

ORIGINAL ARTICLE 

Year : 2015  Volume
: 2
 Issue : 3  Page : 7987 

Early math learning with tablet PCs: The role of action
Peter J.N. Dejonckheere^{1}, Ad W Smitsman^{2}, Annemie Desoete^{3}, Birgit Haeck^{1}, Kimberly Ghyselinck^{1}, Kevin Hillaert^{1}, Katleen Coppenolle^{1}
^{1} Teacher Department, University College of Vives, Tielt, Belgium ^{2} Department of Developmental Psychology, Radboud University, Nijmegen, The Netherlands ^{3} Department of Clinical and Health Psychology, Ghent University, Gent, Belgium
Date of Web Publication  13Sep2016 
Correspondence Address: Peter J.N. Dejonckheere VIVES, Beernegemstraat 10, 8700 Tielt Belgium
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/23952555.190477
Context: The present study is about computer assisted learning (CAI) and how it facilitates early math learning in 46yearold children. Aim: Trying to demonstrate how changes in estimation accuracy are a result of different behavioral or action organizations during playing with a numerical board game on a tablet PC. Settings and Design: A preposttest design and a training intervention was used. Statistical Analysis Used: In order to measure childrens' estimation accuracy (N = 179), the percent absolute error scores were calculated and compared in a pretest and a posttest. Further, each child's best fitting linear function (Rlin) was computed in order to find out whether children handled numbers in a linear way. Materials and Methods: A number line estimation task with a 010 interval was used in both the pretest and the posttest. For the intervention training, each child received a tablet computer and could play on a digital number line for four 15min sessions. Children's hand and finger movements were manipulated during instruction in different conditions: Freely jumping or pointing. Results : Children's estimation accuracy increased after playing with the digital number line. However, the way in which behavior was organized during the training period resulted in different accuracy performances. Conclusions: These results show that minor changes in the behavioral system can lead to significantly different learning gains and that numerical knowledge is embodied in the system the child mobilizes. Keywords: Action, embodied cognition, math education, tablet PC
How to cite this article: Dejonckheere PJ, Smitsman AW, Desoete A, Haeck B, Ghyselinck K, Hillaert K, Coppenolle K. Early math learning with tablet PCs: The role of action. Eur J Psychol Educ Studies 2015;2:7987 
How to cite this URL: Dejonckheere PJ, Smitsman AW, Desoete A, Haeck B, Ghyselinck K, Hillaert K, Coppenolle K. Early math learning with tablet PCs: The role of action. Eur J Psychol Educ Studies [serial online] 2015 [cited 2017 Aug 23];2:7987. Available from: http://www.ejpes.org/text.asp?2015/2/3/79/190477 
Introduction   
Mathematics is of central importance to modern society and is becoming increasingly essential in many job profiles. ^{[1],[2]} Research evidence has illustrated the influence of numerical abilities on employment, promotion opportunities and wages, over and above the influence of literacy. Given the high social and individual cost associated with poorly developed mathematical skills, it is essential to gain insight into interventions that can enhance mathematical developments and the way these developments take place. ^{[3],[4]}
In recent times, "computerassisted interventions" (CAI) has received growing interest. ^{[5],[6]} Literature reviews have shown that the use of information and communication technology in teaching has a strong motivational and attentional stimulating effect on students. ^{[7],[8]} However, the introduction of this technology in young children's lives is not without controversy. First, contradictory results have been found concerning the educational effectiveness of CAI games ^{[9],[10]} and there are many public debates about the possible detrimental effects on children's learning. ^{[11]} Second, the processes involved in learning with CAI remain unclear. For instance, it is not clear how learners benefit from action and experience to help them represent the magnitudes of verbally stated or written numericals.
