The aim of the present study was to analyse the relationship between play skills and mathematical skills in toddlers, by examining the correlations between overall scores, the scores for different kinds of play skills and mathematical skills, and how level of play skills is related to mathematical skills.
Correlations between play skills and mathematical skills
To explore the correlations between mathematical skills and play skills Pearson product-moment correlation coefficients were calculated both between the total score for mathematical skills (MIO total) and the total scores for play skills, and between the scores for different play sections and the different sections in MIO (Table 3).
The correlations between Total Play skills and MIO-total are as also the correlations between Total Play skills and four of the mathematical areas (Mathematical language, Logical reasoning, Shape and Space and Pattern and Order) strong. For Counting and Series of Numbers and Enumeration, the correlations were moderate, but in the upper range. These results indicate that when the toddlers’ play skills were summed to a total score, they were relatively strongly correlated with skills in all the mathematical areas.
When it was examined whether any particular type of play skill in toddlers displayed greater correlations with mathematical skills than others, correlations were found between the MIO-total and that for all play skills, and all play sections correlated with all the mathematical sections in the MIO.
Two of the correlations between MIO-total and the play sections were strong (Independence in play and Interaction in play), and the other correlations were of moderate strength. Most of the correlations (22) between the different play skills and mathematical skills were of moderate strength.
The correlations between the play section Exploring and construction play and the mathematical skills were all moderate, similarly to the correlation between the total-MIO and this play skill. The toddlers’ need for sensorimotor experiences in order to learn mathematics is well established (Solem and Reikerås 2017), and this relation was not surprising. In particular, relations with the geometrical areas Shape and Space and Pattern and Order was expected, since these relations were reported in a previous study (Casey et al. 2008). Play with building blocks has also been reported to be linked to increased skills in mathematical language and numeracy (Schmitt et al. 2018). The results in the present study identified even stronger relations between skills in Exploring and construction play and Mathematical language and Logical reasoning than the correlations with the geometrical areas. The weakest correlations with the present play section were observed for two quantitative areas, Counting and Series of Numbers and Enumeration, where the correlations were near being weak. Nevertheless, these mathematical areas correlate with Exploring and construction play, and these correlations may depend on age, since the participants in the present study were toddlers, whereas earlier findings (e.g., Schmitt et al. 2018) were obtained from somewhat older children (pre-schoolers).
The play section Pretend play and the sum of mathematical scores (MIO-total) exhibited a moderate (near strong) correlation. The mathematical areas exhibiting the strongest correlations with this play section were Mathematical language and Logical reasoning. This finding is consistent with the clear links identified between language development and the development of pretend play, as well as between pretend play and problem solving (Bergen 2002). Although the toddlers were in the beginning stages of the development of pretend play (Hännikäinen and Munter 2018), relations to the mathematical areas described above were also present at a moderate strength. Lillard et al. (2013) asked for more evidence of the impact of pretend play on cognitive development. The present study is unable to show causality; however, the results show a relation between mathematical skills and skills in pretend play. This finding supports the theory proposed by Lillard et al. known as the “claim about the relations” that was initially argued for by Vygotskij (1978).
Rule-based play is difficult for the toddlers, which is shown in Table 3 through the comparison of the mean scores for Rule-based play and the other play sections. The low mean score for Rule-based play skills (.17) makes it little meaningful to analyse the correlations with mathematical skills and rule-based skills, as the lowest correlation was observed between these play skills and mathematical skills. Rule-based play in the form of games is often used to stimulate mathematical development in older children (Mononen et al. 2014). The low level of correlations identified between rule-based play and mathematical skills in the present study implies that other types of play may be better suited in the work with toddlers to foster mathematics skills.
Although children’s play was categorised in different types of play and play skills in the present study, these categories are not strictly separated. For example, pretend play is often present in block play, and the children establish rules for pretend play. The intercorrelations between the three specific play skills (see Table 3) also support this hypothesis by showing strong correlations between all of the following skills: Exploring and construction play and Pretend play, Exploring and construction play and Rule-based play, and between Pretend play and Rule-based play. In addition, the toddlers alternate smoothly between different types of play, and therefore more than one play type may be present over short timeslots (Hännikäinen and Munter 2018).
