Multidimensional Reasoning Can Promote 3-Year-Old Children's Performance on the Dimensional Change Card Sort Task

An important aspect of executive functioning is the ability to flexibly switch between behavioral rules. This study explored how considering the multidimensionality of objects affects behavioral rule switching in 3‐year‐old children. In Study 1 (N = 40), children who participated in a brief game separating and aggregating an object's dimensions (i.e., color and shape) showed improved performance on the Dimensional Change Card Sort (DCCS), a measure of behavioral rule switching, relative to controls. In Study 2 (N = 80) DCCS performance improved even when the initial practice involved a different dimension (pattern and shape). Thus, practice thinking about multidimensionality can affect 3‐year‐olds' DCCS performance and therefore may play an important role in the development of flexible thinking.

Executive functioning (EF) refers to a suite of cognitive abilities that support the conscious control of thoughts, actions, and behavior (Miyake et al., 2000) including, working memory, inhibitory control, and set‐shifting. In preschool‐aged children, one of the most commonly used tasks to assess preschoolers' EF skills is the Dimensional Change Card Sort (DCCS; Zelazo, 2006). In this task, children are instructed to sort bivalent test cards—red or blue rabbits or boats—initially based on one dimension (e.g., color) and then switch to sort by another dimension (e.g., shape). Although successful performance on the DCCS relies most obviously on the ability to shift between the sorting rules, the task also clearly requires the ability to inhibit a prepotent tendency to sort according to the initial rule, and the ability to hold in working memory the current task context (Cragg & Chevalier, 2012; Perner & Lang, 2002; Waxer & Morton, 2011). Performance on the DCCS improves substantially over the preschool years (Carlson, 2005). For instance, when asked to switch, 3‐year‐olds tend to perseverate on sorting according to the initial rule whereas 5‐year‐olds shift successfully (Garon, Bryson, & Smith, 2008; Zelazo, 2006). Because of its importance as a principal measure of EF skills, a considerable amount of theoretical and empirical work has been focused on understanding the cognitive and neurocognitive measures that support DCCS performance. The goal of this study was to present novel evidence that conceptual understandings regarding the multidimensional nature of objects (e.g., that objects can be composed of dimensions whose values can vary independently) may play a critical role in DCCS development.c

There have been several accounts of theoretical accounts of what contributes to the age‐related changes in the DCCS. These accounts can be seen as fitting into two categories: (a) rule‐based accounts, and (b) object‐based accounts. A full review of this literature is beyond the scope of this paper and there have been valuable recent summaries (e.g., Buss & Spencer, 2014). To preview, we will be situating our account within the object‐based accounts, with a special focus on developing the hypothesis for how a conceptual understanding of multidimensionality might promote DCCS performance.

Rule‐based accounts hypothesize that young preschoolers' failures in correct postswitch sorting are attributable to difficulties in representing the postswitch rule. One well‐articulated account along these lines is the Cognitive Complexity and Control (CCC, CCC‐Revised) or Iterative Reprocessing theory offered by Zelazo and colleagues (Cunningham & Zelazo, 2007; Zelazo et al., 2003). This model suggests that young preschoolers fail on postswitch trials of the DCCS because they are unable to append the postswitch rule to the preswitch rule in a way that integrates them into a complex conditional (or "if‐if‐then") rule (Cunningham & Zelazo, 2007; Marcovitch & Zelazo, 2009; Zelazo, 2015). This theory is supported by several studies showing that task modifications that reduce the need for forming complex rules by making the separate sorting strategies discrete foster improved performance in preschoolers who fail standard versions of the DCCS (e.g., Zelazo et al., 2003).

A second rule‐based account for DCCS performance stems from the active‐latent account of working memory (see Brace, Morton, & Munakata, 2006). Briefly, latent representations in working memory are those built implicitly from children's direct actions and experiences. In contrast, "active" representations are those that are more explicit and actively maintained to guide behavior. The theory proposes that postswitch sorting failures are the result of children relying too much on the latent representations of the sorting rules relative to the active ones which are more effortful to maintain. In an elegant study, Brace et al. (2006) showed that a scaffolding procedure designed to establish a latent representation of the postswitch rule improved children's performance on the DCCS. Importantly, as the authors point out, it did so without necessarily encouraging the development of a higher‐order rule, thereby suggesting that the creation of a higher order "if‐if‐then" rule is not necessary for successful postswitch sorting.

In contrast to the theories that focus on children's representation of the sorting rules themselves, object‐based accounts focus on children's abilities to understand or attend to the objects involved in the DCCS. For example, the representational re‐description theory suggests that the source of children's perseverative error stems from their inability to label or "describe" a given object in multiple ways (Kloo & Perner, 2003, 2005; Perner & Lang, 2002). Just as young preschool‐aged children typically have trouble acknowledging that things can have two labels at the same time (Clark, 1993; Doherty & Perner, 1998; Markman, 1989) children in the DCCS may have difficulty thinking of the red rabbit as "a red thing" when sorting by color and then as "a rabbit" when sorting by shape (Jordan & Morton, 2008, 2012; Kloo & Perner, 2003; Mack, 2007). As children's understanding that objects can have multiple labels improves, they become more flexible in how they can describe the objects in the DCCS game.

