Opportunities for preschoolers mathematical skills training using a digital mathematical application

Introduction

Currently, the digital devices use is an integral part of the most preschool children’s lives (Veraksa et al., 2021; Kalabina, Progatskaya, 2022; Smirnova et al., 2022; Chichinina et al., 2023; Konca, 2022). Depending on the amount of screen time, the type of digital content consumed, the organization of interaction with digital devices, and the parental involvement presence, the digital devices use can be developmental, including for children's mathematical skills and abilities (Belova, 2022; Denisenkova, Taruntayev, 2022; Belolutskaya, Vachkova, Patarakin, 2023; Benavides-Varela et al., 2020). The mathematical skills development level in preschool children is a significant predictor of the child's subsequent academic success in school (Duncan et al., 2007; Jordan et al., 2009). Thus, this research examined the possibility of improving mathematical skills in preschool children via a digital mathematical application, provided that it is used in situations of joint discussion with an adult or independent use by children.

In senior preschool age, elementary mathematical concepts and skills are actively formed. While learning mathematics, preschool children develop elementary knowledge about the set, number, magnitude and shape of objects, they learn to navigate in time and space, master counting and measuring objects. In addition, children acquire knowledge of special mathematical terminology (i.e. names of geometric figures, mathematical operations with numbers, etc.) and become familiar with certain mathematical relationships, patterns, and dependencies (Gabova, 2014; Jordan et al., 2009). In this work, we focused on studying the mathematical representations of senior preschoolers about quantity and magnitude as the most basic and significant for further successful mastery of mathematics in elementary school (Benavides-Varela et al., 2020; Jordan et al., 2009).

The association between digital device use and mathematical knowledge and skills in preschool children is still poorly underexplored, however it is important to mention several studies that confirm the presence of such an association. In the research by Zaranis and colleagues (Zaranis, 2012; Zaranis, Kalogiannakis, 2011), the effectiveness of traditional mathematics teaching was compared with computer-based teaching built on the Hill model, which assumes the development of geometric thinking at five complexity levels, with only the first two levels used for kindergarten. At the first level, children recognize geometric figures, identify them with surrounding objects (for example, a rectangle is like a door). At the second, descriptive-analytical level, they recognize the geometric figures’ properties. The study was conducted in a Greek kindergarten among children of 4 to 6 years old. The control and experimental groups, which received traditional and computer-based teaching respectively, studied similar material with the same frequency. The lessons included a story/explanation for each of the ten numbers, introduced the child to various aspects of counting situations, and involved the child actively in solving gamified tasks for counting. The computer tasks were selected in accordance with the kindergarten program and were a supplement to the material learnt. The results demonstrated that additional computer training can improve the mathematical skills development in preschool children (Zaranis, 2012; Zaranis, Kalogiannakis, 2011).

Despite the fact that there is very little data on the importance of joint (with parents) digital devices use for teaching preschoolers mathematics (Belova, Shumakova, 2022; Veraksa et al., 2022), a number of studies show that children's digital devices use becomes more developmental when utilizing them together with parents and siblings, when communicating and discussing digital content (Veraksa et al., 2022; Karabanova, 2022; Bukhalenkova, Chichinina, Almazova, 2023; Dore, Zimmermann, 2020; Wannapaschaiyong et al., 2023). Kim's meta-analysis found a link between parental involvement in children's digital devices use and academic achievement of children at school age (from preschool to final-year classes) (Kim, 2022).

There are several mechanisms through which sharing digital devices with adults can help a child learn better via digital content. Firstly, adults can direct a child's attention to important parts in digital content by highlighting information that needs to be mastered. Secondly, adults can help children interpret digital content when it is unclear or more complex than the child could understand on his/her own. Finally, adults can help children understand how media content relates to their own lives and the real world (Dore, Zimmermann, 2020).

Research demonstrates that active mediation by an adult improves children’s understanding and learning (Archer, Wood, De Pasquale, 2021; Dore et al., 2020; Strouse, Ganea, 2021). In a study by Strouse and colleagues, one group of parents was trained to pause an educational video while watching it with their child, ask questions, and encourage their child to recount parts of the story. Another group of parents was asked to watch the video with their child as usual. Results indicated that when parents were encouraged to interact with their child, children understood the story in the video better and learned more new words from it (Strouse, O'Doherty, Troseth, 2013).

