous chapter

34 Symbols and Symbolic Thought

Tara Callaghan, Department of Psychology, St. Francis Xavier University, Canada

• Published: 16 December 2013
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This chapter explores the development of symbol use and symbolic thought across diverse domains (gesture, linguistic, pretense, and the material artifacts of models, pictures, maps, and video). The chapter begins with a clarification of different conceptualizations of central theoretical constructs. Then, evidence to support major theoretical claims in the field is considered. A number of themes emerge from these findings. There is clear evidence that for all domains the onset of symbolic insight is based on solid perceptual, cognitive, learning, and social-cognitive foundations. The importance of social supports from expert symbol users was also evident. New proposals that link symbolic knowledge to the development of consciousness and the uniquely human motive to share promise to generate exciting new developments in this field.

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Preschool Children’s Loose Parts Play and the Relationship to Cognitive Development: A Review of the Literature

Ozlem cankaya.

1 Department of Human Services and Early Learning, MacEwan University, Edmonton, AB T5J 4S2, Canada; ac.nawecam@nnitramnytahor

Natalia Rohatyn-Martin

Jamie leach.

2 Department of Child and Youth Study, Mount Saint Vincent University, Halifax, NS B3M 2J6, Canada; [email protected]

Keirsten Taylor

3 Department of Psychology, MacEwan University, Edmonton, AB T5J 4S2, Canada; ac.nawecamym@49krolyat

4 Centre for Research in Applied Measurement and Evaluation, University of Alberta, Edmonton, AB T6G 2R3, Canada; ac.atreblau@tulub

Associated Data

Not applicable.

Play is an integrative process, and the skills acquired in it—overcoming impulses, behavior control, exploration and discovery, problem-solving, reasoning, drawing conclusions, and attention to processes and outcomes are foundational cognitive structures that drive learning and motivation. Loose parts play is a prominent form of play that many scholars and educators explicitly endorse for cognitive development (e.g., divergent thinking, problem-solving). It is unique among play types because children can combine different play types and natural or manufactured materials in one occurrence. While educators and policymakers promote the benefits of loose parts play, no previous research has explored the direct relationship between preschool-age children’s indoor loose parts play experiences and cognitive development. We address this gap by bringing together the relevant literature and synthesizing the empirical studies on common play types with loose parts, namely object and exploratory, symbolic and pretend, and constructive play. We also focus on studies that examine children’s experiences through loose parts, highlighting the impact of different play types on learning through the reinforcement of cognitive skills, such as executive function, cognitive self-regulation, reasoning, and problem-solving. By examining the existing literature and synthesizing empirical evidence, we aim to deepen our understanding of the relationship between children’s play with loose parts and its impact on cognitive development. Ultimately, pointing out the gaps in the literature that would add to the body of knowledge surrounding the benefits of play for cognitive development and inform educators, policymakers, and researchers about the significance of incorporating loose parts play into early childhood education.

1. Introduction

Play is a foundational and universal phenomenon in the development of young children, often defined as an activity pursued for its own sake and mainly characterized by processes rather than end goals ( Smith 2005 ). Following Burghardt ( 2005 , 2010 ) and Pellegrini ( 2009 ), we define play as a process involving a range of intrinsically motivating activities for enjoyment. Although the exact definition of play is debated ( Smith 2005 ; Wallerstedt and Pramling 2012 ; Whitebread et al. 2012 ; Zosh et al. 2018 ), there is consensus on children’s motivation for involvement in play for exploration and discovery and its exceptional complexity in inducing learning ( Pyle et al. 2017 ; Smith 2005 , 2010 ; Whitebread et al. 2012 ). Play is also an integrating process ( Wood and Bennett 1997 ), where children draw upon and connect previous experiences, represent their ideas in different ways, imagine possibilities, explore, and create new meanings ( Dockett and Perry 2007 ).

Researchers have explored specific types of play (e.g., pretend, construction, sensorimotor) and their capacity to enhance children’s cognitive development ( Lillard et al. 2013 ; Wolfgang et al. 2001 ; Smith 2017 ). The more complex the play, the more it impacts development (e.g., pretend play; Beckwith et al. 1994 ; Lifter et al. 2011 ; Lillard et al. 2013 ; Zosh et al. 2022 ). What is evident is that children acquire foundational cognitive skills that drive learning during play, such as overcoming impulses through cognitive self-regulation, behavior control through emotional self-control, exploration and discovery, problem-solving, receptive and expressive language, social interaction, and attention to processes and outcomes ( Park 2019 ; Wolfgang et al. 2001 ). Many researchers recognize play as a medium for learning and the foundation for exploration ( Bergen 2009 ; Pramling Samuelsson and Johansson 2009 ; White 2012 ; Whitebread et al. 2017 ). There is growing global interest in loose parts play (LPP) to enrich children’s indoor experiences to motivate experimentation and learning (e.g., Beaudin 2021 ; Beloglovsky and Daly 2015 , 2016 ; Caldwell 2016 ; Casey and Robertson 2016 ; Daly and Beloglovsky 2014 ; Eren-Öcal 2021 ; Gençer and Avci 2017 ; Rawstrone 2020 ; Sear 2016 ).

This literature review first provides an overview of loose parts play and highlights its unique characteristics. Subsequently, drawing upon existing research on play and cognitive development, we examine the impact of specific types of play with loose parts on the cognitive development of young children. Through a comprehensive synthesis of the available literature, we explore how different play opportunities influence cognitive capacities, including executive function, cognitive self-regulation, reasoning, and problem-solving. Our review underscores the crucial role of play in facilitating the development of fundamental cognitive abilities, which in turn have long-term implications for learning and cognitive outcomes. This literature review critically integrates research findings to shed light on the potential contribution of loose parts play to cognitive development, emphasizing the significance of play as a means of fostering cognitive skills through the utilization of these specific materials.

1.1. What Is Loose Parts Play?

LPP is defined as children’s play with open-ended and interactive materials (e.g., cardboard, shells, tires, sand, pompoms) not initially intended for play that can be manipulated limitlessly ( Gull et al. 2019 ). LPP is an engaging form of play for children that offers complexity because children can combine different play types and various materials in one occurrence ( Beaudin 2021 ). This form of play emphasizes materials that allow children to play in multiple ways and levels of complexity while experimenting, discovering, inventing, and having fun ( Casey and Robertson 2016 ; Sear 2016 ). Indeed, LPP has many elements of free or unstructured play, as described by other researchers. These play types, like LPP, are often described as springboards for all subsequent learning, where children’s ideas, interests, and desires are respected, nurtured, and expanded into an ongoing, orderly, and recognizable curriculum incorporating knowledge from all disciplines ( Van Camp 1972 ; UNICEF 2023 ). However, free play may include any unstructured activity that inspires a child to use their imagination without constant adult direction. Some examples of free play include children playing together in the backyard, where various activities, such as running, jogging, climbing, jumping, and fine motor movement, help the child develop speed, strength, stamina, flexibility, and coordinative abilities. Likewise, unstructured play may resemble LPP, allowing children to explore, create, and discover without predetermined rules or guidelines. Like free play, however, this is open to a broad scope of activities, including artistic or musical games, imaginative games (e.g., making a fort with boxes or blankets), dressing up or playing make-believe, or exploring new spaces like woods, backyards, parks, and playgrounds.

1.2. What Is Unique about Loose Parts Play?

Nicholson ( 1972 ) coined the term loose parts and described the importance of interactive materials that can have many affordances.. According to Affordance Theory ( Gibson 1979 ), the world is perceived as an object of possibilities for action or affordances. In terms of materials, affordances refer to how an object or material can be used or interacted with. Children’s LPP can involve a variety of materials: everyday synthetic or natural materials, reusable and upcycled materials, and commercial toys that may promote thinking in Science, Technology, Engineering, Arts, and Mathematics (STEAM) ( Beloglovsky and Daly 2016 ; Drew and Rankin 2004 ; Bairaktarova et al. 2011 ). Play materials with many affordances provide children with more opportunities to learn and develop new skills through their play.

We know that children’s play frequently involves objects, materials, or toys ( Gull et al. 2020 ; Tizard et al. 1976 ), and play themes generally follow the ideas inherent in the materials and toys available ( Pellegrini and Smith 1998 ; Pellegrini and Perlmutter 1989 ; Smith and Connolly 1980 ). Thus, LPP is unique because the materials are clearly defined by their affordances compared to those used in other play types (e.g., musical, pretend). It is important for children’s play materials to have many affordances because it allows for a wide range of exploration and creativity. For example, a simple wooden block can be used as a building material, a tool for stacking and balancing, or a prop in imaginative play. Each of these uses can offer a different learning experience and help children develop a range of skills, such as problem-solving, spatial reasoning, and fine motor skills.

According to Trawick-Smith et al. ( 2014 ), quality play encourages children to be involved in critical learning and cognitive development elements such as self-regulation, make-believe, problem-solving, and creative expression. High-quality play offers many educational benefits such as problem solving and learning ( Bergen 2006 ; Gronlund 2010 ). When children have access to play materials with many affordances, they are more likely to engage in open-ended and imaginative play that reinforces these educational benefits. LPP allows children to explore their interests and ideas to develop their creativity and self-expression. Additionally, having access to a variety of play materials with many affordances can help with attention shifts and increase engagement in play, which is essential for children’s development and well-being. Consequently, materials used in LPP are more likely to fulfill quality play opportunities.

Researchers have shown that materials with many affordances in children’s play, such as those used in LPP, also have developmental benefits ( Guyton 2011 ; Bairaktarova et al. 2011 ; Kiewra and Veselack 2016 ; Segatti et al. 2003 ; Shabazian and Soga 2014 ). For example, these materials can inspire, maintain, and spark ideas, support children using symbolic skills to transform ideas into scenarios during play, draw social interaction into a shared play sphere, promote self-esteem, emotional well-being, and resilience, and foster children’s higher mental processes, such as thinking or internal dialogues ( Pellegrini and Bjorklund 2004 ; Pepler and Ross 1981 ; Mundy and Newell 2007 ; Drew and Rankin 2004 ; Whitebread et al. 2012 ; Schaefer 2016 ). Not all toys and materials are equally effective in promoting engaging play, especially for children of different ages ( Cutter-Mackenzie and Edwards 2013 ; Trawick-Smith et al. 2011 ). While it is difficult to define engaging play by age, one parameter can be helpful to define play that sustains children’s attention over a period of time with elaborate themes and ideas. Open-ended materials and toys that do not suggest a play theme allow for many kinds of play, including constructive and pretend play, that can lead to positive outcomes ( Trawick-Smith et al. 2015 ). Trawick-Smith et al. ( 2015 ) also found that play materials and toys with many affordances do not serve younger children well but promote engaging play for older ones. Younger children perform their most frequent pretend-to-play with realistic toys. Furthermore, everyday objects and natural materials can foster cause-and-effect or trial-and-error explorations and positively influence children’s cognitive development by sparking imagination, creativity, and motivation for further exploration and learning ( Bairaktarova and Evangelou 2012 ; Kiewra and Veselack 2016 ).

