Intervention effects on low performing preschoolers ’ early mathematical skills: Adding fundamental motor skill practice as a supporting method

Background: This study examined the effects of (1) combined early numeracy and fundamental motor skills (MovEN), (2) early numeracy, and (3) fundamental motor skills intervention programs on children ’ s early mathematical and fundamental motor skills, and how individual background variables affect the effectiveness of these interventions. Procedure: Together 50 preschoolers participated in the interventions (16 × 45 min sessions). Children ’ s early numeracy, mathematical problem-solving, and fundamental motor skills were measured once before and twice after the interventions. Main findings: The results showed that the MovEN and early numeracy -interventions were effective in improving children ’ s early numeracy, and mathematical problem-solving. Whereas the MovEN and fundamental motor skills interventions improved children ’ s fundamental motor skills. From individual factors, only updating ability predicted the intervention ’ s effectiveness over and above prior performance. Conclusion: The results suggest that children ’ s early mathematical and fundamental motor skills can be supported effectively at the same time with the MovEN -intervention.


Introduction
For many years, children's development has been studied in silos within different disciplines, although it is well-known that children's development is a complex process involving multiple dimensions [1].For instance, it has been shown that the development of cognitive and motor skills is parallel [2,3] and that these skills are related to one another already in preschool years [2,4].There is evidence that fundamental motor skills affect executive function development, and it is suggested that executive functions may mediate the effects of fundamental motor skills on early academic skills [4] such as early mathematical skills [5].Although this relation has been shown, many intervention studies still focus on supporting separately either academic or motor skills [3].Thus, more knowledge is needed about practices that simultaneously promote multiple aspects of children's development.
In recent years, researchers have developed fundamental motor skill interventions to support children's cognitive and academic skills.
Although it has been demonstrated that fundamental motor skill interventions can support preschoolers' cognitive and academic skills, especially when combined with cognitive or academic practices, these intervention studies have had several limitations [6,7].First, some studies have compared the effects of combined interventions to academic interventions [8,9], but there are no studies comparing combined intervention approaches to both academic and fundamental motor skills interventions.Such evaluation is important in order to reveal if the combination is more effective than practicing academic or fundamental motor skills separately.Furthermore, another limitation is that only a few studies have investigated the long-term effects of the combined interventions (e.g., [10]).Since the long-term effects of the interventions are important in securing the learning effects and preventing later difficulties, this should be also investigated in the intervention studies [11].The third limitation is that the effects of fundamental motor skills on early mathematical skills have been rarely looked at [12][13][14][15], although motor skill interventions have been found to be effective on mathematical skills in school-aged children [16].Considering that the early mathematical skills (e.g., early numeracy and mathematical problem-solving) have been shown to be important already in the early years [17], the effects of fundamental motor skill interventions on early mathematical skills should be studied also in preschool-aged children.Finally, individual differences affecting the effectiveness of the combined interventions have not been considered in the previous intervention studies, although it is well known that there are many individual factors affecting children's learning (e.g., [18][19][20][21]).
To address the above-mentioned research gap, in this present study, the effects of an intervention called Movement with Early Numeracy (MovEN) were investigated.The MovEN combines the learning of early numeracy via story reading with fundamental motor skills.The intervention effects were investigated on early mathematical and fundamental motor skills and the effects were compared to two control interventions that included separately early numeracy or fundamental motor skills practices.The children participating in the interventions were identified to be at risk for low performance in early mathematical skills.In addition, it was assessed whether individual background variables such as parental socioeconomic status, child's language skills, and executive functions impact the effectiveness of the interventions.

Early mathematical skills
When considering early academic skills in preschool-aged children, early numeracy can be seen as one of the most important skills in predicting later mathematical skills [22] as well as academic achievement [17].Early numeracy refers to children's ability to understand and operate with quantities [23].Early numeracy includes a variety of skills considering for example quantity, number, and subitizing; verbal, and object counting; comparing, ordering, and estimating; as well as early arithmetic skills [24].After children obtain the basic knowledge of numbers, they start to understand numerical relations [25] such as comparing (e.g., more, less), spatial relations (e.g., under, above), classification (e.g., same, different), and quantity (e.g., none, together [26]).These numerical relational skills have been shown to be important to counting skills, as well as more complex early mathematical skills like mathematical problem-solving [27].
Mathematical problem-solving can be seen as an important 21st-century skill since new and unknown situations in life require applying new and existing knowledge in a creative way [28].There is no unified definition for mathematical problem-solving, but it can be seen as a "nonstandard" skill, meaning that children cannot recall or use familiar solution patterns to solve them, however, they need to apply and combine their previous mathematical knowledge in a new way in order to solve the problems [29,30].Early numeracy skills (i.e., numerical relational and counting skills) have been shown to predict later mathematical problem-solving skills [30].For instance, to solve mathematical problems children need to understand the used language [24] such as numerical relational concepts.In addition, solving mathematical problems requires children to use different counting and reasoning strategies and gives children a meaningful purpose for using mathematics (e.g., One child has this amount of coins and another one this amount.How many coins does that first child have to give to the other in order they both have as many coins?[24]).The ability to solve mathematical problems develops in later preschool years [24,31], however, studies have shown that already four to five-year-old children are able to solve mathematical problem-solving tasks including problems that require arithmetic skills [30,32] as well as geometrics and combinatorics [30].