Thus, the research conducted points to the importance of children using digital devices together with adults, and that more active forms of shared use have a more significant impact on learning (Archer, Wood, De Pasquale, 2021; Dore et al., 2020; Strouse, Ganea, 2021). Although many Russian studies written by V. Davydov, L. Obukhova, N. Talyzina, N. Salmina and other scientists have already revealed the adult’s role in teaching children mathematics, there is very little modern research that would investigate and prove the importance of the joint (with an adult) digital devices use by preschoolers for teaching them mathematics.

Since theoretical analysis of studies has demonstrated the importance of interaction with an adult when using a digital device for teaching preschool children mathematics (Benavides-Varela et al., 2020; Kim, 2022; Konca, 2022; Zaranis, Kalogiannakis, 2011), this research focused on the possibilities identification to improve mathematical skills in preschoolers via a digital math application. For this purpose, a comparison was made of the developmental effect of mathematics classes using a digital math application in the case of joint discussion with an adult or independent application use by preschoolers.

Materials and methods

Data processing methods. At the beginning of the study, the cluster analysis was applied to identify children with different levels of mathematical skills mastery. Non-parametric criteria of statistical analysis were also used, since the distribution differs from normal (Kolmogorov-Smirnov criterion): the Mann-Whitney criterion was used to compare the two experimental groups’ results, the Wilcoxon criterion was used to determine the significance of changes in these groups before and after the classes; the effect size Cohen's d was calculated.

Statistical data analysis was performed via the statistical package SPSS 22.0.

The search and selection of an educational math application was carried out based on the following criteria: 1) the child’s involvement in the interaction with the app’s content, 2) the material’s presentation form as well as the correspondence of the number concept forming method to the age characteristics of preschool age, 3) the mathematical concepts’ formation logic, 4) ensuring the principle of continuity with the school curriculum in relation to mathematical content, 5) the possibility of involving an adult in the process. None of the found applications fully met the described criteria, and none of them implemented the joint use possibility nor involving adults. In accordance with the described criteria, the most suitable for preschoolers was the application called "Luntik. Mathematics" (for more details on the mathematical digital applications’ analysis, see the article (Aslanova et al., 2020). This app is designed to develop mathematical knowledge and skills in children of 4 to 6 years old and includes several mathematical blocks: about quantity and counting, shape, magnitude, time, space orientation. Within each block, the child first listens to a short story about the characters from the famous cartoon “Luntik” followed by an explanation of the material, and then the child completes mathematical tasks that are a logical continuation of the story – this ensures the child’s involvement in interaction with the app’s content. The application has voice-over for tasks and the ability to replay instructions again while completing a task. Thus, the content and the material’s presentation forms correspond to the preschoolers’ age characteristics, and the mathematical concepts’ formation logic is consistent with the requirements of the Federal State Educational Standard (On Approval of the Federal State Educational Standard for Preschool Education..., 2013), which ensures continuity with the primary school educational program. The only criterion that this application does not meet is the ability to involve an adult, which is what we tried to implement in this study.

Based on literature review (Veraksa et al., 2022; Karabanova, 2022; Kim, 2022), we hypothesized that preschoolers who use a digital math app in a joint discussion with an adult will be more successful in completing math tasks on quantity, counting, and magnitude than children who use the app on their own.

Study sample. The research involved 64 preschoolers (out of these 42.2% were boys) of 5 to 6 years old (M = 5,8; Sd = 0,34), pupils of senior groups of kindergartens in Moscow. These senior groups were located in three kindergartens that belonged to the same educational complex, where all pupils were taught according to the same educational program (“From Birth to School”, 2019) in accordance with the Federal State Educational Standard (On Approval of the Federal State Educational Standard for Preschool Education..., 2013).

Among the pupils from seven senior groups, 64 children were selected who regularly attended kindergarten and did not participate in additional math classes. It should be noted that all children who took part in the study had experience using a tablet and did not have difficulties in managing it and working with a digital math application. In addition, (this information was clarified in advance through kindergarten teachers) all research participants were allowed by their parents to play digital games.

