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. Author manuscript; available in PMC: 2020 Oct 1.
Published in final edited form as: J Educ Psychol. 2019 Oct;111(7):1273–1283. doi: 10.1037/edu0000346

Cognitive Predictors of Kindergarten Achievement in African American Children

A Nayena Blankson 1, Jessica A Gudmundson 2, Memuna Kondeh 3
PMCID: PMC6907019  NIHMSID: NIHMS1012678  PMID: 31831914

Abstract

Three aspects of cognition (fluid intelligence, executive functioning, and crystallized intelligence) in pre-K were examined as predictors of math and reading achievement in kindergarten among an economically diverse sample of 198 African American children. From a variable-centered perspective, confirmatory factor analysis revealed that the three aspects of cognition can be distinguished. Subsequent regression analyses indicated that only executive functioning and crystallized intelligence predicted math and reading achievement in kindergarten. From a person-centered perspective, three profiles of cognition were identified: low fluid and crystallized intelligence with average executive functioning, average abilities in all three areas, and high abilities in all three areas, but particularly higher in executive functioning. Children with low fluid and crystallized intelligence during pre-K had the lowest math and reading skills in kindergarten, whereas children with the highest cognitive skills had the highest math and reading skills in kindergarten. Together, the variable-centered and person-centered results suggest that perhaps there should be increased focus on crystallized intelligence in early education programs, policies, and interventions in addition to a focus on executive functioning.

Keywords: Crystallized intelligence, fluid intelligence, executive functioning, academic achievement, intelligence

When children enter school with strong cognitive skills, they perform better throughout their school years (Duncan et al., 2007). However, it is not clear if certain aspects of cognition serve as better predictors of kindergarten math and reading achievement specifically in African American children. Moreover, do different patterns of cognitive skills differentially predict kindergarten achievement in African American children? The answers to these questions can have a profound impact on the way we instruct African American children in their early years. Although the US demographic is quickly changing, our understanding of the factors that predict achievement in African American children remains limited. Most of what we know regarding the relation between early cognitive processes and achievement comes from research on samples in which the majority of participants are Caucasian (although some of these samples have been representative of the US population at the time data were collected) or samples of exclusively low-income African American children.

It could be that underlying processes are no different for Caucasian children than for African American children; but, there is very little data on the cognitive processes of minority children across a range of socioeconomic statuses (García Coll, 2013). We do not know whether the processes that have been uncovered thus far in the literature regarding school readiness and achievement generalize across a broader socioeconomic spectrum of African American children. Most importantly, however, is the fact that research on African American children has often been comparative in nature, with conclusions that African American children are inferior to their Caucasian counterparts-- i.e., the deficits model has often been used (García Coll et al., 1996).

Although much is known about African American children from lower income backgrounds, African American children across the broader spectrum of SES are at risk for academic failure. Rather than focusing on deficits, it is important to identify the cognitive factors that lead to optimal development in these children. The present study exclusively focuses on African American children, allowing us to identify factors that promote development, rather than identifying ways in which African American children underperform compared to Caucasian children. By isolating this population and exploring their reasoning and achievement in greater depth, we can learn ways to improve their educational outcomes.

In the present study we take both a variable-centered as well as person-centered approach to understanding the relation between cognition and achievement. Variable-centered analyses (e.g., factor analyses and regression analyses) assume that all participants are the same. The focus is on identifying how variables are related (Muthén & Muthén, 2000). Person-centered analyses (e.g., latent profile analyses), on the other hand, allow the examination of heterogeneity in the data (Muthén & Muthén, 2000) and can be used to determine whether there are different groups of children who have different patterns of cognitive skills. Identified profiles can then be used to determine if there are group differences on specific outcome variables. Together, the two approaches can provide greater insight on development than each approach alone. Comparing the results of the variable-centered and person-centered analyses will allow a deeper understanding of the malleable cognitive factors that influence early academic achievement in African American children.

Cognition and Achievement Links: Variable-Centered Perspective

In some approaches to research on cognition and achievement, it is often assumed that there is one ability construct – usually referred to as general intelligence, IQ, or g. However, there is now considerable evidence indicating that, first, a one-factor theory of intelligence does not explain many important observed relationships among intelligence and other variables, and second, that different tests thought to measure the same single factor of intelligence do not measure such a factor (Horn & Blankson, 2012).

It has been argued that greater emphasis should be placed on testing specific abilities rather than testing one general ability in research on achievement (Blankson & Blair, 2016; McGrew & Wendling, 2010). Of focus in the present investigation are three important aspects of cognition that have been found to predict math and reading achievement, namely fluid intelligence, executive functioning, and crystallized intelligence. Based on prior research, all three processes are expected to be independent predictors of achievement, although some evidence suggests that these three cognitive processes may differentially relate to achievement.

Fluid Intelligence and Achievement

The central feature of fluid intelligence is reasoning under novel conditions – i.e., conditions in which the elements of a reasoning problem are equally familiar or equally unfamiliar to all participants, and there are no notable individual differences in practice with the problem or their constituent elements. Fluid intelligence is comprised of a broad range of reasoning abilities (e.g., deductive) to arrive at understanding relations among stimuli, comprehending implications, and drawing inferences. Such reasoning skills do not rely on prior knowledge (Horn & Blankson, 2012). Fluid intelligence is often measured by tests of matrix reasoning. The elements in matrix reasoning tests are often figures or shapes that are related in some manner when examined across the rows and down the columns of the matrix. Usually, one element is missing in the matrix that must be filled in. To fill in the missing element requires that one understand the relationships among the other elements in the matrix. The reasoning of such tasks involves comprehending that there is a problem, apprehending the elements of the problem, educing (figuring out) possible relationships among the elements, and holding the relationships in the span of immediate awareness while figuring out which of the possible relationships best fits the conditions and constraints of the problem (Horn & Blankson, 2012).

Theoretically, fluid intelligence is thought to be a primary ability from which other aspects of ability and achievement spring forth (Cattell, 1987). For example, results by Ferrer and McArdle (2004) suggested that fluid intelligence is a leading predictor of academic achievement and that fluid intelligence may play a stronger role in achievement in the childhood and the adolescent years than in adulthood. Specifically, fluid intelligence may be more strongly related to math achievement than to reading achievement (Evans, Floyd, McGrew, & Leforgee, 2001; Floyd, Keith, Taub, & McGrew, 2007; McGrew & Wendling, 2010; Peng, Wang, Wang, & Lin, in press). The ability to be proficient in all aspects of math require children to be able to reason actively about the problem elements (Blair & Razza, 2007; Geary, Hoard, & Hamson, 1999).

