Basic number knowledge is an important foundation of children’s performance on future mathematics (Cirino, 2011; Koponen et al., 2013; Krajewski & Schneider, 2009; LeFevre et al., 2010; Träff et al., 2020). Children’s development of basic symbolic number skills has been shown largely dependent upon phonological processing (e.g., Yang et al., 2021; Fuchs et al., 2010; Geary, 2013; LeFevre et al., 2010; von Aster & Shalev, 2007). However, rather few researchers have paid attention to whether basic number knowledge could also contribute to the development of phonological processing. The present study would investigate whether the relationship of phonological processing with basic number knowledge could be bidirectional over time in a longitudinal sample of children, using cross-lagged panel analyses.
Krajewski and Schneider (2009a) proposed the developmental levels of basic number knowledge (see also Krajewski & Schneider, 2009). The model described early development of quantity-number knowledge, and development could be divided into three level. Level 1 is the basic numerical skills. When children reached this stage, they can distinguish at least indiscrete amounts (quantity discrimination). For example, they can compare quantities with the terms of “more”, “less” or “same”. At level 2, children acquire the ability of linking quantities to numbers and the ability of understanding the meaning of number words. They can accurately compare the magnitude of two numbers (e.g. 3 and 8). At level 3, the children understand the decomposition and composition of numbers (e.g. 8 can be decomposed into 3 and 5; 3 and 5 compose 8). Considering the current study focuses on kindergarten children, we only examined the basic number knowledge that belongs to the Level 1 and Level 2: number identification and number comparison, respectively.
Contributions of Phonological Processing to Basic Number Knowledge
Phonological processing refers to the ability to use phonological information to decode linguistic information (Wagner & Torgesen, 1987; Kuzmina et al., 2019). Phonological processing includes three main components: phonological awareness, rapid automatic naming (hereafter, RAN) and phonological memory (Lu, 2003; Wagner & Torgesen, 1987). Phonological awareness is an awareness or understanding of the sound structure of spoken language and the ability to manipulate these sounds (Wagner & Torgesen, 1987; Milwidsky, 2008). It requires the skills of an individual to convert the spoken language into sound units and then recompose it into spoken language. RAN refers to children’s ability to record a visual word onto a sound-based representation by retrieving words which often measured by the speed of labeling common items (Blachman, 1984; Torgesen et al. 1990). Phonological memory emphasizes the short-term maintaining and rehearsing of verbal words and phrases (Cameron et al. 2005).
When solving a math problem, we need select, implement, monitor strategies and store representations in the working memory. Therefore, these phonological processing skills might be very important. When children hear a number, they first have to convert the spoken language into sound units, a step where phonological awareness comes in to play. The RAN functions to facilitate retrieval speed when children retrieve phonological number codes in long term memory (Koponen et al., 2016). Finally, children need to store and rehearse the number information in mind when solving a math problem, in which phonological memory is required.
Indeed, several longitudinal studies suggest that phonological processing should predict later basic number knowledge, such as number counting (Krajewski &Schneider, 2009; Koponen et al., 2016; LeFevre et al, 2010). A recent meta-analysis also revealed significant associations between earlier phonological processing and later basic number abilities (e.g., number identification, number comparison) (Peng et al., 2020). For example, a 3-year longitudinal study on 4.5- to 7.5-year-old children found that the phonological awareness independently contributed to future performance in number identification and number comparison (LeFevre et al, 2010). Koponen et al. (2016) followed 378 Finish children from kindergarten to Grade 3, and indicated that RAN predicted arithmetic fluency. The relationship remained even after controlling phonological awareness, vocabulary, phonological memory, working memory, number concept skill and mother’s education. Our own study tracked Filipino children at mean ages of 4.5, 5.0, and 5.5 years old and found that RAN explained significant variance in the growth rate of early numeracy (Yang et al., 2021). We therefore assume that phonological processing should predict later basic number knowledge.
The Possible Role of Basic Number Knowledge in Phonological Processing
Except for the role of phonological processing in basic number knowledge, there might be a reciprocal linkage between phonological processing and basic number knowledge. There are researchers indicating that mathematics development could contribute to specific math vocabulary knowledge that are stored in a language format (e.g., O’Halloran, 2005). For example, the numbers included phonemes/syllable information (e.g., one, two, three…), and when children learn to count numbers, they will manipulate the syllables. A recent meta-analysis conducted with 344 studies found a moderate relation between language (e.g., phonological awareness and RAN) and mathematics (e.g., basic number knowledge, geometry, calculations). They propose that the foundational mathematics could improve the thinking function of language via advanced mathematics (Peng et al., 2020). Therefore, higher performance in basic number knowledge might also promote children’s thinking function of phonological processing, and we deduced that higher performance in basic number knowledge could promote the development of phonological processing.
Altogether, the influence of early phonological processing on later basic number knowledge has been largely established, but the effect of early basic number knowledge on later phonological processing has been mainly discussed at the theoretical level, lacking verification by empirical studies. Thus, the purpose of the present study was to investigate, in a longitudinal sample of Chinese children, whether the basic number knowledge, in addition to being influenced by phonological processing subskills, could also predict the development of phonological processing. The present study would conduct cross-lagged longitudinal path models to establish the direction of the interaction between phonological processing (phonological awareness, RAN, phonological memory) and basic number knowledge (number identification, number comparison).