Cognitive development: Less incremental than what we think

Executive summary

• Cognitive development is less incremental as originally conceived by Jean Piaget.
• Non-linear developmental trajectories in which children, adolescents and adults commit systematic errors in contexts that are supposed to require the same knowledge already mastered by younger children (or even infants) in different cognitive domains is the norm rather than the exception.
• Cognitive development should be viewed as a non-linear dynamic system in which executive functions play a key role in producing cognitive change over time and context.
• Systematic errors do not necessarily reveal a lack of knowledge; rather, they reveal a lack of ability to express a given knowledge in a context in which a prepotent response, and illogical intuition, or misleading strategy interfere with it
• The progressive ability to inhibit misleading automatic strategies supports cognitive development by allowing children, adolescents and adults to understand the domain of the validity of each strategy in various contexts.

Introduction

Models of cognitive development have huge impact on curricula, pedagogy, and more globally on the organization of school systems. Constructivist theories such as the one proposed by Jean Piaget, one of the most well-known developmental psychologists and a former director of the International Bureau of Education, continue to be highly influential in the educational community while no longer being one of the models used to conceptualize cognitive development in the research community. Neither findings from neuroscience nor models of cognitive development should be prescriptive of education policies but educational policies that adhere to the principles of the learning brain and of cognitive development are more likely to be efficient (Immordino-Yang & Gotlieb, 2017). In addition, teachers who have knowledge of the cognitive and brain development of children and adolescents are more likely to design pedagogical interventions tailored to the students’ needs.

In this brief, we first present incremental models of development, such as Piaget’s constructivist (Piaget, 1983), or innate models of development, such as Spelke’s core knowledge (Spelke, 2000) models. We then provide a number of evidence that cognitive development is less incremental as originally assumed and that cognitive development should be viewed as a non-linear dynamic system (Smith & Thelen, 2003) in which executive functions, i.e., “a family of top-down mental processes needed when we have to concentrate and pay attention, when going on automatic or relying on instinct or intuition would be ill-advised, insufficient, or impossible” (Diamond, 2013, p. 136), play a key role in producing cognitive change over time and context (Houdé & Borst, 2014).

Incremental models of cognitive development

Cognitive development is generally conceived as linear and incremental, with more complex knowledge progressively acquired with age. For instance, in the seminal constructivist theory, Piaget (Piaget, 1983) argues that children progressively acquire a logical understanding of the principles that govern the physical world by directly acting in it. According to this theory, the logical structures of children’s mind become increasingly more complex throughout four fundamental shifts (or stages) during which the logical structures at a given stage are combined to create more complex structures at the next stage. These shifts occur at about the same age for all children. They start with a shift from the sensorimotor stage (from birth to 2 years of age), during which perception and motor processes are prevalent, to the preoperational stage (from 2 to 7 years of age), during which children are mainly illogical, according to Piaget. Shifting to the concrete operational stage (from 7 to 12 years of age), children start to reason logically but only on concrete objects, while the shift to the formal operational stage (after 12 years of age) allows children to reason on abstract propositions.

Piaget’s constructivist theory has been widely criticized in part because it underestimates the rich conceptual knowledge of infants on the physical principles of their environment (Spelke, 2000). Indeed, four-month-old infants seem already to possess an understanding of the physical properties of objects, of agents and their actions, of the numerical properties of sets of objects, and of the spatial relations of objects and their geometrical organization in the environment (Spelke, 2000). Evidence that knowledge was similar in infants and in adults led some developmental psychologists to argue that cognitive development essentially consists of the refinement of these four core knowledge systems (Spelke, 2000).

These linear and incremental models of development have been progressively questioned due to their inability to account for non-linear trajectories of cognitive development in which children, adolescents and adults commit systematic errors in contexts that are supposed to require the same knowledge already mastered by younger children (or even infants). In what follows, we present three instances of such non-linear trajectories of cognitive development in three seminal Piagetian tasks.

The paradoxes of cognitive development: from incremental to non-linear trajectories

The A-B problem

In the A-B problem designed by Piaget (Piaget, 1983) to test infants’ (8 to 12 months old) understanding of object permanence (i.e., understanding that an object continues to exist even when out of sight), an infant is placed in front of two equally reachable screens (A and B), and an object is hidden behind A. Infants as young as 8 months can easily find the object under A. After a few repetitions of hiding and finding the object under A, the object is transferred from A to B. Infants up to 12 months old commit the famous A-not-B error, seeking the object under A while the object is hidden under B. For Piaget, succeeding the A-not-B task was a hallmark of the acquisition of object permanence at around 12 months of age. Error in the A-not-B tasks is surprising in light of the fact that 4-month-old infants have already mastered several principles regarding objects and their displacement in the environment (Spelke, 2000).