Taub and colleagues (Taub, Keith, Floyd, & McGrew, 2008) examined the direct and indirect effects of broad and specific cognitive abilities among a nationally representative sample of 5,000 children across four age groups (5–6; 7–8; 9–13; and 14–19 years-old). Although general cognitive abilities were a significant predictor of math achievement, fluid intelligence had the strongest relationship with math achievement among all four age groups. These results were also supported in a recent study by Green and colleagues (Green, Bunge, Chiongbian, Barrow, & Ferrer, 2017) who examined fluid intelligence, spatial skills, and vocabulary in relation to future math achievement among a sample of 6- to 21-year-olds. Utilizing a cohort-sequential design, measures were administered at three time points over a period of 4.5 years. Results indicated that fluid reasoning was a significant predictor of math achievement above and beyond the effects of age, spatial skills, and vocabulary.

Fluid intelligence has been shown to be a less consistent predictor in relation to reading achievement. A recent study by Cormier and colleagues (Cormier, McGrew, Bulut, & Funamoto, 2017) examined the association between broad cognitive abilities and reading achievement among a large, nationally representative sample of children and adolescents ages 6 to 19 years old. Results revealed that fluid intelligence was the strongest predictor of all indicators of reading achievement and this effect held across all ages. However, the results of Quinn (2018) failed to replicate this finding in a meta-analysis of 155 studies examining decoding, linguistic comprehension, and cognitive factors on reading comprehension across a broad age range. Results indicated that for younger students, a two-factor model including decoding and language comprehension accounted for 60% of the variance in reading comprehension, and that other cognitive factors (e.g., reasoning, inference, and working memory) failed to add any additional variance to the prediction of reading comprehension.

Executive Functioning and Achievement

Executive functioning refers to a variety of related cognitive skills that involve the ability to maintain task-relevant information in short-term memory, the ability to manipulate this information through the use of focused attention, and the capability to problem solve for goal directed behaviors in novel or challenging settings (Verdine, Irwin, Golinkoff, & Hirsh-Pasek, 2014). Among these skills are: attentional focusing and cognitive flexibility; cognitive inhibitory control; set-shifting; working memory; planning; and updating (Diamond, Barnett, Thomas, & Munro, 2007; Verdine et al., 2014). Measures that assess executive functioning often require that the individual complete a given task while holding multiple pieces of information in mind simultaneously (Willoughby, Wirth, & Blair, 2012) or inhibiting a prepotent response (Diamond et al., 2007).

In learning situations, children with higher levels of executive functioning may be better able to inhibit distracting stimuli, and thereby focus on the learning task. Evidence indicates that executive functioning skills are related to math and reading achievement (Blankson & Blair, 2016; Bull, Espy, & Wiebe 2008; Foy & Mann, 2013; Ribner, Willoughby, Blair, & The Family Life Project Key Investigators, 2017; Schmitt, Geldhof, Purpura, Duncan, & McClelland, 2017). Executive functioning may be especially relevant to math achievement. In addition, to active reasoning involved in math problems, individuals must also be able to hold potential solutions in mind to arrive at a final solution (Geary et al., 1999). Therefore, executive functioning may be just as important as fluid intelligence in math achievement.

Crystallized Intelligence and Achievement

Unlike fluid intelligence and executive functioning, crystallized intelligence is knowledge that is acquired primarily through social transmission of language and the dominant culture. Crystallized intelligence is measured by tasks indicating such knowledge, such as tests of verbal comprehension and general culturally based information (Horn & Blankson, 2012). Theoretically, crystallized intelligence is more susceptible to environmental influence than fluid intelligence and executive functioning, and there is some research to support this theory. For example, crystallized intelligence has been found to be more strongly correlated with the economic level of one’s parents than fluid intelligence and executive functioning (Dilworth-Bart, 2012).

Crystallized intelligence has consistently been found to be associated with reading (Evans et al., 2001; Floyd et al., 2007) and math achievement (Floyd et al., 2003). In some cases, crystallized intelligence has been found to be more strongly related to reading achievement than have fluid intelligence and executive functioning (Evans et al., 2001). Therefore, when examined simultaneously, it is expected that fluid intelligence and executive functioning will emerge as stronger predictors of math achievement whereas crystallized intelligence will emerge as a stronger predictor of reading achievement.

There is also evidence that supports crystallized intelligence as a moderate to strong predictor of math achievement. Taub and colleagues (Taub et al., 2008) found moderate to large direct effects of crystallized intelligence on math performance, but this relationship only held for children between the ages of 9 and 19 and was not significant for children from 5 to 8 years old.

Cognition and Achievement Links: Person-Centered Perspective

The majority of research that has examined the link between cognition and achievement has typically approached questions from a variable-centered perspective. However, there is less research about early childhood cognition and achievement from a person-centered perspective. In relation to achievement, it may not be sufficient to identify the specific aspects of cognition that promote learning. Instead, it may be important to understand if there are groups that can be identified by strengths and weaknesses of cognitive processes, and then understand whether those groups differ in levels of achievement. For example, profile analysis has been proposed as an alternative method to the use of global scores in assessing cognitive capabilities and achievement in children (Hale et al., 2008).

Research suggests that different underlying patterns of cognitive processes may differentially predict math and reading achievement. For example, in a study by Proctor, Floyd, and Shaver (2005), children with lower math reasoning achievement had cognitive profiles that were lower on fluid and crystallized intelligence compared with children who had average math reasoning skills. On the other hand, short-term memory, an aspect of executive functioning, emerged as a weakness in approximately 50% of the children with low math achievement, and a strength in the other 50%. Thus, at least two cognitive profiles might be identified, one low in fluid and crystallized intelligence but high in executive functioning, and one that is low in all three processes. Other profiles are also plausible, such as one that is high on all three aspects of cognition, and one high in fluid intelligence and executive functioning but low in crystallized intelligence, given neuronal connections between fluid intelligence and executive functioning (Blair, 2006).

Identification of profiles and their relation to achievement can inform development of interventions and educational plans for students (Hale et al., 2008). For example, if children with a pattern of high crystallized intelligence but lower executive functioning and fluid intelligence are found to achieve well in reading but to be challenged by math, then this may suggest individual education plans that focus on strengthening executive functioning and fluid intelligence as building blocks to math achievement. Similarly, if low levels of crystallized intelligence are related to poor performance in early reading even in children with high executive functioning and fluid intelligence, then a focus on acquisition of basic receptive and expressive vocabulary as a precursor to word identification may be a useful strategy that can be implemented for some children. If it is the case that executive functioning skills matter more than other cognitive processes, then it would be expected that children who have weaknesses in their fluid and crystallized intelligence but who have strong executive functioning skills, will show higher academic achievement. In short, the results of the proposed research may highlight the importance of the development and implementation of different intervention strategies or school curricula aimed at addressing specific strengths in children.

Differentiating Cognitive Processes

Although research supports the importance of fluid intelligence, executive functioning, and crystallized intelligence, there are conceptual and measurement issues that persist. Specifically, although crystallized intelligence has consistently been identified as a distinct process from either fluid intelligence or executive functioning as early as in the third and fourth years of life (Blair, 2006; Dilworth-Bart, 2012; Horn & Blankson, 2012), the distinction between processes typically labeled as fluid intelligence or executive functioning is less clear. Some have suggested that executive functioning and fluid intelligence may be the same process (Decker, Hill, & Dean, 2007), while others have argued that fluid intelligence and executive functioning rely on separate processes (Blair, 2006). More recent research indicates that executive functioning is a separate construct that is equally related to fluid and crystallized intelligence (Brydges, Reid, Fox, & Anderson, 2012).

