The connection between challenges in the domains of mathematics and language and deficits in working memory (WM) has been substantiated in numerous studies (Raghubar et al., 2010; Szucs, 2016). Much of this research draws upon Baddeley’s WM model (Baddeley, 2000, 2002), which delineates the WM system into three components: the first is the central executive (complex WM), which is responsible for regulatory functions such as attention, action control, and problem-solving; the other two are subordinate systems controlled by the central executive—the phonological loop (PL) and the visuospatial sketchpad, which respectively handle and manipulate auditory and visual information and are regarded as simple WM.

The WM system plays a pivotal role in supporting learning processes, including the assimilation of new information and the development of novel skills (Baddeley & Hitch, 1974; Holmes et al., 2009; Peng et al., 2016). Learning necessitates concurrent processing and storage of data, thereby making children with WM impairments susceptible to challenges in basic learning processes, knowledge acquisition, and the execution of complex skills (Pickering & Gathercole, 2004). While there is a consensus that WM is closely linked to early literacy and numeracy, the precise contributions of each WM component to distinct early literacy and numeracy skills in kindergarten-aged children remain elusive due to limited research in this age group and inconsistent findings across WM domains.

This study aims to elucidate the associations between different WM profiles and academic achievements in early literacy and early numeracy domains. The findings will enhance our comprehension of the role of WM in acquiring new learning skills and its predictive capacity for success or difficulties across various academic domains. Moreover, the study advocates for the implementation of early intervention programs to support children with WM challenges, thereby mitigating potential difficulties upon entry into formal education.

Theoretical Background

Working Memory

The majority of research on the cognitive processes underlying arithmetic and language cognition has been significantly influenced by Baddeley and Hitch’s WM model, initially proposed in 1974 and subsequently refined (Baddeley, 2000; Baddeley & Hitch, 1974). This model conceptualizes WM as a multifaceted system comprising two domain-specific short-term memory (STM) stores: the PL and the visuospatial sketchpad, which are specialized for the temporary retention of verbal and visual-spatial information, respectively. Additionally, it includes the central executive (CE), responsible for enabling flexible allocation of cognitive resources to meet changing demands, particularly when performing concurrent tasks.

Individual differences in WM capacity exert a profound influence on children’s ability to acquire knowledge and develop new skills (Cowan & Alloway, 2008) and are intricately linked to academic and cognitive performance (Alloway & Alloway, 2010; Peng et al., 2016). This research seeks to investigate how varying levels of proficiency in the three WM components impact early literacy and early numeracy knowledge among preschool-aged children.

It has been found by several studies that working memory interventions, especially which are based on everyday contexts have the potential to improve children’s WM capacity and even have an effect on real-world skills such as attention, language and academic attainment (Rowe et al., 2019). Furthermore, in a meta-analysis conducted by Peijnenborgh et al, (2016) found that WM training improved short-term verbal WM, visuo-spatial WM, and word decoding (effect sizes ranged between 0.36 and 0.63), of children with learning disabilities when compared to the untrained control group. Therefore, it can be assumed that WM can be improved by training when identified to be low among children, to reduce academic difficulties in the future.

Early Numeracy Abilities

Early numeracy encompasses the fundamental mathematical knowledge acquired during early childhood, which serves as the bedrock upon which more complex mathematical skills are built (Baroody & Benson, 2001; Jordan et al., 2007). These skills encompass mastery of the conventional counting system, logical reasoning, and an understanding of the significance of arithmetic operations (Krajewski & Schneider, 2009). Numerous studies have established a strong predictive link between early numeracy proficiency and subsequent success in formal elementary school mathematics (Jordan et al., 2007; Van Der Heyden, 2010).

One prominent theoretical framework for understanding the development of mathematical knowledge is the Triple Code Model (Dehaene & Cohen, 1995). This model posits that numerical processing involves three distinct mental representations: two symbolic forms, wherein numbers are represented as words (e.g., “three”) and Arabic numerals (e.g., “3”), and a non-symbolic analogue system that represents numbers as magnitudes or quantities. According to this developmental hypothesis, children are initially equipped with a system for processing nonsymbolic quantity information (the “analog code”). Exposure to language and mathematical education leads to the acquisition of number words (called the “verbal code”) and number symbols (called the “visual code”), which are eventually mapped onto their corresponding quantities. This mapping process imbues number symbols with meaning, thereby facilitating their use in various mathematical tasks (Dehaene & Cohen, 1995).

Early Literacy Abilities

Early literacy refers to the knowledge of spoken and written language and the interplay between them throughout a child’s developmental journey from infancy (Purpura et al., 2011; Whitehurst & Lonigan, 1998). Early literacy encompasses several components across three major domains: spoken language, phonological awareness, and the visual recognition of printed words (Purpura et al., 2011). Spoken language includes language skills such as vocabulary, grammar, conversation skills, and the ability to clearly and coherently articulate various types of text. Phonological awareness involves recognizing the sound structure of words and encompasses tasks such as sound matching, blending, and segmenting. Print knowledge encompasses familiarity with the alphabet, recognition of letter shapes and names, and understanding print concepts, which involves orienting oneself in books and written texts (Purpura & Ganley, 2014).

Extensive research literature consistently supports the correlation between children’s mastery of early language skills during preschool years and their subsequent success in learning to read and write during elementary school, across various languages (Korat et al., 2003; Catts & Hogan, 2003; Pears et al., 2016; Shamir et al., 2012; Shatil et al., 2000). Thus, children who commence formal education without a foundation in basic early literacy skills may face challenges in bridging this gap (Pears et al., 2016). Early numeracy and early literacy serve as the building blocks for academic development in school; thus, comprehending their developmental underpinnings is of paramount importance.

The Contribution of Working Memory and its Components to Early Numeracy

The role of working memory (WM) in the context of early numeracy skills in preschool-aged children has been extensively investigated, with research consistently demonstrating that preschoolers’ WM abilities predict their mathematical achievement several years later in school (Bull et al., 2008; Friso-van den Bos et al., 2014; Geary, 2011; Raghubar et al., 2010). These studies have revealed a strong correlation between WM abilities and the quality of performance in early numeracy tasks. Specifically, WM has been associated with simple calculations, a relationship attributed to the cognitive resources required by young children when acquiring new mathematical skills and concepts (Passolunghi et al., 2015; Peng & Fuchs, 2016; Peng et al., 2016). However, research that examines the contributions of different WM components to early numeracy skills has not yielded a consensus.