Evidence in support of the representational redescription theory comes from studies showing that children can reverse their responses with respect to a given stimulus when redescription is not necessary. For instance, in one set of studies, children were first asked to sort cards with pictures of either pears or apples to a consistent target card (e.g., sort apple cards to the apple target) and then switch to sort with the inconsistent target (e.g., sort apples to the pear target). Young preschoolers who typically fail the DCCS perform well on the postswitch trials in this alternative task (Brooks, Hanauer, Padowska, & Rosman, 2003; Kloo, Perner, Kerschhuber, Dabernig, & Aichhorn, 2008; Perner & Lang, 2002). Sorting can also be improved when children are asked to sort on two different attributes (e.g., color and shape) so long as they are separated and distinct on the sorting cards (Diamond, Carlson, & Beck, 2005; Kloo & Perner, 2005), though the evidence for this finding is mixed (see Zelazo et al., 2003). The representational redescription theory explains this by suggesting that the separation of the two entities on the card eliminates the need for describing a single object in two ways (Kirkham, Cruess, & Diamond, 2003; Kloo & Perner, 2005; Mack, 2007; Towse, Redbond, Houston‐Price, & Cook, 2000; van Bers, Visser, & Raijmakers, 2014).

More recently, an object‐based approach was offered by Buss and colleagues (e.g., Buss & Kerr‐German, 2019) that focuses on children's capacity for dimensional attention—or, the ability to flexibly switch their attention between the two dimensions of the object. Their approach, inspired by dynamic systems and neural modeling approaches such as dynamic field theory (Buss & Spencer, 2014), reasons that the task requires children to maintain representations of two dimensions of the object—one in terms of its shape and another in terms of its color, each of which is paired with, and activated by the mention of, their labels. Whichever one of these representations reaches some strength threshold within the task context provides the basis for guiding children's actions. For young children, these representations are initially weak and susceptible to dynamic changes based on the task context. In particular, experience with the preswitch dimension in the first part of the task naturally strengthens the representation of that dimension which subsequently makes it a formidable competitor for the weaker representation of the postswitch dimension when children are asked to attend to that one. Over time, however, as the associations between those dimensions and their labels are strengthened, the postswitch dimension can more successfully compete with the preswitch dimension, which in turn makes it more accessible to children's sorting behavior. Buss and Spencer (2014) review the literature and demonstrate that any task manipulation that improves children's posttest sorting (including those that were used to support other theories, such as representational re‐description or the rule‐based theories) may have done so by affecting the contextual salience of the postswitch dimension.

In their work, Buss and colleagues have focused on the role that basic "bottom‐up" mechanisms might play in shaping children's dimensional attention within the DCCS context, such as the extant strength of children's word‐dimension associations, and the perceptual salience of the postswitch dimension. Yet, what has been unexplored in this context is the extent to which relevant conceptual understandings may play a critical role in providing top‐down control over attentional processing in the task context. The candidate conceptual understanding that we explore here is "multidimensionality"—namely that objects composed of their constituent features, into which they can also be decomposed. For example, a red square is a composite that has the separable attributes of color (RED) and its shape (SQUARE). A critical feature of multidimensional understanding is the conceptual understanding that the attributes are variables that can take different values, which in turn would lead to different composites, (e.g., RED could instead be combined with CIRCLE to create a red circle).

Early work on children's understanding of objects suggested that children might have a relatively weak conceptual understanding of the multidimensional nature of objects—when asked to categorize items that either shared salient features or had greater overall similarity, younger preschoolers tended to opt for grouping objects based on overall similarity (e.g., Smith & Kemler, 1977). Early influential hypotheses about why this is the case centered on bottom‐up perceptual factors—for instance, that children could only perceive objects holistically and struggled to separate the perception of objects' features (see Tighe & Shepp, 1983 for a review). Subsequent work, however, showed that when given special instructions, children could sort by features, thereby showing that the difficulty was not a perceptual one, but instead was a difficulty with using those features to guide responses in a given context (see Smith, 1989).

A full conceptual understanding of multidimensionality, however, entails more than an awareness of multiple features of an object, or the ability to attend to one feature or another. Critically, multidimensionality also entails understanding the generative relationship between objects and their constituent, orthogonally variable features. To illustrate this key difference, consider the developmental trajectory of phonemic awareness. Briefly, phonemic awareness is the understanding, important to reading fluency, that words are composed of constituent phonemes (Kenner, Terry, Friehling, & Namy, 2017). Although perceptual skills play a necessary role in separating words into their constituent sounds, those skills are separable from the awareness of the association between words and their constituent phonemes, which itself seems to benefit from scaffolding in relevant contexts (Anthony & Francis, 2005; Kenner et al., 2017; Ukrainetz, Nuspl, Wilkerson, & Beddes, 2011). Extending this same logic to objects, children may be capable of registering the constituent dimensions of objects without an attendant awareness or understanding of the role those constituents play in creating the composite.

With this in mind, our hypothesis was that children's facility with reasoning about the multidimensional nature of objects may act as a top‐down factor that promotes their ability to flexibly shift between the pre and postswitch sorting dimensions in the DCCS. To test this hypothesis experimentally, we developed a brief activity to give children practice reasoning about the multidimensional nature of objects. In the activity, children were asked to both (a) decompose simple objects (e.g., red squares) into their constituent features (e.g., shapes and colors), and (b) combine constituent features to create a composite object. To preview, in Study 1 the activity required them to separate and combine the same dimensions that they would then be asked to switch between in the DCCS (i.e., shapes and colors). In Study 2, the activity required separating and combining pattern and shape, and the DCCS asked children to switch sorting strategies between either pattern and shape (as in training) or color and shape (as in the typical DCCS). In addition to DCCS performance, we included two age‐appropriate measures of EF—the Bear/Dragon task (Kochanska, Murray, Jacques, Koenig, & Vandegeest, 1996) and the Day/Night Stroop task (Gerstadt, Hong, & Diamond, 1994). Including these measures allowed us to determine whether children's practice in thinking about the multidimensional nature of objects affected performance on DCCS specifically, or EF more generally.