By delineating these skills first, and then assessing the connection with achievement, we can better isolate the aspects of cognition that impact achievement. It might be that a two-factor model fits best, with one factor comprising measures of crystallized intelligence and the second factor comprising measures of executive functioning and fluid intelligence. This would indicate that in this population, general reasoning and planning skills are indistinguishable from one another, and targeting both executive functioning and fluid reasoning as a single intervention might be more beneficial than targeting each cognitive ability independently. If a three-factor model fits best, this would indicate that multiple, more precise, interventions would be beneficial to improve achievement outcomes.

The Present Study

The present study will extend previous research about the relations among fluid intelligence, executive functioning, and crystallized intelligence, and how these abilities independently and/or jointly predict math and reading achievement. It is an important step towards identifying normative developmental trends and outcomes within African American children. Previous research has provided a foundation for understanding these relationships. For example, early research by Kennedy, Van de Riet, and White (1963) examined cognition and achievement in an economically diverse sample of African American children in the 1st through 6th grade. In a more recent study, Noble et al. (2005) investigated cognition and achievement in African American children across a range of SES beginning when children were in kindergarten. The current study builds on these investigations by jointly examining fluid intelligence, executive functioning, and crystallized intelligence in the pre-K year as predictors of achievement in the kindergarten year.

We used two analytic perspectives. First, from a variable-centered perspective, we examined whether fluid intelligence, executive functioning, and crystallized intelligence can be distinguished in the pre-K year. We hypothesized that the three factors can be distinguished. Analyses were then conducted to determine whether fluid intelligence, executive functioning, and crystallized intelligence all contribute equally to the prediction of achievement in kindergarten or if one is a stronger predictor of achievement than the others. From a person-centered perspective, we examined whether different cognitive profiles can be identified within our study sample. Using these identified profiles, we examined whether certain patterns of cognitive processes produce higher levels of achievement than other patterns.

By strengthening our understanding of the role that fluid intelligence, executive functioning, and crystallized intelligence play in early academic achievement in a sample of African American children, we can better address issues regarding early academic success in this population to maximize achievement outcomes. How children perform academically early in life is related to how they will perform later in life (Duncan et al., 2007). Thus, a focus on the transition into formal schooling among African American children is crucial.

Method

Participants

Participants were part of a larger study in which 198 African American children were initially recruited through pre-K programs in the southeastern part of the US (mean age = 58.13 months, SD = 4.04). Data were collected from the children in their pre-K year and then again in the spring of the child’s kindergarten year. At the first wave, fifty-four percent of the children were female. Annual income and family size were reported by 190 caregivers. Average income-to-needs ratio, which is derived by dividing the total family income by the poverty threshold for that family size and is a common indicator of socioeconomic status, was 1.85 (SD = 1.62); approximately 63% of the sample had an income-to-needs ratio of less than 2.0, 33% between 2 and 5; and 4% greater than 5. Typically, an income-to-needs ratio of less than 2.0 represents families who are low-income, an income-to-needs ratio between 2 and 5 represents middle-income, and above 5.0 represents high-income families. As such, the present sample is economically diverse, particularly for research on African American children.

Of the original 198 participants, 171 returned for the kindergarten visit, an 86% retention rate. Retention was related to income-to-needs-ratio (t = [188] = −2.78, p < .01), fluid intelligence (t = [195] = −2.81, p < .01), and crystallized intelligence (t = [196] = −2.49, p < .05). Children who returned for the kindergarten visit came from higher income families and had higher fluid and crystallized intelligence scores. All other comparisons were non-significant. At the kindergarten time point (mean age = 72.11 months, SD = 3.57), 53% of the children were female. Average income-to-needs ratio (n = 165) was 2.12 (SD = 1.61); approximately 58% had an income-to-needs ratio of less than 2.0; 37% between 2 and 5; and 6% greater than 5.

Procedures

Participating families were initially recruited from preschools and childcare centers in a small Southeastern city through letters sent home with the children. Families interested in participating returned contact information to the researchers who then called the families to schedule a laboratory visit that lasted approximately two hours at each visit. Caregivers provided written consent before the start of each session. Task order was held constant across children. Caregivers completed a demographics measure while children were completing their tasks. Caregivers received $30 and $35 for the pre-K and kindergarten visits, respectively, and children selected a toy and stickers after the visit as thanks for their participation. All procedures were approved by the Institutional Review Board. For the present study, cognitive measures and covariates were obtained during the pre-K year and achievement measures during the kindergarten year.

Measures

Fluid Intelligence

The Woodcock-Johnson Tests of Cognitive Abilities (WJ III COG; Woodcock, McGrew, & Mather, 2001) Concept Formation subtest (α = .91) and the Raven’s Coloured Progressive Matrices (Carlson & Jensen, 1981; Raven, Court, & Raven, 1986; α = .76) were used to measure fluid intelligence. For the Concept Formation test (sample α = .73), the participant is given a stimulus set for which they must identify the rule (color, size, number, and shape, or some combination of these characteristics) for why one stimulus differs from another stimulus. Throughout the task, participants are given corrective feedback.

For the Raven’s Coloured Progressive Matrices, the participant is shown a geometric image with a missing piece. Participants are provided with a set of choices from which they must select the correct missing piece (sample α = .50).

Executive Functioning

The Hearts and Flowers (Diamond et al., 2007) and Fish Flanker (Rueda et al., 2004) tasks were used to measure executive functioning. The Hearts and Flowers task is a reliable and valid measure of attention shifting and inhibitory control. Children were shown a picture of either a heart or flower on the left or right side of a laptop computer screen. Two “fuzzy” buttons were placed on the laptop keyboard on opposite sides. Children were instructed to press one of the two buttons corresponding with the picture’s location on the screen according to two rules: When a heart was shown, they were to press the button that corresponded to the same side of the picture; when a flower was shown, they were to press the button on the opposite side of picture. The percent correct on 33 trials of mixed hearts and flowers served as the measure of accuracy.

The Flanker task is a reliable and valid (Zelazo et al., 2013) measure of inhibitory control. On a laptop computer screen, children were shown a target fish that was flanked by two fish on either side. Children were instructed to focus on the middle fish and press the fuzzy button corresponding to the direction in which the middle fish was pointing. There were two types of practice trials, congruent and incongruent. All of the fish were pointing in the same direction for the congruent trials whereas the flanker fish were facing the opposite direction of the middle target fish for the incongruent trials. During test trials, congruent and incongruent trials were inter-mixed. The percent correct on 50 mixed trials served as the measure of accuracy.