Certain studies have found that the PL plays a role in counting and enumeration tasks (Geary et al., 2008; Jordan et al., 2010). Its effects have also been observed in data acquisition strategies and the retrieval of numeric facts from long-term memory (Foster et al., 2015) as well as its involvement in mental calculation activities (Holmes et al., 2008). The PL has been linked to automatization and direct extraction strategies for adding and subtracting small numbers and quantities (Martin et al., 2014). Additionally, it has been identified as a significant contributing factor in solving word problems among six-year-olds (Foster et al., 2015), albeit not the sole factor.

The central executive collaborates with the PL during complex tasks that necessitate coordination across various stages, such as translating verbal terms and problems into a language code, extracting phonologically stored solutions from long-term memory, and employing counting-based strategies for performing calculations (Martin et al., 2014). Nonetheless, the contribution of the central executive to early mathematical skills remains a subject of debate. A few studies have found that it contributes to the mathematical performance of kindergarten-aged children across various skills aligned with the appropriate curriculum for their age group (Holmes et al., 2008; Meyer et al., 2010). Conversely, Purpura and Ganley (2014) argue that, in less complex skills, WM does not serve as a predictive factor. They contend that WM is involved in early numeracy skills that require a series of steps or data storage (e.g., calculations and number sequences) but not in basic components such as verbal counting and one-to-one correspondence of numbers.

Further, the role of the visuospatial sketchpad in early numeracy skills is subject to variability in research findings. It has been identified as crucial for representing numbers on the mental number axis (Geary et al., 2008; Meyer et al., 2010), as spatial-numeric information regarding the location of numeric symbols is essential for precise execution of simple counting and enumeration tasks. Young children also employ visuospatial strategies when performing mental calculations (Kroesbergen et al., 2014). Moreover, the visuospatial sketchpad has been associated with children's performance in non-verbal mathematical problems (Krajewski & Schneider, 2009; LeFevre et al., 2010), with researchers suggesting that young children utilize non-verbal models in problem-solving processes.

While a conclusive consensus regarding the precise influence of memory components on early mathematical skills remains elusive, it is evident that lower performance levels in working memory (WM) tasks are closely associated with difficulties in acquiring early numeracy skills. WM appears to play a crucial role in the development of counting abilities, as children with poor WM often resort to basic finger-counting strategies, which impose relatively low demands on WM resources (Geary et al., 2004). Insufficient WM capacity hampers the acquisition of fundamental number facts (Geary et al., 2004) and computational skills (Wilson & Swanson, 2001). Moreover, it poses challenges in solving mathematical problems expressed in everyday language (Swanson & Sachse-Lee, 2001).

In a comprehensive investigation conducted by Gathercole and Alloway (2008), the academic profiles of a sizable cohort of children with low WM capacity were examined. This study identified over 300 children aged 5 and 6 as well as 9 and 10 who scored in the lowest decile on WM tasks. Among these children, a substantial proportion faced difficulties in both reading and mathematics, with 75% of the 5- and 6-year olds and 83% of the 9- and 10-year olds experiencing challenges in both domains. An additional 5% of the 5- and 6-year olds displayed struggles specifically in mathematics.

These findings emphasize the pivotal role of WM in early mathematical development and its broader implications for academic achievement. While questions persist regarding the precise contributions of different WM components to early numeracy skills, it is evident that addressing WM capacity in young learners is of paramount importance for fostering mathematical proficiency and academic success.

The Contribution of Working Memory and its Components to Early Literacy

Numerous studies and theoretical models have explored the development of working memory (WM) and its link to individual differences in language and reading abilities. While consensus exists among researchers regarding the importance of WM in the development of language, reading, and writing skills (Gathercole et al., 2016; Purpura et al., 2017; Schuchardt, Maehler, & Hesselhorn, 2008), there is no unanimous agreement regarding the specific contributions of various WM components to these skills. A few studies report connections between each memory component and reading skills, while others highlight only a single component. The discrepancies in findings may stem from differences in task designs, evaluations of memory components, or variations in study samples, all of which can influence WM functions (Schuchardt et al., 2008).

In the realm of early literacy skills, several studies have established correlations between phonological WM and phonological awareness as well as reading abilities (Gathercole & Baddeley, 1995). Verbal WM has been identified as a key determinant in both typically developing children and those with reading disabilities (Gathercole et al., 2006; Peng et al., 2016). It has also been proposed that verbal WM exerts an influence on metalinguistic abilities, including phonological awareness, and contributes to the long-term acquisition of letter-sound rules crucial for phonological processing—a prerequisite for developing reading and writing skills (Alloway & Gathercole, 2004).

The function of the PL has been deemed pivotal in the acquisition of reading skills among children (Gathercole et al., 2006; Moll et al., 2016; Peng et al., 2016) and found to be significantly associated with reading and vocabulary development during early childhood (e.g., Swanson & Jerman, 2007). In contrast, the role of the visuospatial component in reading skills remains a subject of debate, with certain studies suggesting that it has no effect (Kibby et al., 2004; Schuchardt et al., 2008) and others indicating deficits in this component among individuals with reading disabilities, including both adults and children (Gathercole et al., 2006; Menghini et al., 2011). A few researchers have proposed that visuospatial WM may compensate for limited language storage and processing capacity, thereby enabling individuals to utilize imaginative or various visuospatial representations to overcome difficulties (Pickering & Gathercole, 2004).

While numerous studies have emphasized the importance of phonological processing in language and reading, the central executive component of WM has received comparatively less attention; thus, its role remains contentious. The link between the central executive and reading skills is not entirely clear. A few researchers argue that the quality of central executive performance distinguishes typical readers from those with reading disabilities (Gathercole et al., 2006; Schuchardt et al., 2008; Smith-Spark et al., 2007). Nevertheless, it is worth noting that the central executive processes and manages information that originates from the PL, thereby implying that deficits in the central executive or an interplay between the central executive and PL functions may impact language skills (Pickering & Gathercole, 2004).

