Children's working memory: Its structure and relationship to fluid intelligence

Intelligence 39 (2011) 210–221

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Intelligence

Children's working memory: Its structure and relationship to fluid intelligence Caroline Hornung ⁎, Martin Brunner, Robert A.P. Reuter, Romain Martin University of Luxembourg, Research Unit for Educational Measurement and Applied Cognitive Science (EMACS), Luxembourg, Luxembourg

a r t i c l e

i n f o

Article history: Received 25 February 2010 Received in revised form 12 January 2011 Accepted 11 March 2011 Available online 5 April 2011 Keywords: Working memory Short-term storage Fluid intelligence Children Structural equation models

a b s t r a c t Working memory (WM) has been predominantly studied in adults. The insights provided by these studies have led to the development of competing theories on the structure of WM and conflicting conclusions on how strongly WM components are related to higher order thinking skills such as fluid intelligence. However, it remains unclear whether and to what extent the theories and findings derived from adult data generalize to children. The purpose of the present study is therefore to investigate children's WM (N = 161), who attended classes at the end of kindergarten in Luxembourg. Specifically, we examine different structural models of WM and how its components, as defined in these models, are related to fluid intelligence. Our results indicate that short-term storage capacity primarily explains the relationship between WM and fluid intelligence. Based on these observations we discuss the theoretical and methodological issues that arise when children's WM is investigated. © 2011 Elsevier Inc. All rights reserved.

Working memory (WM) is an essential cognitive function in everyday life: it enables people to store and process important information, to inhibit irrelevant information, and to take the necessary incremental steps to achieve goals. This holds for people of all ages. It therefore comes as no surprise that WM has emerged to be strongly related to fluid intelligence (GF) in adult samples (Colom, Abad, Quiroga, Shih, & Flores-Mendoza, 2008; Colom, Abad, Rebollo, & Shih, 2005; Colom, Rebollo, Abad, & Shih, 2006; Colom, Shih, Flores-Mendoza, & Quiroga, 2006; Conway, Cowan, Bunting, Therriault, & Minkoff, 2002; Conway, Kane, & Engle, 2003; Engle, Tuholski, Laughlin, & Conway, 1999; Kane & Engle, 2002; Krumm et al., 2009; Oberauer, Süß, Wilhelm, & Wittmann, 2008). Although WM is critical for successful complex cognitive functioning across the lifespan, most previous studies in this research field have focused on adult samples and considerably less research attention has

⁎ Corresponding author at: University of Luxembourg, The Faculty of Language and Literature, Humanities, Arts and Education, Research Unit for Educational Measurement and Applied Cognitive Science (EMACS), Campus Walferdange, B.P. 2, L-7201 Walferdange, Luxembourg. Tel.: +352 466 644 9511. E-mail address: [email protected] (C. Hornung). 0160-2896/$ – see front matter © 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.intell.2011.03.002

been paid to WM in children. Despite the general consensus that WM capacities develop significantly during childhood (Cowan et al., 2005; Engel de Abreu, Conway, & Gathercole, 2010; Gathercole, 1999), surprisingly little is known about whether and to what extent theories and empirical findings on WM derived from adult data generalize to children. Drawing on key theories and findings on WM and data obtained from 5-to7-year-old children, this article therefore rigorously investigates (1) the structure of WM and (2) the relationship between WM components and fluid intelligence in children. 1. The structure of WM components 1.1. Definitions and measurement Working memory (WM) refers to a complex cognitive system of limited capacity that stores information while simultaneously processing the same or additional information (Baddeley & Hitch, 1974; Cowan, 1999; Tuholski, Engle, & Baylis, 2001). Two essential structural components of WM are therefore (a) a short-term storage component (i.e., short-term memory, STM) that holds information briefly, and (b) a nonstorage component responsible for further processing, generally

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referring to executive attention control (Conway et al., 2003). Short-term storage capacity is limited to about 3–5 chunks of information in adults and to about 3 chunks of information in children (Ricker, AuBuchon, & Cowan, 2010). To overcome this capacity limit, additional processes, such as executive attention control, are therefore required to store larger amounts of information, to combat interference and decay (Cowan, 2008; Engle et al., 1999). While STM is usually measured by simple span tasks that require the storage and direct recall of information, WM is usually measured by complex span tasks that require the simultaneous storage and additional processing of information (in terms of a secondary processing component) (Conway et al., 2003; Gathercole, 1999). Higher scores on simple spans are indicative of higher STM capacity, while higher scores on complex spans are indicative of higher WM capacity (i.e., executive attention control) (Engle et al., 1999). Even though, STM and WM refer to theoretically distinct concepts, usually assessed separately, both concepts are measured by tasks that tap short-term storage, and non-storage processes such as executive attention control and domain-specific skills and strategies to some extent (Conway et al., 2003; Engle et al., 1999). Thus, the distinction between STM and WM seems ambiguous and it might primarily translate the degree to which storage and non-storage processes are implicated in the tasks assessing both concepts. The next section therefore draws on different conceptualizations of WM and recent research findings to develop different structural models of WM. These structural models make different assumptions about how children's individual differences on these tasks can be explained.

1.2. Structural models of WM for children In this section we have identified 6 different models for WM in children. Model 1 tests the hypothesis of a unitary WM component that is that STM and WM are indistinguishable in early childhood (potentially becoming increasingly differentiated with age). Recent empirical findings indicate that WM and STM measures might reflect the same latent construct (Colom, Rebollo, et al., 2006; Colom, Shih, et al., 2006; Kyllonen & Christal, 1990; Unsworth & Engle, 2006, 2007). For example, Unsworth and Engle (2007) suggest that simple and complex span tasks assess the same basic cognitive processes (active maintenance through primary memory and retrieval through secondary memory) and, as a matter of parsimony, conclude that STM and WM are indistinguishable. Model 2 tests the opposing theoretical position that STM and WM are distinct constructs. Shah and Miyake (1996) suggested that simple span tasks involve short-term storage processes, whereas complex span tasks involve both storage and executive attention control processes. An important observation in previous studies of WM is that adults' individual performances on tasks measuring WM and STM differ considerably, which further underscore their distinction (Ackerman, Beier, & Boyle, 2005; Engle et al., 1999). Engel de Abreu et al. (2010) found distinct STM and WM components in 5-to-9-year-old children. Likewise, Gathercole and Pickering (2000) found separate systems for executive and verbal storage processes in 6- and 7-year-old children.