Crystallized Intelligence

Two subtests from the WJ III COG (Woodcock et al., 2001) were used to measure crystallized intelligence: Verbal Comprehension (α = .90) and General Information (α = .89). For the Verbal Comprehension test, children were asked to identify objects, synonyms, and antonyms, and to complete verbal analogies (sample α = .84). For General Information, children were asked to identify where named objects are found and to state what people typically do with a named object (sample α = .73).

Reading Achievement

Two subtests from the Woodcock-Johnson Tests of Achievement (WJ III ACH; Woodcock et al., 2001) were used to measure reading achievement. For the Picture Vocabulary test (α = .77), children were shown pictures of objects and asked to name the object (sample α = .69). For the Letter-Word Identification test (α = .91), children were asked to identify letters and words that were visually presented (sample α = .94).

Math Achievement

Two subtests from the WJ III ACH (Woodcock et al., 2001) were used to measure math achievement. For the Applied Problems test (α = .92), problems were presented orally or visually, and children were asked to perform mathematical calculations in response to the presented problems (sample α = .82). For the Quantitative Concepts test (α = .90), the children were asked to identify mathematical terms and formulae, and to identify missing numbers in a presented number sequence (sample α = .87).

Covariates

Child age in months, child gender, and socioeconomic status (measured by family income-to-needs ratio in this study) have been found to be related to the variables of interest and were therefore explored as potential covariates. Mothers reported the child’s age, gender, and family income variables at the pre-K visit.

Results

Preliminary Analyses

Missingness ranged from 0% to 4% (family income) for the pre-K measures. As previously mentioned, 86% of the participants returned for the kindergarten visit. Missingness was 0% for the kindergarten measures among the participants who returned (See Table 1). Aside from attrition, missingness was primarily due to participant non-response (income) or experimenter error (e.g., no ceiling reached before discontinuing testing). Analyses were conducted using full-information maximum likelihood to account for missing data (Widaman, 2006).

Table 1.

Descriptive Statistics for Study Variables

Wave N M SD Min Max
Income-to-needs ratio 1 190 1.81 1.62 .08 6.29
Fluid Intelligence 1
 Concept Formation W 190 445.21 11.85 418.00 486.00
 Raven’s 196 7.16 1.69 1.00 11.00
 Composite 197 0.00 0.79 −2.97 1.72
Executive Functioning 1
 Hearts and Flowers 196 0.48 0.18 0.03 .97
 Fish Flanker 197 0.48 0.28 0.00 1.00
 Composite 197 0.00 0.86 −2.14 2.23
Crystallized Intelligence 1
 Verbal Comprehension W 198 453.66 12.59 427.00 489.00
 General Information W 198 451.14 12.69 411.00 483.00
 Composite 198 0.00 0.89 −2.56 2.30
Reading Achievement 2
 Picture Vocabulary W 171 475.39 9.01 452.00 501.00
 Letter-Word Identification W 171 421.89 36.65 314.00 503.00
 Composite 171 0.00 0.88 −2.33 2.02
Math Achievement 2
 Applied Problems W 171 443.61 19.72 318.00 481.00
 Quantitative Concepts W 171 455.39 14.72 403.00 491.00
 Composite 171 0.00 0.93 −4.86 2.16
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Note. W = W Score.

A subsidiary aim of the present study was to determine if the cognitive skills under investigation can be distinguished. To address this aim, we conducted confirmatory factor analyses to determine whether the pre-K cognitive measures fit a one-, two-, or three-factor model. Analyses were conducted using Mplus 8.2 (Muthén & Muthén, 1998–2017). The chi-square statistic, Root Mean Square Error of Approximation (RMSEA; Steiger & Lind, 1980), and Comparative Fit Index (CFI; Bentler, 1990) were examined to estimate the goodness of fit of the models. Results suggested that the 3-factor model (χ2 [6] = 7.72; RMSEA = .04; CFI = .99) fit better than the 1-factor (χ2 [9] = 36.16; RMSEA = .12; CFI = .88) and 2-factor (χ2 [8] = 18.93; RMSEA = .08; CFI = .95) models.

Substantive Analyses

Given that a three factor model held for the primary variables, composites were formed and used in all substantive analyses. To form composites, we standardized all variables to put them in the same metric and scores were averaged within each construct. Next, we identified covariates. Only income-to-needs ratio met the requirement of being correlated with a predictor and an outcome for inclusion in subsequent analyses. The means and standard deviations for the study variables are in Table 1. For the Woodcock-Johnson tests, W scores are presented because of their link to normative data. Correlations are in Table 2. Income-to-needs ratio was positively associated with all variables except executive functioning. Additionally, each of the three pre-K cognitive measures correlated positively with children’s kindergarten math and reading achievement.

Table 2.

Correlations among Study Variables

Variable 1 2 3 4 5
1. Fluid Intelligence --
2. Executive Functioning .33** --
3. Crystallized Intelligence .43** .38** --
4. Reading Achievement .34** .32** .70** --
5. Math Achievement .42** .38** .64** .73** --
6. Income-to-needs ratio .31** .08 .35** .53** .47**
7. Child age (mos.) −.03 .33** .17* −.01 −.05
8. Male −.03 .09 .00 −.06 −.01
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**

p < .01.

Variable-Centered Perspective

From a variable-centered perspective, multiple regression analyses were conducted in Mplus (Muthén & Muthén, 1998–2017) to test the independent contribution of each pre-K cognitive skill to kindergarten achievement, controlling for income-to-needs ratio. Results are presented in Table 3. Income-to-needs ratio was a significant predictor of math and reading achievement. Of focus in the present investigation, however, was the impact of cognition on achievement. When considered simultaneously, executive functioning and crystallized intelligence predicted both math and reading achievement, over and above income-to-needs ratio, whereas fluid intelligence was not a significant predictor of math and reading. Crystallized intelligence was the strongest predictor for both math and reading achievement.

Table 3.

Full Information Maximum Likelihood Regression Estimates

Math Achievement (R2 = .56) Reading Achievement (R2 = .63)
Predictors Estimate SE Beta Est./SE 95% CI Estimate SE Beta Est./SE 95% CI
Income-to-needs ratio 0.17 0.03 .29 5.37** 0.11, 0.23 0.20 0.03 .36 7.29** 0.14, 0.25
Fluid Intelligence 0.12 0.07 .10 1.68 −0.02, 0.26 −0.04 0.06 −.03 −0.55 −0.16, 0.09
Executive Functioning 0.21 0.06 .19 3.38** 0.09, 0.33 0.13 0.06 .13 2.44** 0.03, 0.24
Crystallized Intelligence 0.48 0.07 .45 7.33** 0.35, 0.61 0.57 0.03 .56 7.29** 0.46, 0.68
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**