A study that examined the relationship between memory abilities and early language literacy in children aged 3.5 to 5 years found a connection between verbal auditory WM and phonological awareness. However, no such connection was observed with print knowledge and vocabulary. Researchers have posited that these skills do not necessitate complex execution and, thus, they do not heavily involve WM. Purpura et al., (2017) suggested that only more complex aspects of language skills can be attributed to WM. Additionally, a study conducted by Gathercole et al. (2003), which examined verbal WM skills in children entering the educational system (aged 4–5 years), revealed a strong correlation between these skills and their subsequent academic achievements at age 7, thereby emphasizing the enduring impact of WM on scholastic development.

The Current Study

As elucidated in the preceding literature review, memory deficiencies related to storing and processing information during the execution of complex tasks can significantly contribute to difficulties in acquiring the skills and knowledge essential for success in various academic domains during the early school years. Consequently, children with limited WM capacity are at an increased risk of underachieving during their initial years of formal education. Although it has been shown that WM has to remain relatively stable over time, it is plausible that the cumulative impact of low WM capacity may disrupt learning processes as children progress through various developmental phases.

Building upon the findings highlighted in the literature review, it becomes evident that memory capacity plays a crucial role in the early identification of children at risk for various types of learning disabilities. Nevertheless, due to the inconsistencies in previous research findings, it is imperative to investigate which specific early language and mathematical abilities are linked to the performance of distinct WM mechanisms, particularly at an early age—prior to formal schooling and the potential onset of learning difficulties.

The primary objective of this study is to explore how heterogeneous abilities that are part of each of the memory components—including simple visual-spatial WM, simple verbal auditory WM, and complex WM—influence various aspects of early literacy and early numeracy skills in kindergarten-aged children. Individual variations in WM capacities and profiles can significantly impact the learning experiences of children. Therefore, this investigation aims to provide insights into these individual differences, ultimately facilitating the development of personalized learning approaches that consider learners’ WM strengths and weaknesses, thereby enabling the provision of tailored support and instruction.

Given the strong correlation observed between measures of simple and complex WM in children (Alloway et al., 2006; Gathercole et al., 2016), it is anticipated that both simple and complex WM measures exhibit associations with performance in linguistic and mathematical domains. The study hypothesizes that diverse WM profiles emerge among kindergarteners, thereby reflecting varying levels of performance across memory components. Specifically, children who demonstrate high performance in all memory components are expected to exhibit high achievement levels in both early literacy and early numeracy tasks. Conversely, those displaying low performance across all memory components are likely to manifest lower levels of proficiency in both knowledge domains.

Furthermore, in line with previous research (e.g., Caviola, et al., 2020; De Vita et al., 2021; Holmes & Adams, 2006), it is hypothesized that the involvement of the visuospatial WM domain is more pronounced than that of the verbal auditory WM domain in early numeracy skills among preschoolers; conversely, in early literacy, the involvement of these memory domains exhibit the opposite pattern.

In sum, this study endeavors to shed light on the intricate interplay between WM and early literacy and numeracy skills in kindergarten-aged children, thereby providing valuable insights into the potential role of distinct WM components in shaping early academic development. Thus, the findings may inform early intervention strategies and personalized educational approaches to support children’s learning needs based on their WM profiles.

Method

Participants

The study included 250 children aged 5 to 7 years (M = 5.78 years, SD = 0.36), with 50.8% boys and 49.2% girls. All participants were typically developing Hebrew-speaking children with no known developmental disorders. They came from diverse socioeconomic backgrounds and attended 30 different kindergartens in the northern region of Israel. Written informed consent was obtained from the parents or guardians of all participants, and the children provided verbal agreement before participation. Additionally, the study received approval from the Ministry of Education and the ethics committee of the university.

Measures

Early Numeracy

Sixteen mathematics tasks were employed to evaluate various numeracy constructs related to early mathematical knowledge, encompassing different aspects of numeracy development, as previously outlined. In all tasks, children received one point for each correct response. The task sequence was randomized. All tasks were based on tasks used by Purpura et al. (2017).

Verbal Counting (Forward or Backward)

Children were instructed to count forward from 6 to 20, with the task halting after one error. Similarly, they were asked to count backward from 20 to 0. Each correctly pronounced number word received one point, with separate scores calculated for each subtest (maximum = 14 or 20). Those who counted correctly from 6 to 20 also received a full score for the series from 1 to 20.

Verbal Counting—Skips of two numbers

Children continued a counting sequence (skipping two numbers) initiated by the examiner, until they reached 20. The task stopped after one error, with one point awarded for each correctly pronounced number word (maximum total score = 10).

One-to-One Counting

Children were presented with four sets of game discs (3, 6, 11, and 14) and instructed to count them. One point was granted for each correct count, thereby resulting in a total of four items (α = 0.51).

Cardinality and Conservation Ability

In the context of the one-to-one counting task, children placed the abovementioned discs into a transparent glass and indicated how many they had counted without re-counting the set. This section comprised of two items (α = 0.54).

Composition—Disassembly of a Group into Parts

Children were given a set of game discs (6, 9) and asked to separate the quantity into two groups in two different ways (α = 0.54). One point was awarded for each correctly arranged set.

Subitizing

Children briefly viewed a few sets of dots (ranging from two to five) arranged linearly and were tasked with stating the number in each group (α = 0.43).

Ordinality

Children were presented with a line of game discs and asked to identify “last,” “first,” “before last,” and the tenth disc. This section consisted of six items (α = 0.51).

Symbolic and Non-Symbolic Magnitude Comparison

Based on the numeracy screener test (Nosworthy et al., 2013), children were required to symbolically identify the larger number in single-digit numerical pairs and non-symbolically identify the larger magnitude of two arrays of dots. Each subtest assessed the total number of correct answers within a one-minute time limit, with high test–retest reliability (symbolic comparison = 0.96; non-symbolic comparison = 0.94).

Numeral Identification

Children were presented with a card containing five numbers (3, 6, 4, 9, and 5) and had to point to the number they heard when the examiner stated a number. The numbers were presented randomly (α = 0.77).

Number Naming

Children verbally named 13 numbers ranging from 0 to 12, presented in random order (α = 0.89).