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Model 3 investigates two domain-specific WM components for verbal and visuo-spatial information respectively (Park et al., 2002). Verbal and visuo-spatial storage processes are viewed as separate developing components in WM that rely on distinct neural substrates (Becker, MacAndrew, & Fiez, 1999; Gathercole, 1998; Gathercole, Pickering, Ambridge, & Wearing, 2004; Pickering, Gathercole, & Peaker, 1998; Smith & Jonides, 1997). Previous findings indicate distinct verbal and visuo-spatial components of STM and WM in 4-to-13year-old children (Alloway, Gathercole, & Pickering, 2006; Tillman, Nyberg, & Bohlin, 2008). Model 4 investigates the standard WM model (Baddeley & Hitch, 1974) that comprises a central executive and two domain-specific storage systems—the phonological loop and the visuo-spatial sketchpad—representing either verbal or visuo-spatial STM (Awh et al., 1996). Importantly, in this model, storage refers to an attention-free function. A study with 6-year-old children (Gathercole et al., 2004) and even younger children supported this WM model (Alloway, Gathercole, Willis, & Adams, 2004). Model 5 tests Cowan's (1995, 1999, 2001) WM framework, according to which WM capacity refers to a core storage capacity. While in Model 4 storage is interpreted as an attention-free function, Model 5 suggests that storage may draw on attention. Here, short-term storage capacity reflects the focus or scope of attention. More specifically, a task at hand might activate a vast bank of long-term memory representations. Attention is needed to focus on the relevant information in order to store it. Thus, variance in memory tasks can be explained by a core storage capacity and further specific processes engaged in the task. To reflect these ideas, Model 5 defines a domain-general component (COMMON) that affects all memory span tasks and that is interpreted as short-term storage (see Colom, Rebollo, et al., 2006; Colom, Shih, et al., 2006; Engle et al., 1999). Furthermore, the model includes two domain-specific components (verbal specific and visuo-spatial specific) that affect either verbal or visuo-spatial span tasks. Both specific components are interpreted as task-relevant and domain-specific processes reflecting specific activations of either language-based or visual-based networks (D'Esposito, 2007; Zimmer, Münzer, & Umla-Runge, 2010). They may also represent long-term memory representations (e.g., specific skills and strategies) activated by the task at hand (Cowan, 1995, 2001, 2008; Cowan et al., 2005). Model 6 capitalizes on recent structural conceptions of WM in adults (Unsworth & Engle, 2007) and attempts to separate storage from executive attention control processes. More specifically, Model 6 comprises a common short-term storage factor (STM common) that affects all verbal span tasks, and a WM residual factor that represents executive processes that are needed in addition to STM processes to complete complex span tasks (Engle et al., 1999). Model 6 further includes a general visuo-spatial WM factor (VSWM) that affects simple visuo-spatial span tasks (cf. Gathercole & Pickering, 2000). Overall, the components in Models 5 and 6 are more process-based and seem to be easier to interpret than the components in the modular WM model (cf. Model 4) that have been applied in most previous research in developmental and educational psychology. Furthermore, Models 5 and 6 align well with recently tested structural models of WM in

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adults striving for a better understanding of the processes underlying memory span tasks. Comparison of the competing WM models will elucidate which WM structures generalize to children.

2. The relationship between WM components and fluid intelligence (GF) As outlined above, WM involves both storage and nonstorage processes. Crucially, higher order thinking skills (e.g., reasoning) are highly dependent on these cognitive functions. Previous research in adults has paid particular attention to how WM components are related to fluid intelligence (GF). GF refers to abstract reasoning abilities in order to adapt to novel complex situations (Heitz, Unsworth, & Engle, 2004). The results of this research are mixed: some studies indicate that WM and GF are identical constructs (Kyllonen & Christal, 1990), while other studies indicate that WM and GF are related but distinct constructs (Ackerman et al., 2005; Heitz et al., 2004). Engle and colleagues (Engle et al., 1999; Kane & Engle, 2002) suggest that WM and GF are driven by the same underlying executive processes (cf. Conway et al., 2002), whereas Colom and colleagues argue that short-term storage drives the relationship between WM and GF (Colom et al., 2008; Colom, Rebollo, et al., 2006). What do we know about the relationship of WM components and GF in children? The few studies conducted to date have shown that WM and GF are related but distinct constructs (Alloway et al., 2004; Cowan, Fristoe, Elliott, Brunner, & Saults, 2006; Engel de Abreu et al., 2010) and that both STM and WM are independently relevant to GF in 6-to-13-year-old children (Tillman et al., 2008). Crucially, previous studies on the relationship between WM and GF in children have rarely compared different structural models of children's WM. Thus, it is not entirely clear to what extent these results depend on the particular WM model applied. Furthermore, it remains unclear which WM components underlay the relation between WM and GF in children. In this article, we therefore investigate children's WM by carefully examining the relationship between the various WM components (as defined in Models 1 to 6) and GF. To this end, we extend Models 1 to 6 by including a latent construct representing GF. Consequently, Model 1 & GF studies the relationship between a single general WM component and GF. Model 2 & GF investigates how distinct STM and WM components relate to GF and whether the relation between WM and GF is stronger than that between STM and GF (cf. Alloway et al., 2004; Engel de Abreu et al., 2010; Engle et al., 1999). Based on these authors' findings, WM tasks are more strongly related to GF than STM tasks—the additional executive attention processes that are involved in WM tasks and that reflect individual differences in WM capacity are thought to account for the strength of the relationship between WM and GF. Model 3 & GF investigates how domain-specific WM components (verbal and visuo-spatial WM) relate to GF. We expect both factors to relate to GF, because both represent WM components measured by span tasks that involve storage and non-storage processes (e.g., executive attention control) important to GF (Tillman et al., 2008).