p < .01

Person-Centered Perspective

From a person-centered perspective, unconditional latent profile models were tested using Mplus (Muthén & Muthén, 1998–2017). The number of profiles was increased until the model was not well identified, such as class sizes with fewer than 20 individuals (Masyn, 2013), which in this case was 4 classes. Latent profile analysis is an exploratory technique. Several indicators have been developed to help in determining the number of optimal classes. Among these are the Bayesian Information Criterion (BIC) and the Bootstrap Likelihood Ratio Test (BLRT), which have been found to be the best indicators of the number of classes (Jung & Wickrama, 2008; Nylund, Asparouhov, & Muthén, 2007). Lower BIC values indicate a better model fit. The BLRT is a likelihood ratio test that compares the K class model to the K+1 class model and provides a p value. If the p value is non-significant, this indicates that the K model fits better than the K + 1 model (Jung & Wickrama, 2008). Additionally, we computed the correct model probability (cmP) value and the Bayes Factor (BF). The cmP approximates the probability that the model under consideration is the correct model relative to the other models in the set (Masyn, 2013). Any models with cmP values greater than .10 should be considered further. The BF is an index that represents the comparative fit between two models. When the BF is greater than 10, this is evidence that model A is a better model than model B (Masyn, 2013). Bayes Factors were computed comparing the K model to the K + 1 model (e.g., model 2 with 3). Finally, we considered interpretability, parsimony, and class proportion size in deciding on the number of classes (Masyn, 2013).

A three-profile solution was found to be best using the rules of thumb described above (See Table 4 & Figure 1). Specifically, the 3-class solution had the lowest BIC value. Additionally, the BLRT value for the 4-class solution was not significant, indicating that a 4-class solution was not significantly better than a 3-class solution. The 3-class solution had a cmP value greater than .10, indicating that among the four models, it was the best candidate for consideration. Finally, the BF value for the 3-class model was greater than 10, indicating that it was a better model than the 4 class model. Class sizes were all greater than 20 for the 3-class solution in contrast to the 4-class solution, in which one class had fewer than 20 participants. Children in profile 1 (Low fluid and crystallized; n = 24) had lower scores on all three aspects of cognition, but they were especially lower in fluid and crystallized intelligence. Children in profile 2 (Average cognition; n = 132) had average scores on all three aspects of cognition. Children in profile 3 (High executive functioning; n = 42) had the highest scores on all three aspects of cognition, but especially higher on executive functioning.

Table 4.

Fit Statistics for Latent Profiles Analyses

Number of Classes BIC BLRT cmP BF
1 1507.94 NA < .01 < .01
2 1467.52 61.58, p <.05 .02 .02
3 1459.87 28.80, p < .05 .98 776.66
4 1473.18 7.84, p = .58 < .01 NA
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Note. BIC = Bayesian information criterion; BLRT= Bootstrap Likelihood Ratio Test.; cmP= correct model probability; BF= Bayes Factor.

Figure 1. Cognitive Profiles.

Figure 1

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Note: EF= executive functioning; GF= fluid intelligence; GC= crystallized intelligence; Profile 1= Low fluid and crystallized; Profile 2= Average cognition; Profile 3= High executive functioning.

Once the classes were identified, analyses were conducted using the Bolck, Croon, and Hagenaars (BCH) method (Bakk & Vermunt, 2016) in Mplus to evaluate the relation between the profiles and kindergarten reading and math achievement. The BCH method has been found to supersede other approaches for testing continuous distal outcomes in latent class analyses (Muthén & Muthén, 1998–2017). Results indicated that reading achievement scores were significantly different across the three profiles, as were math achievement scores (See Figure 2). Children with average executive functioning but low fluid and crystallized intelligence during pre-K had the lowest math and reading scores in kindergarten, whereas children with the highest scores in all three aspects of cognition (Profile 3) had the highest scores in reading and math.

Figure 2. Kindergarten Achievement by Preschool Cognitive Profile.

Figure 2

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Note: Profile 1= Low fluid and crystallized; Profile 2= Average cognition; Profile 3= High executive functioning.

Discussion

Research has consistently demonstrated that children who enter formal schooling with better cognitive skills have higher achievement in math and reading (Blair & Razza, 2007; Duncan et al., 2007), and that math and reading skills at school entry are the strongest predictors of later academic achievement (Duncan et al., 2007). However, several issues regarding the relation between cognition and achievement remain. Importantly, little is known about whether specific aspects of cognition (e.g., fluid intelligence, executive functioning, and crystallized intelligence) matter more for either math or reading achievement within samples of African American children. Additionally, it is not clear whether there are specific patterns of cognitive function that differentially predict math and reading achievement in these children. The present study aimed to fill these gaps in the literature by providing both variable-centered and person-centered perspectives on cognitive processes and academic achievement among African American children across a broader range of socioeconomic status.

The results of the present research may inform the development and implementation of different intervention strategies or school curricula aimed at addressing specific skills in children. Importantly, the cognitive processes are all malleable factors that can be improved through training and intervention. Children’s fluid intelligence has been shown to improve through computerized training tasks, such as non-verbal reasoning games and speed training programs (Au et al., 2015). Children’s executive functioning can also be increased through diverse activities that include CogMed computerized training, task-switching computerized training, and Tae-Kwon-Do (Diamond & Lee, 2011). Additionally, studies show that crystallized abilities can also be improved by training working memory (Alloway & Alloway, 2009; Au et al., 2015) and through game-based tasks, although the game-based tasks have only been tested in adolescents (Neugnot-Cerioli, Gagner, & Beauchamp, 2017). There is some evidence that improving these skills can subsequently improve academic outcomes (Karbach & Unger, 2014), and that the impacts of these training and intervention programs are most beneficial to low performing children (Diamond & Lee, 2011).

Variable-Centered Perspective

From a variable-centered perspective, we examined if fluid intelligence, executive functioning, and crystallized intelligence can be delineated among African American children during the pre-K year and if these aspects of cognition have independent effects on early math and reading achievement when examined simultaneously. The three aspects of cognition were distinguished. Additionally, only executive functioning and crystallized intelligence predicted math and reading achievement in kindergarten, over and above any effects of income-to-needs.

Cognitive research highlights the importance of executive functioning and crystallized intelligence skills in relation to early academic achievement. The variable-centered results corroborate as well as extend previous findings regarding the links between cognitive abilities and later achievement. In particular, executive functioning is a central aspect of cognitive development during the preschool period and developmental increases in executive functioning generally reflect advances in an underlying cognitive ability to represent complex rule structures. Children with higher executive functioning are better able to pay attention in class, inhibit distracting stimuli, and communicate their needs to teachers, all of which are important skills for success in school (Blair & Razza, 2007; Fitzpatrick & Pagani, 2012).

The findings of this study are also consistent with previous research indicating that crystallized intelligence is an important predictor of achievement (Evans et al., 2001; Floyd et al., 2007). For example, Floyd et al. (2007) found that general cognitive factors influence reading achievement indirectly through specific factors, such as crystallized intelligence. Crystallized intelligence is acquired through the social and cultural transmission of information (Horn & Blankson, 2012). Children who have enriching early language experiences, have objects and experiences labeled for them at a young age, and who are exposed to a wider variety of words, have better vocabularies than children who do not have these enriching experiences with language (Callanan & Sabbagh, 2004). The ability to access this verbal and general information is quite important for children’s early math and reading abilities. Having a store of information and an ability to label objects and experiences assists children with memorizing, retaining, and later recalling words and concepts that are essential to later reading and math achievement.