Several studies have demonstrated that the A-not-B error reflects not a lack of object permanence but a lack of maturation of the prefrontal cortex, allowing infants before 12 months of age to inhibit the prepotent gesture (i.e., a motor heuristic) of reaching for the object under A, reinforced by the repetition of hiding the object under A (Dimaond, 1998). Convergent evidence for the role of inhibitory control in succeeding in the A-B problem was provided by an electroencephalographic study showing a relation between infants’ improvement in this task and an increase in the electric activity of the frontal areas of the brain (Bell & Fox, 1992).

The number conservation task

In the number-conservation task, designed by Jean Piaget at the beginning of the 20^th century (Piaget, 1983), two alignments of tokens of equal length are presented, and children are asked whether the two alignments contain the same number of tokens. At age 5, children acknowledge the so-called initial equivalence, stating that the two alignments indeed contain the same number of tokens. Then, the experimenter transforms the length of one of the two alignments and asks once again whether the two alignments contain the same number of tokens. Piaget observed that children under 7 years of age stated that the two alignments did not contain the same number of tokens after the transformation of the length of one of the two alignments, disregarding the fact that the transformation affected one physical quantity (i.e., length) without affecting the other (i.e., numerosity). As for the A-not-B task, Piaget considered that succeeding the number conservation task was a sign of children’s mind reaching a new stage of development (i.e., the concrete operational stage). Surprisingly, in the 1980s, studies demonstrated that infants already understood at age four months that length did not covary with number (Antell & Keating, 1983).

Several studies have provided evidence that success in the number-conservation task for both children and adults relies on inhibiting a very automatic but misleading strategy, the “length-equals-number” strategy (Borst, Simon, Vidal, & Houdé, 2013; Houdé & Guichart, 2001; Houdé et al., 2011). Indeed, children under 7 years of age erroneously think that the longer alignment contains more tokens after tokens have been spread apart in the number-conservation task. The “length-equals-number” strategy is most likely created during childhood because our brain detects in our visual environment that longer alignments tend to have more objects (Houdé & Borst, 2014). Interestingly, this strategy is sometimes reinforced at school when teaching preschoolers to count: illustrations in the classroom or in textbooks depict the 1-to-10 Arabic numbering series with rows of animals of increasing length, reinforcing the “length-equals-number” strategy. A functional magnetic resonance imagery (fMRI) study on 60 children aged 5 to 9 provided convergent evidence for the role of inhibitory control in the number-conservation task by showing that the progressive ability to perform the number-conservation task elicits increasing activation not only in the intraparietal sulcus (an area dedicated to number and length processing, Dormal & Pesenti, 2009) but also in the right inferior frontal gyrus (an epicenter of inhibitory control, Aron et al., 2014) (Houdé et al., 2011). Finally, a high-density event-related potential (ERP) study demonstrated that adults still need to inhibit the misleading “length-equals-number” strategy to perform the number-conservation task (Borst, Simon et al., 2013).

Interestingly, one study recently demonstrated that 6-year-old children are more prone to accept the numerical equivalence in an adaptation of the number-conservation task when the difference in length of the two rows increased (Viarouge, Houdé, & Borst, 2019). In this adaptation of the number-conservation task, children were asked to perform a computerized same-different numerical estimation task with horizontally arranged dots (as in Piaget’s number-conservation task after the length of one row is transformed). The spacing of the dots in one row (and thus the length ratio between the two rows) varied systematically. Children’s ability to make a “same” judgment when the two rows contained an equal number of dots decreased progressively as the difference in the lengths of the two rows increased. Thus, children’s performance on this task decreased as the interference between the non numerical and numerical magnitudes increased. In addition, children who orient more spontaneously toward numerosity in a card sorting task were more likely to succeed the number-conservation task. Spontaneous orientation toward different dimensions of magnitude (i.e., numerosity spacing, or item size in a set of dots) was measured by using a card-sorting task (i.e., the SOMAG, see Viarouge et al., 2018). In each trial, children were presented with three images depicting arrays of dots: Two cards (targets) were horizontally aligned at the top of the screen, while the third card (reference) was centered at the bottom of the screen. Children were asked to spontaneously pick one target card to go with the reference card. The collections of dots shown on the cards could be sorted according to the number of dots, aspects of the dot size or of the spacing of the dots (the Size and Spacing dimensions were defined following DeWind, Adams, Platt, & Brannon, 2015).Taken together these findings suggest that it becomes easier for children to succeed the number-conservation task (a) as the misleading “length-equals-number” strategy becomes less salient (by increasing the difference in length between the two rows) and/or (b) as they spontaneously rely on the numerical dimension of the task. Using such card-sorting task in the classroom might be a good way to assess quickly and efficiently the spontaneous orientation of students toward numbers and thus propose dedicated activities for the one more spontaneously oriented toward different dimensions of magnitude.