Model 4 & GF examines the relationship between a central executive system and two specific storage systems—verbal STM and visuo-spatial STM—on the one hand, and GF, on the other. Because the three systems are measured by span tasks that involve storage and non-storage processes, we expect all three constructs to be substantially related to GF. This, however, makes it difficult to distinguish the role of storage and non-storage processes for GF. Model 5 & GF may provide more detailed insights into this matter. WM components are defined as distinct, independent cognitive processes involved in memory span tasks. Contrary to Model 4 & GF, Model 5 & GF conceives short-term storage as a domain-general cognitive capacity, not dependent on a domainspecific buffer (e.g., Colom et al., 2008; Colom, Rebollo, et al., 2006; Cowan, 2008; Engle et al., 1999; Krumm et al., 2009). The specific components in Model 5 & GF refer to domain- and taskspecific representations, and not to limited stores. To our knowledge, no previous correlational study has investigated this kind of structural WM model in children (Model 5) and its relationship to GF. We are therefore particularly interested in how domain-general and domain-specific WM components relate to GF. Model 6 & GF distinguishes between the storage and the non-storage component in the verbal domain. The common variance factor represents short-term storage while the WM residual represents executive attention control (Colom et al., 2008; Unsworth & Engle, 2007). While Colom et al. (2008) emphasize that short-term storage explains the relation between WM and GF, others suggest that the specific WM residuals (i.e., executive attention control) explain the relation between WM and GF (e.g., Engle et al., 1999, in adults; Engel de Abreu et al., 2010, in children). Model 6 & GF will further investigate this question to provide a clearer view on the processes underlying the WM and GF relation in children. As a whole, our central research objective is to examine different conceptualizations of WM in children. To this end, we first examine different structural models of WM. In a second step, we investigate how WM components as defined in these structural models are related to GF in children. 3. Method 3.1. Participants One hundred and sixty-one children (78 girls, 83 boys) from seven preschools in the city and suburbs of Luxembourg participated in the study. The children were tested in their third year of preschool, 5 months before entering first grade of primary school. The mean age was 74.8 months (SD = 3.80 months; range = 67 to 86 months). Written parental consent was obtained for all participating children. Most participants spoke Luxemburgish (36%) or Portuguese (40.4%) as their first language. This multilingual situation is typical for schools in Luxembourg (i.e., majority of children coming either from a Luxemburgish or Portuguese language background). Note that all Portuguese-speaking children of this sample spoke Luxembourgish as their second language/first foreign language. Prior discussions with the preschool teachers revealed that children mastered the number words from 1 to 10 and the 9 color words used in the task. The task instructions were brief and standardized in Luxemburgish. The training examples

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revealed that all the children appeared to understand the task instructions. Children's socio-economic background (as measured by a parent questionnaire assessing occupation) was diverse: 33.8% of mothers and 51.3% of fathers were blue-collar workers; 20.5% of mothers and 23.7% of fathers were employed in the private sector; 11.9% of mothers and 13.2% of fathers worked for the government or in the public sector; 5.3% of mothers and 9.2% of fathers were self-employed; 26.5% of mothers and 1.3% of fathers were not employed. 3.2. Procedure Most of the participating children (98.1%) completed assessments of WM and GF in two separate test sessions at an interval of 3 h to 4 days. Exceptions were made for three children who were sick on the second day of testing and who were administered the second test at a later date. All children worked on the assessments individually in a quiet room at their preschool. Most of the testing sessions (87%) took place in the morning between 8:00 and 11:30 a.m. The remaining sessions were held in the afternoon between 2:00 and 3:30 p.m. Before each task, the experimenter told a brief story, gave instructions, and presented the children with several training trials. The test or task did not start until the children had understood the instructions. Children were not given any performancecontingent feedback during the test sessions, but the experimenter provided general encouragement, independent of a child's performance. In test session 1, children performed verbal simple and complex span tasks (see Section 3.3 “Measures” for details). In test session 2, children first performed visuo-spatial span tasks, followed by an abstract reasoning test. Most tasks were presented on a mobile computer. The auditory items were digitally recorded by a female speaker. The sound recordings were then inserted into four PowerPoint presentations, each corresponding to a different verbal span task. Children performed the verbal span tasks orally; the experimenter wrote down their answers. In the visuo-spatial span tasks, developed with Quest Net (Allen Communication, 1996) [multimedia authoring system], children used a pen to identify the recalled locations on a touch-sensitive computer screen. The participants' answers were automatically encoded. Standardized verbal instructions were given for all tasks and the experimenter was the same for all the children and test sessions. Each test session lasted from 20 to 30 min per child and the assessment language was Luxemburgish. 3.3. Measures We identified tasks that were considered to be appropriate and comprehensible for young children based on prior research (Pickering & Gathercole, 2001), and intensive discussions with research colleagues and preschool teachers. Task stimuli and instructions were translated into Luxembourgish. The items of two verbal span tasks were then pretested on 45 4-to-6-yearold children before they were included in the present test battery. 3.3.1. Verbal simple span tasks To measure short-term storage of verbal information we administered the digit recall and the pseudo-word recall.

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The digit recall task was translated from the WM Test Battery for Children (WMTB-C, Pickering & Gathercole, 2001). Participants have to store a list of single digits presented at a 1-second interval and to recall them in the same order directly after presentation. The task starts with 2-digit sequences and progresses to sequences of 3 to 5 digits. Six trials were presented for each span list; a child correctly recalling three successive trials in a list moved on to the next list. The digit recall task score was the sum of correct trials on span lists 3, 4, and 5 (maximum score = 18). The procedure of the pseudo-word recall task was identical to that of the digit recall task. The only difference was that participants had to recall lists of syllables in the order given (e.g., “SU ME SPA,” “BI GA LE RO”). The pseudoword recall task score was the sum of correct trials on span lists 3, 4, and 5. Two trials of list lengths 3 and 4 were replaced after the pretest because the syllables proved too difficult for most of the children to differentiate and recall. 3.3.2. Verbal complex span tasks To evaluate short-term storage and additional processing of verbal information, we administered the backward digit recall and the backward color recall. In the backward digit recall task children were asked to recall a list of single digits in reverse order (2 7 … 7 2). The procedure was otherwise identical to that of the digit recall task. The backward digit recall task score was the sum of correct trials on span lists 2, 3, and 4. In the backward color recall task, the experimenter asked children to recall a list of color words in the reverse order. To design this task, we grouped nine monosyllabic color words at random. Color words were monosyllabic to ensure that word length did not interfere with recall (Monnier & Ejarque, 2008). The backward color recall task score was the sum of correct trials on span lists 2, 3, and 4. 3.3.3. Visuo-spatial span tasks Visuo-spatial short-term storage capacity was assessed by two location span tasks. Both tasks were presented on a tablet PC screen. Children had to memorize and recall the positions of a dwarf that appeared and disappeared again soon afterwards. After presentation, children used a pen to indicate the locations where they had seen the dwarf appear on the touch-sensitive screen. The task began with two training trials, the first with one dwarf and the second with two dwarves. There were two blocks of 11 test trials, each block comprised of three trials with 2, four trials with 3, and four trials with 4 targets. The task trials were presented in fixed order in two distinct conditions. In the first condition, targets appeared and disappeared in a visible grid on the screen. The grid had four columns and four rows, yielding a total of 16 cells. In the second condition, targets appeared and disappeared on a simple black screen (no grid). The child had to rely on features other than the grid to find the hidden targets. Importantly, the cognitive demands of these two conditions differ. The mean scores show that children's performance was considerably higher in the grid condition than in the black screen condition (see Table 1). A major reason for these differing cognitive demands is that the black screen condition requires more executive attention control processes to actively structure the screen and to encode