Fluid intelligence was not related to math and reading achievement once income and the other cognitive variables were taken into account, which is in line with some past research (e.g., Floyd et al., 2007) but contrary to others. Fluid intelligence is often considered the sine qua non of intelligence, and has been equated with g, or general intelligence by some (e.g., Kvist & Gustafsson, 2008). The present results indicate that basic reasoning skills may not be sufficient for the acquisition of math and reading skills in the kindergarten year, beyond the impacts of the other variables examined in the present study. Past research has often focused on a general intelligence factor, which combines both fluid and crystallized intelligence into one. The results of the present research illustrate that a focus on a general intelligence factor in research might serve as a hindrance in learning more about the ways in which cognition impacts achievement. These results therefore highlight the importance of examining the independent influence of different cognitive processes on different aspects of academic achievement rather than a sole focus on a general cognitive ability factor.

Additionally, the findings of the present research suggest that further research is needed on the specific role that fluid intelligence might play in achievement in these children. Cattell’s (1987) investment hypothesis specified that fluid abilities are invested in learning to bring about other abilities, which contribute to academic achievement. It might be that crystallized intelligence or executive functioning serve as a mediator in the link between fluid intelligence and achievement. Future research can examine the extent to which this is the case using data with more than two time points.

Person-Centered Perspective

From a person-centered perspective, three profiles of cognition were identified and differences in math and reading achievement were examined. The fact that children with the lowest fluid and crystallized intelligence and average executive functioning scored the lowest in math and reading achievement when compared to children with comparable executive functioning scores, but higher scores in crystallized and fluid intelligence is interesting and challenges the importance of executive functioning over other aspects of cognition. One explanation for these results is that executive functioning does not help children’s achievement when they have weaknesses in other aspects of cognition. On the other hand, when children have higher, or even average, scores in fluid and crystallized intelligence, the children with higher executive functioning benefit the most. That is, executive functioning may help to maximize children’s achievement only when children have at least average skills in other cognitive domains. Even if children can pay attention to stimuli and control impulses to take full advantage of their learning environments, they may not be as successful academically if they do not have the previous knowledge or foundation that is required for learning. Likewise, children who have more exposure to language or possess better problem-solving skills may be better able to utilize their skills in executive functioning to reach their full academic potential.

Restrictions and Strengths

There are a few potential restrictions in the present study that should be noted. Foremost, although the models that were tested accounted for a substantial amount of the variance in kindergarten math and reading achievement, additional variance may be accounted for by other cognitive and linguistic variables or variables related to other child characteristics, such as motivation and self-efficacy. Additional research can examine the extent to which this is the case. Furthermore, because our research design is not a randomized controlled trial, caution is warranted in drawing any causal conclusions. Additionally, the use of latent profile analysis is an exploratory technique and there were fewer than 200 participants in the study, which might impact the enumeration of classes. However, this potential restriction might be minimized in the present study because sample size has not been found to have a strong effect on power in detecting the correct number of profiles in simulation studies (Tein, Coxe, & Cham, 2013). Nevertheless, further research with larger samples should be conducted to determine if the profiles replicate.

Despite these potential limitations, the results of the present research fill an important gap in the research literature regarding the extent to which important cognitive factors predict both reading and math achievement among a more economically diverse sample of African American children than has been studied in the past, with approximately 40% of the sample being middle to upper income. Our results indicated that income-to-needs ratio was associated with fluid and crystallized intelligence, as well as math and reading achievement, which is consistent with previous research; it has been found that individuals with higher levels of socioeconomic adversity tend to have lower scores on tests of cognition and achievement. However, income-to-needs ratio was not significantly related to executive functioning, as has been found in other studies (e.g., Dilworth-Bart, 2012). Also, contrary to expectations was the finding that income-to-needs ratio was as strongly related to crystallized intelligence as to fluid intelligence in this sample. Socioeconomic status is a complex variable that is comprised of multiple components (e.g., parent education, income, etc.). Any one or all of these aspects can play a role in any one or all of the cognitive and achievement variables investigated in the present study. The present study highlights the need for further research to carefully unpack the role of socioeconomic status in cognition and achievement among African American children.

Conclusion

Overall, the findings give insight on the extent to which cognitive factors predict academic achievement, particularly among children who are often framed in the research literature as having deficits when compared to Caucasian children. By understanding which cognitive factors predict academic achievement among African American children, policy and intervention programs can focus on how to promote these factors to enhance achievement. Together, the variable-centered and person-centered results from the present study suggest that perhaps there should be increased focus on crystallized intelligence in early education programs, policies, and interventions in addition to a focus on executive functioning. Although there are several intervention programs that target executive functioning in preschoolers (e.g., Tools of the Mind; Diamond et al., 2007), there are fewer interventions that directly focus on training crystallized intelligence in preschoolers. It might be that recently developed game-based methods for training crystallized intelligence in adolescents (Neugnot-Cerioli et al., 2017) might be extended down to younger children. Many early education policies are targeted at children from low-income families. The results of this research suggest that policies and interventions should be expanded to encompass African American children across a broader range of socioeconomic status. Ultimately, high quality early interventions and education programs that help support improvements in executive functioning and crystallized intelligence might make the most impact on achievement for these children.

Educational Impact and Implications Statement.

Results of the present research indicate that fluid intelligence, executive functioning, and crystallized intelligence can be distinguished in the Pre-K year, and three profiles of cognition can be identified: low fluid and crystallized intelligence with average executive functioning, average abilities in all three areas, and high abilities in all three areas, but particularly higher in executive functioning. Children with the highest cognitive skills had the highest math and reading skills in kindergarten, whereas children with low fluid and crystallized intelligence had the lowest scores in reading and math. However, in regression analyses, fluid intelligence did not predict achievement. Together, these results suggest that increased attention should be paid to the training of crystallized intelligence in addition to executive functioning training during the preschool period.

Acknowledgments

This research was supported by grant no. R15HD077511 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development awarded to A. N. Blankson. The content is solely the responsibility of the authors and does not necessarily represent the official views of the Eunice Kennedy Shriver National Institute of Child Health and Human Development or the National Institutes of Health. The authors thank Clancy Blair for his assistance with this manuscript, the students who assisted with data collection, and the families who participated in the study.

Footnotes

Author Note

Contributor Information

A. Nayena Blankson, Spelman College.

Jessica A. Gudmundson, Spelman College

Memuna Kondeh, Temple University.