In addition, Howe et al. ( 2022 ) investigated how open-ended versus closed-ended toys impact children’s pretend play. They found that open-ended toys are particularly important in supporting children’s play and learning, as they encourage divergent and convergent thinking, imagination, and problem-solving skills. The nature of toys determines children’s patterns of communication and behavior. The authors concluded that although the toy themes are somewhat suggestive, they may not promote similar behaviors and outcomes in pretend play. Therefore, the type of toys and play materials children can access can significantly impact their play experiences, the play types they involve in, and their learning outcomes. Open-ended materials and toys that allow for many kinds of play have been found to have developmental benefits, foster creativity, and encourage problem-solving skills. Thus, considering play materials with many affordances provide opportunities for LPP to promote children’s growth and development. Researchers have heavily investigated the developmental benefits of playing with individual open-ended materials, i.e., play with blocks, LEGO ® , or sand in isolation (e.g., Kiewra and Veselack 2016 ; Schulz and Bonawitz 2007 ; Segatti et al. 2003 ; Shabazian and Soga 2014 ; Zippert et al. 2019 ). However, LPP can involve interactive materials used simultaneously in various play types ( Casey and Robertson 2016 ; Daly and Beloglovsky 2014 ).

1.3. What Is the Status of Research on Loose Parts Play?

As already highlighted, broad interest in LPP to enrich children’s play experiences has grown ( Beaudin 2021 ; Beloglovsky and Daly 2015 ), with claims to be a developmental foundation for creativity, problem-solving, and divergent thinking. However, research has not kept pace with the enthusiasm of childcare professionals and policymakers (e.g., Nova Scotia Department of Education and Early Childhood Development 2018 ). Recent systematic and scoping reviews document that, thus far, there are only a handful of empirical studies on children’s LPP, and the focus on the developmental benefits of this type of play is limited, especially for cognitive development ( Gibson et al. 2017 ; Gull et al. 2019 ; Houser et al. 2016 ). Instead, researchers have focused primarily on outdoor LPP, examining physical and social development ( Houser et al. 2016 ; Maxwell et al. 2008 ; Spencer et al. 2019 ). Indoor play environments offer unique opportunities for young children to engage in imaginative, creative, and sensory-rich activities. However, despite the prevalence of indoor play spaces and the common recommendation of loose parts play for the preschool age group, there is limited scientific research available to support these practices ( Gibson et al. 2017 ). Studies on young children’s indoor LPP are limited to a few non-empirical studies ( Beaudin 2021 ; Sear 2016 ; Rawstrone 2020 ). No empirical work considers children’s cognitive functioning (e.g., verbal IQ, executive function). Furthermore, the influence of critical factors such as a child’s age, family income, and educational attainment on parent/child play types, duration, and engagement with loose parts has not yet entered the research dialogue. Thus, there is a noticeable research gap when it comes to understanding the specific benefits of indoor play for children under the age of 6.

The types of play children commonly utilize with loose parts have yet to be documented or explained. Such knowledge would support understanding which materials are most conducive to specific types of progressively complex play, allow children to design their own learning goals, and prepare young children for learning. The evidence that illustrates the developmental benefits of this type of play is very limited. For example, Gibson et al. ( 2017 ) robustly indicated the lack of research on the benefits of LPP. They highlighted that little is known about how LPP influences children’s development beyond physical and social domains ( Flannigan and Dietze 2017 ; Gibson et al. 2017 ). Early studies have focused narrowly on children’s outdoor LPP ( Flannigan and Dietze 2017 ; Gull et al. 2019 ; Houser et al. 2016 ; Spencer et al. 2019 ; Olsen and Smith 2017 ) and mostly on physical and social development ( Dobbins et al. 2013 ; Engelen et al. 2013 ; Flannigan and Dietze 2017 ; Houser et al. 2016 ; Maxwell et al. 2008 ; Ridgers et al. 2011 ; Spencer et al. 2019 ). Furthermore, the existing empirical studies focus mainly on older children (c.f. McLoyd 1983 ; Maxwell et al. 2008 ; Oncu et al. 2015 ). Empirical work on young children’s indoor LPP types and their relationship to preschool-age children’s cognitive skills in the current literature is crucially lacking.

• Loose Parts Play (LPP) focuses on utilizing materials that offer multiple possibilities, enabling children to engage in diverse play experiences and develop cognitive capacities like executive function and cognitive self-regulation. LPP provides flexibility and adaptability, allowing children to manipulate, combine, and transform loose parts in countless ways, thereby facilitating open-ended play experiences.
• Research on LPP is limited, especially regarding its developmental benefits for cognitive development. Existing studies primarily focus on outdoor LPP and its impact on physical and social development. More research is needed, particularly on young children’s indoor LPP and its influence on cognitive functioning, considering factors such as the child’s age or family socio-economic status.
• Play, including loose parts play, is fundamental in childhood and significantly impacts children’s cognitive development. The open-ended nature of loose parts play fosters divergent thinking and flexible problem-solving approaches.
• Symbolic and pretend play promote cognitive skills such as symbolic substitution, dual representation, language development, executive function, self-regulation, and problem-solving. Loose parts play also supports constructive play, stimulating cognitive advancement, problem-solving, and higher-level thinking, while enhancing social interaction and communication skills.
• Further research is needed to explore the specific impact of loose parts on children’s play while considering the effects of a child’s cognitive development, age, socio-economic status, and cultural differences.

2. How Do Specific Types of Play with Loose Parts Impact Young Children’s Cognitive Development?

2.1. object and exploratory play with loose parts.

Object play is an infant or child’s playful exploration of an object and or engagement with it to learn about its properties ( Hughes 2021 ; Smith 2010 ) and progresses from early sensorimotor explorations to symbolic objects (i.e., using objects to represent other objects, such as a banana as a telephone) for communication, language, and abstract thought ( Yogman et al. 2018 ). Hughes ( 2021 ) describes object play as encompassing problem-solving, considering it ‘problem-solving play’. Problem-solving can be defined as a cognitive process through which individuals identify, analyze, and apply solutions to overcome obstacles or challenges that hinder the achievement of a desired goal. It involves systematically exploring and evaluating different strategies, information, and resources to find the most effective and efficient way to solve a problem or address a complex situation. Certainly, object play is viewed as a window to cognitive processes—a means for children to express their knowledge and interpret new knowledge by exploring objects at hand ( Lifter et al. 2022 ). Piaget and Cook ( 1952 ) described children’s object play as originating from sensorimotor explorations and termed it sensorimotor play. This early exploratory play is the first form of object play and typically begins around five months of age ( White 2012 ). Within a year, simple reflexes turn into intentional, coordinated movements of exploration. Concerning cognitive developmental stages, Piaget and Cook ( 1952 ) postulated that children’s external actions to understand how the world operates eventually become internal representations.

Through manipulating objects, toddlers begin to have cognitive representations of the world that can be evident in how they relate to the representations of objects and people around them. For instance, if a young child wants an obstructed object, they reach for it directly. These trial-and-error sessions for younger children transform into deliberate planning for older children ( Smith 2010 ). Pellegrini ( 2013 ) describes the benefits of children’s object play as part of learning behavioral “modules”. He emphasized that modules are novel and recombined behavior and cognitive routines constructed by individuals in response to new ecological demands. With experience, these diverse behavioral routines become more focused and relevant to the environment. Pellegrini ( 2013 ) speculated that children’s play experiences with objects generate behavioral modules.

Object play has a strong presence in children’s lives and remains a large part of the daily routine, occupying approximately 10–15% of children’s waking hours by conservative estimation ( Smith and Connolly 1980 ). Its cognitive developmental contribution includes learning about the nature of objects, problem-solving, creativity, and foundational skills for science, technology, engineering, and mathematics ( White 2012 ). Through exploratory object play, children are introduced to the function of objects and how to control them ( Bjorklund and Gardiner 2011 ). They use object exploration to test their hypotheses about their environments and how those objects operate by touching and manipulating parts of the toy ( Schulz and Bonawitz 2007 ), even in infants ( Baldwin and Moses 1994 ; Gweon 2012 ; Schulz 2015 ). Indeed, the quality of the evidence children observe affects their exploratory play. Schulz and Bonawitz ( 2007 ) found that preschool children distinguish confounded and unconfounded evidence and selectively engage in more exploration when the causal structure of events is ambiguous. Thus, the exploratory play of even very young children appears to reflect some of the logic of scientific inquiry and give them a basis to practice the life-long skill of learning about the properties of and uses for objects that they can touch, hear, and see. More crucially, it helps them to make inferences about properties that are not as easy to ascertain ( Gweon 2012 ; White 2012 ).

Given play’s imaginative and flexible nature, another core cognitive skill facilitated by exploratory and object play is problem-solving ( Cankaya 2022 ), particularly divergent problem-solving skills. By engaging in problem-solving tasks, individuals develop their analytical capabilities, enhance their adaptability, and acquire valuable problem-solving skills that can be applied in various aspects of life and learning ( Lillard et al. 2013 ). For example, Pepler and Ross ( 1981 ) assigned young children to play with a puzzle, considered a convergent toy due to its single solution to the problem. In another condition, children were offered a multiple-option block set, considered a divergent toy. In later tasks, children who played with the blocks were more innovative and flexible in their problem-solving approaches than their peers who played with convergent toys. The researchers emphasized that children benefit from divergent experiences and that those experiences can be transferred and generalized more broadly. They also found that children who played with the divergent toys were generally successful on various divergent and convergent problem-solving tasks, suggesting that engaging in divergent playful activities might instill the idea of numerous creative solutions to a problem ( Pepler and Ross 1981 ; White 2012 ).

Furthermore, Solis et al. ( 2017 ) documented that experiencing and manipulating physical principles through objects allows young children to formulate scientific intuitions, serving as potential precursors to learning in STEAM subjects. Crucially, this supports children’s reasoning skills with materials. Through naturalistic observations of preschool children’s free play, they demonstrated that children encountered various physics concepts while engaging in spatial–mathematical activities. This occurred as children engaged in planning and executing play sequences, solving problems, and exploring the objects available. During play, children discover physical principles through object affordances ( Nicholson 1972 ). Similarly, Bjorklund and Gardiner ( 2011 ) asserted that children could explore and learn about the properties of and uses for objects they can see, touch, and hear through solitary object play.