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Table 1 Intercorrelations, means, standard deviations, and reliabilities for measures of short-term memory (STM), working memory (WM), and fluid intelligence (GF). Measure

1.

Verbal STM 1. Pseudo-word recall 2. Digit recall

– .67

2.

3.

4.

–

5.

6.

Verbal WM 3. Backward color recall 4. Backward digit recall

.44 .48

.55 .61

– .76

Visuo-spatial WM 5. Location recall (grid) 6. Location recall (no grid)

.11 .06

.19 .20

.29 .25

.27 .29

– .59

–

.27 .19 .16 .30 7.74 3.99 .90

.40 .28 .29 .38 6.88 3.73 .90

.43 .35 .36 .31 7.62 3.19 .84

.45 .32 .33 .43 6.61 2.95 .84

.36 .27 .36 .21 5.11 2.18 .74

.34 .29 .26 .28 3.30 1.92 .66

Fluid intelligence GF 7. CPM total sum score 8. CPM Set A score 9. CPM Set AB score 10. CPM Set B score M SD Reliability (α)

7.

8.

9.

10.

– .63 .89 .80 19.24 4.28 .74

– .41 .31 8.39 1.17 –

– .54 6.41 2.40 –

– 4.44 1.75 –

Note. Correlations not reaching significance at the .05 level are indicated in bold. STM = short-term memory; WM = working memory; CPM = Raven's Coloured Progressive Matrices.

and recall the hidden targets. For example, Martin and colleagues' neuroimaging data (Martin, Houssemand, Schiltz, Burnod, & Alexandre, 2008) showed that the recall of three squares in a grid paradigm (categorical condition) involved only visuo-spatial storage, whereas the recall of three squares in a black screen paradigm (coordinate condition) additionally involved executive attention control processes. Further, it seems likely that the task is easier in the grid condition because it is limited to 16 possible locations, whereas the black screen condition yields an unlimited number of possible locations. We used the absolute scoring (ABS) method—the method predominantly used in child WM research—to score the children's performances on all tasks. Children received 1 point for each correctly recalled trial. If they missed out an item or made errors in recall, they received 0 point. Because no individual differences were found on span list 2 in either verbal simple span task, we decided to exclude these data from the analysis. Thus, the maximum possible score on each of the verbal span tasks was 18, and the maximum possible score on each of the visuo-spatial span tasks was 11. Presentation of verbal span tasks was stopped as soon as a child made three consecutive errors on a list. Presentation of the visuo-spatial span tasks was stopped after completion of all 22 trials. 3.3.4. Fluid intelligence measure To investigate the relation among WM components and GF, we administered Raven's Coloured Progressive Matrices (Raven, Raven, & Court, 1998), a figural reasoning task to assess the children's GF. The test items were abstract shapes and patterns, from each of which a piece was missing. Six response options were offered below the test item. The children were instructed to choose the best-fitting one into the blank space. The test is comprised of three parts (A, AB, and B), each containing 12 items. At the beginning of each subset, children were encouraged to look at all response options offered. In cases where children responded too fast without looking at all the options or pointed to the same

location repeatedly over several trials, the experimenter reminded them to take their time and to look at all the possible answers. All children completed the three parts of the test; their score on each part corresponded to the number of correctly solved items (up to a maximum of 12 on each part). Raw scores were used for statistical analysis. The tasks assessing WM components and the three scores obtained for Raven's Coloured Progressive Matrices demonstrated good reliabilities (see Table 1). 3.4. Statistical analyses All structural equation models were estimated with the software Mplus 5.2 (Muthén & Muthén, 1998–2007). Model fit was evaluated by various indices: the χ2 goodness-of-fit statistic, the root-mean-square error of approximation (RMSEA), the comparative fit index (CFI), and the standardized root-meansquare residual (SRMR). A non-significant χ2 goodness-of-fit statistic indicates a good fit. The corresponding probability value indicates the probability of finding a multivariate difference of a certain size between the specified model and the sample data given that the specified model is the “true” model in the population. RMSEA values below .05 indicate a good model fit and that values between .05 and .07 indicate a reasonable model fit (Browne & Cudeck, 1993). Values greater than .10 indicate a poor approximation of the model (Jöreskog, 1993). CFI values larger than .95 and SRMR values close to .08 indicate a good fit (Hu & Bentler, 1999). 4. Results The results are presented in two sections. In the first section, we present the different structural equation models investigating the structure of WM components in children. In the second section, we extend these WM models to include GF in order to determine how the distinct components of WM relate to GF in children.