References

  1. Alloway TP, & Alloway RG (2009). The efficacy of working memory training in improving crystallized intelligence. Nature Precedings. [Google Scholar]
  2. Au J, Sheehan E, Tsai N, Duncan GJ, Buschkuehl M, & Jaeggi SM (2015). Improving fluid intelligence with training on working memory: A meta-analysis. Psychonomic Bulletin & Review, 22, 366–377. doi: 10.3758/s13423-014-0699-x [DOI] [PubMed] [Google Scholar]
  3. Bakk Z & Vermunt JK (2016). Robustness of stepwise latent class modeling with continuous distal outcomes. Structural Equation Modeling, 23, 20–31. doi: 10.1080/10705511.2014.955104 [DOI] [Google Scholar]
  4. Bentler PM (1990). Comparative fit indices in structural equation models. Psychological Bulletin, 107, 238–246. [DOI] [PubMed] [Google Scholar]
  5. Blair C (2006). How similar are fluid cognition and general intelligence? A developmental neuroscience perspective on fluid cognition as an aspect of human cognitive ability. Behavioral and Brain Science, 29, 109–125. doi: 10.1017/S0140525X06009034 [DOI] [PubMed] [Google Scholar]
  6. Blair C, & Razza RP (2007). Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. Child Development, 78, 647–663. doi: 10.1111/j.1467-8624.2007.01019.x [DOI] [PubMed] [Google Scholar]
  7. Blankson AN, & Blair C (2016). Cognition and classroom quality as predictors of math achievement in the kindergarten year. Learning and Instruction, 41, 32–40. doi: 10.1016/j.learninstruc.2015.09.004 [DOI] [Google Scholar]
  8. Bull R, Espy KA, & Wiebe SA (2008). Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years. Developmental Neuropsychology, 33, 205–228. doi: 10.1080/87565640801982312 [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Brydges CR, Reid CL, Fox AM, Anderson M (2012). A unitary executive function predicts intelligence in children. Intelligence, 40, 458–469. doi: 10.1016/j.intell.2012.05.006 [DOI] [Google Scholar]
  10. Callanan MA, & Sabbagh MA (2004). Multiple labels for objects in conversations with young children: Parents’ language and children’s developing expectations about word meanings. Child Development, 40, 746–763. doi: 10.1037/0012-1649.40.5.746 [DOI] [PubMed] [Google Scholar]
  11. Carlson JS, & Jensen CM (1981). Reliability of the Raven Colored Progressive Matrices Test: Age and ethnic group comparisons. Journal of Consulting and Clinical Psychology, 49, 320–322. [Google Scholar]
  12. Cattell RB (1987). Intelligence: Its structure, growth, and action. New York: Elsevier. [Google Scholar]
  13. Cormier D, McGrew K, Bulut O, & Funamoto A (2017). Revisiting the relations between the WJ-IV measures of Cattell-Horn-Carroll (CHC) cognitive abilities and reading achievement during the school-age years. Journal of Psychoeducational Assessment, 35, 731–754. doi: 10.1177/0734282916659208 [DOI] [Google Scholar]
  14. Decker SL, Hill SK, & Dean RS (2007). Evidence of construct similarity in executive functions and fluid reasoning abilities. International Journal of Neuroscience, 117, 735–748. doi: 10.1080/00207450600910085 [DOI] [PubMed] [Google Scholar]
  15. Diamond A, Barnett WS, Thomas J, & Munro S (2007). Preschool program improves cognitive control. Science, 318, 1387–1388. doi: 10.1126/science.1151148 [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Diamond A, & Lee K (2011). Interventions shown to aid executive function development in children 4 to12 years old. Science, 333, 959–964. doi: 10.1126/science.1204529 [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Dilworth-Bart JE (2012). Does executive function mediate SES and home quality associations with academic readiness? Early Childhood Research Quarterly, 27, 416–425. doi: 10.1016/j.ecresq.2012.02.002 [DOI] [Google Scholar]
  18. Duncan GJ, Dowsett CJ, Claessens A, Magnuson K, Huston AC, Klebanov P, … & Japel C (2007). School readiness and later achievement. Developmental Psychology, 43, 1428–1446. doi: 10.1037/0012-1649.43.6.1428 [DOI] [PubMed] [Google Scholar]
  19. Evans JJ, Floyd RG, McGrew KS, & Leforgee MH (2001). The relations between measures of Cattell-Horn-Carroll (CHC) cognitive abilities and reading achievement during childhood and adolescence. School Psychology Review, 31, 246–262. [Google Scholar]
  20. Ferrer E, & McArdle JJ (2004). An experimental analysis of dynamic hypotheses about cognitive abilities and achievement from childhood to early adulthood. Developmental Psychology, 40, 935–952. doi: 10.1037/0012-1649.40.6.935 [DOI] [PubMed] [Google Scholar]
  21. Fitzpatrick C, & Pagani LS (2012). Toddler working memory skills predict kindergarten school readiness. Intelligence, 40, 205–212. doi: 10.1016/j.intell.2011.11.007 [DOI] [Google Scholar]
  22. Floyd RG, Evans JJ, & McGrew KS (2003). Relations between measures of Cattell-Horn-Carroll (CHC) cognitive abilities and mathematics achievement across the school-age years. Psychology in the Schools, 40, 155–171. [Google Scholar]
  23. Floyd RG, Keith T,Z, Taub GE, & McGrew KS (2007). Cattell-Horn-Carroll cognitive abilities and their effects on reading decoding skills: g has indirect effects, more specific abilities have direct effects. School Psychology Quarterly, 22, 200–233. doi: 10.1037/1045-3830.22.2.200 [DOI] [Google Scholar]
  24. Foy JG, & Mann VA (2013). Executive function and early reading skills. Reading and Writing, 26, 453–472. [Google Scholar]
  25. García Coll C (2013). The colorization of North America’s children: Science, policy, and practice. Paper presented at the 2013 Biennial Meeting of the Society for Research in Child Development, Seattle, WA. [Google Scholar]
  26. García Coll C, Lamberty G, Jenkins R, McAdoo HP, Crnic K, Wasik BH, & García HV (1996). An integrative model for the study of developmental competencies in minority children. Child Development, 67, 1891–1914. doi: 10.2307/1131600 [DOI] [PubMed] [Google Scholar]
  27. Geary DC, Hoard MK, & Hamson CO (1999). Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for a mathematical disability. Journal of Experimental Child Psychology, 74, 213–239. doi: 10.1006/jecp.1999.2515 [DOI] [PubMed] [Google Scholar]
  28. Green CT, Bunge SA, Chiongbian VB, Barrow M, & Ferrer E (2017). Fluid reasoning predicts future mathematics among children and adolescents. Journal of Experimental Child Psychology, 157, 125–143. doi: 10.1016/j.jecp.2016.12.005 [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Hale JB, Fiorello CA, Dumont R, Willis JO, Rackley C, & Elliott C (2008). Differential Ability Scales- Second Edition (Neuro) psychological predictors of math performance for typical children and children with math disability. Psychology in the Schools, 45, 838–858. doi: 10.1002/pits.20330 [DOI] [Google Scholar]