The class-inclusion task

In the class-inclusion task, children are presented with 8 daisies and 2 roses and asked whether there are more daisies than flowers. To succeed at this task, children must understand that there are more elements in the superordinate class (i.e., flower) than in the subordinate classes (i.e., daisies). At 7 years of age, children typically succeed the class-inclusion suggesting that they grasp the underlying logic of class inclusion, a hallmark of children’s mind shifting to the concrete operational stage according to Piaget. Surprisingly, adults are systematically biased in very simple logical problems that require logical reasoning similar to the one displayed by 7-year-old children in the class-inclusion task (Kahneman, 2011). In one such problem, the so-called Linda conjunction fallacy problem, Linda is described as a woman who was a feminist activist in 1970s, and participants are asked whether it is more likely that Linda would today be a banker or a banker and a feminist. Most adults think that Linda is more likely to be a banker and a feminist, disregarding the principles of probabilities (i.e., the probability of a conjunction of events is always lower than the probability of a single event). Strikingly, children have already mastered the class-inclusion logic needed to succeed in the Linda conjunction fallacy problem at age 7, as demonstrated by their ability to succeed in the class-inclusion task designed by Piaget (Piaget, 1983). Indeed, in the Linda problem, one must understand that there are always more bankers (i.e., superordinate class) than bankers and feminists (i.e., subordinate class) just as one must understand in the class-inclusion task that there are always more flowers (i.e., superordinate class) than daisies (i.e., the subordinate classes). Just as in other Piagetian tasks, two studies revealed that the inhibition of a misleading heuristic (here, the direct perceptual comparison of the number of daisies and roses) was also critical for success in this Piagetian task for both school-aged children and adults (Borst, Poirel, Pineau, Cassotti, & Houdé, 2013; Perret, Paour, & Blaye, 2003). Indeed, children under 7 years of age erroneously think that there are more daisies than flowers in the class-inclusion task because children spontaneously compare the visuospatial extensions (the number of elements) of the two subordinate classes (e.g., daisies and roses) rather than comparing the superordinate class (flowers) to its subordinate class (daisies).

Non-linear models of cognitive development

In light of these non-linear development trajectories that more likely constitute the norm than the exceptions, a growing number of researchers argue that cognitive development should be conceived as a non-linear dynamic system (Siegler, 1999; Smith & Thelen, 2003) in which errors can appear at any age and in any context when children, adolescents or adults rely on prepotent responses, illogical intuitions, or misleading strategies to solve a task rather than on deliberate, analytical strategies adapted to the context. Importantly, executive functions such as inhibitory control are one of the core mechanisms of intelligence that allows one to overcome systematic errors in a given task by inhibiting misleading prepotent responses and strategies (Houdé & Borst, 2014). This assumption is consistent with studies showing that the ability of children to succeed in theory of mind (Benson, Sabbagh, Carlon, & Zelazo, 2013), counterfactual reasoning (Becks, Riggs, & Gorniak, 2009) and strategic reasoning (Apperly & Caroll, 2009) tasks might be in part related to the growing inhibitory control ability between the ages of 3 and 5 years. Inhibitory control is conceived within this theoretical framework as a process that allows children and adults to resist habits or automatisms, temptations, distractions, or interference and to adapt to conflicting situations (Diamond, 2013).

Several strategies with different degrees of complexity and sophistication can be used to solve a task (Siegler, 1999) and individuals tend to rely spontaneously on fast, effortless, automatic strategies rather than on slow, effortful, analytical strategies to perform such tasks. In most contexts, automatic strategies are the most adapted strategies and provide a faster way to reach a solution, but in other contexts, they can be misleading when they interfere with the proper analytical strategy to use. Thus, systematic errors do not necessarily reveal a lack of knowledge; rather, they reveal a lack of ability to express a given knowledge in a context in which a misleading automatic strategy constructed previously interferes with it. According to this theoretical framework, the progressive ability to inhibit misleading automatic strategies sustains cognitive development by allowing children, adolescents and adults to understand the domain of the validity of each strategy in various contexts (Houdé & Borst, 2014).

The development of inhibitory control ability is necessary but is not sufficient to produce conceptual development during childhood and adolescence. Indeed, the development of other executive functions such as working memory (Halford, Cowan & Andrew, 2007) might also be critical to support conceptual development and reasoning (Morsanyi & Handley, 2008). Finally, inhibiting misleading automatic strategies remain challenging throughout childhood, adolescence and adulthood because of the slow maturation (until 25 years of age) of the prefrontal cortex (Casey, Tottenham, Liston, & Durston, 2005), an area of the brain devoted to inhibitory control (Aron, Robbins, & Poldrack, 2014) and more generally to executive functions (Diamond, 2013).

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