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4.1. The structure of WM in children Initial analyses indicated some potential empirical underidentification of the most complex model, namely Model 5. To obtain unique parameter estimates for this model, we therefore introduced two additional constraints: We fixed both factor loadings of (a) the two visuo-spatial tasks on the specific visuospatial specific factor and (b) the two verbal simple span tasks on the specific verbal factor to 1. All model solutions were then “properly identified” as the estimation procedures converged, no parameter estimates were out of the range of admissible parameter estimates (e.g., negative variances), and all matrices of parameter estimates were positive definite. These findings strongly supported further investigation of the results yielded by the seven structural models of WM. Standardized parameter estimates for Models 1 to 6 are shown in Fig. 1; dashed lines indicate non-significant model parameters (p b . 05). Fit indices for all models are shown in Table 2. Model 1 investigated a unique and general WM factor in children. Statistically significant standardized factor loadings ranged from λ = .32 to λ = .88 for WM. However, Model 1 provided a poor fit to the data (see Table 2). This result is not in line with the idea of a unitary WM component in children. Thus, it was intriguing to examine whether Models 2 to 6, which predict WM to comprise distinct components, provided a better explanation of the data. Model 2 tested distinct STM and WM components. Because the initial fit of this model was very poor, we introduced a correlation between the residual terms of the visuo-spatial span tasks. This modification yielded a substantial improvement in model fit and seemed justified because (a) both tasks measure visuo-spatial processes and (b) the correlation of the residual

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Table 2 Fit statistics of the models capturing the structure of working memory (WM). Model

χ2

df p

Model 1 (WM) 105.08 9 76.95 8 Model 2 (STM-WM) a Model 2 (STM-WM) 14.08 7 Model 3 (VEWM-VSWM) 47.30 8 Model 4 5.11 6 (VSSTM-VESTM-EXEC) Model 5 4.68 5 (VSSP-VERBAL-COMMON) Model 6 (VSWM-STM 4.86 5 common-WM residual) Cutoff criterion

CFI

RMSEA SRMR

.00 .76 .00 .82 .50 .98 .00 .90 .53 1.00

.26 .23 .08 .18 .00

.13 .13 .06 .07 .02

.46

1.00

.00

.02

.43

1.00

.00

.02

N.05

N.95

b.05

b.08

Note. χ2 = chi-square goodness-of-fit statistic; df = degrees of freedom; CFI = comparative fit index; RMSEA = root-mean-square error of approximation; SRMR = standardized root-mean-square residual. Values that fail to meet cutoff criteria necessary to support the model for that row are shown in bold. A non-significant χ2 statistic (p N .05) indicates a good fit of the model to the data. a Initial fit statistics for Model 2 (see text for details).

terms was strong (r = .57). The correlation between STM and WM was high (r = .73). Statistically significant standardized factor loadings ranged from λ = .22 to λ = .92 for STM and from λ = .83 to λ = .92 for WM. The overall fit of Model 2 was adequate. These data suggest that the structure of children's working memory may be reasonably well represented by an STM and a WM component. Nevertheless, both factors may reflect the same underlying processes because both were measured by span tasks involving primarily short-term storage. This further explains the strong association between STM and WM in this model.

Fig. 1. Six conceptually different structural equation models testing distinct WM components in children. Note. Latent variables: WM = working memory; STM = short-term memory; VSWM = visuo-spatial working memory; VEWM = verbal working memory; VS STM = visuo-spatial short-term memory; EXECUTIVE = central executive; VE STM = verbal short-term memory; VSSP = visuo-spatial specific; COMMON = common variance; VERBAL = verbal specific. Manifest variables: VS_GR = visuo-spatial span task grid; VS_NG = visuo-spatial span task no grid; VE_BC = verbal backward color recall task; VE_BD = verbal backward digit recall task; VE_FPS = verbal pseudo-word recall task; VE_FD = verbal digit recall task.

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Model 3 investigated the domain specificity of WM by testing whether a verbal WM component could be differentiated from a visuo-spatial WM component. The correlation between the two constructs was moderate, r = .39, demonstrating that they are related but clearly distinct. Statistically significant standardized factor loadings ranged from λ = .60 to λ = .88 for verbal WM and from λ = .76 to λ = .78 for visuospatial WM. However, the fit of Model 3 was poor. Consultation of the modification indices showed that allowing the residual terms of the two complex verbal span tasks to correlate would produce a significant improvement in overall model fit. We did however not introduce this modification because we had no plausible theoretical justification for it. More specifically, the two verbal complex tasks place heavy demands on storage and executive attention control. Thus, both represent excellent markers of verbal WM. Accordingly, the common variance of the two tasks should be completely represented by the verbal WM factor as specified in Model 3. Our findings do not support distinct domain-specific WM systems. Model 4 was derived from the standard three-factor WM model. Verbal STM correlated positively with visuo-spatial STM (r = .26) and highly with the central executive (r = .72). Visuospatial STM correlated moderately with the central executive (r = .41). Statistically significant standardized factor loadings ranged from λ = .73 to λ = .92 for verbal STM, from λ = .77 to λ = .78 for visuo-spatial STM, and from λ = .83 to λ = .91 for the central executive. The fit of this model was very good. The weak correlation between verbal and visuo-spatial STM supports Baddeley's (1986) view that the phonological loop and the visuo-spatial sketchpad are independent of one another and that both STM systems involve domain-specific processes. The strong relation between verbal STM and the central executive may be explained by the fact that both constructs were measured with verbal span tasks that require the shortterm storage of verbal information. Model 5 tested a common variance factor model including a shared short-term storage component (COMMON) and two domain-specific components. The three factors were specified to be mutually uncorrelated to reflect the operation of distinct cognitive resources. The fit of this model was excellent (see Table 2). Statistically significant standardized factor loadings ranged from λ = .66 to λ = .71 for the verbal specific factor, from λ = .66 to λ = .74 for the visuo-spatial specific factor, and from λ = .33 to λ = .87 for the COMMON factor. Two factor loadings on the verbal specific factor were non-significant. These loadings concerned the two verbal complex span tasks, which loaded particularly heavily on the COMMON factor. We interpret the COMMON factor as shared processes resulting in a core storage capacity (Colom, Rebollo, et al., 2006) that according to some reflects the capacity of the scope of attention (Cowan, 2008; also see Cowan et al., 2006). Furthermore, the specific verbal and visuo-spatial factors may be best interpreted as domain- and task-specific processes that might refer to activated long-term representations and build the essential link between WM and long-term memory (cf. Cowan, 1999, 2008). Furthermore, it appears that both complex span tasks are excellent markers of the domain-general storage capacity, but not of verbal-specific processes. Finally, Model 6 tested a model with a shared short-term storage factor (STM common), a WM residual factor (WM residual) and a general visuo-spatial WM factor (VSWM). The fit