  30. Horn JL, & Blankson AN (2012). Foundations for better understanding of cognitive abilities. In Flanagan DP & Harrison PL (Eds.), Contemporary intellectual assessment: Theories, tests, and issues (3rd ed.). New York: The Guilford Press. [Google Scholar]
  31. Jung T, & Wickrama KAS (2008). An introduction to latent class growth analysis and growth mixture modeling. Social and Personality Psychology Compass, 2, 302–317. doi: 10.1111/j.1751-9004.2007.00054.x [DOI] [Google Scholar]
  32. Karbach J & Unger K (2014). Executive control training from middle childhood to adolescence. Frontiers in Psychology, 5, 1–14. doi: 10.3389/fpsyg.2014.00390 [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Kennedy W, Van de Riet V, & White J (1963). A normative sample of intelligence and achievement of Negro elementary school children in the southeastern United States. Monographs of the Society for research in Child Development, 28, 1–112. [PubMed] [Google Scholar]
  34. Kvist AV, & Gustafsson J (2008). The relation between fluid intelligence and the general factor as a function of cultural background: A test of Cattell’s Investment Theory. Intelligence, 36, 422–436. doi: 10.1016/j.intell.2007.08.004 [DOI] [Google Scholar]
  35. Masyn K (2013). Latent class analysis and finite mixture modeling. In Little T (Ed.), The Oxford handbook of quantitative methods in psychology (Vol. 2, pp. 375–393). Oxford, UK: Oxford University Press. doi: 10.1093/oxfordhb/9780199934898.013.0025 [DOI] [Google Scholar]
  36. McGrew KS, & Wendling BJ (2010). Cattell-Horn-Carroll cognitive-achievement relations: What we have learned from the past 20 years of research. Psychology in the Schools, 27, 651–675. doi: 10.1002/pits.20497 [DOI] [Google Scholar]
  37. Muthén BO, & Muthén LK (2000). Integrating person-centered and variable-centered analysis: Growth mixture modeling with latent trajectory classes. Alcoholism: Clinical and Experimental Research, 24, 882–891. [PubMed] [Google Scholar]
  38. Muthén LK, & Muthén BO (1998–2017). Mplus user’s guide. Eighth Edition. Los Angeles, CA: Muthén & Muthén. [Google Scholar]
  39. Neugnot-Cerioli M, Gagner C, Beauchamp MH (2017). Training of fluid and crystallized intelligence: A game-based approach in adolescents presenting with below average IQ. Cogent Psychology, 4, 1284360. doi: 10.1080/23311908.2017.1284360 [DOI] [Google Scholar]
  40. Noble KG, Norman MF and Farah MJ (2005). Neurocognitive correlates of socioeconomic status in kindergarten children. Developmental Science, 8, 74–87. [DOI] [PubMed] [Google Scholar]
  41. Nylund KL, Asparouhov T, & Muthén BO (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling, 14, 535–569. doi: 10.1080/10705510701575396 [DOI] [Google Scholar]
  42. Peng P, Wang T, Wang C, & Lin X (in press). A meta-analysis on the relation between fluid intelligence and reading/mathematics: Effects of tasks, age, and social economics status. Psychological Bulletin. [DOI] [PubMed] [Google Scholar]
  43. Pigott TD (2001). A review of methods for missing data. Educational Research and Evaluation, 7, 353–383. [Google Scholar]
  44. Proctor BE, Floyd RG, & Shaver RB (2005). Cattle-Horn-Carroll broad cognitive ability profiles of low math achievers. Psychology in the School, 42, 1–12. doi: 10.1002/pits.20030 [DOI] [Google Scholar]
  45. Quinn JM and Wagner RK (2018). Using meta‐analytic structural equation modeling to study developmental change in relations between language and literacy. Child Development. doi: 10.1111/cdev.13049 [DOI] [PMC free article] [PubMed] [Google Scholar]
  46. Raven JC, Court JH, & Raven J (1986). Manual for Raven’s Progressive Matrices and Vocabulary Scales (Section 2) - Coloured Progressive Matrices. London: Lewis. [Google Scholar]
  47. Ribner AD, Willoughby MT, Blair CB, & The Family Life Project Key Investigators. (2017). Executive function buffers the association between early math and later academic skills. Frontiers in Psychology, 8, 869. doi: 10.3389/fpsyg.2017.00869 [DOI] [PMC free article] [PubMed] [Google Scholar]
  48. Rueda MR, Fan J, McCandliss BD, Halparin JD, Gruber DB, Pappert Lercari L, & Posner MI (2004). Development of attentional networks in childhood. Neuropsychologia, 42, 1029–1040. doi: 10.1016/j.neuropsychologia.2003.12.012 [DOI] [PubMed] [Google Scholar]
  49. Schmitt SA, Geldhof GJ, Purpura DJ, Duncan R, & McClelland MM (2017). Examining the relations between executive function, math, and literacy during the transition to kindergarten: A multi-analytic approach. Journal of Educational Psychology, 109, 1120–1140. doi: 10.1037/edu0000193 [DOI] [Google Scholar]
  50. Steiger JH & Lind JC (1980). Statistically-based tests for the number of common factors. Paper presented at the Annual Spring Meeting of the Psychometric Society. Iowa City, IA. [Google Scholar]
  51. Taub GE, Keith TZ, Floyd RG, & McGrew KS (2008). Effects of general and broad cognitive abilities on mathematics achievement. School Psychology Quarterly, 23, 187–198. doi: 10.1037/1045-3830.23.2.187 [DOI] [Google Scholar]
  52. Tein JY, Coxe S, & Cham H (2013). Statistical power to detect the correct number of classes in latent profile analysis. Structural Equation Modeling, 20, 640–657. doi: 10.1080/10705511.2013.824781 [DOI] [PMC free article] [PubMed] [Google Scholar]
  53. Verdine BN, Irwin CM, Golinkoff RM, & Hirsh-Pasek K (2014). Contributions of executive function and spatial skills to preschool mathematics achievement. Journal of Experimental Child Psychology, 126, 37–51. doi: 10.1016/j.jecp.2014.02.012 [DOI] [PMC free article] [PubMed] [Google Scholar]
  54. Widaman KF (2006). Missing data: What to do with or without them. Monographs of theSociety for Research in Child Development, 71, 42–64. [Google Scholar]
  55. Willoughby MT, Wirth RJ, & Blair CB (2012). Executive function in early childhood: Longitudinal measurement invariance and development change. Psychological Assessment, 24, 418–431. doi: 10.1037/a0025779. [DOI] [PMC free article] [PubMed] [Google Scholar]
  56. Woodcock RW, McGrew KS, & Mather N (2001). Woodcock-Johnson III. Itasca, IL: Riverside Publishing. [Google Scholar]
  57. Zelazo PD, Anderson JE, Richler J, Wallner-Allen K, Beaumont JL, & Weintraub S (2013). NIH toolbox cognitive battery (CB): Measuring executive function and attention. Monographs of the Society for Research in Child Development, 78, 16–33. doi: 10.1111/mono.12032 [DOI] [PubMed] [Google Scholar]

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