Object play has been found to have a positive impact on children’s visuospatial skills, which are crucial for their numerical reasoning abilities ( Caviola et al. 2014 ; Fanari et al. 2019 ; Holmes et al. 2008 ; LeFevre et al. 2010 ; Sella et al. 2016 ). Several studies have directly linked early object play to better math outcomes ( Caldera et al. 1999 ; Verdine et al. 2019 ; Wolfgang et al. 2001 ). Longitudinal research conducted by Wolfgang et al. ( 2001 ) suggests that engaging in complex object play during early childhood can lay the foundation for later mathematical understanding in formal learning contexts. Additionally, Verdine et al. ( 2019 ) explain that tangible toys with various geometric shapes can enhance children’s spatial language use and facilitate interactions between adults and children, thereby supporting the development of early geometric knowledge. These findings highlight the significance of object play in promoting children’s mathematical skills and the importance of providing them with opportunities to engage with toys and materials that foster spatial thinking and geometric understanding.

Riede et al. ( 2021 ) created a framework for understanding the role of play objects and object play for innovative behavior. They emphasized that children’s play strongly reflects adult behaviors, and play that involves imagination encourages children to explore the consequences of potential benefits of social and technological action schemata before enacting them. Some toys offer a powerful opportunity as an innovation primer, allowing children to explore the complex, emergent mechanical and material affordances of associated adult technologies ( Lancy 2017 ). Riede et al. ( 2021 ) suggested that play objects offered by adults to their youngsters significantly affect children, adolescents, and young adults’ possibility of becoming innovative. Teachings and pedagogical interventions may help maintain long-term traditions, and playing with objects may function as a primer for innovation ( Riede et al. 2021 ). Even children’s brief frequencies of experimentation increase propensities to innovate in late childhood, adolescence, and later life. These trial-and-error activities scaffold children to develop creativity and strategies to tackle novel problems successfully.

Children involve loose parts in their object and exploratory play by incorporating and manipulating objects with multiple uses ( Scott-McKie and Casey 2017 ). Loose parts can be moved, combined, designed, redesigned, taken apart, and put together in endless ways ( Nicholson 1972 ). Children involve loose parts in their object play differently from other objects due to the unique characteristics and possibilities they offer ( Nicholson 1972 ; Beloglovsky and Daly 2015 ). Loose parts include various materials in combination ( Cankaya 2023 ) that are predominantly open-ended and can be used in multiple ways, while other objects may have a specific intended purpose or limited functionality. In that regard, loose parts offer greater flexibility and adaptability in play. They can be combined, arranged, and modified in various ways, allowing children to create unique structures, designs, or scenarios.

In contrast, other objects may have limited possibilities for manipulation or customization. For example, a toy car typically serves a specific role and function. In contrast, a loose part, such as a stacking cup, can be a building element, a prop in pretend play, or a part of a sorting activity. Children can explore and engage in both object and exploratory play, but loose parts give them more options for how objects can be used in various ways. Also, children can transform and repurpose loose parts based on their imagination, whereas other objects may have predetermined uses or fixed representations. Thus, loose parts give children more opportunities for flexibility and adaptability in object and exploratory play, as they need to figure out how to use loose parts effectively, experiment with different combinations, and overcome challenges. Other objects often have a more prescribed use (e.g., puzzles; Scott-McKie and Casey 2017 ), limiting the need for problem-solving in the same way. Loose parts give children greater freedom, flexibility, and open-ended possibilities compared to other objects, making them unique components of children’s play experiences.

2.2. Symbolic and Pretend Play with Loose Parts

Symbolic and pretend play activities are characterized by an ‘as-if’ stance ( Garvey 1990 ), and the playful set of behaviors and activities often involve nonliteral actions ( Weisberg 2015 ). In the context of pretend play, the child taking on the role of the pretender consciously and purposefully projects a mentally represented alternative onto the current situation, fostering a playful atmosphere ( Lillard et al. 2013 ). Children’s involvement in symbolic or pretend play is depicted by an active transformation of the here and now. It involves a living agent who is aware that they are pretending, a reality that is pretended, and a mental representation projected onto reality. For example, a child may use a stick as a sword and pretend to strike a playmate who then pretends to be injured. This type of play is alternatively called imaginary play or pretense. Furthermore, Holmes et al. ( 2019 ) definition of creative play encompasses pretend and symbolic play, wherein children think creatively through these types of play; in a sense, creative play may occur as a result of pretend or symbolic play.

Like other kinds of play, pretend play is connected to children’s cognitive development although, uniquely, it appears to be distinctively human ( Smith 2010 ; Whitebread et al. 2017 ). Symbolic substitution is a cognitive benchmark for young children that manifests as language skills and emerges after the first 12 months ( Whitebread et al. 2017 ). Around this time, children start mastering various symbolic systems such as spoken language, numbers, and music. Some examples are when a child pretends a cup is a party hat (not immediately clued in the environment), locating objects from a map, reading words, and understanding their reference points. This dual representation is the ability to think about an object in different ways simultaneously ( DeLoache 2000 ; Uttal et al. 2009 ). This ability first appears around age 2, increases rapidly, and signals an awareness that the child has begun representational activity ( Whitebread et al. 2017 ). Therefore, pretending and language development grow with children’s ability to think symbolically. Children’s symbolic or pretend play gradually includes more complex schemes in the appearance of sociodramatic or role play. Consequently, preschoolers are observed to spend more time in pretend play than younger children ( Howes and Matheson 1992 ).

Researchers have also demonstrated that children’s pretend play has both short-term and long-term benefits for cognitive development ( Copple and Bredekamp 2009, p. 15 ; Lillard et al. 2013 ; Savina 2014 ). In particular, a significant body of evidence shows that children involved in complex pretend play have executive function skills ( Coelho et al. 2020 ; Garon et al. 2008 ; Germeroth et al. 2019 ; Kelly et al. 2011 ; Walker et al. 2020 ). Executive function (EF) is a set of high-level cognitive processes that facilitate new ways of behaving and optimize one’s approach to unfamiliar circumstances ( Baddeley 2002 ; Barkley 2001 ; Cumming et al. 2022 ; Diamond 2013 ; Garon et al. 2008 ; Happaney and Zelazo 2022 ; Zelazo et al. 2003 ). It includes basic cognitive processes such as attentional control, cognitive inhibition, inhibitory control, working memory, and cognitive flexibility. EF is often explained with the analogy of an “air traffic control system at a busy airport that safely manages the arrivals and departures of many aircraft on multiple runways” ( Center on the Developing Child at Harvard University 2011 ). These mental processes play a critical role in a person’s ability to manage daily life tasks such as sustaining attention, keeping goals and information in mind, refraining from responding immediately, resisting distraction, tolerating frustration, considering the consequence of different behaviors, reflecting on past experiences, planning for the future, and balancing multiple tasks successfully ( Diamond 2013 ; Garon et al. 2008 ; Zelazo et al. 2016 ). Thus, they are necessary for the cognitive control of behavior: selecting and successfully monitoring behaviors that facilitate the attainment of chosen goals.

Although the direction of the relationship between children’s EF and pretend play is still subject to debate ( Lillard et al. 2013 ), several play-centered interventions have successfully enhanced children’s executive function ( Coelho et al. 2020 ; Elias and Berk 2002 ; Thibodeau et al. 2016 ; Walker et al. 2020 ). Children involved in short amounts of pretend play regularly (e.g., less than 10 min daily) show improvements in performance on subsequent executive function tasks ( Carlson and White 2013 ). Walker et al. ( 2020 ) developed a pre–post design intervention study where educators embedded targeted activities and role-playing with a problem to solve collectively over ten weeks, resulting in significant behavior improvements in children’s executive function performance. Similarly, Kelly and colleagues observed 4- and 5-year-old children in their free play to explore the role of inhibitory control in symbolic play. They found that greater inhibitory control positively correlated with more symbolic play. These studies indicate that encouraging children to engage in pretend play, particularly more mature forms, could be a natural vehicle by which adults can promote EF and self-regulation ( Lillard et al. 2013 ; White 2012 ).

Furthermore, growing evidence shows the development of self-regulation skills through pretend play ( Elias and Berk 2002 ; Savina 2014 ; Slot et al. 2017 ). Self-regulation, the ability to understand and manage one’s behavior and reactions ( Savina 2014 ), develops rapidly in the first years of life and continues to develop into adulthood. EFs are presumed to be the general forms or classes of self-directed actions we use in self-regulation ( Barkley 2001 ). In children’s play, self-regulation may manifest in a variety of ways, such as regulating reactions to intense emotions such as frustration or excitement, calming down after something exciting or upsetting happens, focusing on a task, refocusing attention on a new task, controlling impulses, or learning a range of behaviors to engage in social play (i.e., play with others; Eisenberg and Sulik 2012 ; Post et al. 2006 ). EF and self-regulation may produce an overall net maximization of social consequences when considering response alternatives’ immediate and delayed outcomes. They are also instrumental in purposive, intentional behavior such as learning, experimenting with new ideas, or verbal communication ( Barkley 2001 ). Significantly, Weintraub et al. ( 2013 ) showed that EF skills build throughout childhood and adolescence, with early childhood having the most dramatic growth. Since proficiency in numerous EFs decline later in life ( Weintraub et al. 2013 ), mastering such skills during the early years may be essential for daily life functioning in later adulthood.

Slot et al. ( 2017 ) differentiated between cognitive and emotional self-regulation and investigated how 3-year-olds demonstrated each in a naturalistic play setting. ‘Hot’ executive functions refer to self-management skills when emotions run high, while ‘cool’ executive functions refer to skills when emotions are not a factor. They found that in neutral or cool situations, children’s EF typically includes working memory, inhibitory control, and cognitive flexibility and that 3-year-olds showed aspects of cognitive and emotional self-regulation ( Blair and Ursache 2011 ; Slot et al. 2017 ). Cool EFs appeared significantly related to emotional self-regulation, whereas hot EFs were not significantly related to cognitive or emotional self-regulation. Specific to our discussion in this paper, they found that the quality of pretend play was strongly associated with cognitive self-regulation and, to a lesser extent, emotional self-regulation. These findings further suggest that pretending may encourage the flexible thinking required for children to overcome impulses and successfully control cognitive behaviors ( Slot et al. 2017 ; White and Carlson 2016 ).

Loose parts allow children to use their imagination and assign symbolic representations to objects (e.g., please compare building a house with Magna-Tiles versus including a dollhouse in children’s pretend play; Gronlund 2010 ). They can transform a simple loose part, such as a stick or a fabric, into a pretend object with multiple meanings. For example, a stick can become a magic wand, a fishing rod, or a sword. Other objects often have specific and fixed representations that limit their transformative potential (e.g., Elsa’s or Harry Potter’s magic wand). Children can adapt and incorporate loose parts into various roles and scenarios during pretend play ( Gronlund 2010 ; Scott-McKie and Casey 2017 ). They can easily change the purpose and function of loose parts based on the evolving storyline or their imaginative needs. In contrast, other toys and play materials often have predefined roles and are less adaptable to different pretend play situations. Halfway through a pretend or symbolic play scenario, if children see the idea or opportunity, they can combine loose parts, rearrange them, or add additional elements to create props or set designs for their imaginative scenarios.

