^{*}

^{a}

^{a}

^{b}

^{a}

The present study investigated the predictive role of spatial skills for arithmetic and number line estimation in kindergarten children (N = 125). Spatial skills are known to be related to mathematical development, but due to the construct’s non-unitary nature, different aspects of spatial skills need to be differentiated. In the present study, a spatial orientation task, a spatial visualization task and visuo-motor integration task were administered to assess three different aspects of spatial skills. Furthermore, we assessed counting abilities, knowledge of Arabic numerals, quantitative knowledge, as well as verbal working memory and verbal intelligence in kindergarten. Four months later, the same children performed an arithmetic and a number line estimation task to evaluate how the abilities measured at Time 1 predicted early mathematics outcomes. Hierarchical regression analysis revealed that children’s performance in arithmetic was predicted by their performance on the spatial orientation and visuo-motor integration task, as well as their knowledge of the Arabic numerals. Performance in number line estimation was significantly predicted by the children’s spatial orientation performance. Our findings emphasize the role of spatial skills, notably spatial orientation, in mathematical development. The relation between spatial orientation and arithmetic was partially mediated by the number line estimation task. Our results further show that some aspects of spatial skills might be more predictive of mathematical development than others, underlining the importance to differentiate within the construct of spatial skills when it comes to understanding numerical development.

The acquisition of early numerical abilities in kindergarten is important for later mathematical learning, school achievement and more general life outcomes such as adult socioeconomic status (

In the context of numerical development, domain-specific and domain-general abilities can be distinguished.

Basic numerical abilities such as quantitative knowledge, counting abilities and numeral knowledge are considered as domain-specific precursors of mathematical abilities. The pivotal role of these number-specific abilities has been shown across different studies (e.g.

Development of numerical cognition occurs, according to

Besides the afore-mentioned factors, the literature suggests that

Spatial skills play a special role in mathematical development and a clear classification, as either domain-general or domain-specific abilities, is not straightforward. As spatial skills do not a have a numerical component per se, they could be considered as domain-general abilities. On the other hand, the relation between spatial skills and mathematics has been shown to hold throughout development (for a review see

Providing a concise definition of spatial skills is particularly challenging as it is not a unified construct and rarely a precise definition is provided. Studies investigating the same underlying construct of spatial skills differ with regard to the term they use, even when using the same assessment tasks. Terms such as “visuo-spatial abilities”, “visual perception” and “spatial skills” are often used interchangeably (e.g.

On a general level,

Considering the development of spatial skills in early childhood, the importance of a related ability arises: visuo-motor integration (VMI). The main distinction between VMI and the three spatial categories defined by

The relation between spatial skills and mathematics is generally considerd as “(…) one of the most robust and well-established findings in cognitive psychology” (

An influential research strand, studying the link between spatial skills and mathematics, focuses on the systematic interaction between space encoding and numbers in adults. This interaction is commonly explained through the spatial organization of numerical magnitude on a mental number line (

Another strand of research, within the broad research area investigating the relation between spatial skills and mathematics, is focusing on “pure” spatial skills: spatial skills without a numerical component (e.g. mental rotation abilities, mental paper folding etc.) (see

One approach to assess children’s spatial skills is by using assembly and pattern construction tasks.

Taking these findings together, spatial skills and VMI should both be considered when investigating the predictive value of spatial skills for mathematical learning (see also

One explanation ^{st} and 2^{nd} grade are predictive of their improvement in number line knowledge over the school year. Children’s mental transformation skills at age five predicted their performance on an approximate calculation task at age eight. Moreover, they found that children’s linear number line knowledge at age six mediated this relation.

A further tentative explanation why spatial skills and mathematics are related, is based on the findings that mental rotation positively influences children’s performance on equations or missing term problems (

Whereas all of the studies cited up to now are correlational in nature, first attempts have been made to determine whether training spatial skills has a direct impact on mathematics. If spatial training would prove to transfer to mathematics, this would support the assumption that spatial skills have a causal role in mathematical development. Up to now, data on this topic remains inconclusive.

When studying the role of different aspects of spatial skills for mathematical learning, it is important to keep in mind that spatial skills and mathematics are both multifaceted. In view of the componential nature of mathematics, different spatial skills might only relate to specific aspects of mathematics and not to other aspects (

To investigate the relation between spatial skills and mathematics, it is not sufficient to identify the relevant spatial predictors of mathematics. The choice of measures of mathematical knowledge with regard to its componential nature, also needs to be critically reflected. Due to the componential nature of spatial skills and mathematics, certain spatial skills might relate differentially to certain components of mathematics. A profound understanding of the aspects of spatial skills that are primarily related to mathematical development would provide vital information for early education. This knowledge will provide researchers, teachers and educators with valuable information for the development and implementation of early interventions.

There is currently a shortcoming of empirical data on the differential relation between distinct aspects of spatial skills and early mathematics. Our aim was to investigate the relation between three different spatial tasks and two measures of early mathematics when taking number-specific and domain-general abilities into account. The predictive power of a specific aspect of spatial perception (namely

To evaluate the specific relation between spatial skills and early mathematic knowledge, we included further variables that are potentially predictive of early mathematics. Adding measures of verbal short-term memory and verbal intelligence, should allow us to disentangle the relation between different aspects of spatial skills and different aspects of early mathematics while controlling for the influence of other domain-general abilities. Parent’s occupational status, school affiliation, children’s age in months and gender were considered as control variables (see also

Considering the heterogeneity regarding the operationalization of spatial skills throughout different studies, the present study was mainly exploratory concerning the relation between different spatial tasks and different aspects of early mathematics.