Supporting early mathematical skills
Considering the importance of early numeracy and mathematical problem-solving skills for later life, it is important to study how these skills can be fostered effectively already during preschool years.Mathematical problem-solving in preschoolers is a less studied topic and there are only a few intervention studies conducted on preschoolers (e. g., [33]) and most with qualitative research methods [34][35][36].Whereas research-based interventions with different kinds of instructional strategies, such as explicit instruction, corrective feedback, concrete manipulatives, or computer-assisted approaches, have been developed to support the learning of early numeracy [37].The effectiveness of these interventions on low-performing children's early numeracy has been demonstrated previously highlighting the importance of early support [11,37].
Early mathematical skills have been found to be related to language skills [38], and thus language skills should be also considered when planning interventions.One potential way to support children's early mathematical skills would be by supporting children's numerical relational skills which are important when understanding math-related language [39].One natural way to increase the use of numerical relational skills with preschool-aged children is during story reading [40].A previous review study demonstrated that story-reading interventions are an effective way to support children's early numeracy [39], and especially numerical relational skill learning [40].In addition, story-reading interventions have been found to improve mathematical problem-solving (i.e., tasks that require geometry [33]).Indeed, numerical relational skills have been found to be closely related to mathematical problem-solving and thus it is suggested that when supporting mathematical problem-solving, also numerical relational skills should be practiced [30].
As discussed above, intervention programs can differ in terms of intervention content, however, interventions can also differ in their study design.When conducting intervention research, it is preferred to include a control group, since otherwise, it is difficult to determine whether the improvements are due to the intervention or normal development [41].The control groups can be either passive control groups that do not participate in any additional practices or active control groups, where the intervention effects are compared to other types of interventions.When using only passive control groups, it is difficult to conclude whether the effects stem from the intervention content or the extra attention given to children [41].Including active control groups enables the comparison of different intervention contents with each other, and thus it is preferred to use active control groups in the intervention studies [11].Another important intervention design aspect is including delayed post-measurement that reveals if the intervention effects hold after the intervention is finished.A common limitation of the previous early mathematical interventions is that the long-term effects of the interventions have not been investigated or found often [11,42].However, the long-term effects of the interventions are important in terms of preventing later difficulties and thus should be also investigated in the intervention studies [11].

Early mathematical and fundamental motor skills
For children, a natural way to explore new things is by moving [43].While engaging in different environments and activities, children start to learn a group of gross motor skills called fundamental motor skills [44].Fundamental motor skills, which consist of balance, manipulative, and locomotor movement skills [45], are important skills to develop during preschool years since later, more complex motor skills are developed upon them [46].These skills are needed for example when participating in different physical activities such as playing games with peers [47].
The development of fundamental motor skills usually occurs during the age of two to seven years [45] making the development of fundamental motor skills and cognitive skills parallel during the early years [3].It has been argued that practicing these skills may activate the same brain areas, making these skills highly interrelated [4,48].For example, one study found that improvements in fundamental motor skills during the intervention partly explained the improvements in early mathematical skills, indicating that there is a relation between these skills [10].One explanation for this connection can also be the contextual aspects of fundamental motor skills practices since fundamental motor skill activities are usually performed in groups and require children to P. Jylänki et al. actively shift their attention between different rules or environments [4,49].Thus, during this context, children also engage and practice their executive functions.Empirical research has also found evidence that underlines this connection by revealing the relation between fundamental motor skills and executive functions [50].In addition to executive functions, there is also evidence that fundamental motor skills may be related to mathematical problem-solving skills [51] and that executive functions may mediate the effects of fundamental motor skills on early mathematical skills in preschool-aged children [5].
In line with the previously presented evidence, systematic reviews have demonstrated that fundamental motor skill interventions are effective in supporting typically developing children as well as children with special educational needs, especially when the fundamental motor skills and cognitive or academic skill learning are combined [6,7].In preschool-aged children, the evidence of the effectiveness of fundamental motor skill interventions on executive functions is well-established [6,50].However, only a few studies investigate the effects of fundamental motor skill interventions on early mathematical skills [12][13][14][15], and no studies on mathematical problem-solving although longitudinal evidence indicates that improvements in fundamental motor skills were related to improvements in mathematical problem-solving [51].Since studies with school-aged children have demonstrated that fundamental motor skill interventions can be effective, especially for children's mathematical skills [16], and there is evidence from cross-sectional studies of the connection between fundamental motor and early mathematical skills in preschoolers [5,52], the effectiveness of fundamental motor skill interventions on preschool-aged children's early mathematical skills should be studied more.