Furthermore, loose parts can facilitate the use of language, in particular, productive language through narrative expansion in pretend play. Children can introduce new loose parts into their play to enrich the storyline or add complexity to their pretend world. They can bring in additional loose parts to represent characters, objects, or settings, enhancing the depth and breadth of their imaginative play. An active play partner in pretend or symbolic play can benefit young children’s LPP, resulting in longer and more complex play episodes than when they play alone ( Balfanz et al. 2003 ; Ramani and Eason 2015 ; Schmitt et al. 2018 ). Children frequently involve others in their play in early learning environments. Pramling Samuelsson and Johansson ( 2009 ) explored why children involve teachers in their play and learning through video recording children’s play in preschool and primary schools. They found five reasons for involving teachers: getting help from the teacher, acknowledging teachers as competent persons, making the teachers aware of other children breaking the rules, getting information about and confirmation of how things work, and involving teachers in play. Pramling and colleagues reasoned that children see educators as knowledgeable and that they can contribute to their learning processes. As children age, they mobilize educators as resources to learn about something or ask questions to expand and continue with the task. Children’s time playing with others can be a time to learn new skills, practice existing abilities, and build interests ( Ramani and Eason 2015 ). The continuum of playful learning shows the different levels of social interaction involved in experiences. The flexible component of loose parts allows children to play, explore, and discover independently in their pretend play. By involving loose parts in their pretend play, children have the freedom to transform objects, adapt them to different roles, and engage in imaginative and flexible play scenarios. The open-ended nature of loose parts can promote creativity, symbolic representation, narrative expansion, and collaborative play experiences that may differ from the limitations imposed by other objects.

2.3. Constructive Play with Loose Parts

Constructive play, characterized by manipulating materials to create things, is a commonly observed form of play during preschool and kindergarten free play periods ( Gronlund 2010 ; Park 2019 ). It typically begins around the age of 2 and becomes the most prevalent form of play between the ages of 4 and 6, accounting for a significant portion of children’s playtime ( Rubin 2001 ). During constructive play, children experiment with materials, manipulating and constructing objects ( Maxwell et al. 2008 ). They create something by combining basic elements, arranging them in various ways, and achieving a goal through these processes ( Forman 2006 , 2021 ). Examples of constructive play include building forts, stacking blocks, constructing LEGO sets, making sandcastles, and shaping playdough figures, which can be both static and dynamic in nature. Constructive play with basic elements, such as blocks, offers opportunities for children to develop cognitive skills, including symbolic awareness and problem-solving abilities ( Han and Park 2010 ). It allows children to produce patterns, objects, and functional systems and engage in pretend sequences, fostering creativity and imaginative thinking ( Forman 2006 ). Moreover, constructive play provides insights into children’s thinking processes as they pretend, invent, improvise, and design their own rules at their own pace ( Forman 2006 ). Overall, constructive play stimulates cognitive advancement and promotes higher-level thinking in children ( Ness and Farenga 2016 ; Park et al. 2008 ).

Children’s play themes generally follow the ideas inherent in the materials and toys available. However, materials and toys used for children’s play have changed significantly over the years, reflecting societal changes, technological advancements, and shifts in understanding child development ( Cankaya 2023 ). Loose parts can be offered in many combinations, but the impact of material choice on children’s play types and engagement is unknown ( Gibson et al. 2017 ). Children can incorporate loose parts materials into their constructions, adding a sense of authenticity and connection to the natural world ( Beloglovsky and Daly 2016 ). They also need to consider the spatial relationships, balance, and structural integrity of their constructions ( Scott-McKie and Casey 2017 ).

According to researchers, the most prominent cognitive skills involved in early childhood science involvement in constructive play are problem-solving, critical thinking, and scientific inquiry using trial and error ( Campbell et al. 2018 ; Soylu 2016 ; Yücelyiğit and Toker 2021 ). This can increase children’s understanding of geometry, physics, and architectural principles. Other construction toys (e.g., Lincoln Logs) may not incorporate other toys in the same way that would allow various design elements that originally did not have a place in the construction. Ness and Farenga ( 2016 ) suggest that the specific qualities of some play materials (e.g., blocks, bricks, and planks) may help establish the scientific, mathematical, and technological foundations for children’s cognitive development, as opposed to scripted play properties may have the opposite effect that the use of products manufactured with specialized, commercialized themes prevents children from self-regulation and even ideation. Loose parts often encourage collaboration and social interaction, particularly with peers during constructive play.

Collaborative building requires them to create and establish joint goals using receptive and expressive language, such as what they would build and how they would build it ( Vriens-van Hoogdalem et al. 2016 ). It also necessitates communicating actions, representations of the blocks, and the significance of the structures they create. During peer play, children must also coordinate their behaviors, communicate effectively to establish the interaction’s goals and rules, and work through disagreements by understanding each other’s views ( Pellegrini 2009 ; Ramani et al. 2014 ). Through discussion, children attempt to resolve their differing perspectives and advance their understanding of difficult, complex problems. Thus, peer involvement and cooperative play activities are characterized by this common understanding of the goals and processes to execute them ( Bratman 1992 ). Children can share loose parts, negotiate roles, and work together to create and develop their pretend play scenarios. Other objects may not foster the same level of collaboration and shared imagination. Children engage in open-ended exploration, creative problem-solving, and collaborative building experiences that differ from other objects or toys’ more structured and limited possibilities. Thus, loose parts’ constructive play capacity is qualitatively different from other play materials and toys. Table 1 below presents research findings that establish connections between specific play types, as explained in this article, and their impact on young children’s cognitive development. Each play type contributes to various aspects of cognitive growth, highlighting the diverse benefits associated with different types of play.

Research connecting specific play types to young children’s cognitive development.

3. Conclusions and Future Directions

Play is fundamental in childhood and consumes a large portion of children’s unstructured time ( Haight and Miller 1993 ). There is a clear developmental progression of children’s ability to engage in play from sensorimotor play during infancy to the emergence of pretend play in early childhood. A child’s engagement in various types of play with open-ended materials and play partners leads to qualitative changes in their play complexity and core cognitive skills that are critical in learning and motivation, even in adulthood.

Children’s cognitive development proceeds rapidly in the early years, which mirrors the dynamic changes in their play. The ability to play, specifically pretend play, appears to be an early expression of children’s understanding of symbols and symbolic relations ( Piaget 1962 ). The discussion regarding the direction of the relationship between play and cognitive development is complex (e.g., Duncan and Tarulli 2003 ). However, there is growing evidence that some play types have the potential to facilitate core cognitive functions ( Coelho et al. 2020 ; Garon et al. 2008 ; Germeroth et al. 2019 ; Kelly et al. 2011 ; Walker et al. 2020 ). In particular, play experiences facilitate the development of various cognitive skills, including executive function, problem-solving, and critical thinking ( Andersen et al. 2022 ; Hirsh-Pasek et al. 2004 , 2009 , 2020 ; Jaarsveld et al. 2012 ; Koerber et al. 2005 ; Lillard et al. 2013 ; Schulz and Bonawitz 2007 ; Weisberg et al. 2016 ; Whitebread et al. 2017 ). As children acquire these complex cognitive capacities, their play becomes more multifaceted, thus reflecting and supporting the underlying mechanisms for core cognitive skills.

Play serves as a foundation for the development of lifelong learning skills. Individuals with well-developed executive function skills are better equipped to engage in independent learning, self-directed study, and effective time management. These skills also support academic achievement by facilitating sustained attention, impulse control, and emotional regulation during challenging tasks. Moreover, researchers also document that play facilitates cognitive self-regulation skills ( Elias and Berk 2002 ; Savina 2014 ; Slot et al. 2017 ), which are crucial skills for learning, school achievement, and building and maintaining social relationships. Executive function and cognitive self-regulation are necessary for optimal cognitive development, as they provide the cognitive abilities needed to navigate complex tasks, set goals, adapt strategies, and make informed decisions. Strengthening these skills during early development lays a solid foundation for continued learning and success throughout life. While further research is needed to deepen our understanding, the existing evidence highlights the potential of engaging in specific types of play with indoor loose parts to positively influence young children’s cognitive development and equip them with essential skills for lifelong learning.

Play provides opportunities for children to actively engage in activities that require them to plan, strategize, and make decisions, thereby enhancing their cognitive abilities. Furthermore, play serves as a catalyst for learning, allowing children to explore their interests, acquire new knowledge, and develop a deeper understanding of concepts. The intrinsic motivation inherent in play promotes active engagement, curiosity, and a positive attitude toward learning, in particular, if the materials are conducive to various types of play ( Trawick-Smith et al. 2015 ). Although research on loose parts play is currently limited, studies focusing on specific types of play with open-ended materials provide compelling evidence that engaging in play with indoor loose parts can potentially have a significant impact on the cognitive development of young children ( White 2012 ; Baldwin and Moses 1994 ; Bjorklund and Gardiner 2011 ; Caviola et al. 2014 ; Fanari et al. 2019 ; Gweon 2012 ; Holmes et al. 2008 ; LeFevre et al. 2010 ; Schulz and Bonawitz 2007 ; Schulz 2015 ; Sella et al. 2016 ).

Researchers have consistently shown that play fosters cognitive skills such as problem-solving and reasoning. The open-ended nature of loose parts play promotes divergent thinking and flexibility in problem-solving approaches. Children manipulate and interact with a variety of loose parts, allowing them to experiment, explore, and make connections, which supports their cognitive development. Moreover, through this type of play, children develop cognitive flexibility, innovation, and a deeper understanding of cause-and-effect relationships. The versatility and adaptability of loose parts play enable children to engage in self-directed learning experiences, promoting agency in their cognitive growth. Educators and parents should recognize the value of incorporating indoor loose parts play into children’s environments as a means to enhance their cognitive development and promote holistic learning experiences.

Discussing children’s play in international and diverse communities requires careful consideration of social, cultural, and political contexts impacting children’s lives ( Shimpi and Nicholson 2014 ; Thibodeau-Nielsen et al. 2020 ). Adults (e.g., caregivers, parents, educators) must provide children with balanced opportunities for different kinds of play (e.g., constructive, pretend play) to nurture overall development. Providing a variety of materials to stimulate different types of play is necessary. For example, offering a variety of loose parts in rotating order could support cognitive development through quality play and engagement opportunities. It is also essential for adults to play with children on children’s terms. While there are benefits for children to be left on their own to free play, there are positive benefits of some active adult involvement in the play, such as supporting longer, more complex episodes of play ( Ward 1994 ). Lastly, ensuring equity in all children’s access to play and play materials is essential for future success as a society. Equal access to play is vital for children’s sense of belonging and ensures all children can fulfill their potential for lifelong learning and success.

As society continues to change, research on play must be mobilized to ensure early learning educators, families, community advocates, and health and education professionals draw on the most current evidence to optimize children’s development and support their learning and cognitive growth ( Barnett and Owens 2015 ). In particular, given the popularity of LPP, it is vital to investigate further its specific impacts on children’s development, such as the relationship between children’s cognitive development and LPP duration and complexity and the possible unintended outcomes of LPP on children’s cognitive, social, and physical development.