Number to Quantity Matching

Children matched the number of objects in a picture to the correct number, ranging from 1 to 4, printed on a card. This section included five items (α = 0.56).

Number Order

Children arranged cards numbered from 0 to 10 in ascending order. One point was awarded for each correctly placed number, with the overall score being the total of all points earned.

Formal Addition

This task involved simple single-digit addition sums (e.g., 1 + 1, 3 + 2) with a maximum sum of 5. Children were presented with the sum orally and were asked, “How much is…?” Five items were included (α = 0.79).

Formal Subtraction

Similar to formal addition, this task featured simple single-digit subtraction sums where the sum of parts did not exceed five. Children were presented with the sum orally and asked, “How much is…?” This section included five items (α = 0.95).

Verbal Story Problems

Children were presented with five basic addition (α = 0.57) and five subtraction (α = 0.64) problems that were read aloud. They were required to verbally provide the answers.

Early Literacy

Word Recognition

Adapted from a Dutch test (Van der Kooy-Hofland et al., 2012), this Hebrew version assessed word recognition. The examiner presented a list of four real words, including a target word and three distractors differing in terms of one, two, or all letters from the target word. Children identified the target word spoken by the examiner. The test comprised 12 items, with each being scored from 0 to 3 points (α = 0.77).

Letter Naming

Children were asked to name 10 Hebrew letters presented individually on A4 paper. The total number of correctly named letters was calculated (α = 0.87).

Letter Identification

This test consisted of 10 items where children had to identify a target letter from four presented letters. The total number of correctly identified letters was calculated (α = 0.82).

Phonological Awareness

Three phonological awareness tasks were administered, including two initial consonant isolation tasks in CVC (α = 0.81) and CCVC syllables (α = 0.84) as well as a final phoneme isolation in CVC syllables task (α = 0.89). The words in each task were presented orally, and children vocalized the initial or final consonant syllable. Testing ceased after five sequential errors, and the total number of correct answers were calculated separately for the initial consonant isolation tasks (CVC and CCVC syllables, maximum = 10).

Vocabulary

This task was based on the vocabulary subtest from a language screening test for Hebrew-speaking preschool children. It included 14 color pictures printed separately on A4 paper. Children were asked to name each picture aloud following the examiner’s instruction (e.g., “What is this?” or “What is he doing?”). The score was based on the total number of pictures named correctly (α = 0.75).

Morpho-Syntactic Skills—Nonwords Derivation

This task consisted of 10 orally presented sentences by the examiner, each containing a novel verb that represented a nonsense word in Hebrew. Children were required to complete the sentences by modifying and producing the verb with the correct inflection and derivation based on Hebrew morpho-syntactic structures and rules (α = 0.65).

Noun Plural Production

Children were shown an A4 paper with two colored pictures—one with a singular count noun item and the other with four exemplars of the same item. The examiner said a sentence while pointing to the single count noun item (e.g., “Here is a cherry”). Then, the examiner pointed to the second picture with four cherries and asked, “These are a lot of…?” The total number of correct answers was calculated (maximum = 15, α = 0.74).

Consequential Adjective Production

This test included 10 items presented on an A4 paper, each with two colored pictures. The examiner began by saying a sentence with a target verb (e.g., “They broke the window”) and asked the children to complete the sentence by deriving the consequential adjectives from the verb (e.g., “Now the window is…?” with the expected response being “broken”). Two practice items preceded the test (α = 0.74).

Consequential Verbs Production

This task comprised eight sentences read aloud by the examiner. Children completed each sentence by deriving the consequential verb from a noun (e.g., “What are we doing with the paint?” [Tzeva] with the expected response being “With the paint, we are…?” [Tsovei’em]). The total number of correct answers was calculated (α = 0.74).

Simple Working Memory Skills

Simple Verbal Auditory Memory

Digits Forward (WISC-3R; Wechsler, 1991)

This test assessed short-term auditory memory. Children repeated a series of numbers spoken by the examiner in ascending order of difficulty, beginning with two numbers and increasing if successful. The score was based on the number of correctly remembered digits (α = 0.67).

Word Repetition Test (based on Alloway, Gathercole, & Pickering, 2006)

This task evaluated the ability to repeat a sequence of words in the order presented. It began with a series of two words and expanded if the child succeeded. The score was calculated based on the number of words in the sequence that was correctly remembered by the child (α = 0.61).

Auditory-Visual Memory

Word Order Test (Kaufman & Kaufman, 2004)

This test assessed the integration between auditory and visual memory. Children indicated a sequence of images displaying objects whose names were read aloud to them. The task began with a series of two words and increased if the child succeeded. The score was based on the number of words in the sequence correctly remembered by the child (α = 0.75).

Visuospatial Memory

Spatial Memory—Matrices (Kaufman & Kaufman, 2004)

This test examined short-term visuospatial working memory. Children repeated a sequence of locations of illustrations on a matrix of squares. It began with a series of two stimuli in a nine-square matrix and increased if the child succeeded. The score consisted of the number of items that were correctly remembered (α = 0.86).

Spatial Sequential Memory—Corsi Frog adapted from DEST-2 (Nicolson & Fawcett, 2004)

This task involved a card with seven lily pads arranged randomly and a toy frog. Children were required to observe the frog’s jumps and then copy the sequence. The task difficulty increased from two jumps to seven jumps. The capacity score was calculated based on the longest list length correctly recalled (α = 0.81).

Hand Movement Test (Kaufman & Kaufman, 2004)

This test assessed the ability to repeat a sequence of hand movements. It began with a series of two hand movements and increased if the child succeeded. The score was based on the number of movement sequences correctly remembered (α = 0.86).

Complex WM Skills

Complex Visuospatial WM

Corsi Frog Backward, Adapted from DEST-2 (Nicolson & Fawcett, 2004)

This was similar to the forward test, but children had to copy the frog’s jumps in reverse order (α = 0.81).

Series of Numbers (Bayliss, et al., 2003): This test examined the ability to retain number sequences while naming colors. Children viewed numbers and colored dots and were asked to name the color of the dot while remembering the number sequence. They then repeated the numbers in order (α = 0.63).