Based on an a priori power analysis assuming a medium effect size with power to detect at.8, we set a target sample size of 40 participants (20 per cell). To reach this target, we recruited 52 preschool‐aged children were recruited from a database consisting of families from a predominantly white (90.8%) middle‐class military and mixed‐professional community centered in Southeastern Ontario, Canada. Data were collected between 02/2015—09/2015. Six of the original children who were recruited could not be included because they refused to complete the procedure. An additional four were excluded because they failed the preswitch trials of the DCCS. An additional two could not complete the multidimensional activity—one in the experimental condition and one in the control condition. These six participants who were excluded because of their performance did not differ from the full sample in terms of their gender distribution or vocabulary scores, but they were significantly younger, t(51) = 2.34, p = .023.

Thus, the final sample consisted of 40 children (18 girls and 22 boys, age range 38–47 months). Participants were randomly assigned to participate in either the control (n = 20; Mage = 41.10 months, SD = 3.40; 9 girls, 11 boys) or the experimental condition (n = 20; Mage = 41.00 months, SD = 3.00; 9 girls, 11 boys).

Children were randomly assigned to either the control or experimental condition. Children were tested individually in a quiet room by the same experimenter while parents remained outside watching the session via a live feed. The testing session began with either the control or experimental color and shape game. The experimenter then administered an EF battery, including the DCCS, the order of which was randomized for each participant. Finally, participants completed the Peabody Preschool Vocabulary Test (PPVT), a measure of receptive language ability.

Children were shown a rectangular board filled with detachable cards. On the left side, there was a column of five cards depicting line drawings of different shapes, and another column with five cards showing amorphous scribbles. On the other side of the board, there were 10 cards, each depicting a different color shape composite (purple circle, blue square, etc.; see Figure 1).

The game began with children being asked to find the composite shape from the right side of the board that would result from combining a specific shape and color from the left side (e.g., "If I give you this shape and this color [removes pentagon line drawing and red scribble from the display] and if we put these together, which one would we get from over here [indicate a section of the display with colored shapes]?"). After successfully finding five composite cards from their separate components they were then asked to perform the task in reverse; that is, they were to find the two pieces that together made up a specific colored shape. For example, children might be shown a purple circle and asked to select its corresponding line drawing (circle) and color scribble (purple). Each shape and color were displayed twice in the combined colored shape display to prevent the child from merely matching on a single feature. There were five combination trials and five separation trials, each child played the complete game once in the same order.

The purpose of this condition was to provide a one‐dimensional control that allowed for similar exposure to the stimuli used in the experimental condition. Here, children were asked to match cards from the left and right sides of the board, but instead of integrating dimensions, children were asked to focus on only one. For example, on one trial the experimenter selected a purple scribble and asked, "Can you find me two cards that are the same color as this one?" As with the experimental condition, there were 10 trials. Children were asked to first find all five colors (red, light blue, pink, purple, navy) followed by all five shapes (circle, trapezoid, square, parallelogram, pentagon). Thus, while they had to consider both the shape and color dimensions of objects equally while playing the control game, they did not have to integrate them or consider their multidimensionality. The experimental and control conditions took on average about 7 min to complete.

After participating in either the experimental or the control game, children were given the DCCS (Zelazo et al., 2003). The child was shown two different trays, one with a picture of a blue rabbit and one with a picture of a red boat. Children were then instructed to sort bivalent cards according to either the color rule or the shape rule (counterbalanced across participants). After the experimenter demonstrated the appropriate sorting technique, children were asked to sort five new cards, presented sequentially by the experimenter. Following the original, and more challenging, protocol for this task the experimenter labeled each card presented to the child with reference to both the relevant and irrelevant dimension of the card in the form with a color‐shape label (e.g., "red rabbit"). Children who correctly sorted at least four out of the five trials were then asked to sort another five cards based on the other dimension (e.g., if previously sorting by color, they were now asked to sort by shape). There were five postswitch trials where the experimenter again repeated the postswitch rule and continued to label the cards according to both dimensions. Following previous work (see Espinet, Anderson, & Zelazo, 2013), children passed the DCCS if they correctly sorted at least four of the five postswitch trials. Prior work has shown that about 20% of children in the age group tested here (3.5‐year‐olds) typically show passing performance, thereby making it a reasonable baseline from which we might observe improvement (see Carlson, 2005).

The experimenter and child began by talking about when the sun rises (daytime) and when the moon and stars come out (nighttime; Gerstadt et al., 1994). The experimenter then showed the child a white card with a yellow sun on it and a black card with a white moon and stars. The child was instructed to say "day" when shown the card of the night sky and to say "night" when shown the card of the sun. Children were given two practice trials, after which 16 cards were presented in a fixed, pseudorandom order. At no point during the testing were children reminded of the rules. The score was the number of correct responses (range: 0–16).