Furthermore, relatively little is known about the effects of socio-economic status and ethnic and cultural differences in children’s play. Further research on culturally specific play materials, their impact on children’s growth, the role of adults in play across cultural contexts, and even types of play in multicultural communities would provide much-needed context and understanding for professionals and educators working across or in mixed cultural communities. These areas represent just a few that are critical for investigation. Knowing how to promote learning through play must recognize the whole play continuum to ensure optimal conditions for children’s growth and development.

Acknowledgments

We would also like to acknowledge a volunteer research assistant, Alyssa Ma, for reviewing the literature on STEM with us on earlier manuscript versions.

Funding Statement

This research was funded by MacEwan University, grant number RES0000756 (Project Grant).

Institutional Review Board Statement

Informed consent statement, data availability statement, conflicts of interest.

The authors declare no conflict of interest.

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Piaget’s Theory and Stages of Cognitive Development

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

Key Features

• Constructivist approach to learning : Piaget believed that children actively construct their understanding of the world rather than passively absorbing information. This emphasizes the child’s role as a “little scientist,” exploring and making sense of their environment.
• Developmental Stages : Piaget proposed four sequential stages of cognitive development, each marked by distinct thinking patterns, progressing from infancy to adolescence.
• Schemas : Schemas are mental frameworks that help individuals organize and interpret information. As children grow and learn, their schemas become more numerous and sophisticated, allowing for more complex understanding of the world.
• Assimilation : Incorporating new information into preexisting ideas and schemas.
• Accommodation : Modifying existing schemas or creating new ones to fit new information.
• Equilibration : This is how children progress through cognitive developmental stages. It involves balancing assimilation and accommodation, driving the shift from one stage of thought to the next as children encounter and resolve cognitive conflicts.

Stages of Development

Jean Piaget’s theory of cognitive development suggests that children move through four different stages of intellectual development which reflect the increasing sophistication of children’s thought

Each child goes through the stages in the same order (but not all at the same rate), and child development is determined by biological maturation and interaction with the environment.

At each stage of development, the child’s thinking is qualitatively different from the other stages, that is, each stage involves a different type of intelligence.

Although no stage can be missed out, there are individual differences in the rate at which children progress through stages, and some individuals may never attain the later stages.

Piaget did not claim that a particular stage was reached at a certain age – although descriptions of the stages often include an indication of the age at which the average child would reach each stage.

The Sensorimotor Stage

Ages: birth to 2 years.

During the sensorimotor stage (birth to age 2) infants develop basic motor skills and learn to perceive and interact with their environment through physical sensations and body coordination.

Major Characteristics and Developmental Changes:

• The infant learns about the world through their senses and through their actions (moving around and exploring their environment).
• During the sensorimotor stage, a range of cognitive abilities develop. These include: object permanence; self-recognition (the child realizes that other people are separate from them); deferred imitation; and representational play.
• Cognitive abilities relate to the emergence of the general symbolic function, which is the capacity to represent the world mentally
• At about 8 months, the infant will understand the permanence of objects and that they will still exist even if they can’t see them, and the infant will search for them when they disappear.

At the beginning of this stage, the infant lives in the present. It does not yet have a mental picture of the world stored in its memory, so it does not have a sense of object permanence.

If it cannot see something, then it does not exist. This is why you can hide a toy from an infant, while it watches, but it will not search for the object once it has gone out of sight.

The main achievement during this stage is object permanence – knowing that an object still exists, even if it is hidden. It requires the ability to form a mental representation (i.e., a schema) of the object.

Towards the end of this stage the general symbolic function begins to appear where children show in their play that they can use one object to stand for another. Language starts to appear because they realise that words can be used to represent objects and feelings.

The child begins to be able to store information about the world, recall it, and label it.

Individual Differences

• Cultural Practices : In some cultures, babies are carried on their mothers’ backs throughout the day. This constant physical contact and varied stimuli can influence how a child perceives their environment and their sense of object permanence.
• Gender Norms : Toys assigned to babies can differ based on gender expectations. A boy might be given more cars or action figures, while a girl might receive dolls or kitchen sets. This can influence early interactions and sensory explorations.

Learn More: The Sensorimotor Stage of Cognitive Development

The Preoperational Stage

Ages: 2 – 7 years.

Piaget’s second stage of intellectual development is the preoperational stage , which occurs between 2 and 7 years. At the beginning of this stage, the child does not use operations (a set of logical rules), so thinking is influenced by how things look or appear to them rather than logical reasoning.

For example, a child might think a tall, thin glass contains more liquid than a short, wide glass, even if both hold the same amount, because they focus on the height rather than considering both dimensions.

Furthermore, the child is egocentric; he assumes that other people see the world as he does, as shown in the Three Mountains study.

As the preoperational stage develops, egocentrism declines, and children begin to enjoy the participation of another child in their games, and let’s pretend play becomes more important.

Toddlers often pretend to be people they are not (e.g. superheroes, policemen), and may play these roles with props that symbolize real-life objects. Children may also invent an imaginary playmate.

• Toddlers and young children acquire the ability to internally represent the world through language and mental imagery.
• During this stage, young children can think about things symbolically. This is the ability to make one thing, such as a word or an object, stand for something other than itself.
• A child’s thinking is dominated by how the world looks, not how the world is. It is not yet capable of logical (problem-solving) type of thought.
• Moreover, the child has difficulties with class inclusion; he can classify objects but cannot include objects in sub-sets, which involves classifying objects as belonging to two or more categories simultaneously.
• Infants at this stage also demonstrate animism. This is the tendency for the child to think that non-living objects (such as toys) have life and feelings like a person’s.

By 2 years, children have made some progress toward detaching their thoughts from the physical world. However, have not yet developed logical (or “operational”) thought characteristics of later stages.

Thinking is still intuitive (based on subjective judgments about situations) and egocentric (centered on the child’s own view of the world).

• Cultural Storytelling : Different cultures have unique stories, myths, and folklore. Children from diverse backgrounds might understand and interpret symbolic elements differently based on their cultural narratives.
• Race & Representation : A child’s racial identity can influence how they engage in pretend play. For instance, a lack of diverse representation in media and toys might lead children of color to recreate scenarios that don’t reflect their experiences or background.

Learn More: The Preoperational Stage of Cognitive Development

The Concrete Operational Stage

Ages: 7 – 11 years.

By the beginning of the concrete operational stage , the child can use operations (a set of logical rules) so they can conserve quantities, realize that people see the world in a different way (decentring), and demonstrate improvement in inclusion tasks.

Children still have difficulties with abstract thinking.

• During this stage, children begin to think logically about concrete events.
• Children begin to understand the concept of conservation; understanding that, although things may change in appearance, certain properties remain the same.
• During this stage, children can mentally reverse things (e.g., picture a ball of plasticine returning to its original shape).
• During this stage, children also become less egocentric and begin to think about how other people might think and feel.

The stage is called concrete because children can think logically much more successfully if they can manipulate real (concrete) materials or pictures of them.

Piaget considered the concrete stage a major turning point in the child’s cognitive development because it marks the beginning of logical or operational thought. This means the child can work things out internally in their head (rather than physically try things out in the real world).

Children can conserve number (age 6), mass (age 7), and weight (age 9). Conservation is the understanding that something stays the same in quantity even though its appearance changes.

But operational thought is only effective here if the child is asked to reason about materials that are physically present. Children at this stage will tend to make mistakes or be overwhelmed when asked to reason about abstract or hypothetical problems.

• Cultural Context in Conservation Tasks : In a society where resources are scarce, children might demonstrate conservation skills earlier due to the cultural emphasis on preserving and reusing materials.
• Gender & Learning : Stereotypes about gender abilities, like “boys are better at math,” can influence how children approach logical problems or classify objects based on perceived gender norms.

Learn More: The Concrete Operational Stage of Development

The Formal Operational Stage

Ages: 12 and over.

The formal operational period begins at about age 11. As adolescents enter this stage, they gain the ability to think abstractly, the ability to combine and classify items in a more sophisticated way, and the capacity for higher-order reasoning.

Adolescents can think systematically and reason about what might be as well as what is (not everyone achieves this stage). This allows them to understand politics, ethics, and science fiction, as well as to engage in scientific reasoning.

Adolescents can deal with abstract ideas; for example, they can understand division and fractions without having to actually divide things up and solve hypothetical (imaginary) problems.

• Concrete operations are carried out on physical objects, whereas formal operations are carried out on ideas. Formal operational thought is entirely freed from physical and perceptual constraints.
• During this stage, adolescents can deal with abstract ideas (e.g., they no longer need to think about slicing up cakes or sharing sweets to understand division and fractions).
• They can follow the form of an argument without having to think in terms of specific examples.
• Adolescents can deal with hypothetical problems with many possible solutions. For example, if asked, ‘What would happen if money were abolished in one hour?’ they could speculate about many possible consequences.
• Piaget described reflective abstraction as the process by which individuals become aware of and reflect upon their own cognitive actions or operations (metacognition).

From about 12 years, children can follow the form of a logical argument without reference to its content. During this time, people develop the ability to think about abstract concepts, and logically test hypotheses.

This stage sees the emergence of scientific thinking, formulating abstract theories and hypotheses when faced with a problem.

• Culture & Abstract Thinking : Cultures emphasize different kinds of logical or abstract thinking. For example, in societies with a strong oral tradition, the ability to hold complex narratives might develop prominently.
• Gender & Ethics : Discussions about morality and ethics can be influenced by gender norms. For instance, in some cultures, girls might be encouraged to prioritize community harmony, while boys might be encouraged to prioritize individual rights.

Learn More: The Formal Operational Stage of Development

Piaget’s Theory

• Piaget’s theory places a strong emphasis on the active role that children play in their own cognitive development.
• According to Piaget, children are not passive recipients of information; instead, they actively explore and interact with their surroundings.
• This active engagement with the environment is crucial because it allows them to gradually build their understanding of the world.

1. How Piaget Developed the Theory

Piaget was employed at the Binet Institute in the 1920s, where his job was to develop French versions of questions on English intelligence tests. He became intrigued with the reasons children gave for their wrong answers to the questions that required logical thinking.

He believed that these incorrect answers revealed important differences between the thinking of adults and children.

Piaget branched out on his own with a new set of assumptions about children’s intelligence:

• Children’s intelligence differs from an adult’s in quality rather than in quantity. This means that children reason (think) differently from adults and see the world in different ways.
• Children actively build up their knowledge about the world . They are not passive creatures waiting for someone to fill their heads with knowledge.
• The best way to understand children’s reasoning is to see things from their point of view.

Piaget did not want to measure how well children could count, spell or solve problems as a way of grading their I.Q. What he was more interested in was the way in which fundamental concepts like the very idea of number , time, quantity, causality , justice , and so on emerged.

