Keywords

Introduction

Through the toddler period (from 1 to 3 years of age), children develop many central mathematical skills (Reikerås et al., 2012; Reikerås, 2016). At the same period, they have an extensive development of their language (Slot et al., 2020). Although relations between development in mathematics and language were noted several decades ago (e.g., Durkin & Shire, 1991), there is still a lack of research on the topic, especially regarding children as young as toddlers. The present study aims to examine how the relations are between toddlers’ skills in mathematics and language. This includes the relations between different parts of mathematics and language, as well as the relations between mathematics and different aspects of language. It will also be explored how the relations between mathematical skills and language skills are for children with different levels of mathematical skills.

Mathematics and Language

In early childhood and care institutions (ECECs), toddlers are surrounded by staff and children who use language to explain sizes, shapes, numbers, relations, directions, quantities, etc. Such social use of language forms an interactive and linguistic context that is important for children’s learning of mathematics (Björklund, 2008; Durkin et al., 1986).

Toddlers express their mathematics mainly through action since they are not fully able to express themselves verbally (Björklund, 2007). They show that they have an understanding of mathematical content related to, e.g., size, shapes and numbers before they start to use language to express their understanding in the later part of the toddler period (Reikerås et al., 2012; Solem & Reikerås, 2017). Language comprehension is found to be the best predictor for variations in number tasks in 7–9-year-olds (Cowan et al., 2005), and Bower et al. (2020) found spatial language comprehension in three-year-olds to be strongly associated with mathematical skills. The importance of children’s expressive language skills for mathematical development was investigated in a study of 3–5-year-olds by Purpura et al. (2011) and in a study of 5–6-year-olds by Praet et al. (2013). Both studies found that vocabulary and other expressive language skills were central factors in explaining the variance in mathematical skills; therefore, these language skills are crucial for mathematical development.

The largest challenge when studying the relation between the development of mathematical skills and language skills is related to how mathematics is defined and whether mathematical language is seen as a part of mathematical skills or not. Mathematical language is classified in some taxonomies in the problem-solving area together with logical reasoning (Magne et al., 2019), even though this language develops through interaction with the acquisition of skills in most other mathematical areas. Verbal counting is, for instance, central in quantitative development (Mix et al., 2002), and relational language is found to be a powerful contribution to spatial learning (Gentner, 2008). In the same way, quantitative development affects geometrical development and not only arithmetical development (Mix et al., 2002). Geometrical development also supports the learning of numbers and later arithmetic (Arcavi, 2003). However, some researchers find language skills of lesser importance for mathematical development based on neuroscientific research (e.g., Gelman & Butterworth, 2005).

The differences in the findings may also be due to what kind of language the children’s mathematical skills are compared with. Purpura and Reid (2016) found that although general language performance was initially a significant predictor of numeracy performance, when both mathematical language and general language were included in the model, only mathematical language was a significant predictor of numeracy performance.

In a study by Reikerås and Salomonsen (2019) comparing skills in children with different levels of mathematics, the group of toddlers with weak mathematics had the largest variation of results within the mathematical area of mathematical language. Kleemans et al. (2011), who conducted research on children with language difficulties, found that these difficulties were not restricted to language acquisition but also had serious consequences for the development of key concepts in early numeracy skills. Durkin et al. (2013) showed that the weaker the language skills children have, the more difficult it is to master number skills. However, Arvedson (2002) found that children with language difficulties differ from children with typical development only in verbal numeral skills but not in nonverbal number skills.

The Present Study

Earlier studies about the relations between mathematics and language, as presented above, underline the need for more research, both on the relation between the developmental areas’ mathematics and language for all children and for children with different skill levels. Most earlier studies are based on research with few children, and few of the studies included toddlers. The present study has a large group of toddlers as participants, and the data were collected in social interactions in the ECEC by their teachers. The study aims to answer the research questions

  1. 1.

    How are the relations between mathematical skills and language skills in toddler age?

  2. 2.

    If and in which way does the relationship differ between language and mathematics for children at different skill levels?

Method

The present study is part of The Stavanger Project – The Learning Child following children’s development from 2½ to 10 years of age, and the 1086 participating toddlers (534 girls, 552 boys) were recruited through the project (for a description see Reikerås et al., 2012). The parents gave written consent to let their children participate, and the project was approved by the Norwegian Social Science Data Services.

Data on the toddler’s mathematical skills and language skills were collected by the staff in the ECECs using structured observation of the toddlers in play and everyday situations over a three-month period (from the toddlers being 2 years and 6 months to they turning 2 years and 9 months). This method is based on authentic assessment, a recommended and accepted practice, and a nonintrusive way of assessing children’s skills in ECECs (Bagnato et al., 2014).