of the model was excellent and suggested that similar to adults, complex memory span tasks measure a short-term storage component on the one hand and a non-storage component (i.e., executive attention control) on the other hand. VSWM correlated significantly with STM common (r = .26) and with WM residual (r = .33). This suggests that similar to complex verbal span tasks, simple visuo-spatial span tasks tap a storage and a non-storage component. Statistically significant standardized factor loadings ranged from λ = .59 to λ = .92 for STM common, from λ = .58 to λ = .62 for WM residual, and from λ = .76 to λ = .78 for VSWM. Similar to Model 5, Model 6 suggests that simple and complex span tasks involve shared processes for storing and processing information. This finding corroborates prior findings suggesting that both simple and complex span tasks tap WM capacity in children (Cowan, 2008; Engle et al., 1999; Hutton & Towse, 2001). In summary, our results suggest that WM in children involves storage and non-storage processes. Next, we focus on the relationship between WM and GF in children. 4.2. The relationship between WM components and GF The second central objective of this article was to study how the components of WM as defined in Models 1 to 6 would relate to GF. To this end, we extended Models 1 to 6 by including a factor representing GF; this factor was represented by the three subsets from Raven's Coloured Progressive Matrices (see Fig. 2). The evaluation of model fit indicated that Model 4 & GF and Model 5 & GF provided the best fit to the data (see Table 3). Table 4 summarizes the key results. Crucially, none of the models investigated supported the hypothesis that WM (or any of its components) is identical to GF. Neither the correlations nor the corresponding upper limits of the 95% confidence intervals were close to 1. Several additional results are noteworthy. First, in Model 1 & GF, WM and GF were strongly associated (r = .64); however, this correlation was clearly different from 1. Second, Model 2 & GF investigated the relationship between distinct STM and WM components and GF. In line with previous studies (e.g., Tillman et al., 2008 in children; Unsworth & Engle, 2007 in adults), there were similar strong correlations between STM and GF (r = .52) and between WM and GF (r = .59) suggesting that STM and WM share variability in predicting GF. It appears that the correlations found between STM, WM and GF depend primarily on short-term storage capacity. WM is slightly more strongly related to GF, which can be explained by the complex span tasks measuring WM in this model, which are supposed to draw on additional executive attention control. Third, Model 4 & GF showed that Baddeley's three WM components (i.e., verbal STM, visuo-spatial STM, and the central executive) were strongly related to GF, with correlations larger than .50. This finding supports our hypothesis that the three standard components share common variance due to the storage component inherent in all memory span tasks and that may be recruited by the administered GF measure. Fourth, in line with the recent findings among adults (Colom et al., 2008; Unsworth & Engle, 2007), the COMMON factor in Model 5 & GF, representing the common variance of simple and complex span tasks, was more strongly related to GF (r = .58) than was either domain-specific factor (verbal,

C. Hornung et al. / Intelligence 39 (2011) 210–221

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Fig. 2. Six conceptually different structural equation models illustrating the relationship between WM components and GF. Note. Latent variables: WM = working memory; GF = fluid intelligence; STM = short-term memory; VSWM = visuo-spatial working memory; VEWM = verbal working memory; VS STM = visuospatial short-term memory; EXECUTIVE = central executive; VE STM = verbal short-term memory; VSSP = visuo-spatial specific storage; COMMON = common variance; VERBAL = verbal specific storage. Manifest variables: VS_GR = visuo-spatial span task grid; VS_NG = visuo-spatial span task no grid; VE_BC = verbal backward color recall task; VE_BD = verbal backward digit recall task; VE_FPS = verbal pseudo-word recall task; VE_FD = verbal digit recall task.

r = .24; visuo-spatial, r = .31). Unsworth and Engle (2007) have suggested that simple and complex span tasks largely measure the same cognitive processes (e.g., rehearsal, Table 3 Fit statistics of the models investigating the link between working memory (WM) components and fluid intelligence (GF). Model

χ2

Model 1 & GF (WM & GF) 141.80 Model 2 & GF (STM-WM 53.18 & GF) Model 3 & GF (VEWM74.04 VSWM & GF) Model 4 & GF (VSSTM31.19 VESTM-EXEC & GF) Model 5 & GF (VSSP31.33 VERBAL-COMMON & GF) Model 6 & GF (VSWM-STM 30.89 common-WM residual & GF) Cutoff criterion

df

p

CFI

RMSEA SRMR

38 37

.00 .04

.81 .97

.13 .05

.11 .09

37

.00

.93

.08

.06

36

.70 1.00

.00

.04

36

.69 1.00

.00

.04

20

.06

.06

.04

N.05 N.95 b.05

b.08

.98

Note. χ2 = chi-square goodness-of-fit statistic; df = degrees of freedom; CFI = comparative fit index; RMSEA = root-mean-square error of approximation; SRMR = standardized root-mean-square residual. Values that fail to meet cutoff criteria necessary to support the model for that row are shown in bold. A nonsignificant χ2 statistic (p N .05) indicates a good fit of the model to the data.

maintenance, and controlled retrieval) and that STM and WM are equally good at predicting GF in adults when variability from long list lengths is taken into account. Note, however, that Model 5 & GF is slightly different from Unsworth and Engle's (2007) structural model. They suggested that the specific latent factor reflects the residual variance common to the complex span tasks. In the present study, we used diverse task material (verbal and visuospatial) to account for domain-specific residual factors. These residual factors, nevertheless, do not represent the residual variance from complex span tasks only as in the Unsworth and Engle's model (2007), but also the residual variance from simple span tasks. In doing so, we studied how domaingeneral and domain-specific WM components relate to GF in children. Model 5 & GF indicates (a) that simple and complex span tasks relate substantially to GF in children and, more importantly, (b) shared variance form simple and complex span tasks interpreted as short-term storage primarily drives the relationship between WM and GF in 5-to-7-year-old children. This finding corroborates previous research among adults (e.g., Colom et al., 2008; Colom, Rebollo, et al., 2006). Furthermore, verbal and visuo-spatial processes are also relevant to perform Raven's Matrices, suggesting that GF in

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Table 4 Correlations between working memory components and fluid intelligence GF as obtained for the different structural models of working memory. WM component Model 1 & GF WM Model 2 & GF STM WM Model 3 & GF VSWM VEWM Model 4 & GF VS STM EXEC VE STM Model 5 & GF VSSP COMMON VERBAL Model 6 & GF VSWM WM residual STM common