Movement with Early Numeracy -intervention
As demonstrated by previous studies, both numerical relational skills practicing (e.g., within a story-reading context [39,53]), as well as fundamental motor skill interventions that are integrated into academic skill practicing [6,7], have been found to be effective ways to improve children's early numeracy or more broadly early academic skills.Based on this evidence, the Movement with Early Numeracy (MovEN) -intervention was developed to combine the learning of numerical relational skills via story reading with fundamental motor skills practice.The MovEN -intervention demonstrated positive immediate and long-term effects on children's early numeracy skills in the pilot study [13].However, the effectiveness of the MovEN -intervention was not possible to compare to early numeracy or fundamental motor skills practice alone, which has been a common limitation in other combined fundamental motor skill interventions as well [6,7] highlighting the need for further research.In addition, in previous studies, individual background variables were not considered in light of the effectiveness of the intervention.

Individual differences affecting intervention effectiveness
Although there are positive findings from previous interventions on early mathematical skills, it is not expected that a universal response to the interventions can be accomplished, meaning that all children will not benefit from the interventions provided [54].Thus, it is important to investigate the individual differences that affect the intervention's effectiveness.Previous studies have suggested several potential causes for individual differences in children's early mathematical skills and fundamental motor skills.Individual differences in mathematical skills may occur due to cognitive skills [18] or opportunities for home math interactions, for instance [55][56][57].Especially higher-order cognitive skills, such as executive functions, are found to be important for learning mathematics [18,58].According to recent results from preschoolers, executive functions can be divided into two components: inhibition and switching, and updating [59].Inhibition and switching enable children to control their attention and behavior while inhibiting irrelevant stimuli [60] and switching between tasks or mental sets [61].These skills are important for early mathematical skills since children need to carefully examine the problems or tasks rather than answering the first impulse, and switch to different mental sets for example when counting by different units like minutes and hours [24].Inhibition and switching have also been found to predict later mathematical skills [62,63].Updating refers to the ability to update relevant information in working memory [64].Working memory is important when solving mathematical tasks since those tasks require holding and processing information in short-term memory [24].Working memory capacity is found to be an important predictor of mathematical skills already in the preschool years (e.g., [65,66]).It is important to be able to update the working memory capacity by replacing old, unnecessary, information with relevant information, to free mental "space" to solve mathematical tasks [24,64].In addition to mathematical skills, executive functions have been found to be important in fundamental motor skills learning, and it has been suggested that inhibition and switching ability drives the development of fundamental motor skills [21].
One variable that affects early mathematical skills is language skills.Usually in this age group, early mathematical tasks are presented orally, and thus children need receptive and expressive language skills to understand the presented tasks [19,27,67].Early numeracy and language skills have been found to be related [38], and general language skills have been shown to predict early mathematical skills [17].Especially, numerical relational skills (also referred to as mathematical language [53]) have an important role in this relation [26], and math-related language skills have been found to predict early numeracy more than general language [26,68].The importance of understanding used language is also important when understanding mathematical problems, and it has been shown that language skills are related to mathematical problem-solving [30].
Also, parental socioeconomic status has been found to be related to children's early mathematical skills [56], and many studies have shown that children from low-income families lag behind in their early mathematical learning [69,70].This relation may be caused by the lower educational level of the parents [71], parental learning difficulties [72], or parent-child interactions [73].In addition, the home environment influences children's mathematical learning [71,72,74].For example, the rich use of numerical relational concepts in everyday talk at home (i.e., counting objects or recognizing which number is greater) supports children's early mathematical skills [55,57].
Related to fundamental motor skills learning it has been shown that socioeconomic status also affects development [20].For instance, opportunities to practice fundamental motor skills in a home environment affect motor development and thus there can be large variability in children's fundamental motor skills at a young age [47].Preschools play a crucial role as a supporter of essential fundamental motor skills development for children, who have fewer opportunities to develop their fundamental motor skills in their home environment [75].
In sum, individual variables such as parental socioeconomic status, child's language skills, and executive functions impact early mathematical skills (e.g., [18,56]) and fundamental motor skills development (e.g., [20,21]).Since all these individual background variables are related to children's learning, it would be important to investigate if these factors also affect intervention effects.

The present study
Early mathematical skills are important to develop during early years [17].Individual differences in early mathematical skills have been shown already in the preschool years [71] highlighting the importance of developing effective interventions to support the development early on.Different kinds of early numeracy interventions have been studied over the years with positive effects [37], however, long-term effects of these interventions as well as individual differences that affect the effectiveness of the interventions are rarely investigated.

P. Jylänki et al.
In recent years, it has been suggested that children's learning should be studied in a more holistic manner and one possibility could be by combining the learning with fundamental motor skills [6].Indeed, there is evidence that fundamental motor skills are related to early mathematical skills [5,51].However, this relation should be studied more with intervention design and, there is a lack of evidence about which kind of interventions (i.e., early numeracy intervention, fundamental motor skills intervention, or combined fundamental motor skills and early numeracy intervention) are most effective to support the learning of preschool-aged children's early mathematical skills.In order to reveal the most effective practices, active control groups should be included in the intervention studies [11].
To answer above mentioned research gap, in this present study, we aimed to examine the immediate and long-term effects of combined early numeracy and fundamental motor skill intervention called MovEN, on children's early numeracy and mathematical problemsolving with two active control groups.Since there are findings suggesting that the improvements in the fundamental motor skills partly explain the improvements in early mathematical skills [10], the intervention effects were also investigated on fundamental motor skills.The children in the active control groups participated in the interventions that included separately either early numeracy or fundamental motor skills learning.In addition, it was assessed whether individual background variables such as parental socioeconomic status, child's language skills, and executive functions impact the effectiveness of the interventions.More specifically we aimed to answer the following research questions:

Participants
This study was conducted as a part of Active Early Numeracy (AEN) -project.Preschools from Southern Finland were contacted, and teachers who recognized that children in their group are at risk for low performance in early numeracy were asked to volunteer for the study.Together six volunteering preschools were included in this study, including a total of 50 children (M = 5.07 years, SD = 0.85); 29 girls, and 21 boys.Children were divided into three groups at the preschool level: 22 children from three preschools in the MovEN -intervention, 14 children from one preschool in the early numeracy control group, and 14 children from two preschools in the fundamental motor skills control group.The sample size remained rather low since this study was conducted during the Covid-19 pandemic, limiting preschools possibilities to participate in the study as well as research group to conduct assessment during restrictions.
Five of the six participating preschools were located in the metropolitan area of Finland and were included in the AEN -project.These children's parental, as well as the municipality's consents, were obtained before the start of the study.However, one preschool outside the metropolitan area volunteered to participate in the MovEN -intervention.In this municipality, with the agreement of the head of the preschool, the preschool teachers were trained to conduct the intervention measurements to collect the data anonymously, and thus parents' and municipality's consent was not needed.The AEN -project got university ethics approval on August 28, 2019.Participation was voluntary, and withdrawal from the study was possible at any time.
The participating children's parents filled out a questionnaire concerning their parents' socioeconomic status.This included questions about parents' education, employment status, total net income as well as home language.The baseline characteristics as well as the socioeconomic background of the participating children are presented in Table 1.In the MovEN and fundamental motor skill groups, the participants' parents displayed a greater representation of higher education whereas in the early numeracy group higher presentation of high school or vocational school degrees compared to the socioeconomic status factor Note. Information about the family's socioeconomic status is missing from one preschool in the MovEN -intervention group (n = 7).* Mean household net income in [Finland] was 44 781 euros/year in 2021 [76].
P. Jylänki et al. distribution in the respective municipality.The household's net incomes were similar to the municipality's overall distribution in every group.However, the parents' employment status in MovEN and fundamental motor skill groups displayed a greater representation of part and fulltime employment and lower unemployment in the fundamental motor skills group, whereas in the early numeracy group higher representation of students.In all intervention groups, Finnish as a home language was slightly over-presented compared to the distribution in the respective municipality.

Early numeracy
Children's early numeracy was measured with the Early Numeracy Test [77], which measures children's numerical relational and counting skills.The first 20 items of the Early Numeracy Test measure numerical relational skills.These items are related to numerical concepts of comparison, classification, one-to-one correspondence, and seriation.The latter 20 items measuring children's counting skills are related to the use of number words, structured counting, resultative counting, and a general understanding of numbers [78].The Early Numeracy Test was performed individually with each child.For a correct answer, one point was given whereas for the wrong answer, zero point was given.The child did not get feedback from their answers.The Early Numeracy Test has been previously found to be a valid tool to measure early numeracy in Finnish children [78] as well as reliable in this sample α = 0.937 (N = 48).

Mathematical problem-solving
The mathematical problem-solving was measured with the Mathematical Problem-Solving Measure which has been shown to be a reliable measure to assess 4-to 5-year-olds mathematical problem-solving skills [30].The measure includes 21 items covering different mathematical domains, but only 10 items were used in this study for practical reasons.The items that were chosen to include in this study were the items that correlated most strongly with the sum variable of the entire measure in the 5-year-olds in AEN -project sample (N = 123).These items were designed to measure reasoning (6 items), arithmetics (3 items), and combinatorics (1 item) [30].The used 10 items demonstrated good reliability α = 0.806 (N = 39) in the current sample.

Fundamental motor skills
Fundamental motor skills were measured with a jumping sideways task from the KTK-test battery (Körperkoordinationstest für Kinder [79]).The jumping sideways task has been shown to be a good predictor for the total fundamental motor skills score (locomotor and object control skills measured with the Test of Gross Motor Development − 3 [80] and balancing skills measured with KTK-test) in the whole sample in the AEN -project.The correlations to the total sum in 5 to 6-year-olds (N = 416-450) were r = 0.610.
In the jumping sideways task, children were asked to jump over a wooden bar (60 × 4 × 2 cm) as many times as possible for 15 seconds.The jumping area was limited to 100 × 60 cm.Children performed the task twice and the number of correct jumps (i.e., the child's toes are pointing forward and the jump stays inside the jumping area) was counted.Children had five practice jumps before the actual test to ensure that they had understood the assignment.The jumping sideways task demonstrated very good reliability α = 0.958 (N = 48) in the current sample.The sum score of the two trials was used in the analysis.