Verbal Auditory WM

Children’s Sorting Object Task (CSOT) (based on McInerney, Hrabok, & Kerns, 2005)

The examiner read a list of words to the child, beginning with two words and increasing if the child succeeded. The child was asked to reorder the words in accordance with size. Scores ranged from 0 to 2 for each item (α = 0.79).

Digit Span Backward Test (WISC-III, Wechsler, 1991)

This was similar to the digit forward test, but children repeated the digits in reverse order, from the last number heard to the first one (α = 0.72).

Procedure

Data were collected at a single point of time in the middle of the kindergarten year. Tasks were administered individually in a quiet kindergarten space by a research assistant in two sessions, each of which lasted 20–30 min. Data encompassed linguistic, reading, numeric, and memory abilities, which were administered in random order. The study had received approval from the Israeli Ministry of Education’s chief scientist (approval file #9667) and the Research Ethics Committee of the University of Haifa’s Faculty of Education (approval #043/18). Signed consent forms from parents of participating children were obtained for data collection.

Data Analysis

To test our hypotheses regarding the relationships between working memory (WM) components and early literacy and numeracy, we employed structural equation modeling (SEM). We established a measurement model that involved nine latent variables, with each concept measured by a single indicator. Independent measurement errors were estimated for all indicators.

The nine latent variables (LVs) corresponded to each of the following aspects:

  1. 1.

    Working Memory: This comprised simple verbal auditory WM (VASimple WM), simple visuospatial WM (VISimple WM), and complex WM.

  2. 2.

    Early Literacy: This comprised phonological awareness (PHON), orthographic knowledge (ORTH), and morphological knowledge and vocabulary (MORPH).

  3. 3.

    Early Numeracy: This comprised verbal auditory symbolic math knowledge (VASYMB), non-symbolic math knowledge (NONSYMB), and visuospatial symbolic math knowledge (VISSYMB).

The analysis aimed to investigate the strength of relationships between WM and language LVs and the relationships between WM and math LVs. Model fit was assessed using structural modeling, and independent measurement errors were estimated for each latent variable. The parameters were estimated based on all available data.

Further, model fit was evaluated in two steps: The models were individually fitted to each sample using maximum likelihood estimation (MLE), a method that performs well with missing data.

The models’ fit was evaluated using several goodness-of-fit indices, including Chi-square (χ^2), root mean square error of approximation (RMSEA), normed fit-indices (NFI), and comparative fit indices (CFI). Typically, RMSEA values below 0.07 are considered acceptable, while NFI and CFI values above 0.90 are indicative of a good fit. The χ^2 statistic should also be examined in relation to the degrees of freedom, where values between one and three are considered acceptable. However, the interpretation of the χ^2 statistic can be influenced by sample size.

The information regarding the fit of all the models is presented in Table 1 below.

Table 1 Model Comparisons
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This comprehensive analysis enabled us to explore the relationships between WM components and early literacy and numeracy, while rigorously evaluating the fit of the model to the data.

Results

In accordance with Baddeley’s theoretical framework (2000), the various memory abilities were categorized into three factors: simple verbal auditory WM, visual spatial WM, and complex WM. In order to understand the relationships within and among the different memory components, a Pearson correlation matrix was generated, as presented in Table 2.

Table 2 Correlations among verbal auditory WM and visual spatial WM
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For verbal auditory WM, the intradomain correlations ranged from 0.40 to 0.51, thereby indicating moderate to relatively strong relationships among the different measures within this domain.

In the visual spatial WM domain, the intradomain correlations were somewhat lower, ranging from 0.16 to 0.28, thereby suggesting moderate relationships among the measures in this domain.

Complex WM exhibited robust correlations with most memory components, with values between 0.23 and 0.48, thereby indicating strong associations.

These findings provide insights into the interrelationships among different memory abilities and lay the foundation for further analysis of their impact on early literacy and numeracy skills.

Measurement Models

In order to investigate the connection among the different WM components and early literacy and numeracy skills, three CFA models were implemented. Table 3 below presents the relationships among the different components of WM and early math and language capabilities. The relationship is presented based on calculated structural models.

Table 3 The Relationship Between WM Components and Academic Domains
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The models of relationships between simple and complex WM and early literacy fit the data: χ^2 (180, N = 250) = 368.822, p < 0.001; CFI = 0.91; NFI = 0.91; RMSEA = 0.07 and χ^2 (146, N = 250) = 349.003, p < 0.001; CFI = 0.90; NFI = 0.90; RMSEA = 0.07, respectively. The models of relationships between simple and complex WM and early numeracy fit the data, \({\chi }^{2}\) (158, N = 250) = 246.935, p < 0.001; CFI = 0.95; NFI = 0.95; RMSEA = 0.05. and \({\chi }^{2}\) (127, N = 250) = 237.620, p < 0.001; CFI = 0.93; NFI = 0.93; RMSEA = 0.06., respectively.

Group Division

To examine the differences in academic performance among children with diverse memory abilities, they were divided into three groups according to their performance in each cluster of the memory tests. Children who performed in the lowest 25% were defined as the low group (the number of children in this group ranged between 54 and 71), children between the 25th and 75th percentiles were the average (middle) group (the number of children in this group ranged between 98 and 124), and those above the 75th percentile were the high group (the number of children in this group ranged between 81 and 90). This cut of point has been used in previous studies as the cut-off point of children with difficulties (e.g., Barnes et al, 2020; Willcutt et al., 2019). In order to examine the differences in performance of the different memory profiles groups an analysis of variance (ANOVA) was performed on each memory component separately for early academic skills as well as post-hoc LSD comparison to understand the differences among the different profiles. The effect size was measured using the Eta square analysis. The results are presented in the following tables and figures.

Simple Visual-Spatial WM

Table 4 presents the means of early numeracy and early literacy variables for the three profiles of simple visual-spatial WM. Figure 1 displays a graphical representation of this.

Table 4 Descriptive Statistics and Simple Visual Spatial Subgroup Comparisons with One-Way ANOVA Analyses of Variance and LSD Post-Hoc Tests
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Fig. 1
figure 1

Memory Profiles of Simple Visual Spatial WM Subgroups on Early Numeracy and Early Literacy Variables

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The results reveal that children in Profile 1 (low) exhibited the lowest levels of academic performance, while those in Profile 3 (high) exhibited the highest. The group of children with moderate memory levels (Profile 2, middle) achieved moderate academic achievement and were similar in their performance to the low group in all the early literacy abilities. All effect sizes of this analysis were medium and ranged between 0.02 and 0.09. It is important to note that there was no main effect for morphological processing among the three groups.