Piaget studied children from infancy to adolescence using naturalistic observation of his own three babies and sometimes controlled observation too. From these, he wrote diary descriptions charting their development.

He also used clinical interviews and observations of older children who were able to understand questions and hold conversations.

2. Piaget’s Theory Differs From Others In Several Ways:

Piaget’s (1936, 1950) theory of cognitive development explains how a child constructs a mental model of the world.

He disagreed with the idea that intelligence was a fixed trait, and regarded cognitive development as a process that occurs due to biological maturation and interaction with the environment.

Children’s ability to understand, think about, and solve problems in the world develops in a stop-start, discontinuous manner (rather than gradual changes over time).

• It is concerned with children, rather than all learners.
• It focuses on development, rather than learning per se, so it does not address learning of information or specific behaviors.
• It proposes discrete stages of development, marked by qualitative differences, rather than a gradual increase in number and complexity of behaviors, concepts, ideas, etc.

The goal of the theory is to explain the mechanisms and processes by which the infant, and then the child, develops into an individual who can reason and think using hypotheses.

To Piaget, cognitive development was a progressive reorganization of mental processes as a result of biological maturation and environmental experience.

Children construct an understanding of the world around them, then experience discrepancies between what they already know and what they discover in their environment.

A schema is a mental framework or concept that helps us organize and interpret information. It’s like a mental file folder where we store knowledge about a particular object, event, or concept.

According to Piaget (1952), schemas are fundamental building blocks of cognitive development. They are constantly being created, modified, and reorganized as we interact with the world.

Wadsworth (2004) suggests that schemata (the plural of schema) be thought of as “index cards” filed in the brain, each one telling an individual how to react to incoming stimuli or information.

According to Piaget, we are born with a few primitive schemas, such as sucking, which give us the means to interact with the world. These initial schemas are physical, but as the child develops, they become mental schemas.

For example:

• Babies have a sucking reflex, triggered by something touching their lips. This corresponds to a “sucking schema.”
• The grasping reflex, elicited when something touches the palm of a baby’s hand, represents another innate schema.
• The rooting reflex, where a baby turns its head towards something which touches its cheek, is also considered an innate schema.

When Piaget discussed the development of a person’s mental processes, he referred to increases in the number and complexity of the schemata that the person had learned.

When a child’s existing schemas are capable of explaining what it can perceive around it, it is said to be in a state of equilibrium, i.e., a state of cognitive (i.e., mental) balance.

Operations are more sophisticated mental structures that allow us to combine schemas in a logical (reasonable) way. For example, picking up a rattle would combine three schemas, gazing, reaching and grasping.

As children grow, they can carry out more complex operations and begin to imagine hypothetical (imaginary) situations.

Operations are learned through interaction with other people and the environment, and they represent a key advancement in cognitive development beyond simple schemas.

As children grow and interact with their environment, these basic schemas become more complex and numerous, and new schemas are developed through the processes of assimilation and accommodation .

4. The Process of Adaptation

Piaget (1952) believed child development results from maturation and environmental interaction. Adaptation is the process of changing mental models to match reality, achieved through assimilation and accommodation.

• Assimilation is fitting new information into existing schemas without changing one’s understanding. For example,  a child who has only seen small dogs might call a cat a “dog” due to similar features like fur, four legs, and a tail.
• Accommodation occurs when existing schemas must be revised to incorporate new information. For instance, a child who believes all animals have four legs would need to accommodate their schema upon seeing a snake. A baby tries to use the same grasping schema to pick up a very small object. It doesn’t work. The baby then changes the schema using the forefinger and thumb to pick up the object.

When schemas explain our perceptions, we’re in equilibration. New, unexplainable situations create disequilibrium, motivating learning. This cognitive conflict, where contradictory views exist, drives development.

Piaget viewed intellectual growth as an adaptation to the world through assimilation, accommodation, and equilibration. These processes are continuous and interactive, allowing schemas to evolve and become more sophisticated.

Jean Piaget (1952; see also Wadsworth, 2004) viewed intellectual growth as a process of adaptation (adjustment) to the world. This happens through assimilation, accommodation, and equilibration.

5. Equilibration

Piaget (1985) believed that all human thought seeks order and is uncomfortable with contradictions and inconsistencies in knowledge structures. In other words, we seek “equilibrium” in our cognitive structures.

Equilibrium occurs when a child’s schemas can deal with most new information through assimilation. However, an unpleasant state of disequilibrium occurs when new information cannot be fitted into existing schemas (assimilation).

Piaget believed that cognitive development did not progress at a steady rate, but rather in leaps and bounds. Equilibration is the force which drives the learning process as we do not like to be frustrated and will seek to restore balance by mastering the new challenge (accommodation).

Once the new information is acquired the process of assimilation with the new schema will continue until the next time we need to make an adjustment to it.

Equilibration is a regulatory process that maintains a balance between assimilation and accommodation to facilitate cognitive growth. Think of it this way: We can’t merely assimilate all the time; if we did, we would never learn any new concepts or principles.

Everything new we encountered would just get put in the same few “slots” we already had. Neither can we accommodate all the time; if we did, everything we encountered would seem new; there would be no recurring regularities in our world. We’d be exhausted by the mental effort!

Applications to Education

Think of old black-and-white films you’ve seen where children sat in rows at desks with inkwells. They learned by rote, all chanting in unison in response to questions set by an authoritarian figure like Miss Trunchbull in Matilda.

Children who were unable to keep up were seen as slacking and would be punished by variations on the theme of corporal punishment. Yes, it really did happen and in some parts of the world still does today.

Piaget is partly responsible for the change that occurred in the 1960s and for your relatively pleasurable and pain-free school days!

“Children should be able to do their own experimenting and their own research. Teachers, of course, can guide them by providing appropriate materials, but the essential thing is that in order for a child to understand something, he must construct it himself, he must re-invent it. Every time we teach a child something, we keep him from inventing it himself. On the other hand that which we allow him to discover by himself will remain with him visibly”. Piaget (1972, p. 27)

Plowden Report

Piaget (1952) did not explicitly relate his theory to education, although later researchers have explained how features of Piaget’s theory can be applied to teaching and learning.

Piaget has been extremely influential in developing educational policy and teaching practice. For example, a review of primary education by the UK government in 1966 was based strongly on Piaget’s theory. The result of this review led to the publication of the Plowden Report (1967).

In the 1960s the Plowden Committee investigated the deficiencies in education and decided to incorporate many of Piaget’s ideas into its final report published in 1967, even though Piaget’s work was not really designed for education.

The report makes three Piaget-associated recommendations:

• Children should be given individual attention and it should be realized that they need to be treated differently.
• Children should only be taught things that they are capable of learning
• Children mature at different rates and the teacher needs to be aware of the stage of development of each child so teaching can be tailored to their individual needs.

The report’s recurring themes are individual learning, flexibility in the curriculum, the centrality of play in children’s learning, the use of the environment, learning by discovery and the importance of the evaluation of children’s progress – teachers should “not assume that only what is measurable is valuable.”

Discovery learning, the idea that children learn best through doing and actively exploring, was seen as central to the transformation of the primary school curriculum.

How to teach

Learning should be student-centered and accomplished through active discovery in the classroom. The teacher’s role is to facilitate learning rather than direct tuition.

Because Piaget’s theory is based upon biological maturation and stages, the notion of “readiness” is important. Readiness concerns when certain information or concepts should be taught.

According to Piaget’s theory, children should not be taught certain concepts until they have reached the appropriate stage of cognitive development.

Consequently, education should be stage-specific, with curricula developed to match the age and stage of thinking of the child. For example, abstract concepts like algebra or atomic structure are not suitable for primary school children.

Assimilation and accommodation require an active learner, not a passive one, because problem-solving skills cannot be taught, they must be discovered (Piaget, 1958).

Therefore, teachers should encourage the following within the classroom:

• Consider the stages of cognitive development : Educational programs should be designed to correspond to Piaget’s stages of development. For example, a child in the concrete operational stage should not be taught abstract concepts and should be given concrete aid such as tokens to count with.
• Provide concrete experiences before abstract concepts : Especially for younger children, ensure they have hands-on experiences with concepts before introducing more abstract representations.
• Provide challenges that promote growth without causing frustration : Devising situations that present useful problems and create disequilibrium in the child.
• Focus on the process of learning rather than the end product : Instead of checking if children have the right answer, the teacher should focus on the students’ understanding and the processes they used to arrive at the answer.
• Encourage active learning : Learning must be active (discovery learning). Children should be encouraged to discover for themselves and to interact with the material instead of being given ready-made knowledge. Using active methods that require rediscovering or reconstructing “truths.”
• Foster social interaction: Using collaborative, as well as individual activities (so children can learn from each other). Implement cooperative learning activities, such as group problem-solving tasks or role-playing scenarios.
• Differentiated teaching : Adapt lessons to suit the needs of the individual child. For example, observe a child’s ability to classify objects by color, shape, and size. If they can easily sort by one attribute but struggle with multiple attributes, tailor future activities to gradually increase complexity, such as sorting buttons first by color, then by color and size together.
• Providing support for the “spontaneous research” of the child : Provide opportunities and resources for children to explore topics of their own interest, encouraging their natural curiosity and self-directed learning. Create a “Wonder Wall” in the classroom where children can post questions about topics that interest them. 

Classroom Activities

Sensorimotor stage (0-2 years):.

Although most kids in this age range are not in a traditional classroom setting, they can still benefit from games that stimulate their senses and motor skills.

• Object Permanence Games : Play peek-a-boo or hide toys under a blanket to help babies understand that objects still exist even when they can’t see them.
• Sensory Play : Activities like water play, sand play, or playdough encourage exploration through touch.
• Imitation : Children at this age love to imitate adults. Use imitation as a way to teach new skills.

Preoperational Stage (2-7 years):

• Role Playing : Set up pretend play areas where children can act out different scenarios, such as a kitchen, hospital, or market.
• Use of Symbols : Encourage drawing, building, and using props to represent other things.
• Hands-on Activities : Children should interact physically with their environment, so provide plenty of opportunities for hands-on learning.
• Egocentrism Activities : Use exercises that highlight different perspectives. For instance, having two children sit across from each other with an object in between and asking them what the other sees.

Concrete Operational Stage (7-11 years):

• Classification Tasks : Provide objects or pictures to group, based on various characteristics.
• Hands-on Experiments : Introduce basic science experiments where they can observe cause and effect, like a simple volcano with baking soda and vinegar.
• Logical Games : Board games, puzzles, and logic problems help develop their thinking skills.
• Conservation Tasks : Use experiments to showcase that quantity doesn’t change with alterations in shape, such as the classic liquid conservation task using differently shaped glasses.