The way in which action occurs and in which knowledge is obtained is often viewed as disconnected in traditional cognitive psychology and constructivism. ^{[12]} However, they may also be conceived as two different aspects of the same behavioral system that creates information instead of reading out representations. Learning can be thought of as selforganization by the system, and new knowledge as an emergent property of that selforganizing activity. ^{[13]} Thus, to study learning and development we need to address the organizations of behavioral systems that generate knowledge and insight instead of the knowledge itself. Every task evokes a particular organization of the system that creates information, irrespective of whether the task is meant for assessing knowledge or learning.
Number line estimation
This study addresses ways CAI may furnish to facilitate early math learning, and to investigate processes that get facilitated in learning in more detail. Concretely, we trained children with a number line estimation task. ^{[14]} In a number line estimation task children are presented a series of lines with a number at each end (e.g., 010) and no other numbers or marks in between. They have to estimate the location on the line of a given number. ^{[15]} We trained children with such a task for several reasons. First, it enabled us to unravel how particular action organizations affect the way early number knowledge develops. Second, several studies have supported the hypothesis that number estimation accuracy significantly predicts later mathematics performance ^{[16],[17],[18],[19]} which makes number estimation training meaningful. A third reason is that training children to estimate numbers on a number line may encourage them to handle these numbers in a more linear way instead of a logarithmic one. A logarithmic representation compresses the distance between magnitudes at the middle and upper ends of the interval, whereas a linear representation provides an adequate reflection of the actual interval distances of numbers. In addition, it was found that linearity of number line judgments are positively correlated with children's math achievement test scores. ^{[17]}
Accomplishing whatever estimation task demands the mobilization of a behavioral or action organization. Insights from infancy research on action development indicate that these behavioral organizations form complex systems. ^{[20]} Two main characteristics of complex systems are their selforganizing dynamics (which means that organizations are formed on the spot as a result of local interactions) and their nonlinearity (which means that organizations are stable within boundaries, and that tasks that stretch the adaptive qualities of the organization beyond its limits will push behavior into a different form). For this study, it is of importance to note that the organization does not process information, but instead creates it, depending on the variables it regulates with respect to a task. These variables become available depending on the way the system gets organized. Of course, what we ordinarily conceive as information, such as earlier experiences, and the tasks itself play a significant role too. However, their role is that of constraints, that among other constraints and interdependencies together push the selforganizing processes into a particular behavioral organization. Their ongoing interactions form the dynamics that create the organization that the child uses to create information to accomplish a task, such as number line estimation. Learning greatly depends on the information that is created. Learning involves the change of state of nonawareness into awareness. Without the capacity to create information, such a transition would be unfeasible.
For this study, the complex systems view means that the focus of analysis of the task and learning involved should shift from the read out of representations to the act of representing itself. In number line estimation, irrespective of whether the task is used to assess a child's competence or foster learning, the patterned behaviors the child uses to position numbers on a line segment and variables they regulate to do so are at stake. As complex systems, these patterned behaviors create information, and may get attuned to the information they create about the interdependency of numbers, which involves their ordinal relation and their interdistances.
The intrinsic relation between the way behavior gets organized, the information that is created and estimation has been documented in earlier studies, including in the one by Smitsman. ^{[21]} In this study, adults overestimated proportions of circles or squares shown on a TVscreen, interspersed with another, when one category of figures was arranged in small, easily countable groups of 2 or 4 figures and the other category was shown ungrouped. An estimation bias favoring grouped figures above ungrouped figures did not show up in children of about 6 years old. Children whose estimations did not show such a bias, revealed this bias when they were taught the adult's supposed way of estimating. The bias resulted from sampling and counting the figures of both categories for a short period, and the difference in ease of countability between grouped and ungrouped figures. Research of Tversky and Kahneman provides abundant evidence that a person's estimations are based on and biased by the behavioral organizations, by them called heuristics, persons mobilize for their judgments. ^{[22]}
This study uses physical activities to represent numbers on a number line. A considerable amount of authors recognizes that mathematics is linked to patterning of activities. ^{[23]} Bautista and Roth for instance showed that mathematical sense may be expressed both for the producer as for the recipient through action. ^{[24]} They observed that embodied rhythmic patterns emerged in children's transactions with geometric objects and that dynamic contrasts (e.g., intensity, duration, and rhythm) could specify conceptual properties of the object. The authors then argued that the development of knowledge arose from unintended action that could not be reduced to merely abstract ideas. They further argued that the temporal separation of the child's beats on an object and intensity were used to describe the object in terms of its geometric distinctions and similarities. Another example is the research of Cook et al. ^{[25]} The authors showed that when children were encouraged to produce gestures with their hands to instantiate a new math concept, learning was more lasting than when they were asked to instantiate it in words alone.