Latent correlation

95% confidence interval

.64

[.50, .77]

.52 .59

[.36, .68] [.45, .74]

.54 .61

[.36, .71] [.47, .75]

.54 .59 .50

[.36, .71] [.45, .74] [.34, .66]

.31 .58 .24

[.13, .49] [.41, .75] [.00, .49]

.54 .34 .50

[.36, .71] [.15, .52] [.34, .66]

Note. WM = working memory; STM = short-term memory; VS = visuospatial; VE = verbal; EXEC = central executive; COMMON = common variance factor; VSSP = visuo-spatial specific; VERBAL = verbal specific.

children involves more than a core storage capacity and draws on additional domain-specific processes. Lastly, Model 6 & GF further strengthens the above results by reaffirming the importance of shared processes engaged in simple and complex span tasks for GF. Crucially, short-term storage appears to drive the relationship between WM and GF. As noted by Unsworth and Engle (2006) the common variance factor appears to be affecting all memory spans representing maintenance and controlled retrieval from secondary memory. In sum, our findings suggest that WM and GF are related in children—both constructs draw primarily on a core storage capacity and moreover on specific verbal and visuo-spatial processes. 5. Discussion This study rigorously investigated children's WM by assessing domain-general and domain-specific processes in the verbal and visuo-spatial domains. Our research objective was twofold. First, we examined 6 different structural models of WM in children. Second, we investigated how components of WM as defined in these models are related to GF. 5.1. The structure of WM in 5-to-7-year-old children Our study was motivated by the question of whether and to what extent theories on the structure of WM derived from adult data generalize to children. We find that children's WM involves distinct cognitive processes (cf. Alloway et al., 2004). Our findings, based on our best-fitting Models 4 to 6, suggest that—like adults—children draw on storage and non-storage processes when completing memory span tasks (Baddeley, 1986; Conway et al., 2003; Engle & Kane, 2004). In other words, WM may involve similar cognitive processes through-

out the lifespan and these processes may already be in place in 5-to-7-year-old children. Crucially, Model 4 has a contrasting conception of the shortterm storage function compared with more recent WM approaches as represented by Models 5 and 6. Model 4 views short-term storage as a domain-specific, attention-free function, while Models 5 and 6 conceive short-term storage as a domain-general, attention-demanding function (see Cowan, 2008; Cowan et al., 2006) not dependent on multiple localized storage buffers (see D'Esposito, 2007). From this view, shortterm storage capacity refers to the number of items that currently lie in the focus of attention. Moreover, Model 4 has a modular conceptualization, including mutually correlated components. As indicated by the strong correlations between the storage components, on the one hand, and the central executive, on the other, it seems that the three components in this model reflect a mixture of storage, executive attention control, and domain-specific processes (cf. task impurity problem, van der Sluis, de Jong, & van der Leij, 2007). Models 5 and 6 on the other hand, include a COMMON factor affecting simple and complex span tasks. The COMMON factor was conceived to operate independently from the specific factors. This structural conception of WM allowed storage processes to be separated from non-storage ones. In line with prior research we interpret the COMMON factor in Models 5 and 6 as domaingeneral storage capacity (Colom et al., 2008; Colom, Rebollo, et al., 2006; Colom, Shih, et al., 2006; Engle et al., 1999). Others interpreted it in terms of a combination of active maintenance, attention control and controlled retrieval (Unsworth & Engle, 2007) or even as executive attention control (Kane et al., 2004). Interestingly, Cowan (1995, 1999, 2008) does not emphasize a clear-cut distinction between short-term storage and attention in terms of scope of attention. This may also explain why simple span tasks correlate highly with higher-order thinking measures, especially in children who do not yet engage in rehearsal and grouping strategies (Cowan, 2008; Ricker et al., 2010). Hence, the core storage capacity in Model 5 and Model 6 may translate children's capacity to focus their attention in order to hold information, a capacity that has been repeatedly related to intelligence in children and adults (Cowan et al., 2005, 2006). In sum, our results for Models 5 and 6 suggest that theories and key findings on the structure of WM derived from adult data indeed generalize to children with an emphasis on domaingeneral processes supporting the storage function. Likewise, Gathercole et al. (2004) found that preschool children's visuospatial task performance draws more on domain-general systems that gradually differentiate and become specific as knowledge and skills develop. But there are certainly also differences in the way young children and adults solve simple and complex span tasks. Compared with adults, young children have lower memory spans due to lower storage capacity and less efficient mnemonic strategies, which are developing later in the elementary school years (Cowan & Alloway, 2009; Ricker et al., 2010). 5.2. The relationship between WM components and GF Our second research goal was to examine how WM components as defined in different structural models of WM are related to GF. One important finding is that children's WM (or any of its components) is not identical to fluid intelligence

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GF. This observation corroborates previous findings among adult populations, as summarized by Ackerman et al. (2005) in their influential meta-analyses. The findings of previous research, however, have been inconsistent in terms of which components of WM were identified as underlying the relationship between GF and WM. Some scholars conceive this relationship to be dependent on the storage component (e.g., Colom et al., 2008); others on executive attention control (e.g., Conway et al., 2003; Engel de Abreu et al., 2010; Engle & Kane, 2004), others on both (Tillman et al., 2008) or other sources of variance, such as controlled retrieval from secondary memory (Unsworth, Spillers, & Brewer, 2009). Our findings from Models 5 & GF and 6 & GF are in line with Colom, Rebollo, et al. (2006), Colom, Shih, et al. (2006), and Colom et al.'s (2008) view that short-term storage capacity underlies primarily the relation between WM and GF. In line with Cowan et al. (2006), to us short-term storage is an attention-demanding process. These authors distinguish between attention for storage and attention for processing. While the scope of attention is necessary for storage, the control of attention is involved in the processing component. Unfortunately, our testing did not include any conventional attention measure to test this hypothesis (e.g., visual array task, Cowan et al., 2006; Attention Network Test, Rueda et al., 2004) and to study the association between the COMMON factor and different forms of attention (control, scope, and sustained attention). The present findings do not allow us to conclude what kind of attention short-term storage in children draws on. Future studies among children should investigate these questions further. Model 5 & GF also revealed that some of the relationship between WM and GF is driven by non-storage components (also see Model 6 & GF). The small but substantive correlations obtained for the domain-specific factors indicate that domainspecific processes are related to GF over and above a domaingeneral storage function. From this perspective, GF draws on domain-general storage and also on domain-specific nonstorage processes that reflect verbal processing on the one hand and visuo-spatial processing on the other hand. To sum up, as with adult populations, STM, WM and GF are strongly (but not perfectly) related in children. Further, the relationship between children's WM and GF is primarily driven by the short-term storage component. Consequently, we suggest that (a) simple span tasks are equivalently good indicators of children's core storage capacity as complex span tasks, and that (b) this capacity is essential for reasoning and problem solving. Hence, our findings support the view that storage capacity is a core capacity explaining individual differences in fluid intelligence. 5.3. Limitations of the present study Most complex span tasks suitable for adults or older children are inappropriate for younger children. They often require cognitive skills (e.g., reading or arithmetic) that children only acquire through formal education. Consequently, we administered two backward span tasks, free of operation and reading processing because the children of our sample did not yet start formal primary education. Thus, it is important to bear in mind—when interpreting our findings on the generalizability of research on adult WM to children—that we used (age-appropriate) measures (i.e.,