Simple Verbal-Auditory WM

Table 5 presents the means of early numeracy and early literacy variables for the three profiles of simple verbal auditory WM. Figure 2 displays a graphical representation of this.

Table 5 Descriptive Statistics and Simple Verbal Auditory WM Subgroup Comparisons with One-Way ANOVA Analyses of Variance and LSD Post-Hoc Tests
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Memory Profiles of Simple Verbal Auditory WM Subgroups on Early Numeracy and Early Literacy Variables

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A similar pattern was found for simple verbal-auditory knowledge with the level of memory ability correlating with the level of achievement, as indicated in the table. All effect sizes of this analysis were large and ranged between 0.11 and 0.27.

Complex WM

A similar pattern was found for the simple verbal-auditory knowledge with the level of memory ability correlating with the level of achievement, as indicated in Table 5. Significant differences were found among the different profiles in all the early academic abilities. All effect sizes of this analysis were large and ranged between 0.11 and 0.27. There was no significant difference among the low and middle groups only in the orthographic processing.

Complex WM

Table 6 presents the means of early numeracy and early literacy variables for the three complex WM profiles. Figure 3 depicts a graphical representation of this.

Table 6 Descriptive Statistics and Complex WM Subgroup Comparisons with One-Way ANOVA Analyses of Variance and LSD Post-Hoc Tests
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Fig. 3
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Memory Profiles of Complex WM Subgroups on Early Numeracy and Early Literacy Variables

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The results reveal that children in Profile 1 (low) exhibited the lowest levels of academic performance. The children in Profile 3 (high) exhibited the highest levels of achievement. The group of children with moderate memory levels (Profile 2, middle) exhibited moderate academic achievements. A significant group effect was found for all math abilities and language abilities. Post hoc tests did not reveal a significant group effect in complex WM between the middle and low groups for phonological awareness. All effect sizes of this analysis was large, ranging between 0.09 and 0.28.

Discussion

Numerous studies have emphasized the pivotal role of WM in the development of both numerical and language skills (see Raghubar et al., 2010 for a comprehensive review). This study aimed to investigate the contributions of different WM systems to various early literacy and numeracy skills. While previous research has explored the impact of specific WM components on skills acquisition, such as reading and mathematics (e.g., Ketelsen et al., 2010; Kyttälä et al., 2019; Meyer et al., 2010; Peng et al., 2016), there is no consensus on the influence of memory components on early literacy and numeracy. Thus, our study sought to classify children into subgroups based on their WM profiles in kindergarten and determine whether these profiles could explain their achievements in early numeracy and early literacy.

Consistent with our hypotheses, our findings revealed significant group differences between low and high capacity of simple WM and complex WM in early mathematics and language knowledge among children. Similar results have indicated that all WM components are equally strongly associated with math and language performance (Caviola et al., 2020; Friso-Van Den Bos et al., 2013; Peng et al., 2016).

Simple Verbal Auditory WM

With regard to simple verbal-auditory WM, it is commonly believed that the PL plays a limited role in math learning during preschool years (Caviola et al., 2020; Kolkman et al., 2014; Mammarella et al., 2018). However, contrary to our initial assumptions, our study revealed significant differences among subgroups defined by simple verbal-auditory WM (VASimple WM) abilities across all domains of early numeracy. Children with high VASimple WM profiles demonstrated superior achievements in verbal auditory symbolic math knowledge, visual spatial symbolic math knowledge, and non-symbolic math knowledge compared to those with average or low VASimple WM profiles. Moreover, children with average VASimple WM profiles outperformed those with low VASimple WM profiles in early numeracy.

These differences among the VASimple WM profiles of children align with the results of previous studies. Measures of the PL have been shown to correlate with number sense performance (Jordan et al., 2010), counting and addition skills (Noël, 2009), and basic fact retrieval (Holmes & Adams, 2006). Moreover, children with verbal memory impairment struggle more with counting skills compared to typically achieving children (Toll & van Luit, 2013). These findings support our conclusion that VASimple WM is instrumental in acquiring verbal-auditory symbolic math knowledge among kindergartners. The influence of VASimple WM on visual-spatial symbolic math knowledge and non-symbolic math knowledge may be attributed to the oral (verbal) instructions and responses involved in these tasks. Furthermore, kindergarten curricula place a significant emphasis on academic tools and skills development based on verbal auditory memory, potentially impacting children’s performance in this area (Aram & Ziv, 2018).

In the context of early literacy, our study revealed significant differences among subgroups defined by VASimple WM abilities across all domains of early literacy. Children with high VASimple WM profiles excelled in phonological awareness, orthographic knowledge, morphological knowledge, and vocabulary compared to those with low VASimple WM profiles. Additionally, children with average VASimple WM profiles outperformed those with low VASimple WM profiles in phonological awareness, morphological knowledge, and vocabulary. Notably, there were no differences in orthographic knowledge between children with low and average VASimple WM profiles, thereby suggesting that a low or average profile indicates lower achievements, while a high profile signifies higher skills.

Previous research has highlighted the role of phonological memory in various phonological processing skills and vocabulary acquisition (Engel de Abreu et al., 2011; Fancourt & Holmes, 2020). Additionally, phonological memory has been moderately correlated with phonological awareness in young children (Alloway et al., 2005). These findings support our conclusion that VASimple WM plays a crucial role in phonological awareness, morphological knowledge, and vocabulary acquisition. While the precise function of VASimple WM in the acquisition of orthographic skills remains unclear, it is evident that phonological WM is closely related to reading skills (Gathercole & Baddeley, 1995). Nevertheless, there is an ongoing debate regarding whether phonological WM causally influences literacy development or simply provides access to representations underlying phonological awareness tasks, as is the case with reading skills (Melby-Lervåg et al., 2012).