The interconnection of action and cognition has recently received increased attention within debates about embodied cognition, arguing that human capabilities dealing with abstraction are grounded in the body's interaction with the world. ^{[26],[27]} From this perspective, the focus is not to attain maximal transparency between physical materials and hypothetical internal representations to achieve a maximal learning output. ^{[28]} It is rather about the complex behavioral systems that generate information and as a consequence of their capacity foster learning. It is unconceivable how a system that cannot create information and novelty ever would be able to learn and develop.
Study goals and research hypotheses
In this study, we investigated 46yearold children's changes in estimation accuracy as a result of a short training intervention that varied the way the estimation was organized. We used a simple number line task in both the pre and posttest. Children were asked to point to exact locations on a digital number line. The training varied the way children execute estimation. All training sessions consisted of reading aloud a series of random numbers (010). In a jumping training condition, each time a number was articulated, children moved a marker from one position to another on a digital number line. In this condition, the variable the children regulated was the interdistance of the readout numbers on the number line as well as their positions. In a pointing training condition, children were instructed to move the same marker to a location of their consent on the number line and to put it back to its initial location waiting for the next number. Jumping between numbers was not allowed. The variable children learned to regulate in the pointing condition involved the locations of a readout digits, but not their interdistances.
We expected that when accuracy would increase as a consequence of learning, it would change differentially because of the difference in information behaviors both trainings would generate. We expected a higher increase in accuracy for the jumping condition compared to the pointing condition, because this condition would create information about positions as well as distances whereas the other condition would create information about position and not necessarily interval distances.
Subjects and Methods   
Participants
Hundred and seventynine preschool children of 46yearold participated in the experiment (88 boys; 91 girls). Children were recruited from five different schools in the western part of Flanders (Belgium). Parents received a letter explaining the research and submitted informed consent in order for their children to participate. The ages of the children ranged from 54 to 73 months old (mean = 61.5; standard deviation [SD] =5.7). The children were randomly allocated to any of the three conditions: The jumping group (n = 81), the pointing group (n = 55), or the control group (n = 43). No rewards were received after the experiment.
Materials and Procedure   
The number line task
A horizontal number line estimation task with a 010 interval was used in both the pre and posttest, in line with Berteletti et al. and Booth and Siegler. ^{[29],[30]} This task was presented on a tablet PC and used trials in three different formats [Figure 1]: (1) as Arabic numerals (with anchors 0 and 10 and approximately 2 cm above the center of the line an Arabic number of 110 was shown), (2) as spoken number words (with anchors "zero" and "ten" and approximately 2 cm above the center of the line a number word was shown) and (3) as dot patterns (with anchors of zero dots and anchors of ten dots and approximately 2 cm above the center of the line a number of dots was shown). Irrespective of the representation that was used, the aim of the pretest (and posttest) was to estimate where the presented number had to be located as well as possible. To that end, the child had to touch the correct location on the tablet PC. Each child was pretested (and posttested) individually by means of a single tablet PC in a separate room within the child's own school. The test started with a red star on a white canvas that was depicted in the center of the screen. This star had a diameter of about 6 cm and each time a point of the star was touched a green correction mark appeared. Then, three practice trials were given with the number line, one for each condition (Arabic, word, dots). For the Arabic condition, the following instructions were given: "Look, here you can see a black line (pointing), here is zero, and there is ten (pointing), above the line, there is a number." "I will ask you to show me where the number should be located on the line. When you know where the number should be located, you can tap that location with your finger. When the number is closer to zero, then you should tap more on this side (pointing), when the number is closer to ten, then