The last two Play skill areas, Independence in play and Interaction in play, are more general skills than the play skills related to specific types of play. These two skills are the Play skill areas with the highest mean and the largest correlations both with the MIO-total and with the mathematical areas, supporting the hypothesis that these skills are more general skills required for toddlers to learn. Four of the correlations between mathematical skills and Interaction in play were strong, and one of the correlations in Independence in play was strong. Three of the remaining correlations were in the upper range of the moderate category. The abilities to be active in solitary play and parallel play, as well as to initiate play (two of the three items in the Independence of Play section) show that the toddler wants to explore his or her surroundings, which is very important for learning mathematics (Solem and Reikerås 2017) and may explain some of the relations found in the present study. The toddlers’ ability to stay in play (the third item within the Independence in Play category) mirrors the toddlers’ self-regulation skills, which are related to the level of activity of children in play and their academic skills, such as mathematics (Becker et al. 2014). This may explain the relatively high correlations found between Independence in Play and the mathematical skills.
The play section displaying the highest correlation with the total score for mathematical skills was Interaction in play. This correlation confirmed previous findings describing the importance of social interaction for children’s learning of mathematics. During play with other children, which is one of the items in this play section, children often take turns (a second item). Turn-taking requires both self-regulation (which is related to mathematical skills) and an understanding of order. Children with a varied play repertoire (the third item) are more often popular play-mates and participate more frequently in interplay than children with a more limited play repertoire (Stangeland 2017).
The mathematical areas exhibiting the highest correlation with Independence in Play and Interaction in Play were Shape and Space, Mathematical Language, Logical Reasoning and Pattern and Order. Five of these correlations were large, and the remaining correlations were in the upper range of moderate. The remaining correlations with Counting and Series of Numbers and Enumeration were all moderate. Why the correlations between these two more general play skills and the quantitative areas were somewhat lower than the other areas is not known. For most play skills, the pattern with the lowest correlations were quantitative skills, the only exception was the correlation between Pretend Play and Counting and Series of Numbers, which was greater than the correlation between Pretend Play and the two geometrical areas.
Table 3 also shows the intercorrelations between the play skills and between the mathematical skills. The correlation between Independence in play and Interaction in play was high (.81) and may indicate that these skills measure a similar general social play skill. The correlations between the three types of play, namely, Exploring and construction play, Pretend play and Rule-based play, were also high, indicating that these skills also possess strong relationships. The relations between the two general play skills and the three different types of play skills were low to moderate. The intercorrelations between the mathematical skills were generally high, and only two were of medium strength, indicating that the MIO measures an overall level of mathematical skills, consistent with a previous report (Reikerås et al. 2012). Consequently, the findings of the correlations between the different types of mathematical skills and play skills should be interpreted with caution.
Levels of play skills and mathematical skills
The relations between the levels of play skills and mathematical skills were further examined by comparing the mathematical skills of groups with different levels of play skills. The total sample was divided into three groups based on the children’s results on the assessment of Play skills (weak, moderate and strong play skills), and each group included approximately one-third of the total sample. We accepted some differences in the group size to include all children with a certain test score in the appropriate group. The scores used for grouping and results of the play skills in ALLE MED and for MIO for the total sample and for each of the groups are presented in Table 4.
As hypothesised, ANOVA revealed significant differences in the total score for the Play skills between the groups F(2,1085) = 2522.71, p < .01. A Bonferroni correction was applied to prevent a Type I error. The significance level of .05 was divided by three and thus the significance level was adjusted to .017. The effect size eta square was .82 and considered large (Cohen 1988). The Bonferroni post hoc test showed that this result applies to all differences between weak, moderate and strong groups (p < .01). Based on these results, the criteria selected for creating the groups were efficient.
Possible differences in mathematical skills between the groups with weak, moderate and strong play skills were explored using ANOVA. As above, the significance level was adjusted to .017. The statistically significant difference at p < .017 was found for MIO-total F(2,1085) = 293.52, p < .001. The effect size, eta squared, was .35 and considered large according to Cohen (1988).