Formal Operational Stage (11 years and older):

• Hypothesis Testing : Encourage students to make predictions and test them out.
• Abstract Thinking : Introduce topics that require abstract reasoning, such as algebra or ethical dilemmas.
• Problem Solving : Provide complex problems and have students work on solutions, integrating various subjects and concepts.
• Debate and Discussion : Encourage group discussions and debates on abstract topics, highlighting the importance of logic and evidence.
• Feedback and Questioning : Use open-ended questions to challenge students and promote higher-order thinking. For instance, rather than asking, “Is this the right answer?”, ask, “How did you arrive at this conclusion?”

While Piaget’s stages offer a foundational framework, they are not universally experienced in the same way by all children.

Social identities play a critical role in shaping cognitive development, necessitating a more nuanced and culturally responsive approach to understanding child development.

Piaget’s stages may manifest differently based on social identities like race, gender, and culture:

• Race & Teacher Interactions : A child’s race can influence teacher expectations and interactions. For example, racial biases can lead to children of color being perceived as less capable or more disruptive, influencing their cognitive challenges and support.
• Racial and Cultural Stereotypes : These can affect a child’s self-perception and self-efficacy . For instance, stereotypes about which racial or cultural groups are “better” at certain subjects can influence a child’s self-confidence and, subsequently, their engagement in that subject.
• Gender & Peer Interactions : Children learn gender roles from their peers. Boys might be mocked for playing “girl games,” and girls might be excluded from certain activities, influencing their cognitive engagements.
• Language : Multilingual children might navigate the stages differently, especially if their home language differs from their school language. The way concepts are framed in different languages can influence cognitive processing. Cultural idioms and metaphors can shape a child’s understanding of concepts and their ability to use symbolic representation, especially in the pre-operational stage.

Overcoming Challenges and Barriers to Implementation

Balancing play and curriculum.

• Purposeful Play: Ensuring that play is not just free time but a structured learning experience requires careful planning. Educators must identify clear learning objectives and create play environments that facilitate these goals.  
• Alignment with Standards: Striking a balance between child-initiated play and curriculum expectations can be challenging. Educators need to find ways to integrate play-based learning with broader educational goals and standards.
• Pace of Learning: The curriculum’s focus on specific content by certain ages can create pressure to accelerate student learning, potentially contradicting Piaget’s notion of developmental stages. Teachers should regularly assess students’ understanding to identify areas where they need more support or challenge.
• Assessment Focus: The emphasis on standardized testing can shift the focus from process-oriented learning (as Piaget advocated) to outcome-based teaching. Educators should use assessments that reflect real-world tasks and allow students to demonstrate their understanding in multiple ways.
• Parental Expectations: Some parents may have misconceptions about play-based learning, believing it to be less rigorous than traditional instruction. Educators may need to address these concerns and communicate the value of play. 
• Parental Involvement: Involving parents in understanding Piaget’s theory can foster consistency between home and school environments. Providing resources and information to parents about child development can empower them to support their child’s learning at home.

Other challenges

• Individual Differences: Piaget emphasized individual differences in cognitive development, but classrooms often have diverse learners. Meeting the needs of all students while maintaining a play-based approach can be demanding.
• Time Constraints: In some educational settings, there may be pressure to cover specific content or prepare students for standardized tests. Prioritizing play-based learning within these constraints can be difficult.    
• Cultural Sensitivity: Recognizing and respecting cultural differences is essential. Piaget’s theory may need to be adapted to fit the specific cultural context of the children being taught.

Can Piaget’s Ideas Be Applied to Children with Special Educational Needs and Disabilities?

Yes, Piaget’s ideas can be adapted to support children with special educational needs and disabilities (SEND), though with important considerations:

• Individualized Approach : Tailor learning experiences to each child’s unique strengths, needs, and interests, recognizing that development may not follow typical patterns or timelines (Daniels & Diack, 1977).
• Concrete Learning Experiences : Provide hands-on, multisensory activities to support concept exploration, particularly beneficial for children with learning difficulties or sensory impairments (Lee & Zentall, 2012).
• Gradual Scaffolding : Break down tasks into manageable steps and provide appropriate support to help children progress through developmental stages at their own pace (Morra & Borella, 2015).
• Flexible Assessment : Modify Piagetian tasks to accommodate different abilities and communication methods, using multiple assessment approaches.
• Strengths-Based Focus : Emphasize children’s capabilities rather than deficits, using Piaget’s concepts to identify and build upon existing cognitive strengths.
• Interdisciplinary Approach : Combine Piagetian insights with specialized knowledge from fields like occupational therapy and speech-language pathology.

While Piaget’s theory offers valuable insights, it should be part of a broader, evidence-based approach that recognizes the diverse factors influencing development in children with SEND.

Social Media (Digital Learning)

Jean Piaget could not have anticipated the expansive digital age we now live in.

Today, knowledge dissemination and creation are democratized by the Internet, with platforms like blogs, wikis, and social media allowing for vast collaboration and shared knowledge. This development has prompted a reimagining of the future of education.

Classrooms, traditionally seen as primary sites of learning, are being overshadowed by the rise of mobile technologies and platforms like MOOCs (Passey, 2013).

The millennial generation, the first to grow up with cable TV, the internet, and cell phones, relies heavily on technology.

They view it as an integral part of their identity, with most using it extensively in their daily lives, from keeping in touch with loved ones to consuming news and entertainment (Nielsen, 2014).

Social media platforms offer a dynamic environment conducive to Piaget’s principles. These platforms allow interactions that nurture knowledge evolution through cognitive processes like assimilation and accommodation.

They emphasize communal interaction and shared activity, fostering both cognitive and socio-cultural constructivism. This shared activity promotes understanding and exploration beyond individual perspectives, enhancing social-emotional learning (Gehlbach, 2010).

A standout advantage of social media in an educational context is its capacity to extend beyond traditional classroom confines. As the material indicates, these platforms can foster more inclusive learning, bridging diverse learner groups.

This inclusivity can equalize learning opportunities, potentially diminishing biases based on factors like race or socio-economic status, resonating with Kegan’s (1982) concept of “recruitability.”

However, there are challenges. While social media’s potential in learning is vast, its practical application necessitates intention and guidance. Cuban, Kirkpatrick, and Peck (2001) note that certain educators and students are hesitant about integrating social media into educational contexts.

This hesitancy can stem from technological complexities or potential distractions. Yet, when harnessed effectively, social media can provide a rich environment for collaborative learning and interpersonal development, fostering a deeper understanding of content.

In essence, the rise of social media aligns seamlessly with constructivist philosophies. Social media platforms act as tools for everyday cognition, merging daily social interactions with the academic world, and providing avenues for diverse, interactive, and engaging learning experiences.

Criticisms of Jean Piaget’s Theories and Concepts

Criticisms of research methods.

• Small sample size : Piaget often used small, non-representative samples, frequently including only his own children or those from similar backgrounds (European children from families of high socio-economic status). This limits the generalizability of his findings (Lourenço & Machado, 1996).

The lack of inter-rater reliability and potential issues with clinical interviews (e.g., children misunderstanding questions or trying to please the experimenter) may have led to biased or inaccurate conclusions.

Using multiple researchers and more standardized methods could have improved reliability (Donaldson, 1978).

• Age-related issues : Some critics argue that Piaget underestimated the cognitive abilities of younger children. This may be due to the complex language used in his tasks, which could have masked children’s true understanding.
• Cultural limitations : Piaget’s research was primarily conducted with Western, educated children from relatively affluent backgrounds. This raises questions about the universality of his developmental stages across different cultures (Rogoff, 2003).

As several studies have shown Piaget underestimated the abilities of children because his tests were sometimes confusing or difficult to understand (e.g., Hughes , 1975).

Challenges to Key Concepts and Theories

Fixed developmental stages.

Are the stages real? Vygotsky and Bruner would rather not talk about stages at all, preferring to see development as a continuous process.

Others have queried the age ranges of the stages. Some studies have shown that progress to the formal operational stage is not guaranteed.

For example, Keating (1979) reported that 40-60% of college students fail at formal operational tasks, and Dasen (1994) states that only one-third of adults ever reach the formal operational stage.

Current developmental psychology has moved beyond seeing development as progressing through discrete, universal stages (as Piaget proposed) to view it as a more gradual, variable process influenced by social, genetic, and cultural factors.

Current perspectives acknowledge greater variability in the timing and sequence of developmental milestones.

There’s greater recognition of the brain’s plasticity and the potential for cognitive growth throughout the lifespan.

This challenges the idea of fixed developmental endpoints proposed in stage theories.

Culture and individual differences

The fact that the formal operational stage is not reached in all cultures and not all individuals within cultures suggests that it might not be biologically based.

• According to Piaget, the rate of cognitive development cannot be accelerated as it is based on biological processes however, direct tuition can speed up the development which suggests that it is not entirely based on biological factors.
• Because Piaget concentrated on the universal stages of cognitive development and biological maturation, he failed to consider the effect that the social setting and culture may have on cognitive development.

Cross-cultural studies show that the stages of development (except the formal operational stage) occur in the same order in all cultures suggesting that cognitive development is a product of a biological maturation process.

However, the age at which the stages are reached varies between cultures and individuals which suggests that social and cultural factors and individual differences influence cognitive development.

Dasen (1994) cites studies he conducted in remote parts of the central Australian desert with 8—to 14-year-old Indigenous Australians.

He gave them conservation of liquid tasks and spatial awareness tasks. He found that the ability to conserve came later in the Aboriginal children, between the ages of 10 and 13 (as opposed to between 5 and 7, with Piaget’s Swiss sample).

However, he found that spatial awareness abilities developed earlier among Aboriginal children than among Swiss children.

Such a study demonstrates that cognitive development is not purely dependent on maturation but on cultural factors as well—spatial awareness is crucial for nomadic groups of people.

Underemphasis on social and emotional factors

While Piaget’s theory focuses primarily on individual cognitive development, it arguably underestimates the crucial role of social and emotional factors.

Lev Vygotsky , a contemporary of Piaget, emphasized the social nature of learning in his sociocultural theory.

Vygotsky argued that cognitive development occurs through social interactions, particularly with more knowledgeable others (MKOs) such as parents, teachers, or skilled peers.

He introduced the concept of the Zone of Proximal Development ( ZPD ), which represents the gap between what a child can do independently and what they can achieve with guidance.

Furthermore, Vygotsky viewed language as fundamental to thought development, asserting that social dialogue becomes internalized as inner speech, driving cognitive processes. This perspective highlights how cultural tools, especially language, shape thinking.

Emotional factors, including motivation, self-esteem, and relationships, also play significant roles in learning and development – aspects not thoroughly addressed in Piaget’s cognitive-focused theory.

This social-emotional dimension of development has gained increasing recognition in modern educational and developmental psychology.

Underestimating children’s abilities

Piaget failed to distinguish between competence (what a child can do) and performance (what a child can show when given a particular task).

When tasks were altered, performance (and therefore competence) was affected. Therefore, Piaget might have underestimated children’s cognitive abilities.

For example, a child might have object permanence (competence) but still be unable to search for objects (performance). When Piaget hid objects from babies, he found that it wasn’t until after nine months that they looked for them.