Executive functions
Two components of executive functions were measured using computer-based tests in the ePrime software.Inhibition and switching were measured with the Flanker task and updating with the pictorial updating task [81].Both tests have been previously used to measure EF in preschool-aged children (e.g., [59]).In the Flanker task, children were presented with a row of five fish.Children needed to identify the direction of the middle fish by pressing a key that points in the same direction.The task includes 36 congruent trials when the middle fish is facing in the same direction and 36 incongruent trials when the middle fish is facing in the opposite direction than the other four fish.Both correct answers with a total score of 72, as well as reaction time, were used in the analysis.The Flanker task demonstrated very good reliability α = 0.964 (N = 48) in the current sample.In the pictorial updating task, children were presented with pictures of different animals once at a time.Children needed to remember from one to three last animals they saw by pressing the picture of those animals in the correct order from the touchscreen.Correct answers with a maximum score of 36 were used in the analysis.The pictorial updating task demonstrated good reliability α = 0.854 (N = 48) in the current sample.

Language skills
Children's receptive and expressive language skills were measured with age-specific tasks from the LENE (i.e., Leikki-ikäisen neurologinen arvio [Preschool-aged children's neurological evaluation]; [82,83]).The LENE is a language skill screener intended to measure children's receptive and expressive language skills.The number of items varied between age groups including 12, 19, 16, and 21 items for 3, 4, 5, and 6-year-olds respectively.There was only one 3-year-old in the current sample, hence the reliability was calculated for the whole sample in the AEN -project: the internal consistency for LENE was α = 0.833 (N = 132) in 3-year-olds, α = 0.847 (N = 174) in 4-year-olds, α = 0.859 (N = 157) in 5-year-olds, and α = 0.671 (N = 147) in 6-year-olds.Since language skills were measured with age-specific tasks with different maximum scores, z-scores were used in the analysis in order to compare children's language skills.

Intervention program and control conditions
This study used Movement with Early Numeracy (MovEN) -intervention with two control interventions focusing only on early numeracy or fundamental motor skills training.All intervention programs included 16 sessions that lasted approximately 45 minutes and were held two to three times a week.The sessions were held in children's preschools by their teacher.All conditions included story-reading activity following either early numeracy, fundamental motor skills, or combined early numeracy and fundamental motor skills practice.
The MovEN -intervention (see the full description of the intervention program [13]) is an 8-week intervention that combines the learning of numerical relational skills with fundamental motor skills.The intervention program is developed for 4 to 6-year-old children.The intervention program combines the learning of numerical relational skills and fundamental motor skills: The numerical relation skills were practiced through five story books with rich numerical relational concepts (Table 2).The numerical relational concepts that were practiced included concepts that are used to describe for example comparing (e.g., more, less), spatial relations (e.g., under, above), classification (e.g., same, different), and quantity (e.g., none, together).After the story-reading, children participated in the fundamental motor skills activities, which included the same numerical relational concepts as the storybooks.The fundamental motor skills activities included practices for locomotor skills (e.g., jumping or sliding), object control skills (e.g., throwing and catching a ball), and stability skills (e.g., standing on one leg).Each intervention session followed the same structure including beginning with an overview of the following activities and ending with a relaxation.The intervention was held in a group by preschool teachers.
Children in the early numeracy intervention participated in the 8week intervention, which included the same story-reading activity as the MovEN intervention.After the story reading activity, children performed early numeracy tasks that included the same numerical relational concepts as the books while sitting.These activities included different kinds of games and activities with concrete items such as P. Jylänki et al. pictures, blocks, and number or dot cards that have been used also in previous intervention studies [e.g., 84].The intervention structure followed as much as possible the MovEN -intervention without the fundamental motor skills training.
Children in the fundamental motor skills intervention group participated in the 8-week intervention.The fundamental motor skills intervention included also a story-reading activity, however, the used story books were related to fundamental motor skill activities (e.g., football or yoga; see Table 2) rather than numerical relational concepts.After the story-reading activity, the children participated in fundamental motor skill activities that followed the same activities as in the MovEN intervention without the use of numerical relational concepts.

Procedure
This study followed a quasi-experimental study design with the main intervention (i.e., MovEN-intervention) and two control interventions.Children's early numeracy, mathematical problem-solving, and fundamental motor skills were measured once before and twice after the intervention.The post-measurements were conducted immediately after the intervention and the delayed post-measurement on average nine and half weeks after the immediate post-measurement.In addition, children's executive function and language skills were measured only before the intervention and were used as background variables.In one preschool, the preschool teachers were trained to collect the data, and for practical reasons, it was not possible to gather executive functions and language skills data.All other measurements were conducted by the first author or trained research assistants in the children's preschools.
The preschool teachers were trained to conduct the intervention in their preschools.The teachers were provided with one training session (about 1 hour) before the intervention.To ensure the fidelity of the intervention, the first author had an online meeting (about 30 minutes) with the teacher every second week.During the meetings, any questions that the teachers had were discussed, as well as the implementation of the intervention was followed.In addition, the teachers filled in logbooks.In the logbooks, teachers reported for each session the participating children, any general remarks, and rated the tasks based on the instruction as well as implementation.On average children in the MovEN -intervention group participated in 13 out of 16 sessions whereas in the early numeracy and fundamental motor skill control groups the children participated on average in 14 out of 16 sessions.Together three children dropped out of the study since they moved to different preschools during the intervention.Missing data occurred in some measurement points due to children not being present during the measurement day or disagreeing to perform the tests.The data was missing completely at random (p > .548)according to missing data analysis by Little's MCAR Test.