The experimenter and child began by going through a series of "silly" movements (Reed, Pien, & Rothbart, 1984). For example, "stick out your tongue," "touch your ears," etc. The child was then introduced to two puppets, the "naughty" dragon and the "nice" bear. The child was told that in this game, (a modified Simon Says), they should listen to the bear (voiced soft and high‐pitched), but not the dragon (voiced gruff and low‐pitched). Children were given a practice trial with each puppet, followed by 10 test trials. The dragon and bear were used in an alternating order, and children received a score based on their performance on each of the dragon trials on which they successfully withheld their response (i.e., did not do what the dragon said).

The PPVT, 4th ed. (Dunn & Dunn, 2007) assesses children's receptive vocabulary abilities. In this test, children were presented with four pictures and then asked to point to the picture that corresponded to a given vocabulary word. Items became progressively more difficult as children continued through the measure. The task was administered, and raw scores were computed according to the procedures provided in the manual accompanying the task.

The raw data and the scripts used to analyze the data for Studies 1 and 2 are available on our OSF project site (https://osf.io/fg7uq/).

The experimental and control groups did not differ in age (t(38) = 0.097, p = .963) or gender distribution. Likewise, raw PPVT scores were similar across groups (Mexp = 64.94, SD = 17.18; Mcon = 71.10, SD = 16.65; t(37) = 1.136, p = .263). Across all measures, performance was approximately as expected for the age group tested here (see in the following section).

For our focal analyses, we found evidence in favor of our hypothesis regarding the effects of supporting multidimensional reasoning: significantly more children passed the DCCS in the experimental condition (11/20, 55%) than in the control condition (4/20, 20%), χ2(1, _I_N_i_ = 40) = 5.26, p = .022. Further descriptive analysis suggested that passing the DCCS was unrelated to preswitch condition—8/15 passers switched from color to shape and 7/15 switched from shape to color.

If children had performed nonsystematically on any given trial of the postswitch DCCS, achieving a passing score on the test (either 4 or 5 correct) would have a baserate probability of.1875. Binomial tests showed that children significantly exceeded this chance baserate of passing the DCCS in the experimental condition (p = .0003), but not in the control condition (p = .532). Thus, more children in the experimental condition showed systematic correct responding than would be expected by chance, but not in the control condition.

In our secondary analyses, we found no evidence to suggest that the DCCS advantage for the experimental group generalized to the other EF tasks that we administered; performance in the Bear/Dragon task (Mexp = 11.89, SD = 7.84; Mcon = 9.95, SD = 8.36; t(37) = −0.749 p = .459) and the Day/Night Stroop task Mexp = 8.40, SD = 3.68; Mcon = 8.45, SD = 4.14; t(38) = 0.040, p = .968) were similar across conditions.

Although we did not find general evidence of transfer, it seemed possible that those who benefitted from the multidimensional activity would also demonstrate improved outcomes on the other measures of EF. To explore this possibility, we tested whether the children who passed the DCCS (and thus, may have benefitted from the multidimensionality activity) differed from nonpassers in their performance on other EF tasks. Again, we found no evidence of an association. Children who passed the DCCS did not outperform children who failed on either Bear/Dragon (t(17) = 1.125, p = .276) or Day/Night (t(18) = 1.459, p = .161).

The aim of this study was to provide evidence that giving children practice reasoning about the multidimensionality of objects would facilitate their performance on the DCCS. Results showed that children in the experimental group who engaged in the multidimensionality activity performed significantly better on the DCCS relative to controls. These findings suggest that encouraging children to tap into their capacity to reason about the multidimensionality of objects can improve their abilities to use that knowledge in the DCCS and flexibly change from one sorting rule to another.

There was not, however, evidence that the activity affected EF skills broadly. There are several possible explanations for this lack of transfer. First, though there is debate about the extent to which different aspects of EF are separable in preschool‐aged children (see Bardikoff & Sabbagh, 2017 for a review), it is notable that the Day/Night and Bear/Dragon tasks are typically classified as inhibitory control tasks, while the DCCS is a measure of shifting abilities (Garon et al., 2008). It is possible that the factors affecting performance on the three tasks in question differ during this age range, and so the multidimensional practice may not aid in EF broadly but instead may be more important for representing the competing dimensions of the object which in turn promotes more flexible attentional shifting. We will return to this issue in the general discussion.

With respect to our focal finding, an important question concerns whether our intervention supported children's emerging understanding of multidimensionality broadly, or instead facilitated DCCS performance by providing experience with the specific sorting dimensions themselves. Recall that a key mechanism for development offered in the dimensional attention account (Buss & Kerr‐German, 2019) account is the strengthening of the connection between the attributes and their labels, which in turn makes the representations of the object attributes more available in the postswitch phase. Some evidence that it could be from experience with the dimensions themselves comes from Perone, Molitor, Buss, Spencer, and Samuelson (2015). In their work, children who played a simple preliminary matching game with color then went on to perform better on the DCCS when color was the postswitch dimension compared to children who did not play the preliminary game.

This explanation does not, at least on its surface, provide a clear account of our findings. Within both the experimental and control conditions, color and shape attributes were talked about equally, and there was no difference between conditions in the extent to which this was so. Thus, there was no reason to think that our multidimensionality game specifically enhanced the inherent salience of the postswitch dimension or sorting rule. Yet, it could well be that practice with reasoning about the separability of color and shape specifically, and not the conceptual understanding of multidimensionality was driving the boost in some children's DCCS performance.