The assessment material used for mathematics was MIO - The Mathematics, the Individual and the Environment (Davidsen et al., 2008). The structure in MIO is based on Olof Magnes taxonomy (Magne & Thørn, 1987; Magne et al., 2019), and the research grounds for choosing the included items can be found in the handbook (Davidsen et al., 2008). The MIO scheme consisted of six sections (mathematical areas), each including six items (36 items in total): Mathematical language, Logical reasoning, Shape and space, Pattern and order, Counting and series of numbers and Enumeration. The children’s language skills were assessed using the observation material TRAS - Early registration of language development (Espenakk, 2003). The material consists of a total of 72 items divided into three main language areas Social Language (with the sections Communication, Interaction, and Attention), Language Comprehension (with the sections Language comprehension and Linguistic awareness), and Expressive Language (with the sections Sentence production, Word production, and Pronunciation). These assessment materials were developed for use in Norwegian ECECs. The sections in the materials were selected on a theoretical basis. Both MIO and TRAS had been repeatedly piloted in ECECs, with observation of several hundred children to find items suitable for finding valid measures of math and language skills for the age range 2–5 years in ECECs. The data from the pilot were unable to be validated by comparison with data from other assessment materials because at the time, there was no other assessment material for the age groups available in Norwegian that mapped the same fields. However, the calculation of Cronbach’s alpha showed scores ≥0.90 for both materials, indicating good internal consistency. To ensure the reliability of the materials, 90 children were observed by two different ECEC teachers. The Wilcoxon signed rank test showed good interrater reliability for both TRAS and MIO (for more details, see Espenakk, 2003; Reikerås et al. 2012).

TRAS and MIO are both based on a social cultural approach to learning, as it assesses the children’s functional skills: the skills they show in play and interaction with peers and staff in the ECECs and provides ecologically valid data (Keilty et al., 2009). In addition, both materials included the assessment of skills in the child’s proximal zone, in line with Vygotsky (e.g., Vygotskij & Kozulin, 2001). Several studies have documented the advantages of authentic assessment compared with standardised assessments, and authentic assessment has become a recommended and accepted practice (Bagnato et al., 2014). The staff was trained in scoring, and in addition, detailed descriptions of each item in the registration form and directions for scoring were available to facilitate data collection and increase the reliability of the data collection procedure (Helvig & Løge, 2006; Davidsen et al., 2008). Both MIO and TRAS have three difficulty levels, with level 1 as the easiest and level 3 as the most difficult. An example of an item in MIO: Have started with pointing when saying the number sequence. If the child points and says the number sequence (not necessarily the correct link between numbers and things), the staff should mark with show competence (two points). For example, Karine plays alone in the playroom. She mutters the number sequence as she points to the teddy bears and dolls. “I need to know how many you are for us to have enough food!” she says. If the child has begun to show interest in other people’s pointing when they count, the staff should mark with partial competence (one point). For example, Per is closely monitoring when Jasmine points at the cars and says the number sequence. Not yet showing competence (zero point): If the child does not show interest in the relation between pointing and the number sequence. When summing up for each child, the results were normally distributed.

The first analysis is correlation analysis since such analysis is suitable when describing relations between variables. Next, a graphic presentation between the sum scores in mathematics and language is presented to see if there is a linear relation between these variables. If the graph is not linear, it is necessary to divide the children into skill groups and look at the relation between MIO and TRAS for each group. Dividing into quartiles, four groups with approximately the same size, will in the present study be suitable to maintain a certain group size appropriate for statistical analysis (Tabachnick & Fidell, 2014).

Results

To answer the research question about how the relations between mathematical skills and language skills in toddler age are, correlation analyses were performed between the MIO-total and TRAS-total, as well as analyses between the different MIO-sections and the TRAS-sections.

As seen from Table 1, all sections in MIO and all sections in TRAS correlate, and in line with Cohen (1988), all the effect sizes are large. This indicates that across all mathematical areas included in MIO, the mathematical skills in toddlers are related to their language skills.

Table 1 Relations between mathematical skills and language skills in toddler age
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The relationship between language and mathematics varies for children at different skill levels and was first examined by a graph with the sum score in mathematics on one axis and the sum score of language on the other for all the participants (see Fig. 1).

Fig. 1
A scatter plot of T 1 total T R A S versus T 1 total M I O with a fit line. The points are densely plotted between (20, 50) and (50, 100). A best-fit line is drawn between (0, 0) and (70, 140). The line is labeled R squared linear = 0.603. The values are approximate.

Plot of the participants’ results in mathematics (MIO total) and language (TRAS total)

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The graph indicates a more complex picture than a linear relationship, and to be able to answer the second research question, the toddlers’ results on MIO were divided into quartiles, which give us four groups with approximately the same size (see Table 2).