219

recall of information in the forward or backward order) to assess children's working memory processes that differ from those used in adult research (e.g., operation span). Another limitation is that we administered a relatively limited set of measures to investigate children's WM: 2 verbal simple span, 2 verbal complex span and 2 visuo-spatial span tasks. The selection of tasks used in this study was initially based on the standard WM model generally referred to in educational and developmental psychology. Unfortunately, we did not include tasks that tapped only executive functions, further visuo-spatial complex span tasks (Tillman et al., 2008), or simpler visuo-spatial tasks (e.g., the spatial recognition task in Luciana, Conklin, Hooper, & Yarger, 2005) to assess visuospatial storage and additional attention control processes more in detail. The present methodological approach, however, accommodated two constraints imposed by the present sample. First, assessments in children at this age need to be brief. Children cannot concentrate for as long as adults and can easily lose motivation in the context of a scientific study. Hence, the two testing sessions (each lasting about 25 min) seemed to be closer to the upper than the lower limit of numbers of simple and complex span tasks that can be administered to 5-to-7year-old children. Second, simple span tasks have confirmed being good indicators of children's WM capacity because they do not yet (or not efficiently) draw on rehearsal and grouping strategies supporting short-term storage in older children and adults (Cowan, 2008). This also explains why simple span measures were equally strongly related to GF than complex span measures. Particularly when children need to recall long lists of items in simple span tasks, the cognitive effort required (e.g., to maintain and retrieve items) may place heavy demands on additional processes (e.g., attention). This interpretation is in line with recent research results in adult populations (Unsworth & Engle, 2007). It seems that the cognitive demands of both simple and complex span tasks depend on the amount of information that needs to be processed. Specifically, the first items in simple and complex span tasks can be completed with little effort and low demands on executive attention control. As memory load continuously increases in (simple and complex) span tasks, storage capacity limits are reached, recruiting executive attention control for maintenance and retrieval. This combination of cognitive demands in simple and complex span tasks renders the unidimensional measurement of STM or WM components very challenging. Hence, even the inclusion of a wider range of STM and WM tasks might not have allowed us to adequately assess STM and WM functions in both the verbal and visuo-spatial domains and to identify the corresponding factors. From this perspective, we consider the statistical conceptualization of WM components by means of uncorrelated factors (cf. Models 5 and 6) to be a reasonable solution, because these models allowed us to separate individual differences in WM functions. Further, we found a strong positive relationship between children's WM and GF that was, however, clearly different from r = 1. Some studies with adult samples show a considerably stronger or even a perfect relationship between these constructs (Kyllonen, 2002). One explanation for these inconsistent findings may be that we drew on a sample of children and not on an adult sample. A second rationale may be that we used the Raven Test as a single measure of GF. Thus, the latent

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construct representing GF in our study may—in addition to GF— also comprise test-specific variance and variance due to visuospatial processing which can be assumed to be unrelated or only modestly related to (domain-independent) WM. This in turn may have weakened the relationship between WM and GF. Note that we used the Raven's Coloured Progressive Matrices as measure of GF for two major reasons. First, we capitalized on the idea that the Raven Test lies at core of the conceptualization of fluid intelligence (Mackintosh, 1996; Snow & Lohman, 1989) and that it is therefore one of the most often applied measures of this construct (Irwing & Lynn, 2005). Second, the few previous studies on the relationship between children's WM and GF (Engel de Abreu et al., 2010; Tillman et al., 2008) used the Raven test and by applying the same measure we could study the generalizability of these results when applying a significantly broader range of structural conceptualizations of WM. Future studies should apply a more diverse set of tasks to measure GF, ideally tapping numerical, verbal and visuo-spatial contents to analyze the hypothesis that the relationship between GF and WM is stronger with a broader range of measures, while keeping in mind the previously noted shorter attention span of children. 5.4. Outlook In the present study, we find that both domain-general and domain-specific cognitive processes are involved when children perform cognitive tasks tapping STM and WM and that both are related to higher order thinking skills (in terms of GF). In light of these findings, we would like to emphasize the need for future educational research to study children's learning, special developmental needs, and interventions in terms of both domain-specific and domain-general processes and abilities. These research endeavors may be guided by questions such as whether preventive and remedial interventions that foster both domain-specific processes (e.g., phonological awareness, visuo-spatial processing, and approximate number sense) and domain-general cognitive processes (e.g., storage and retrieval of information, sustained attention, inhibitory control, and self-monitoring) lead to academic improvement. Such research endeavors may, in the long run, foster a deeper understanding of the relationships between WM and the development of academic competencies in the fields of mathematics and literacy. Acknowledgments The authors thank the children, their parents, and their teachers for participating in this study. We would like to thank Roberto Colom and an anonymous reviewer for their valuable comments and suggestions on a previous version of this article. We further thank Christine Schiltz, Jean-Paul Steinmetz, and Salvador Rivas for helpful remarks on an earlier draft of this article and Susannah Goss for the editorial support. References Ackerman, P. L., Beier, M. E., & Boyle, M. O. (2005). Working memory and intelligence: The same or different constructs? Psychological Bulletin, 131(1), 30−60. doi:10.1037/0033-2909.131.1.30.

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