you should tap more on this side (pointing). Here you see the number 2, show me on the line where 2 is." For the number word condition, the same instructions were given, but it was said "I will read a number for you and then you should show me on the number line where the number belongs. This is 'one', show me on the line where 'one' is." The third practice trial was a trial with dots. The experimenter said "Sometimes, I will show you this. Here you can see the line as you saw before. On this side, zero dots are shown (pointing). On the other side, there are ten dots. Now you can show me again where the dots here above (pointing) should be located on the line". After the practice trials, thirty test trials were given (randomly offered: Ten Arabic numbers, ten word numbers and ten dot numbers). At the start of each trial, the experimenter gave the following instructions: "This line goes from 0 to 10 (pointing). If you know that zero is located here (pointing) and ten is located over here (pointing), where should this number (pointing the number above) be located?" In the word number condition, the word was pointed to and pronounced out loud. In the dot condition the experimenter said: "If you know that there are no dots here (pointing) and here ten (pointing), where should these dots (pointing to the number above) then be located on the line?"  Figure 1: Screen shots of the number line task (pre and posttest). Arabic numbers (on top), word numbers (in the middle), dot numbers (at the bottom)
Click here to view 
For all trials, no feedback or suggestions were given. Scores for each trial were calculated by the application itself.
The training intervention
The training intervention was carried out traditionally, with small groups of children (45). This was guided by a finalyear preschool teacherstudent and started 1 or 2 days after the pretest assessment. In the meantime, other children received their normal activities from their own teacher; their intervention took place at other moments. Each child received a tablet PC and could play on the digital number line for about 15 min. This was done four times spread over two consecutive weeks. The procedure then differed according to the group in which the child was classified: Children were randomly assigned to the jumping group, the pointing group, or the control group. Children of the jumping group used an existing tablet application called 'Teaching Number Lines'. ^{[31]} The tool shows a thick horizontal number line of 015 that is centered at the bottom of the tablet screen. The line is divided into equal parts and is accompanied by the corresponding numbers (015). Different frog cartoons (markers) are positioned in the left upper corner.
A marker can be selected and can be dragged and dropped anywhere on the screen [Figure 2]. The student teacher told the children that they could drag and drop a frog character with one finger and that they could jump with it on the number line. Then, the student teacher showed a random number of 010 that was printed on a sheet of paper and pronounced that number loud and clear. Children could then execute one jump with their marker to the appropriate number. Then, the student teacher pronounced a new number and the children jumped in one move back or forward, depending on the number that was shown. When all numbers were presented, a new series of ten numbers was given. This was repeated for about 15 min. No feedback was given to participants regarding the accuracy of their marks. The percentage absolute error (PAE) was calculated per child as a measure of children's mapping skills and estimation accuracy.
Children of the pointing group used the same teaching tool as in the jumping group, but the instructions differed. After the teacher pronounced a random number, children moved their marker to the point where the number should be located on the number line and then the marker was brought back to its initial position. Jumping on the number line could be executed occasionally but was not encouraged in this condition [Figure 3]. As in the jumping condition, no feedback was given to participants regarding the accuracy of their marks. Finally, in the control condition, children did not do number line exercises. These children played with nonmath applications such as drawing games and making digital puzzles. This was done for the same amount of time as the other groups who played with the number line.  Figure 2: Screen shot of the application and movements in the jumping training condition
Click here to view 
 Figure 3: Screen shot of the application and movement in the pointing condition
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After the intervention phase, the posttest was executed within the same week as the intervention was finished. The posttest measured number estimations of 010 on a tablet PC (individually) and was exactly the same as the pretest.