Based on the mathematical skills’ diagnostics results via cluster analysis, several groups of children were identified that differed in the mathematical skills’ development level: “Low level” (3 people), “Average level” (35 people), “High level with a low arithmetic proficiency level” (15 people), “High level with a high arithmetic proficiency level” (11 people). As a result of this analysis, 14 children were excluded from further research: 3 subjects due to an extremely low mathematical skills level (insufficient for conducting developmental classes) and 11 children with the initially highest mathematical skills level. The remaining 50 children were randomly divided into two experimental groups, in which the ratio of children with average and high mathematical skills levels was maintained. The first group, where children used the tablet independently, included 24 children (13 girls and 11 boys), and the second group, in which children interacted with an adult while working with the tablet, included 26 children (13 boys and 13 girls). Another 13 children were excluded from the study because they did not complete all the classes or were absent during the final mathematical skills’ diagnostics. Thus, only 38 children completed all the developmental classes and the final diagnostics: 18 from the first experimental group (12 girls and 6 boys) and 20 from the second (10 boys and 10 girls).

Research methods. To assess the preschoolers’ mathematical skills, different methods were used: some - to evaluate those skills that were trained via digital application’s tasks, while others - to assess those skills that were not directly trained via the application. In this way, we wanted to look at the transfer of preschoolers' ideas and skills to similar, but not identical tasks within the framework of children's ideas about quantity and magnitude. Most of the methods used in this study were previously tested on a sample of Russian-speaking preschoolers and primary school children (Sidneva, Aslanova, Bukhalenkova, 2022; Vasilieva et al., 2021).

The following methods were used to evaluate preschoolers' mathematical representations of quantity: 1) the "Numbers Comparison" (Vasilieva et al., 2021) technique assessed the ability to compare single-digit and double-digit numbers; 2) the "Arithmetic Skills" technique estimated addition and subtraction skills within 10; 3) the “Numerical Distance Comparison” technique (Laski, Siegler, 2007; Vasilieva et al., 2021) evaluated understanding and ability to compare “distances” between numbers; 4) the “Number Sense” (Ginsburg, Baroody, 1990) technique assessed the non-symbolic sense of number in preschoolers (Kuzmina et al., 2022).

The following methods were used to evaluate preschool children’s mathematical representations of magnitude: 1) the “Houses” technique was developed within the framework of this study to assess children’s ability to find correspondences between objects by magnitude; 2) the “Measuring by Units” technique estimated the development of children’s ability to take measurements using a unit (the detailed description of the methods can be requested from the author (D.A. Bukhalenkova)).

To control the non-verbal intelligence development level, the children were engaged with the “Raven’s Coloured Progressive Matrices” technique (Raven, Raven, Kort, 2012). The method included three series of 12 tasks. For the correct completion of each task, the child received 1 point (maximum = 36 points).

Research procedure. At the first stage of the research, the “Raven’s Coloured Progressive Matrices” method and diagnostics of mathematical knowledge and skills were carried out with all children individually. Although, technically the diagnostics of mathematical skills were conducted in pairs, each child worked on his/her tasks independently. Diagnostics took about 20 minutes on average and took place mainly in the first half of the day. In testing for non-verbal intelligence, all subjects showed results that were within the age norm.

Based on the preliminary mathematical skills’ diagnostics results, the children were divided into two experimental groups. Each of the experimental groups underwent a cycle of 6 developmental lessons, each lasting 15-20 minutes, in subgroups of 3 people. The children attended only one lesson per day, with at least 3 days between lessons.

The study was conducted in the second half of the school year: diagnostics were carried out in February, a series of developmental classes in March and early April, and the final diagnostics at the end of April.

Developmental lessons program. Based on the "Luntik: Mathematics" app there was developed a program of 6 lessons, including tasks on counting, comparing sets, making up sets, arithmetic operations, and comparing objects by magnitude. Each lesson had specific tasks from the educational application, which were combined into groups according to the principle from simple to complex (first, counting the number of objects was mastered, then addition and subtraction). For each lesson, 3-4 games were selected so that the total lesson time did not exceed 20 minutes.

In case of questions and difficulties while playing with the application, children from the group without the participation of an adult were offered to listen again to the voice instruction built into the application. If the child still could not cope with the task, he/she was offered to move on to the next task or, if all the tasks in this lesson were completed, to finish the game. In the event of questions or difficulties, children from the group with an adult’s participation were either asked to listen to the voice instructions again or were given a simplified explanation of the task (for an explanation's wording example, see. After each lesson, a discussion was held with this group of children. They were asked to answer several questions posed by an adult related to the lesson’s content and to complete similar simple tasks using material objects (for example, pencils). The plan for all lessons and an example of a lesson can be requested from the author (D.A. Bukhalenkova).