With this in mind, we conducted a second study with two aims. The first was to test whether the positive effect of participating in the multidimensionality activity that we observed in Study 1 would be confirmed and generalized to a second sample of children. The second was to determine whether we could modify the intervention we developed to focus on shapes and patterns (rather than shapes and colors) and still see an experimental advantage for children on a shape/color version of the DCCS. This would provide some confidence that the effects of the multidimensional training are not attributable to the effects of familiarization about color, per se, but rather are acting on children's facility with multidimensionality more generally.

As in Study 1, an a priori power analysis assuming a medium effect size and power to detect at.8 established a target sample size of 20 participants per cell. To reach that target, ninety‐five preschool‐aged children were recruited through same database as Study 1, though none of the children included in Study 1 also participated in Study 2. Data were collected between 11/2015—09/2016. A total of 15 children were excluded from this original sample. Six were excluded due to noncompliance, one was excluded due to experimenter error, three failed the preswitch condition of the DCCS, five did not understand the rule of the multidimensionality activity—three in the experimental condition, two in the control condition. There were no statistically significant differences between the excluded and included children in their gender distribution, age, or vocabulary scores.

Thus, the final sample consisted of 80 children (43 girls and 37 boys, age range 38–47 months). Children were randomly assigned to one of four cells in which experimental condition (experimental vs. control) was crossed with DCCS type (color/shape vs. pattern/shape; n = 20 per group). Table 1 summarizes the relevant characteristics for participants in each cell.

1 TableParticipant Information by Condition

1 Note

2 PPVT = Peabody Preschool Vocabulary Test; DCCS =Dimensional Change Card Sort.

Children were tested individually in a quiet room after being familiarized with the setting by the same experimenter while parents remained outside watching the session via a live feed. The testing session began with either the experimental or control pattern and shape game. The experimenter then administered an EF battery including the DCCS, in a random order followed by the PPVT, a measure of receptive language ability.

Similar to Study 1, the purpose of the experimental condition was to highlight the multidimensional nature of stimuli and promote the understanding that one can think about objects in different ways. Children were shown a display with separate sections, one with five blank shapes, one with five different patterns imposed on amorphous shapes, and a final section with ten patterned shapes (see Figure 2). Children played a game identical to the multidimensionality activity in Study 1 but with pattern and shape instead of color and shape. The game in the control condition was also the same as in Study 1, except with this new stimulus set.

Children from the experimental and control multidimensionality conditions were randomly assigned to play one of two different versions of the DCCS: either a novel pattern and shape DCCS that involved the patterns used in the multidimensionality game, or and a standard color and shape DCCS (as in Study 1; Zelazo et al., 2003). In the pattern condition, children were asked to sort cards on the basis of shape and pattern as opposed to shape and color, that is, "if it's a striped one it goes here, but if it's a polka dot one it goes here. Here is a polka dot rabbit. Where does this one go?" Both conditions included five postswitch trials where the experimenter again repeated the postswitch rule. Children pass the pattern and standard DCCS if they correctly sorted at least four of the five postswitch trials. The preswitch condition was counterbalanced across conditions.

The Day/Night Stroop, the Bear/Dragon task, and the PPVT were administered as in Study 1.

Due to the bimodal pass/fail nature of the DCCS a logistic regression was conducted with condition (experimental vs. control), DCCS type (pattern‐shape vs. color‐shape) and the condition x type interaction as the predictors and DCCS outcome (pass/fail) as the outcome measure. A test of the full model against a constant only model was significant, showing that the set of independent variables were able to accurately predict performance, χ2(3) = 10.93, p = .012.

Inspection of the individual factors (summarized in Table 2) showed that there was a significant main effect of condition, whereby children in the experimental group were 4.64 times more likely to pass the DCCS than were children in the control group. There was no main effect of DCCS type, and no interaction between DCCS type and condition. Thus, there was no evidence that children's performance varied depending on whether they received the pattern‐shape DCCS or the color‐shape DCCS following the pattern‐shape intervention game.

2 TableLogistic Regression Analysis of Factors Predicting DCCS Performance in Study 2

• 3 Note
• 4 DCCS = Dimensional Change Card Sort.

For comparison with Study 1, we conducted two chi‐square analyses comparing the experimental and the control groups in the pattern‐shape DCCS and in the standard color‐shape DCCS. For the pattern‐shape DCCS, children in the experimental group were more likely to pass (12/20, 60%) than children in the control group (5/20, 25%), χ2(1, _I_N_i_ = 40) = 5.03, p = .025. The same thing was true for the standard color‐shape DCCS; children in the experimental group were more likely to pass (10/20, 50%) than children in the control group (3/20, 15%), χ2(1, _I_N_i_ = 40) = 4.27, p = .038. These findings generalize the findings from Study 1 to a new sample and provide evidence that the effects of training are not attributable to simple familiarization with a pair of specific dimensions.

Finally, binomial tests against a chance baseline of p = .1875 revealed that in each of the experimental groups, children showed higher rates of passing the DCCS than would be expected by chance DCCS (ppattern‐shape = .00005, pcolor‐shape = .002), but children in the control groups did not (ppattern‐shape = .316, pcolor‐shape = .753). Thus, only in the experimental condition did significantly more children show systematic correct performance on the DCCS than would be expected by chance. In keeping with study 1, rate of passing did not differ on the basis of the preswitch dimension, pattern and shape DCCS, χ2(1, _I_N_i_ = 40) = 2.283, p = .131, color and shape DCCS, χ2(1, _I_N_i_ = 40) = 0.173, p = .677.)