In summary, our study emphasizes the significant impact of working memory, particularly VASimple WM, on early literacy and numeracy skills in kindergarten. These findings contribute to our understanding of the complex interplay between working memory and cognitive development in young children, highlighting the importance of considering memory profiles in educational interventions and curriculum design.

Simple Visual Spatial Working

In the existing body of research regarding the role of simple visual-spatial WM (VISimple WM) in the acquisition of mathematical skills among preschool children, several studies (Caviola et al., 2020; Fung & Swanson, 2017; Mammarella et al., 2018; Raghubar et al., 2010) have consistently demonstrated significant differences among subgroups categorized by VISimple WM abilities across all domains of early numeracy. Specifically, children with high VISimple WM profiles displayed superior achievements in verbal auditory symbolic math knowledge, visual-spatial symbolic math knowledge, and non-symbolic math knowledge in comparison to those with average or low VISimple WM profiles. Furthermore, children with average VISimple WM profiles outperformed those with low VISimple WM profiles in all aspects of early numeracy.

Supporting our findings regarding the involvement of VISimple WM in visual-spatial symbolic math knowledge and non-symbolic math knowledge, prior research has highlighted the role of visuospatial short-term memory in early childhood numerical performance (Bull et al., 2008; McKenzie et al., 2003) and initial math abilities during early primary school years (Gathercole & Pickering, 2000). This suggests that the visual-spatial sketchpad is instrumental in processing visual and spatial information, including mathematical symbols, equations, physical shapes, color, and movement (Gathercole & Pickering, 2000; Bisanz et al., 2005). Fanari et al. (2019) have also emphasized the significance of the link between numbers and space in the development of numerical cognition, thereby highlighting the role of spatial active WM in forming early spatial numerical representations. Additionally, Toll & Van Luit, (2013) found that limitations in visual WM correlated with poorer performance in visual code tasks. Moreover, several studies have established the correlation between spatial skills and visuospatial WM and young children’s early counting ability and general mathematical competence (Passolunghi & Mammarella, 2012). The visuospatial sketchpad has been identified as particularly important for the development of mental arithmetic in young children, particularly under the age of seven, as it influences their utilization of the mental number line and reliance on visuospatial encoding (McKenzie et al., 2003).

Our findings align with the suggestion by Holmes et al. (2008) that primary school children initially employ spatial strategies to solve math problems, with spatial passive WM functioning as a workspace that facilitates the transition from early concrete informal knowledge to nascent formal mathematical knowledge.

In the realm of early literacy, significant differences were also observed among subgroups defined by VISimple WM abilities across most domains. Preschoolers with high VISimple WM profiles exhibited higher levels of achievement in phonological awareness and orthographic knowledge compared to those with low VISimple WM profiles. Moreover, substantial differences were noted between children with average and high VISimple WM profiles across all early literacy domains. Our analysis indicates that there is a dichotomy in the context of language skills: low VISimple WM profiles (which include the low and middle profiles) correspond to low language achievements; conversely, high VISimple WM profiles correlate with high language skills. Furthermore, no significant differences were found between the middle and low groups. These results could lead to the conclusion that only high VISimple WM leads to better performance in the linguistic domain and that children from the middle profile do not have the same advantage.

Although research on the relationship between VISimple WM and language skill development is limited, there is some evidence that supports our findings. VISimple WM has been linked to children’s performance in reading and writing domains during the early stages of formal schooling (Bourke, et al., 2013). This subtype of memory appears to influence specific abilities, such as decoding visual stimuli like letters or symbols and their application in various contexts (Woodrome & Johnson, 2009).

Further, contrary to our initial hypothesis, VISimple WM was found to be associated with phonological awareness, morphological knowledge, and vocabulary. Our results align with Baddeley’s (Baddeley & Hitch, 1974; Baddeley, 2000) multicomponent WM model and support prior research that indicates a distinction between verbal and visuospatial short-term storage in children as young as five years old (Alloway et al., 2006). The present study emphasizes the differential effects of the two components of simple WM on the academic achievements of kindergarteners, thereby suggesting that distinct tasks may tap into various cognitive resources. This observation is in line with Alloway et al. (2006), who posited that the two systems are separate and that performance in verbal WM tasks does not predict spatial abilities, nor are spatial WM measures highly associated with verbal skills. Consequently, it is prudent to consider that the resource requirements may vary depending on the task and the instructions provided. Further research is required to confirm this hypothesis.

Complex Working Memory

In our study, we considered the complex WM system as a unified system, thereby acknowledging the suggestion that the verbal and visuospatial subsystems of WM are not distinctly separate in young children. Instead, the central executive is believed to play a pivotal role by supervising and coordinating both visual and verbal information as well as bridging the connection between WM and long-term memory (Alloway et al., 2005). Therefore, we focused on examining complex WM as a holistic system.

In our specific examination of differences between subgroups defined by complex WM, we found significant variations across all domains of early numeracy. Those with high complex WM profiles achieved higher scores than those with low complex WM profiles. This finding is in line with extensive research emphasizing the role of WM in numerical development (Raghubar et al., 2010). Several studies have demonstrated a close relationship between the central executive (CE) abilities of young children (aged 5–7 years) and mathematical performance, including tasks such as global counting (Kroesbergen et al., 2009) and number recognition that involve linear representations of numbers (Geary et al., 2008). Children who struggle with mathematics tend to perform poorly in CE tasks (Passolunghi & Siegel, 2004; Swanson & Jerman, 2006), and weak WM has been associated with difficulties in early numeracy acquisition (Gersten et al., 2005; Toll & Van Luit, 2013), slower learning of counting sequences (Noël, 2009), and lower accuracy in solving simple addition problems (Noël, 2009; Rasmussen & Bisanz, 2005). Mathematical tasks often require children to execute multiple steps to arrive at the correct answer. For example, in a cardinality task, children must not only hold the requested set size in memory but also perform the act of counting items until they reach the specified number—a process that places a considerable demand on WM (Purpura & Ganley, 2014). Noël’s (2009) research further supports our findings, as her study identified CE as the strongest predictor of tasks related to numerical vocabulary and counting, even surpassing the role of the PL.

A similar pattern emerged in the realm of early literacy, where significant differences were observed across most subgroups in all domains. Those with high complex WM profiles achieved higher literacy scores than those with low complex WM profiles. Additionally, children with average complex WM profiles outperformed those with low complex WM profiles in phonological awareness, morphological knowledge, and vocabulary. However, there were no apparent differences in phonological awareness between children with low and average complex WM profiles.