However, Piaget relied on manual search methods – whether the child was looking for the object or not.

Later, researchers such as Baillargeon and Devos (1991) reported that infants as young as four months looked longer at a moving carrot that didn’t do what it expected, suggesting they had some sense of permanence, otherwise they wouldn’t have had any expectation of what it should or shouldn’t do.

Jean Piaget’s Legacy and Ongoing Influence

Piaget’s ideas on developmental psychology have had an enormous influence. He changed how people viewed the child’s world and their methods of studying children.

He inspired many who followed and took up his ideas. Piaget’s ideas have generated a huge amount of research, which has increased our understanding of cognitive development.

• Seminal Theory : Piaget (1936) was one of the first psychologists to study cognitive development systematically. His contributions include a stage theory of child cognitive development, detailed observational studies of cognition in children, and a series of simple but ingenious tests to reveal different cognitive abilities.
• Neo-Piagetian theories : Researchers have built upon Piaget’s stage theory of cognitive development, incorporating information processing and brain development to explain cognitive growth, emphasizing individual differences and more gradual developmental progressions (Case, 1985; Fischer, 1980; Pascual-Leone, 1970).

Impact on Educational Practices

Early Childhood Education : Piaget’s theories underpin many early childhood programs that emphasize play-based learning, sensory experiences, and exploration.

Constructivist Pedagogy: Piaget’s idea that children construct knowledge through interaction with their environment led to a shift from teacher-centered to child-centered approaches. This emphasizes exploration, discovery, and hands-on activities.

By understanding Piaget’s stages, educators can create environments and activities that challenge children appropriately.

The National Association for the Education of Young Children ( NAEYC ) has incorporated Piagetian principles into its DAP framework, influencing early childhood education policies worldwide.

Parenting Practices

Piaget’s theory influenced parenting by emphasizing stimulating environments, play, and supporting children’s curiosity.

Parents can use Piaget’s stages to have realistic developmental expectations of their children’s behavior and cognitive capabilities.

For instance, understanding that a toddler is in the pre-operational stage can help parents be patient when the child is egocentric.

Play Activities

Recognizing the importance of play in cognitive development, many parents provide toys and games suited for their child’s developmental stage.

Parents can offer activities that are slightly beyond their child’s current abilities, leveraging Vygotsky’s concept of the “ Zone of Proximal Development ,” which complements Piaget’s ideas.

• Peek-a-boo : Helps with object permanence.
• Texture Touch : Provide different textured materials (soft, rough, bumpy, smooth) for babies to touch and feel.
• Sound Bottles : Fill small bottles with different items like rice, beans, bells, and have children shake and listen to the different sounds.
• Memory Games : Using cards with pictures, place them face down, and ask students to find matching pairs.
• Role Playing and Pretend Play : Let children act out roles or stories that enhance symbolic thinking. Encourage symbolic play with dress-up clothes, playsets, or toy cash registers. Provide prompts or scenarios to extend their imagination.
• Story Sequencing : Give children cards with parts of a story and have them arranged in the correct order.
• Number Line Jumps : Create a number line on the floor with tape. Ask students to jump to the correct answer for math problems.
• Classification Games : Provide a mix of objects and ask students to classify them based on different criteria (e.g., color, size, shape).
• Logical Puzzle Games : Games that involve problem-solving using logic, such as simple Sudoku puzzles or logic grid puzzles.
• Debate and Discussion : Provide a topic and let students debate the pros and cons. This promotes abstract thinking and logical reasoning.
• Hypothesis Testing Games : Present a scenario and have students come up with hypotheses and ways to test them.
• Strategy Board Games : Games like chess, checkers, or Settlers of Catan can help in developing strategic and forward-thinking skills.

Comparing Jean Piaget’s Ideas with Other Theorists

Integrating diverse theories enables early years professionals to develop a comprehensive view of child development.

This allows for creating holistic learning experiences that support cognitive, social, and emotional growth.

By recognizing various developmental factors, professionals can tailor their practices to each child’s unique needs and background.

Comparison with Lev Vygotsky

Differences:.

• Stage-Based vs Continuous Development : Piaget proposed a stage-based model of cognitive development, while Vygotsky viewed development as a continuous process influenced by social and cultural factors.
• Role of Language : For Piaget, language is considered secondary to action, i.e., thought precedes language. Vygotsky argues that the development of language and thought go together and that the origin of reasoning has more to do with our ability to communicate with others than with our interaction with the material world.

Similarities:

• Both theories view children as actively constructing their own knowledge of the world; they are not seen as just passively absorbing knowledge.
• They also agree that cognitive development involves qualitative changes in thinking, not only a matter of learning more things.

Comparison with Erik Erikson

Erikson’s (1958) psychosocial theory outlines 8 stages of psychosocial development from infancy to late adulthood.

At each stage, individuals face a conflict between two opposing states that shapes personality. Successfully resolving conflicts leads to virtues like hope, will, purpose, and integrity. Failure leads to outcomes like mistrust, guilt, role confusion, and despair.

• Cognitive vs. Psychosocial Focus : Piaget focuses on cognitive development and how children construct knowledge. Erikson emphasizes psychosocial development, exploring how social interactions shape personality and identity.
• Universal Stages vs. Cultural Influence : Piaget proposed universal cognitive stages relatively independent of culture. Erikson’s psychosocial stages, while sequential, acknowledge significant cultural influence on their expression and timing.
• Role of Conflict : Piaget sees cognitive conflict (disequilibrium) as a driver for learning. Erikson views psychosocial crises as essential for personal growth and identity formation.
• Scope of Development : Piaget’s theory primarily covers childhood to adolescence. Erikson’s theory spans the entire lifespan, from infancy to late adulthood.
• Learning Process vs. Identity Formation : Piaget emphasizes how children learn and understand the world. Erikson focuses on how individuals develop their sense of self and place in society through resolving psychosocial conflicts.
• Stage-based theories : Both propose that development occurs in distinct stages  (Gilleard & Higgs, 2016).
• Age-related progression : Stages are generally associated with specific age ranges.
• Cumulative development : Each stage builds upon the previous ones.
• Focus on childhood : Both emphasize the importance of early life experiences.
• Active role of the individual : Both see children as active participants in their development.

Comparison with Urie Bronfenbrenner

Bronfenbrenner’s (1979) ecological systems theory posits that an individual’s development is influenced by a series of interconnected environmental systems, ranging from the immediate surroundings (e.g., family) to broad societal structures (e.g., culture).

Bronfenbrenner’s theory offers a more comprehensive view of the multiple influences on a child’s development, complementing Piaget’s focus on cognitive processes with a broader ecological perspective.

• Individual vs. Ecological Emphasis : Piaget focuses on individual cognitive development through independent exploration. Bronfenbrenner emphasizes the complex interplay between an individual and multiple environmental systems, from immediate family to broader societal influences.
• Stage-based vs. Systems Approach : Piaget proposed distinct stages of cognitive development. Bronfenbrenner’s Ecological Systems Theory views development as ongoing interactions between the individual and various environmental contexts throughout the lifespan.
• Role of Environment : For Piaget, the environment provides opportunities for cognitive conflict and schema development. Bronfenbrenner sees the environment as a nested set of systems (microsystem, mesosystem, exosystem, macrosystem, chronosystem) that directly and indirectly influence development.
• Cognitive Structures vs. Proximal Processes : Piaget focused on the development of cognitive structures (schemas). Bronfenbrenner emphasized proximal processes – regular, enduring interactions between the individual and their immediate environment – as key drivers of development.
• Discovery Learning vs. Contextual Learning : Piaget advocated for discovery learning to challenge existing schemas. Bronfenbrenner would emphasize the importance of understanding and leveraging the various ecological contexts in which learning occurs, from family to cultural systems.
• Both recognize the child as an active participant in development.
• Both acknowledge the importance of the child’s environment in shaping development.

What is cognitive development?

Cognitive development is how a person’s ability to think, learn, remember, problem-solve, and make decisions changes over time.

This includes the growth and maturation of the brain, as well as the acquisition and refinement of various mental skills and abilities.

Cognitive development is a major aspect of human development, and both genetic and environmental factors heavily influence it. Key domains of cognitive development include attention, memory, language skills, logical reasoning, and problem-solving.

Various theories, such as those proposed by Jean Piaget and Lev Vygotsky, provide different perspectives on how this complex process unfolds from infancy through adulthood.

What are the 4 stages of Piaget’s theory?

Piaget divided children’s cognitive development into four stages; each of the stages represents a new way of thinking and understanding the world.

He called them (1) sensorimotor intelligence , (2) preoperational thinking , (3) concrete operational thinking , and (4) formal operational thinking . Each stage is correlated with an age period of childhood, but only approximately.

According to Piaget, intellectual development takes place through stages that occur in a fixed order and which are universal (all children pass through these stages regardless of social or cultural background).

Development can only occur when the brain has matured to a point of “readiness”.

What are some of the weaknesses of Piaget’s theory?

However, the age at which the stages are reached varies between cultures and individuals, suggesting that social and cultural factors and individual differences influence cognitive development.

What are Piaget’s concepts of schemas?

Schemas are mental structures that contain all of the information relating to one aspect of the world around us.

According to Piaget, we are born with a few primitive schemas, such as sucking, which give us the means to interact with the world.

These are physical, but as the child develops, they become mental schemas. These schemas become more complex with experience.

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Further Reading

• BBC Radio Broadcast about the Three Mountains Study
• Piagetian stages: A critical review
• Bronfenbrenner’s Ecological Systems Theory

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Technologies education and development

New research has examined how children engage with technologies education at different stages of development

New research from Professor Therese Keane and Dr Milorad Cerovac has examined how children engage with technologies education at different stages of development.

“We found that a student's developmental age determines their ability to think in abstract ways when solving hands-on technology problems,” explains Professor Keane.

The study was grounded in Jean Piaget’s theory of cognitive development, which explains how children progress through four key stages as they grow: sensorimotor (absorbing information through their senses), preoperational (understanding symbolic representation), concrete operational (problem-solving things they can see) and formal operational (using abstract thinking and hypothetical problem-solving).

“Consistent with Piaget’s model, our study found that a student’s developmental age does influence their ability to complete tasks that require spatial reasoning and abstract thinking, particularly when moving back and forth between the stages when solving hands-on technology problems.”

Professor Keane says that their findings highlight the important role that STEM teachers play in helping students develop spatial reasoning and abstract thinking skills.

“Technologies teachers are at the forefront of building students' capabilities to think and act as creators and innovators.”

“Our study points to the need for regular exposure to tactile hands-on tasks, the development of students' technical vocabulary, and explicit teaching of how students can work collaboratively.”

The next step in the research will be to examine the role of gender in abstract and spatial inferential reasoning.

“Given the lack of gender diversity in both secondary and tertiary STEM-related courses, and the under-representation of women in STEM careers, addressing gender stereotypes is particularly important in the junior primary school years.”

Read the paper .

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