As with Study 1, we conducted a secondary analysis to determine whether participation in the experimental condition had any effect on performance in the nonfocal EF tasks—Bear/Dragon and Day/Night Stroop. A pair of factorial analyses of variance were conducted with condition (experimental vs. control) and test type (pattern‐shape vs. color‐shape) as independent measures and performance on either Bear/Dragon or Day/Night as the dependent measure. Of particular interest is the main effect of condition. We found no evidence of a main effect of condition for Bear/Dragon (Mexp = 10.36, SD = 8.87; Mcon = 9.18, SD = 9.35), F(1, 74) = .365, p = .548, nor for Day/Night (Mexp = 8.50, SD = 4.54; Mcon = 8.95, SD = 4.73), F(1, 73) = .158, p = .692. There was also no main effect of test type, nor test type by condition interaction.

As with Study 1, we again tested whether the children who passed the DCCS (and thus, may have benefitted from the multidimensionality activity) differed from nonpassers in their performance on other EF tasks. Again, we found no evidence of transfer. Children who passed the DCCS did not outperform children who failed on either Bear/Dragon (t(37) = 0.339 p = .737) or Day/Night (t(36) = 1.149 p = .258).

Consistent with results from Study 1, children who participated in the multidimensionality activity were more likely to pass the DCCS than children in the control condition. This was true regardless of whether the DCCS involved the same or partially different dimensions as those that were used in the scaffolding game. This important extension supports the claim that the scaffolding game improved DCCS performance by giving practice with thinking about multidimensionality rather than experience with specific attributes.

Although technically different, pattern and color are similar insofar that they are surface characteristics that are projected on a shape. One question is whether this similarity is necessary to see the benefits of the scaffolding game. To test this in future research, it would be useful to use a scaffolding game that involved separating and aggregating, for example, shape and size, or orientation and location, to see whether these too improve performance on a standard color‐shape DCCS. This would provide still stronger evidence that it is scaffolding experience with multidimensionality, per se, that leads to improvements in DCCS performance.

In two studies, we found evidence that participating in an activity designed to encourage reasoning about the multidimensional nature of objects promoted performance on postswitch trials of the DCCS. In both studies, the activity focused on separating and aggregating the attributes of objects, either shape and color (Study 1) or pattern and color (Study 2). Regardless of the specific nature of the game, children's performance on the DCCS improved relative to controls after they played the game. We interpret these findings as evidence that explicitly thinking about the multidimensionality of objects—that is, that objects can be composed of constituent attributes—can support children's performance on the DCCS.

Before discussing the broader implications of these findings and our interpretation, it is important to consider alternative explanations. One possibility is that the children in the experimental groups performed significantly better on the DCCS relative to controls because the multidimensionality activity was more cognitively engaging than the control activity. Although for the most part, research has shown that first participating in a cognitively demanding task has negative effects on subsequent tasks (see Oeri & Roebers, 2020; Peverill, et al., 2017), there is evidence that under some circumstances, children tend to perform better on EF tasks after first participating in cognitively demanding tasks that engage their EF abilities (Lavie, 2010). Our focal task of separating objects into their constituent features or aggregating those features to create a composite is arguably more demanding than our control task of simply matching single dimensions. Although we cannot rule that these demands boosted subsequent performance independent of their effects on multidimensionality, the concern is mitigated by several factors. First, the control game was designed to be as engaging as the experimental game. Children in all groups interacted with the same number of cards, heard the same sort of language, were required to match cards on the basis of the same number of attributes. Moreover, the experimental and control games had similar durations. Further evidence for the fact that the games were comparable in terms of difficulty was that roughly similar numbers of children were excluded for being unable to complete the experimental or control games. Finally, if it was simply a general effect of cognitive engagement, then we might have expected experimental effects on the nonfocal EF tasks. The fact that we did not get these effects provides further reason to favor our hypothesis that it was training with multidimensionality per se, rather than participation in a generally demanding task, that promoted children's performance on the DCCS.

A second alternative explanation for our findings relates to a limitation related to our experimental design. We did not measure DCCS performance in the absence of participating in either the control or experimental conditions. This limitation leaves some room for ambiguity with respect to our interpretation. That is, although our preferred interpretation is that children who participated in the experimental condition were advantaged (i.e., showed stronger performance than they would otherwise), it could also be that for some unexpected reason, children who participated in the control condition were disadvantaged. Our design does not allow us to rule this possibility out and it is, thus, a limitation that must be addressed in future studies. Nonetheless, we do not think that this alternative is correct. Across the three control cells of the studies reported here (1 in Experiment 1, and 2 in Experiment 2) children passed the DCCS approximately 20% of the time. The version of the DCCS that we used was the one in which following each postswitch trial, the postswitch rule is repeated and the card is labeled with using the appropriate color‐shape description (e.g., "Here is a red rabbit"). We used this version of the task because it was also included in a published report (Carlson, 2005) that included data from a large sample of children in the age group that we used here. Specifically, we aimed for a version of the task that would have a relatively low pass rate to begin with that would enable us to index improvement due to our training. In that report (see Carlson, 2005, table 3), 10% of young 3‐year‐olds passed the task and 25% of older 3‐year‐olds pass. Averaging these two (as we included both groups) gives an expected pass rate of around 18%, just as we found. These comparisons give us confidence that children in our control condition performed as we would expect from untreated children at the same developmental level.