Involvement
Each time a group of children played with the number line or with the nonmath games, an involvement score was assigned for each child in line with Laevers. ^{[32]} This was executed after 10 min of training by the student teacher herself. Involvement results were used to find out whether differences in motivation existed between conditions and groups (jumping, pointing, nonmath games). Scores ranged from 1 to 5. Score 1 was assigned to children who did not participate: These children often stared into space, showed absence or were listless and showed no activity. They could be busy but not with the subject of interest. Score 2 was assigned when the child's activity was often interrupted. Moments of activity could be observed, but this was approximately only half of the time. The rest of the time was filled with dreaming, looking away, etc., Score 3 assigned to the child when its activity was constant. However, the child did not seem to be really intensely working on it. It was rather factory work, lacking commitment, and passion. Score 4 was given to children who showed activity with intense moments. This code was appropriate when the child was intensely busy with the activity for at least half of the time. Finally, Score 5 was assigned to a child that showed permanent intense activity. These children showed the maximum degree of involvement, they did not show interest for other things and were strongly focused on the activity in question. The child showed mental efforts.
Results   
Involvement
First, a mean involvement score for each child and over different training trials was calculated, ranging from 1 (minimal involvement) to 5 (maximal involvement). Then, the involvement scores were used in a data analysis with involvement as dependent variable and group (jumping, pointing, control; between subjects) and gender (between subjects) as independent variables. Mean children's involvement scores were mean = 3.64; SD = 0.98. Involvement was different for boys and girls, in which boys showed less involvement than girls, F (1178) =21.27; P < 0.01 (Mboys = 3.32; SD = 0.89; Mgirls = 3.95; SD = 0.96). Involvement was not significantly different in the control group, the pointing group and the jumping group, F < 1, ns. Twentytwo children had Score 2, 63 children 3, 52 children 4 and 42 children had Score 5. For further data analysis, we opted to exclude all children with an involvement score <3 (as outliners). The remaining dataset consisted then of 157 children (jumping group, n = 72; pointing group, n = 46; control group, n = 39).
Percent absolute errors
In the preand posttest, children's estimation accuracy was measured (number line task). Therefore, the PAE was calculated by means of the following formula:
For instance, a child has to estimate the location of number 6 on the number line, but in reality, it places a mark at the location that corresponds to 2. The PAE then equals:
= 0.4 or 40%
Thus, the higher the percent, the worse the estimation accuracy.
PAEs were calculated for each child for Arabic numbers, word numbers and dot numbers. Means were compared with a 2 (pretest vs. posttest) × 3 (controls, pointing group, jumping group) mixed model of variance (ANOVA) with repeated measures. Pre and posttest (within subjects) and group (between subjects) acted as independent variables, whereas PAE was the dependent variable.
Results showed a main effect of pretest versus posttest, in which significantly less errors were made in the posttest, F (1, 54) =16.13; P < 0.001, partial η² = 0.10, (MPAEpre = 28.7; SD = 10.3; MPAEpost = 24.8, SD = 9.1). The main effect of group (controls, pointing, jumping) was not significant, F < 2. However, the interaction of pretest versus posttest with group for PAE revealed appeared to be significant, F (2, 154) =7.98; P = 0.001. Further, a posthoc Tukey test (HSD) for the posttest revealed that controls and the pointing group did not differ from each other in contrast to differences between controls and the jumping group (P < 0.003) and differences between the pointing group and the jumping group (P < 0.02). In the pretest, no significant differences emerged [Figure 4]. When the analysis was repeated for the three types of representation formats separately, the same pattern of results emerged. For Arabic numbers F (1, 154) =7.40; P = 0.007, partial η² =0.046, (MPAEpreArabic = 28.39; SD = 12.27; MPAEpostArabic = 25.01, SD = 9.83). The interaction of pretest versus posttest with group for PAE showed significance, F (2, 154) =3.35; P < 0.038.  Figure 4: Mean percent absolute errors in the pretest and the posttest for controls and experimentals
Click here to view 
For number words, F (1, 154) =15.08; P = 0.000, partial η² =0.089, (MPAEprenumber = 28.97; SD = 12.13; MPAEpostnumber = 24.21, SD = 10.00). The interaction of pretest versus posttest with group for PAE was significant, F (2, 154) =7.67; P = 0.001. For dots, F (1, 154) =11.89; P = 0.001, partial η² =0.072, (MPAEpredot = 28.73; SD = 10.38; MPAEpostnumber = 25.17, SD = 10.22). The interaction of pretest versus posttest with the group for PAE showed significance, F (2, 154) =6.22; P = 0.003.