Data analysis
The data analyses were performed using IBM SPSS Statistics 29.In preliminary analysis, a one-way analysis of variance (ANOVA) was used to reveal if there were any differences between the intervention and active control groups in the pre-measurements.This analysis included outcome variables such as early numeracy, mathematical problemsolving, and fundamental motor skills as well as background variables: executive functions (inhibition and switching, and updating), and language skills.
The main data analyses were conducted in three phases: First, within-group effects in the MovEN intervention and active control groups were investigated.Here a paired samples t-test was used individually for each group.The intervention effects were investigated on early numeracy (total score as well as numerical relational and counting skills separately), mathematical problem-solving, and fundamental motor skills.Second, between-group effects of the MovEN -intervention and active control groups were investigated using a one-way ANOVA post hoc analysis (Bonferroni for variables with equal variances and Games-Howell for variables with unequal variances).The intervention effects were compared in early numeracy, mathematical problemsolving, and fundamental motor skills.Since there were significant differences between the intervention and active control groups prior the intervention (see the preliminary analyses), for each outcome variable, gain scores between pre and post-measurements as well as between pre and delayed post-measurements were used in the analysis.Lastly, regression analyses were conducted to reveal if the individual background variables predicted the effectiveness of the interventions.
Here data was analyzed separately for the children who participated in the early numeracy practicing (i.e., MovEN intervention and early numeracy group) and for the children who participated in the fundamental movement interventions (i.e., MovEN intervention and fundamental motor skill group) in order to increase the sample size in the analysis.For the children that participated in the early numeracy practices, the gain in early numeracy, and mathematical problemsolving were used as dependent variables, and individual background variables (prior performance, age, parental socioeconomic status, executive functions, and language skills) as independent variables.Whereas in the group that participated in the fundamental motor skill practices, the gain in the fundamental motor skills was used as a dependent variable.All data analyses were confirmed with the nonparametric tests since the sample size was small.

Preliminary analyses
A series of One-Way ANOVAs were conducted to reveal group differences between the MovEN intervention, early numeracy, and fundamental motor skill active control groups at the pre-measurement (Table 3).There were significant differences between the groups in executive functions.The post hoc comparison revealed that the early numeracy group had a significantly better response time in the inhibition and switching tasks compared to the fundamental motor skills group (p = .002),but there were no significant differences compared to the MovEN group.When analyzing the differences in the inhibition and switching accuracy, the children in the early numeracy group had significantly more correct answers compared to the MovEN group (p = .001).Accordingly, in the updating task, the children in the early numeracy group had significantly more correct answers compared to the fundamental motor skills group (p = .001)and the MovEN group (p = .002).
When evaluating the differences in early numeracy and mathematical problem-solving, children in the early numeracy group had significantly better numerical relational (p = .016),counting skills (p = < 0.004), and total early numeracy (p = .005),as well as mathematical problem-solving skills (p = .043)compared to the MovEN group.However, no differences were found compared to the fundamental motor skills group.When evaluating the differences in the fundamental motor skills, children in the MovEN (p < .001)and fundamental motor skills groups (p < .001)had significantly lower fundamental motor skills compared to the early numeracy group at the pre-measurement.Finally, there were no statistically significant differences in children's language skills between the MovEN, early numeracy, and fundamental motor skill groups.

Within-group comparison (RQ1)
In order to reveal the within-group effects, paired samples t-tests were performed individually for each group.The results show that the early numeracy total score improved significantly during the intervention in both the MovEN group (p = .004)and the early numeracy group (p = .021).However numerical relational skills improved only in the MovEN group (p = <0.001).Mathematical problem-solving skills improved also significantly in both the MovEN group (p = <0.001) and the early numeracy group (p = <0.001).In the fundamental motor skills, significant improvements were found in the MovEN group (p = <0.001) and fundamental motor skills group (p = <0.001),but not in the early numeracy group.All the improvements were sustained in the delayed post-measurement: both the MovEN and early numeracy groups improved significantly in total early numeracy score as well as in numerical relational and counting skills from pre-measurement to delayed post-measurement.In the mathematical problem-solving and fundamental motor skills, all groups demonstrated significant improvements from the pre-measurement.

Between-group comparison (RQ2)
As there were significant differences between the groups in the preassessment, gain scores were used to investigate the differences in the effectiveness of the MovEN intervention, early numeracy, and fundamental motor skill control groups (Table 3).Only statistically significant differences were found in mathematical problem-solving, where the MovEN group improved significantly more during the intervention compared to the children in the fundamental motor skills control group (p = .012).Although the improvements in other variables during the MovEN -intervention did not reach a significant level compared to active control groups, the data suggested a trend in the direction of favoring the MovEN intervention.When the mean gain scores from premeasurement to delayed post-measurement were analyzed, no significant differences were found between the groups.