From the outset, we suggested that the higher‐level mechanism of reasoning about multidimensionality might contrast with other theoretical explanations that have so far relied solely on the dynamic lower‐level processes that are described in the dimensional attention approach (e.g., Buss & Kerr‐German, 2019; Buss & Spencer, 2014). Recall that on this approach, natural developmental changes in children's DCCS performance are thought to be paced by the strengthening of the association between the object dimensions and their labels. If this was the only rate‐limiting factor on children's performance then we might have expected children in the control condition of our study to benefit just as much from the training as those in the experimental condition; after all, children in the control condition were exposed to dimension‐label associations just as often as were children in the experimental condition. The fact that despite these exposures, children's performance in the control condition was at the expected level for an untreated group provides some evidence that it was the higher‐level understanding of multidimensionality that was primed by the task that supported the improved performance of the group.

Our findings from Study 2 are also not straightforwardly predicted by the mechanisms that are featured in current explanations of the dimensional attention approach. In particular, if it were the case that children's performance in the DCCS was affected solely by the strength of the associations between the labels and their attributes (e.g., "color") then there would be no reason to predict that children's performance in a color‐shape DCCS would be affected by experience in our pattern‐shape multidimensionality activity. The fact that we did observe that sort of "transfer" effect further supports our claim that it was the experience reasoning about multidimensionality more abstractly, and not simply a lower‐level account of how the association between properties and their labels contributing to flexible attentional shifting.

An interesting alternative to our more conceptual account concerns another potential difference between our experimental and control activities. Our experimental activity had children match shape and color in conjunction with one another whereas our control activity asked them to do them separately. It is possible is that reasoning about the features in conjunction somehow strengthened the representations of each of the features more than they do when the searches were separated. Some evidence that this might be the case comes from a recent FMRI study showing that conjunction learning had long‐lasting effects on increasing the target‐evoked neural activity relative to simple feature learning (Reavis, Frank, Greenlee, & Tse, 2016). The authors argue that the conjunction learning provided a learning history that affected participants' perception of the salience of the target objects. Although it is not clear about the extent to which the representations of the object features might also have been altered, it certainly raises the possibility that there was something about the conjunction searches they did in the multidimensionality activity that improved their performance on the DCCS, independent of conceptual understandings. We believe that disentangling these issues may be a particularly promising avenue for future work.

In any case, rather than frame our hypotheses about the conceptual understandings of multidimensionality as an alternative to the dimensional attention account, we prefer to consider it an adjunct. The dimensional attention framework offers a plausible account of the cognitive and neurocognitive mechanisms by which postswitch sorting might manifest. What we argue is that in addition to being guided by factors such as the inherent salience of the stimulus, or the children's developmental histories of word‐attribute associations, children's conceptual understandings can also provide a basis for guiding attention. The emerging view from the cognitive neuroscience literature is that attentional shifts can be governed by two distinct systems, sometimes referred to as the ventral versus dorsal attention networks (Fox et al., 2005). In an influential review of the literature comparing the functionality of these two networks, Corbetta, Patel, and Shulman (2008) suggest that the dorsal attention network (including the superior parietal lobes and the frontal eye fields) may be important for orienting to inherently salient (i.e., distinctive) stimuli or stimuli that have accrued substantial orienting in the past. In contrast, the ventral attention network (including the temporal‐parietal junction and the medial prefrontal cortex) are engaged to shift attention toward stimuli that may or may not be inherently salient but are nonetheless relevant to the task at hand. We propose that our multidimensionality activity engaged the ventral attentional network by highlighting the relevance of multidimensionality, which in turn made dimensions more available to attentional switching.

Another relevant question concerns the extent to which our multidimensionality training overlaps with other conceptual understandings, in particular those offered by the representational redescription theory. Recall that the representational redescription theory posits that preschooler's fail the DCCS because of a fundamental difficulty in recognizing that something can be described simultaneously in multiple ways (e.g., that something can be described as a boat and as red). We have no special reason to believe that our target multidimensional activity encouraged children to engage in this sort of labeling practice; the game did not require children to label the cards in their responses, only to select them from the array of options. Nonetheless, it could be that our multidimensionality activity promoted an ability that some have suggested may underlie representational redescription, namely the ability to integrate multiple perspectives or "mental files" of the same object (see Doherty & Perner, 2020). This ability has been theorized to underlie a handful of everyday skills that seem to require the integration of potentially competing perspectives, such as false belief understanding (see also Tomasello, 2018). A key empirical question for future research to address is the extent to which an understanding of multidimensionality may be a part of this general conceptual framework.

The main theoretical contribution of this work is to emphasize the role that a conceptual understanding of multidimensionality plays in preschoolers' flexible application of rules in the DCCS. As reviewed earlier, there is some evidence that an understanding of the multidimensionality of objects is nascent in young preschoolers but gets put to work for decisions in categorization much later (Smith & Kemler, 1977). The findings we present here are generally consistent with this view. Though we tested relatively young children here, almost all children were successful in playing our activity that required multidimensional thinking. That is, almost all children had no trouble combining dimensions to create an aggregate shape or decomposing an aggregate shape into its separate dimensions. Given this, we do not necessarily believe that it is the acquisition of a conceptual understanding of multidimensionality that acts as the conceptual rate‐limiting factor on preschoolers' DCCS performance. Instead, as outlined earlier, we believe that our activity activated children's nascent conceptualization of the inherent multidimensionality of objects, which in turn made it available to the top‐down systems that contribute to flexible attentional shifting.

The multidimensionality game had no effect on the two other tasks measuring EF that we used Bear/Dragon or Day/Night in either of our studies. This finding raises an important question regarding whether multidimensionality is a feature of EF generally, or simply a feature of the DCCS, with both practical and theoretical implications. Importantly, if our intervention effects are task specific, then the findings are arguably of limited utility for understanding EF more generally.