Our findings regarding phonological awareness align with the theoretical framework that suggests that WM plays a critical role in breaking down spoken words into their constituent syllables, onset-rimes, or phonemes as well as in assembling these phonological elements to form words (Peng et al., 2018). The simultaneous processing and storage of these phonological representations, owing to their complexity in various phonological coding tasks, require the involvement of WM (e.g., Oakhill & Kyle, 2000). Moreover, there is evidence that suggests a relationship between WM and vocabulary (e.g., Bowey, 2001). In vocabulary tasks—such as matching a picture to a word or explaining the meaning of a word—WM is used to concurrently process verbal and visual information, activate relevant background knowledge and concepts, and integrate these diverse sources of information (Peng et al., 2018).

Orthographic knowledge involves the processing and manipulation of visual information; consequently, WM is necessary for the simultaneous processing and storage of orthographic representations, particularly when retrieving sounds for sequential displays of symbols and objects. Although our findings align with the notion that the central executive is critical for coordinating and integrating information from text (Baddeley, 2000), we were unable to identify specific research in this area. Thus, further in-depth studies in this domain could yield valuable insights in the future.

In summary, our study emphasizes the crucial role of complex WM in both early numeracy and early literacy. As a supervisory system, the central executive component appears to play a significant role in coordinating cognitive processes across various domains of learning and development in young children. Thus, this research contributes to our understanding of the interplay between complex WM and cognitive abilities, thereby emphasizing the importance of considering the holistic complex WM system in educational contexts.

Conclusion

In this research, we classified preschool children into three subgroups based on their WM profiles in kindergarten, thereby revealing distinct patterns across the three WM components. Children with low WM abilities consistently exhibited the lowest academic performance, while those with high WM skills outperformed the other groups. Effect sizes were notably larger for visual short-term memory compared to auditory and complex memory, thereby highlighting the significant role of memory in early literacy and numeracy skills, although the contribution of simple visual memory appeared somewhat less pronounced.

Our findings align with the notion that children with poor WM functioning are at a heightened risk of educational underachievement (Gathercole & Alloway, 2008). Research has revealed that a substantial percentage of children who achieve below-average scores in English and mathematics tests have WM scores in the deficit range. Moreover, children with general learning difficulties in these subjects are more likely to exhibit poor verbal and visuospatial short-term memory and verbal WM scores (Pickering & Gathercole, 2004). These findings emphasize the importance of identifying and supporting children with WM impairments early on.

Our study also highlighted the significant role of all three WM components in determining children’s memeory profiles. In early literacy, our conclusions are in line with prior research that has demonstrated a relationship between phonological and visual-spatial memory and various literacy-related skills (Welsh et al., 2010; Woodrome & Johnson, 2009). Moreover, our findings support the notion that the central executive, as proposed by Baddeley’s model (2002), plays a substantial role across various tasks in both literacy and numeracy domains. This implies that more complex tasks are likely to be influenced by WM, which is consistent with previous research (Chen & Bailey, 2021; Purpura & Ganley, 2014).

Further, in the field of early numeracy, our findings challenge the notion that the central executive (complex WM in our study) is the sole component that is significantly correlated with early numerical abilities. Our study suggests that simple WM also plays a crucial role in acquiring specific numerical skills. This observation emphasizes the importance of considering both complex and simple WM in understanding early numeracy development. Our findings are consistent with previous research that indicates that VASimple WM and VISimple WM develop differently and influence various aspects of numerical competence (Friso-van den Bos et al., 2014; Gathercole et al., 2016; Kyttälä et al., 2019; Meyer et al., 2010).

Educational Impact and Implications

The identification of distinct WM profiles among preschool children has practical and theoretical significance. The theoretical understanding of memory processes in preschoolers’ mathematics and language performance advances our knowledge of how children learn and enables the identification of and support for at-risk children. It is important that kindergarten teachers will be aware of the important role of WM in order to help and identify children at risk for learning disabilities. Practically, most kindergarten teachers don’t asses working memory abilities, it is important for teachers to be aware that low working memory abilities may lead to lower early literacy and numeracy skills, and children who exhibit these difficulties should undergo a working memory assessment, as well as a linguistic and numeric abilities assessment. Furthermore, children with WM impairments often struggle in classroom activities that place heavy demands on the WM. Hence, educational programs should be designed to compensate for or mitigate WM-related learning difficulties (Davis et al., 2014). Strategies could include modifying curricula to reduce task demands, providing instructional aids, scaffolding, presenting worked examples and gradually eliminating steps, teaching memory strategies, and simplifying instructions. Moreover, combining WM training interventions with activities aimed at enhancing specific skills can be particularly effective, particularly in younger children (Dunlosky et al., 2018; Honoré & Noël, 2017; Kroesbergen et al., 2014; Passolunghi & Costa, 2016; Peng & Fuchs, 2016). Such interventions may help prevent learning difficulties and support the development of cognitive precursors essential for future school learning.

Limitations and Implications for Future Studies

Our study has several limitations that warrant consideration. We primarily focused on typically developing children, while different types of disabilities may present varying cognitive or skill deficit profiles. Future research could explore the relationship between WM and academic performance in children with specific learning disabilities.

Additionally, the tasks in our study were predominantly presented verbally or with pictures of objects, thereby limiting the ability of children to choose their preferred problem-solving method. Future research could investigate children’s preferred mental models when tackling various tasks. Furthermore, due to the large number of tasks performed by each participant, a few measures had relatively low reliability. Future studies could incorporate additional measures to enhance the robustness of the findings.

Further, to expand on our findings, future research could investigate how children’s WM profiles evolve as they progress in academic development and explore whether the contribution of the three WM components varies over time. This could provide valuable insights into the dynamic nature of WM and its relationship with academic skills.

In conclusion, our study sheds light on the significance of WM in early literacy and numeracy skills and emphasizes the importance of considering both complex and simple WM components. The practical implications extend to the development of educational strategies that cater the diverse memory profiles of children, potentially preventing learning difficulties and, thus, facilitating academic success.