Individual differences affecting the effectiveness of the interventions (RQ3)
To reveal individual differences that can affect the effectiveness of the interventions, the data was split into two groups: children who had early numeracy component in the interventions (n = 36; i.e., children in the MovEN intervention and early numeracy control group) and children who had fundamental motor skills component in the interventions (n = 36; i.e., children in the MovEN intervention and fundamental motor skill control group).Regression analyses were conducted to reveal if the individual variables predicted the effectiveness of the interventions (Table 4).The results showed that at pre-measurement, lower early numeracy and better updating ability predicted larger gains in early numeracy during the early numeracy practices.However, inhibition and switching, language skills, socioeconomic status, and age did not predict the gain in early numeracy.Regarding mathematical problem-solving, lower mathematical problem-solving skills, and better early numeracy skills at pre-measurement predicted larger gain during the intervention in mathematical problem-solving.In the group that had fundamental motor skill practice, neither age, fundamental motor skills, socioeconomic status, or executive functions at pre-measurement predicted the gain of fundamental motor skills during the intervention.

Discussion
This study aimed to examine the immediate and long-term effects of combined early numeracy and fundamental motor skill intervention called MovEN, on children's early numeracy, mathematical problemsolving, and fundamental motor skills with two active control groups.The children in the active control groups participated in the interventions that included separately either early numeracy or fundamental motor skills learning.The intervention effects were examined first at a within-group and then at a between-group level.In addition, the individual variables affecting the effectiveness of the interventions were considered.The results demonstrated that children who practiced early numeracy skills either in MovEN intervention or early numeracy control group improved their early numeracy and mathematical problem-solving skills.However, only children who participated in the MovEN intervention improved in their numerical relational skills.The children who practiced their fundamental motor skills, either in MovEN intervention or fundamental motor skill control group, improved their fundamental motor skills.The performance in delayed measurement showed that children maintained the skills they had learned during the intervention practices.When the effectiveness of the MovEN intervention was compared to the active control groups, children's mathematical problem-solving skills improved more in the MovEN intervention compared to the control group practicing only fundamental motor skills.

P. Jylänki et al.
From the individual factors affecting interventions effectiveness, only updating predicted the effectiveness over and above prior performance.
The finding that children who participated in the MovEN -intervention improved their early numeracy, numerical relational skills, and fundamental motor skills is in line with previous findings from the MovEN intervention [13].In that study, children's mathematical problem-solving skills were not measured, and thus our results cannot be fully compared.However, recent results from preschoolers' mathematical problem-solving show that early numeracy was one of the best predictors of mathematical problem-solving skills [30] which is in line with our findings that early numeracy practice also improved children's mathematical problem-solving skills.In addition, in line with the findings of Vessonen et al. [30], children who had better early numeracy skills at baseline improved more in their mathematical problem-solving skills during the interventions.This finding is unsurprising since during mathematical problem-solving children need to use different counting and reasoning strategies and adapt their previous mathematical knowledge to solve the problems [24], and thus better early numeracy skills may enhance mathematical problem-solving development.Interestingly, the children who had lower levels of mathematical problem-solving skills before the intervention improved more in mathematical problem-solving during the intervention.A similar finding was found in early numeracy learning: the children who had lower levels of early numeracy before the intervention improved more during the intervention in early numeracy.These findings suggest that the interventions are most effective in the group of children that have lower initial performance and need additional practice.
When considering other individual factors affecting the effectiveness of the interventions, it was found that children who had better updating ability at the baseline improved more in their early numeracy.Indeed, working memory [65,66] and updating [21] have been found to predict mathematical skills, and the ability to update working memory is involved in different mathematical activities such as arithmetic calculations and reasoning [85].Thus, it might be that a better ability to update information in working memory allows more mental "space" to solve mathematical tasks [24,64] which can help children with better updating ability to learn more during the intervention.However, it was surprising that the updating ability did not predict improvement in mathematical problem-solving.Although there has been found a relation between working memory and mathematical skills, it has been dependent on the mathematical task [66].Thus, it may be that mathematical problem-solving skills do not relay as much to working memory as early numeracy.Since to our knowledge, there are no prior studies assessing the relation between working memory and mathematical problem-solving in preschool-aged children, this should be studied more in the future.
Language skills have been shown to be related to mathematical problem-solving [27] and in this current study, we found that children who had better language skills indeed improved more in their mathematical problem-solving skills.However, this was not the case anymore, when early numeracy was considered suggesting that early numeracy explained the improvements more.Since early numeracy was measured Note. 1 = Pre-measurement, 2 = immediate post-measurement, 3 = delayed post-measurement, Gain 1-2 = Gain between pre and immediate post-measurement, Gain 1-3 = Gain between pre and delayed post-measurement.Significant within-group effects are shown in boldface.
P. Jylänki et al. with the Early Numeracy Test, which also measures children's numerical relational skills, it may be that the numerical relational skills (i.e., concepts related to mathematics) explain mathematical problem-solving learning more than general language.Although language skills are important to early mathematical skills, in line with our findings, previous studies have found that numerical relational skills are more related to early mathematical skills than general language [26,68].In addition, the language skills were measured with a screener test with age-specific tasks and there were no differences found before the intervention in the language skills.Thus, the limited variability in the language skills may also explain why the language skills did not predict the effectiveness of the interventions.Surprisingly, the fundamental motor skills at the pre-measurement did not predict the improvements during the interventions that included fundamental motor skills practicing.However, children who participated in the MovEN intervention and fundamental motor skill control group improved significantly in their fundamental motor skills during the interventions.This finding suggests that regardless of the previous level of fundamental motor skills, the children had the possibility to improve during the intervention in their fundamental motor skills.This is important at least in the MovEN intervention, since one previous combined fundamental motor and early mathematical skill intervention in seven-year-olds, found that the improvements in mathematical skills during the intervention were partly explained by the improvements in the fundamental motor skills [10].Thus, it is important that during combined fundamental motor skills and early mathematical skill interventions, also the fundamental motor skills improve although it is not the main outcome of interest.Another surprising finding was that executive functions did not predict improvements in fundamental motor skills, although recent findings suggest that especially inhibition and switching predict the development of fundamental motor skills [21].Since most of the previous studies [86] have focused on the effects of fundamental motor skills on executive functions, not vice versa, we need more research to understand the developmental relations between executive functions and fundamental motor skills.
When comparing the effects of MovEN and active control groups, it seemed that children's mathematical problem-solving skills improved more in the MovEN intervention compared to the active control group with only fundamental motor skills practice.Young children such as preschoolers benefit from modeling a variety of different types of mathematical problems with concrete objects [24].Thus, using their bodies as well as different manipulatives like balls or bean bags, can help children to understand different mathematical problems.In addition, preschoolers benefit from explaining and discussing their solutions to mathematical problems [24].During the MovEN intervention, children were asked questions where they needed to discuss mathematics as well as solve mathematical tasks using different manipulatives.Thus, this combination of discussing and using their body and manipulatives during the intervention may explain the differences between the MovEN intervention and the fundamental motor skill group.
Although there were no differences between the effectiveness of the interventions in other outcomes than in mathematical problem-solving, the mean gains during the interventions showed a tendency in a way that the children in the MovEN and early numeracy -interventions improved more in early numeracy compared to children in the fundamental motor skills intervention.Since there were no differences between the gains in early numeracy and mathematical problem-solving in the MovEN intervention and early numeracy control group, it can be concluded that both are effective in supporting the learning of early numeracy and mathematical problem-solving.However, with MovEN -intervention, it was possible to also support fundamental motor skills, showing that children's learning can be supported in a more holistic way with the MovEN intervention.