The Levene’s Test of Equality of Variances shows a violation of the homogeneity of variance (p < .05) both for the total score of Play skills and MIO total. As argued in the method section, ANOVA was still relevant and was used. To be sure violating the assumption of homogeneity did not give a falsely significant result, a Welch Robust test of Equality of means was performed and showed significant differences (p < .01) between the groups in line with the ANOVA.
The post hoc tests (Bonferroni) revealed that the differences between the mean scores were statistically significant (p < 0.01) for all differences between the groups. The effect size (Cohen’s d) was calculated to evaluate the importance of these differences between the groups (Cohen 1988). The largest effect on mathematical skills of groups formed according to the level of play skills was found between the weak group and the strong group, where Cohen’s d was 1.78, and according to Sawilowsky (2009), this effect was very large (1.20 ≤ Cohen’s d). Cohen’s d was .91 and .83 for the comparisons between the groups with weak and moderate play skills and between the groups with middle and strong play skills, respectively, which are considered large effects (0.80 ≤ Cohen’s d < 1.20) (Sawilowsky 2009).
The group with moderate play skills also achieved a mean MIO-total score (30.58) similar to the mean score achieved by all participants (30.80), indicating that the children’s play skills were distributed in a similar manner to the mathematical skills. This finding supports a linear relation between play and mathematics, as was also observed in the correlations presented in Table 3.
These findings indicate a relatively strong relationship between the level of play skills and the level of mathematical skills among toddlers. Thus, this imply that the large correlations found between MIO-total and total Play were not the results of strong correlations only for some parts of the groups of toddlers or of many participants. Weak play skills imply weak mathematical skills, moderate play skills imply moderate mathematical skills and strong play skills imply strong mathematical skills.
The large number of people collecting the data might be a limitation of the study. In addition to the training of the staff the reliability could by further strengthened by letting the two observers deliver independent observations. However, the discussion between the observers when seeking agreement contributed to increasing their competence.
The missing SES data should be noted when generalising data, and this is a limitation of the study, although there were not found any differences in mathematical skills between the group with available SES and the group without available SES.
Although the ECECs in Norway are all well equipped, there is not any standardization of what toys they should have. The toddler’s access to play material (blocks, etc.) during the observations was not assessed and could influenced the results. Neither is there information from the parents about children’s play preferences or previous experience with materials such as blocks at home. This lack of information is also a limitation.
There are no data on whether the observations in the present study were recorded during children’s free play, teacher-initiated play or mutual play. This limitation should be accounted for in further research.
Contributions and pedagogical consequences
The present study contribute with new knowledge about the relations between play skills and mathematical skills in toddlers. The large sample size makes the results more generalizable than studies of smaller samples.
The close relations between the toddlers’ play skills and mathematical skills found in the present study have consequences for practice in the ECECs working with toddlers. The findings supports the hypothesis that play and learning should be viewed as related skills, and that the toddlers’ play should be the central focus when teachers are working with mathematics in toddler groups. Previous studies support the use of a combination of play approaches such as free play, teacher-initiated play or mutual play, when supporting young children’s learning of mathematics (Salomonsen 2019).
Regarding different play skills, Interaction in Play and Independence in Play are both more important play skills in toddlers and display the strongest correlations with mathematical skills than the play skills related to specific play types. Few toddlers master Rule-based Play, whereas Pretend Play and Exploring and Construction Play may be play forms that are more suitable for the work with this age group. These two types of play exhibit somewhat higher correlations with mathematics than Rule-based play. The types of play may be related to mathematical skills in other ways when the children are older. More comprehensive studies are needed to follow the children’s play skills and determine how they correlate with different types of mathematical skills.
The findings that the levels of play skills imply the same levels of mathematical skills underscore the importance of considering the toddlers’ play when planning for and implementing mathematical activities in the ECECs. In particular, the play skills of children with weak play skills must be strengthened to help the toddlers develop the tools required for exploring, playing and learning.
The present study is unable to establish conclusions about causality, and more research is needed to determine how different kinds of play skills that develop at an early age predict mathematical skills at older ages. Mathematical skills might also be important for development of play skills, which needs to be explored in further research. As the present study is part of the longitudinal Stavanger Project—The Learning Child, longitudinal data are available for these analyses.