Table 2 The toddlers result on MIO and TRAS divided into quartiles. N, mean and SD for the quartiles, correlations between TRAS-total and MIO-quarttiles, and the proportion of toddlers in the TRAS-quartiles in the MIO-quartiles
Full size table

When examining the correlations between MIO-total and TRAS total for each quartile group of MIO, all are significant, but smaller than when all children were included as in Table 1, now with medium effect size. One cause for this can be that the variance in the results in the quartiles is much smaller than the variance in the whole sample, as seen in the SDs in the table. The children with the lowest mathematical scores (MIO quartile 1) had language scores mostly in TRAS quartile 1 (58.5%) and TRAS-quartile 2 (32.9%). Only 8.6% of toddlers with results in MIO quartile 1 had language scores in one of the TRAS-quartiles 3 and 4. For children with mathematical scores within quartiles 2 and 3, only approximately 50% of the children were in the corresponding language quartile (51.0% and 48.0%, respectively), whereas most of the rest were in their neighbouring quartiles. Of the toddlers with scores in MIO quartile 2, 21.5% had TRAS scores within TRAS quartile 1 and 24.1% in TRAS quartile 3. For MIO quartile 3, the children’s TRAS scores within TRAS quartiles 2 and 4 were 22.3% and 23.8%, respectively. For the children with mathematical scores in the highest quartile, 71.0% also had language scores within the highest language quartile (TRAS-quartile 4), and 21.9% had language scores within TRAS-quartile 3. Only 2 of the children within MIO quartile 4 (under 1%) are in TRAS quartile 1.

Discussion

The present study found strong correlations between toddlers’ different math skills and the aspects of language skills all over when the whole group results were analysed together. The nuances are very small between the size of the correlation coefficients, which makes a meaningful discussion of which is larger than another difficult. However, it may be slightly surprising that the correlations between the section Mathematical language and the three language sections in TRAS do not stand out to a particular extent, although the relation to Language comprehension and Expressive language are among the largest correlations. Another thing worth noting is that the lowest correlations were between the language sections and two mathematical areas related to the numbers Counting and series of numbers and Enumeration. However, the correlations are still due to Cohen (1988) being large.

The findings of these strong relationships between the different kinds of mathematical skills and types of language skills in toddlers are in line with research presented earlier in the paper that supports the close relations between development in mathematics and language for older children (e.g., Cowan et al., 2005; Purpura et al., 2011; Praet et al., 2013).

From the correlation in Table 1, it may be considered that the strong connections between the toddler’s mathematical skills and language skills should give a relatively linear graphic presentation with the sum score in mathematics on one axis and the sum score of language on the other for all the participants. As shown in Fig. 1, this is the case for many of the children. However, the figure shows a messier picture. There are children with high MIO results and much lower language than expected, and there are children with low results in mathematics and high language scores.

When divided into quartiles as displayed in Table 2, this becomes even more visible. There is no 1-1 correspondence between skill level in mathematics and skill level in language. Perhaps the most surprising is that under 60% of the children with MIO results in the lowest quartile are also in TRAS-quartile 1. This stands in contrast to Kleemans et al.’s (2011) research, which found language difficulties to have a high impact on mathematical development. However, if TRAS quartile 2 is included, over 90% of the toddlers in the present study with results in MIO quartile 1 are in the two lowest TRAS quartiles. Nevertheless, there are some toddlers with results in the lowest quartile in mathematics and with language scores above the mean score of TRAS. It should be noted that for children in the next lowest MIO quartile, most of the language scores were within TRAS quartiles 1, 2 and 3, and only 9 of 261 children were in TRAS quartile 4. This implies that it is not common to have under the mean math skills and very good language skills, but for some children, this is the case. When looking at MIO quartile 3, most TRAS scores were within TRAS quartiles 3 and 4, and much fewer were in TRAS quartile 1. For the children with mathematical scores in the highest quartile, 93% also had language scores within the two highest language quartiles. The present study cannot say anything about causality, still, it appears to be children within the highest MIO-quartile are most likely to have over medium language scores. However, there are a few toddlers in MIO-quartile 4 with low to very low language skills.

The variation that appears when dividing a large sample into skill level groups as in the present study shows that the relations between the development of mathematical skills and language skills are much more complex than previously stated. Our results stand in some contrast to earlier research claiming a more 1-1 correspondence between language level and math skills, especially in regard to children with low skills (e.g., Durkin et al., 2013; Kleemans et al., 2011).

In the present study, we used MIO and TRAS to assess mathematics and language respectively. The materials include items based on theoretical terms and concepts central to the two developmental areas. They are not completely separated, e.g., mathematical language is part of MIO, knowing the counting sequence a part of Counting and series of numbers and so on. There are items in TRAS, including relational words and words for the classification of shapes. However, in the language context of TRAS, these items are a part of Language comprehension. This overlap between the assessment materials may be seen as a limitation of the study, but on the other hand, it would be difficult, maybe impossible, to find language-independent assessment material. The present study can therefore only describe how the skills in mathematics and language seem to be related as assessed by MIO and TRAS but cannot say anything about causality.

Although there are relations between the learning of mathematics and language, the results of the present study question whether the two developmental areas can be treated as two sides of the same coin. In further research, children’s skill levels need to be taken into consideration since the relations between mathematics and language may be different related to this. In the ECECs, the staff need to create a rich learning environment where the children have many experiences with play and exploring with a focus on learning mathematics both with an emphasis on language and more language-independent activities to meet children with different language levels.