Strengths and limitations
This is the first study to compare combined early numeracy and fundamental motor skills learning (i.e., MovEN -intervention) to early numeracy, and fundamental motor skills learning alone.Although the MovEN -intervention was not found to be more effective than early numeracy or fundamental motor skill practicing alone, it was possible to support children's learning holistically by demonstrating similar effects on early numeracy and mathematical problem-solving as well as fundamental motor skills than practicing these skills alone.Thus, the results show that in preschools, the learning of mathematical skills can be combined with movement activities effectively and without compromising the effects on mathematical learning.
The main limitation of this study was the small sample size and the heterogeneity of the participants.For example, the children in the early numeracy group were significantly older compared to children in the MovEN or fundamental motor skills group.This is one explanation for the fact that children in the early numeracy intervention performed better at the baseline compared to the children in the MovEN intervention or fundamental motor skills control group.Although the children in the groups differed in age, children's age did not explain the improvements during the interventions.The results showed a tendency in a way that the children in the MovEN intervention group improved more in total early numeracy, numerical relational skills, mathematical problem-solving, and fundamental motor skills compared to the early numeracy and fundamental motor skill groups.However, only in mathematical problem-solving, this difference between MovEN and fundamental motor skill groups was considered significant.In light of the fact that small sample sizes can cause false negative p-values [87], this study should be repeated with a larger sample size and more comparative intervention groups in the future.Finally, since updating ability was shown to affect the effectiveness of the MovEN and early numeracy interventions and previous interventions and cross-sectional studies have found fundamental motor skills and executive functions related [50], future studies should include executive functions measures in the post-measurements also to see if this kind of interventions can also affect children's executive functions ability.

Conclusion
Children's early numeracy and mathematical problem-solving skills can be supported with the MovEN intervention or early numeracy practice alone.However, with combined MovEN -intervention, it was possible to support both early mathematical skills as well as fundamental motor skills.Above and beyond the prior performance of early numeracy, the updating ability predicted the improvements in early numeracy during the MovEN intervention and early numeracy practice.Other individual background variables such as socioeconomic status, inhibition and switching, age or prior performance in fundamental motor skills did not predict the intervention effectiveness.In addition, based on these results, with fundamental motor skills practice, it was not possible to support the learning of early mathematical skills.

Table 1
Baseline characteristics and socioeconomic status of the participants.

Table 2
Used story books in the MovEN, early numeracy, and fundamental motor skill interventions.

Table 3
Between-group comparison at pre-measurement and gain scores during the interventions.