Results

Descriptive statistics for both groups based on preliminary diagnostic results

As a result of the preliminary testing data analysis, no significant differences were found in the success of completing all mathematical tasks in children from the two experimental groups, with the exception of the quantities comparison (Table 1). It is important to highlight that children from the group with the participation of an adult initially coped more successfully with the finding correspondences between objects by magnitude. According to the non-verbal intelligence assessment results, all children participating in the study corresponded to the age norm and no significant statistical differences were found between the experimental groups.

Table 1. Descriptive statistics based on the results of a preliminary assessment of mathematical skills and non-verbal intelligence (N = 38)

Results comparison of preliminary and final mathematical skills testing in two experimental groups

The analysis revealed that in the group of children who played games on the tablet without adult’s participation, there were significant differences between the results obtained before and after the developmental classes in the success of completing such tasks as “Numbers Comparison”, “Number Sense”, “Quantities Comparison”, and there were also significant improvements at the trend level according to the “Arithmetic Skills” technique (Table 2).

Table 2. Differences in the success of mathematical tasks before and after educational activities among children from the group without adult participation

As a result of comparing the completing mathematical tasks success before and after developmental classes in a group with the participation of an adult, significant differences were identified for all diagnostic tasks, with the exception of the “Quantities Comparison” ​​(Table 3).

Table 3. Differences in the success of mathematical tasks before and after educational activities among children from the adult group

Comparison of the changes in the group with adult participation and in the group without adult participation

To analyze changes in mathematical skills, the difference between the scores for each technique obtained by children in the posttest and the scores obtained in the pretest was calculated. Significant differences were discovered in the magnitude of changes between the two groups in the success of completing the “Number Sense” and “Numerical Distance Comparison” tasks. Children from the group with the participation of an adult began to cope with these tasks significantly better than children from the group without the participation of an adult (Table 4).

Table 4. Comparison of the magnitude of changes in the success of mathematical tasks before and after educational classes in two experimental groups

Discussion

It was previously mentioned that the purpose of this study was to identify possibilities to improve mathematical skills in preschool children using a digital mathematical application in situations of joint discussion with an adult or independent use of the application. To achieve the stated goal, a comparison was made of the mathematical application’s "Luntik. Mathematics" developmental effect in situations of joint discussion with an adult and when used independently by preschoolers.

The research results allow us to partially confirm the hypothesis that the success of completing mathematical tasks in children who use a digital mathematical application in a situation of joint discussion with an adult will be higher than in children who used the application independently. Firstly, the results of the experiment show that in the group with the participation of an adult, children significantly improved their performance in completing a greater number of mathematical tasks. Moreover, in the group with the participation of an adult, as opposed to the other group, there were significant improvements in such techniques as “Measuring by units” and “Numerical Distance Comparison”. These differences are particularly interesting and important because the digital app’s games were not directly aimed at mathematical concepts and skills development that these methods assessed. Thus, a correct understanding of how objects can be measured using a unit reflects a correctly formed idea of ​​magnitude (Vasilieva et al., 2021; Veraksa et al., 2022), which seems to us to be an important effectiveness indicator of the developmental activities carried out. The numerical distance comparison technique is more complex than the method of pairs of numbers comparison; it can be classified as a task that is more in the zone of proximal than actual development for preschoolers. Secondly, as a result of comparing the changes magnitude before and after developmental activities in the two groups, it was found that children from the groups with the participation of an adult began to perform the tasks on “Number Sense” and “Numerical Distance Comparison” significantly better than children from the group without an adult.

Therefore, our results demonstrate that in the case of using an educational application with the participation of an adult, the mathematical skills’ effectiveness training in preschoolers was higher and there were more significant improvements than in the case of children playing with the application independently. This highlights the importance of external support when preschoolers use educational applications and indicates the limitations of independent application use by children. Moreover, when using a math app with the help of an adult, a child can not only practice their math skills, but actually improve and deepen their existing skills and basic math concepts.