R²Lin
Each child's best fitting linear function (=R²Lin) was computed on the basis of the scatter plot of the actual and estimated numbers. In this way, it was possible to analyze individual estimation data. Results revealed that for controls 38% of the variance in the pretest is explained by the best fitted linear function, whereas it was 44% in the posttest. For the pointing group, the best linear function accounted for 35% of the variance in the pretest and increased to 55% in the posttest. Finally, the jumping group showed 36% in the pretest and 55% in the posttest.
With the aid of an analysis with repeated measures in which the dependent variable was R²Lin in the pretest and the posttest and group as the independent variable (jumping, pointing, control), a significant interaction of pretest versus posttest and group for R²Lin was found, F (2, 158) =3.92; P < 0.03. In addition, a main effect of pretest versus posttest emerged, F (1, 158) = 52.03; P = 0.000, partial η² = 0.52. The main effect of group was not significant (F < 1) [Figure 5]. However, in the posttest differences (least significant difference) between the jumping group and controls (P < 0.07) and between the pointing group and controls (P < 0.09) tended to be significant, but after a posthoc Tukey test (HSD) these group differences no longer showed up.  Figure 5: Best fitting linear functions (means of R²Lin) from pretest to posttest for experimentals and controls
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Discussion   
In this study, we investigated children's changes in estimation accuracy as a result of a short training intervention program that varied the way in which the behavior was organized and the information the behavior created. Children were 46 years old and repeatedly heard and saw a number of series of random numbers (010) and moved a marker according to their condition. First, children of the jumping training condition moved the marker from one position to another on the digital number line, regulating interdistance of the readout or heard numbers as well as their positions. Second, children of the pointing training condition only moved the marker to the position where the number had to be located. Finally, children of the control group played nonmathematical games (puzzling, drawing, etc.) for the same period of intervention. The estimation accuracy was assessed by means of a pretest and a posttest. In these tests, children had to point exact locations on a digital number line marked by number 0 on one end of the line and number 10 on the other end of the line. It was expected that estimation accuracy would increase to different degrees as a consequence of the information different behaviors of the training conditions generated.
The present study, in line with Desoete and Praet and Ramani and Siegler, revealed that early numeracy can be stimulated by short training sessions. ^{[33],[34],[35]} Indeed, the present results showed that children who played with the number line 4 × 15 min during a limited intervention period already showed better estimation accuracy in a posttest when a number had to be located on a digital number line. However, the way in which behavior was organized during the training period resulted in different accuracy performances. That is, children's PAE scores decreased significantly from pretest to posttest in the jumping condition (where children regulated the interdistance of the readout numbers as well as their positions) but not in the pointing condition (where children regulated the positions of the readout numbers but not their interdistances) nor in the control condition (where children played nonmathematical games).