In response to this concern, we wish to raise two points. First, EF skills are always measured within a particular task context that children may be more or less familiar and practiced. Variability in familiarity and practice with the task context can come from idiosyncratic personal histories or from broader cultural variables (see Sabbagh, Xu, Carlson, Moses, & Lee, 2006). Even if our multidimensionality activity only boosts DCCS performance via a task‐specific conceptual understanding, then it may highlight the role that conceptual understandings play in any context where EF is required, laboratory‐based or otherwise. The insight provided by this work has important implications for designing real‐world interventions designed to improve EF skills. Although there has been substantial focus on training general EF skills in hopes of transfer from the training to EF more broadly, the evidence regarding either near‐ or far‐transfer is mixed (see Scionti, Cavallero, Zogmaister, & Marzocchi, 2019). Our findings suggest that a promising adjunct approach may be to identify aspects of a target context within which EF improvement is a goal and work on strengthening the conceptual understandings critical to successful negotiation of that context.

Third, although we did not find evidence that children in our experimental groups subsequently did better on measures of EF besides the DCCS, it is possible that other measures might have revealed transfer. As many researchers and theorists have pointed out (see e.g., Garon et al., 2008; Miyake & Friedman, 2012), EF is composed of multiple, separable components, typically referred to as inhibition, switching, and updating. The DCCS is thought to especially rely on the switching component whereas the other Stroop‐like tasks that we used are thought to rely more heavily on cognitive inhibition. Accordingly, the theories that have been proposed to account for DCCS performance may be most applicable to understanding the development of flexible switching, and it is less clear about the extent to which they may provide an account for correct performance in other tasks, such as Stroop‐like inhibition tasks, or tasks that especially tax working memory updating. It may be that participating in our multidimensionality activity would show at least near transfer to tasks that also rely on a cognitive flexibility, such as the flexible item selection task (see Blaye & Jacques, 2009). We believe that this is an important direction for future research.

One particularly striking implication of our findings is that we demonstrate that it is possible to promote cognitive flexibility in the DCCS without providing feedback on, or modifying, the task itself. An important question for future research concerns to what extent the type of activity that we used here might generalize beyond the task context. Although we focused here on the multidimensionality of objects, it is possible to conceptualize some behaviors as being multidimensional composites. For instance, in the classroom context of a group discussion, one can make various kinds of contributions (ask a question, comment on another's statement, etc.) and can do so in a number of possible ways (i.e., wait to be called on, interrupt, etc.). Understanding the extent to which any given action can be separated into these constituent dimensions (i.e., outcome and manner) may help children recognize the appropriateness of different actions in different contexts. We think that an important future direction for this work is to better understand the broader application of encouraging multidimensional thinking through aggregation and separation of a given action or object into its constituent features.

Another important implication of our work that we have alluded to throughout this discussion concerns using the DCCS as a measure of children's EF. Although the DCCS certainly has domain‐general EF demands, our work provides evidence that children's facility with the semantic features of that context may constrain their performance. Thus, when considering the factors that go into passing the DCCS, latent domain‐general EF may not be the only one. For the DCCS, and indeed for any other measure of EF, we believe that an important goal for future research is to tease apart the respective contributions of latent domain‐general EF and semantic fluency that shapes the EF demands in the specific task context.

Another important future direction is testing the longevity of the effects that we observed here. Our multidimensionality activity was simple to administer, required minimal materials, and was enjoyable for children. To the extent that understanding multidimensionality may be important for the kind of attentional flexibility that underpins successful DCCS performance, evidence of long‐lived effects could point to the value of using our multidimensionality activity in applied contexts where EF abilities associated with the DCCS are particularly important. It may also be valuable to think of ways in which our brief activity could be both improved and scaled up in order to be incorporated into a more comprehensive program that may be more likely still to promote long‐term benefits.

At the same time, it is important to recognize that there are likely substantial individual differences in the extent to which preschool‐aged children may benefit from our multidimensionality activity. Though our study provided clear evidence that participating in the focal multidimensionality activity raised group performance, there was a sizeable proportion of children who participated in that activity but still did not pass the DCCS. Although our study was not designed to determine why some did and some did not benefit from the focal multidimensionality activity, we can rule out some possible explanations for this finding. For instance, our analyses showed that performance on other IC tasks was similar for those who did versus did not pass the DCCS in the experimental condition, thus making it unlikely that the difference in benefit was attributable to a difference in baseline IC skills. Similarly, all children showed facility with the multidimensionality task itself, thereby suggesting that the difference is not attributable to baseline differences in children's multidimensionality understanding. One possibility, in line with our speculations on the mechanisms underlying our effect, is that individual differences in benefit may be attributable to individual differences in the developmental of the ventral attentional network that is important for top‐down modulation of attention across a variety of contexts. Future work exploring this possibility is crucial for understanding whether and how multidimensional training can benefit cognitive flexibility for a given child.

The results from these two studies provided evidence that requiring young preschool‐aged children to think about the multidimensional nature of objects can promote their DCCS performance. These findings help us to understand the conceptual mechanisms that might underlie DCCS performance and show that providing a context that foregrounds those conceptual understandings can improve DCCS performance without explicit feedback on the task. These findings shed light on the developmental processes important for shifting performance during the preschool age range and raise intriguing possibilities for the different ways in which we can foster this important set of abilities.