To better understand how an adult can participate in a child's interaction with a digital app, we should clarify that in our experiment in the group with an adult, the tester was nearby and observed the children's play, if difficulties arose, the child could turn to an adult for an explanation and help; after each lesson, the adult initiated a discussion of the material covered and offered the child several small tasks to complete, similar to the tasks from the application, but using material objects from the space surrounding the children (for example, pencils). It can be said that the adult’s role consisted of some generalization and practice of the acquired knowledge through ordinary practical activities familiar and understandable to children, which is very important for consolidating knowledge in preschoolers (“From Birth to School”..., 2019). This study shows that a digital device can only be an effective tool in children's acquisition of mathematical concepts and skills, but cannot completely replace an adult and fulfill his/her functions in transmitting cultural experience to a child (Karabanova, 2022; Solovieva et al., 2023; Veraksa et al., 2021).

Conclusion

The conducted research demonstrated the possibility of improving mathematical skills in preschoolers via the digital educational applications’ use and confirmed the importance of cooperation with an adult in the process of preschoolers’ interaction with digital devices.

The results obtained allow us to formulate some recommendations for parents and teachers to ensure that the digital educational applications’ use has the most developmental effect on children:

• It is important to familiarize yourself with the digital educational application, its features, capabilities and content before offering it for use to your child. If necessary, it is worth organizing the process of the application use (for example, think through the order of completing games and tasks; set up voice guidance and prompts).

• An adult's involvement in a child's use of a digital educational application contributes to a greater developmental effect. Even just being nearby and observing, an adult already supports the child to some extent and can help him/her in case of both technical and semantic difficulties, explain what needs to be done in the task, which increases the child’s understanding of the tasks being performed.

• The adult's participation can also be manifested in subsequent discussions with the child about the material covered and the tasks completed in the application. Thus, a child can be asked to tell what he/she has learned, or asked to act as a teacher (for example, asked to explain the essence of some mathematical operation, to teach another to perform it).

• In addition, to help the child better assimilate the knowledge and skills acquired, an adult can offer him/her to complete practical tasks similar to what the child did in the digital application (for example, counting toys/furniture in a room together, comparing their sizes, etc.).

Thus, the active participation and involvement of an adult in the child’s interaction with digital educational applications plays a significant role in the acquisition and consolidation of mathematical knowledge and skills in preschoolers.

Limitations. It is important to note the limitations and prospects of this study.

Firstly, the most significant limitation in this experiment is the absence of a control group with which no educational classes were conducted. The inclusion of such a group in the study will further allow us to evaluate and take into account the learning effect as a result of repeated completion of mathematical tasks during the posttest. In addition, it will allow us to compare how much the digital application itself, without taking into account the participation of an adult, affects the results compared to traditional kindergarten education.

Secondly, we note the small sample size, which does not allow us to generalize the results obtained to all modern Russian preschoolers. In the future, it will be necessary to test the results obtained on more children.

Thirdly, children with extremely low mathematical skills levels (3 people) and children with initially high levels (11 people) were excluded from the study, which limits the research results application to a wider population of children with different mathematical skills levels. However, from our point of view, children with a high mathematical knowledge level simply did not need this application, and for children with an extremely low mathematical knowledge level, its use would be difficult.

Fourthly, due to a decrease in the sample of children during the experiment, the final analysis of the results revealed some shortcomings in the distribution of children into two groups: 1) in the group with adult participation, preschoolers initially performed significantly better with the “Houses” task; 2) in the group without adult participation, girls turned out to be twice as many as boys. These factors could also affect the reliability of the results obtained, and they need to be monitored when repeating the experiment on a larger sample.

Fifthly, we note the short duration of this study, which consisted of only six sessions. To assess the sustainability and long-term effect of using the digital application, it is necessary to further conduct a longer study and a delayed assessment of the children's results.

Sixthly, these results were obtained for a specific digital mathematical application and further require verification on other digital applications, both mathematical and teaching other skills.

Seventhly, the study did not control some external and internal factors that could affect the results of the mathematical skills development in preschoolers (for example, parents conducting additional classes at home, the individual characteristics of children, etc.).

In addition, the prospects of this study include studying the extent to which the digital application’s use can develop cognitive abilities related to mathematical skills (e.g., logical thinking, spatial perception) and how their development can be associated with the effectiveness of teaching mathematics in this way.

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