These PAE data are in line with other studies with analog tasks. For instance, Siegler and Ramani showed that children performed significantly better on a number line task after playing on a physical number board for a number of sessions. ^{[15]} In such a case, playing on the number board is comparable with the present data of our jumping training group. However in Siegler and Ramani's experiment, children could only make jumps of one or two numbers at a time creating less information about interdistances compared to the jumping group of the present study. At first sight, children's best fitting linearity functions not only improved in the jumping training group but also in the pointing training group. In the control group, no such improvement was observed. Indeed, the interaction between pre and posttest with group was significant, indicating that the change of means from pretest to posttest depends on the kind of intervention the child received. However, group differences in the posttest showed no significant results after a post hoc Tukey test (HSD) nor with a planned comparison. This is in contrast to Siegler and Ramani, who found that linearity of individual children's number line estimates varied significantly per session. Children who played the numerical board game showed the greatest pre and posttest change in contrast to children who played the same game but with colors instead of numbers. Since Siegler and Ramani only tested children with lowincome backgrounds, it is not recommended to further speculate on these different results.
Together, our results show that minor changes in the behavioral system can lead to significantly different learning gains. This indicates that numerical knowledge is embodied in the system the child mobilizes. Behavior is patterned. This is because a behavioral system is active underneath. The present research shows that the patterned behavior of the system, and more specifically the variables the behavioral pattern enables to regulate, in combination with the task setting determine the information it generates and consequently the learning of the system. The research also shows that the feedback the system receives when placing the marker on the appropriate position, not necessarily determines learning, because the feedback about the end result was similar in both the training conditions. The patterned behavior and the sensory consequences the behavior generates were the important factors that determined learning. This is a different conclusion than one would expect from the ideomotor view as advocated by action researchers. ^{[36]} This view also emphasizes the importance of behaviors and their sensory consequences as drivers of learning rather than stimuli but seemingly ignores the patterned behavior of a behavioral system which regulation of variables generates information about what to do and how to reach intended results.
Implications for education
Many children, especially with poor families, children with impoverished backgrounds and often nonnative speakers start elementary school with academic skills far beneath their peers. ^{[37]} According to Siegler and Ramani such differences in preschoolers' knowledge come to the surface during tasks with verbally stated or written numerals. ^{[28]} Using methods to this group of children is therefore of great importance. In addition, the value of short periods of intensive training and gaming might also be a lookahead approach to enhance arithmetic in children with dyscalculia. However, additional research on these children comparing both CAIs is certainly necessary.
Whatever target group is of interest, teachers must pay attention to the behavioral patterns and the variables they provoke learners to regulate when designing learning settings. They reveal the behavioral system learners mobilize when engaging in a learning setting and task, and the learning or nonlearning that may proceed by the engagement. The growing accessibility of digital tools on the market may enlighten this task and therefore be useful to facilitate the design of learning settings. In the present research a simple application allowed us to vary children's play with numerals and number lines. The research shows that an apparently slight variation in the task had a considerable effect on learning. However, digital tools are only useful with a thorough analysis of the learning task itself and the behaviors it evokes. An additional advantage of digital tools may be the challenge they may entail for teachers to move on developing the skill to analyze learning behaviors in more detail and to design learning settings accordingly. ^{[38]}
Conclusion   
Four6 year old children took part of a short training intervention through playing on a digital number board. The training intervention varied the way behavior was organized through manipulation of hands and finger movements on a tablet computer. Results show that numerical knowledge is embodied in the system the child mobilizes and that mathematical abstraction is grounded in the body's interaction with the environment.
Limitations of the present study
The results mentioned above should be interpreted with care since there are some limitations to the present study. We only assessed a small group of preschool children. Additional research with larger groups of participants comparing both CAIs is necessary. Furthermore, context variables, such as home and teacher content knowledge and expectations and parental involvement should be included. These limitations indicate that only part of the picture was investigated and that further studies should focus on these aspects. In addition, it is important to notice that kindergarten classrooms are sometimes understaffed. However, children in this study were able to play alone or with very little instruction.
Acknowledgment
This study could not have been possible without the commitment and the assistance of the following people: Erik Halsberghe (former CEO of Vives), Geert De Fauw (VB Zulte), Pieter De Vos (KBO Tielt), Veronique Mesure (Sint Henrik Petegem), Nico Van Poucke (VB Het Spoor). We also would like to express our deep appreciation to the children and the teachers of the participating schools.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]