First, we attempted to determine the predictive power of three spatial tasks respectively, namely spatial orientation, spatial visualization and VMI, for early mathematics when being considered concurrently. The current state of research does not allow us to formulate any precise hypotheses, about the importance of one specific spatial aspect over the other, as most studies considered these aspects isolated from each other. Nevertheless, considering recent literature on the importance of spatial skills for early mathematics in the pre-school years, we hypothesized, according to

In a second step we attempted to elucidate the nature of the relation between spatial skills and early mathematics more thoroughly. One explanation for the relationship between spatial skills and mathematics in children is that better spatial skills lead to a more refined representation of the mental number line, which in turn should lead to better performance in mathematics (

Data were collected in two public kindergartens in Luxembourg. Children from ten different classrooms participated in the present study. In Luxembourg, children visit kindergarten for two years, when they are between four and six years old. Formal structured mathematics instruction in the Luxembourgish schooling system starts after kindergarten, when children enter first grade. A total sample of

Children’s socio-economic and cultural background was measured by a parental questionnaire adapted from

Children were tested in a quiet place in their school building during regular school hours. Assessment took place at two measurement time points, in the middle of the school year (t1) and four months later, at the end of the school year (t2). Tasks were administered in two separate testing sessions of approximately 20 minutes. Task administration, within a testing session, occurred in fixed order. All the tests were administered in Luxembourgish, the language of instruction. Data collection was carried out in the context of a larger research project, in which additional measures have been administered during both sessions at both measurement time points. For the purpose of the present study, only a part of the tasks administered at the two measurement time points will be considered. The relevant measures of the present study are described in the following section.

Parents or caregivers gave their informed written consent and children gave their verbal assent for their participation in the present study. The study was authorized by the Ethics Review Panel of the University of Luxembourg.

Three different measures of spatial skills and number-specific abilities, respectively, were administered. Further, brief measures of verbal short-term storage and intelligence were included. No feedback was provided on any of the test items.

The measure of spatial orientation was adapted from the subtest “position in space” of the developmental test of visual perception (^{i}. The test consisted of eight items in total. The first part of this measure (Items 1 to 4) is an “odd one out” task requiring children to detect one picture out of five pictures that is different (a rotated version of the other four pictures). The second part (Item 5 to 8) is a “matching” task requiring children to find the picture out of four similar, but mirror reversed or rotated, pictures that matches the target picture. A sample item for each part is provided in

Spatial visualization was assessed by a mental transformation task. A shortened 12-item version of the Children’s Mental Transformation Task (CMTT;

The measure of VMI was adapted from the “spatial relations” subtest of the developmental test of visual perception (

Sample Items of the a) First and the b) Second Part of the Spatial Orientation Task, c) the Spatial Visualization Task and the d) Task of Visuo-Motor Integration. (

To assess children’s quantitative knowledge, the first step in the developmental model of

Children’s counting abilities were assessed through five brief counting and cardinality tasks: a free counting task, a “how many” task, a “give a number” task, a backward counting task and a forward counting task. In the free counting task, children were instructed to count as high as possible, starting at 1, thus reflecting children’s knowledge of the verbal number chain. Each child had two attempts, the best out of these two attempts was considered for analysis. Children were stopped when they could count up to 30. When children could not count up to 10, the scoring for this task was 0, for counting up to a number between 10 and 14 they were awarded 1 point, for counting up to 15 – 19 they were awarded 2 points, between 20 – 29 they were awarded 3 points and counting up to 30 was scored as 4 points on this task. In the “how many task”, the experimenter laid out a given number of marbles in front of the child and the child was asked to tell the experimenter how many marbles there were in total. The number of marbles for these trials were: 4, 5 and 7 respectively. Correct answers were coded as 1, wrong answers as 0. Answers were considered correct if children counted out the marbles correctly or gave the cardinal answer correctly. In the “give a number” task, children were instructed to hand the verbally requested number of marbles to the experimenter. Children were given 12 marbles in total. They were instructed to give the requested number of marbles to the experimenter. The numbers requested in these trials were 3, 5 and 10 respectively. Correct answers were coded as 1, wrong answers as 0. In the backward counting task children were given three test trials with starting points at 4, 6 and 10 and they were instructed to count back to 1. In the forward counting task children were asked to count forward from a given number. This task consisted of two trials with starting points at 3 and 5. Children were stopped when they counted correctly for subsequent numbers. For each task, correct answers were coded as 1, wrong answers as 0. A total score was calculated. The maximum score that could be reached on this scale was 15. Cronbach’s alpha was

Children’s symbolic knowledge of Arabic numerals was assessed through a number comparison task and a number naming task. The

In addition to measures of spatial skills and early mathematics, the ordered digit span task (“

To assess children’s verbal intelligence, we administered the information subtest from the French version of the

The number line estimation task was adapted from

To assess children’s early arithmetic skills we adapted the first part of the arithmetic subtest from the TEDI-Math test battery (

To investigate the predictive value of spatial skills, number-specific abilities, verbal STM, and verbal intelligence for children’s performance in early arithmetic and acuity in number line estimation, hierarchical regression analyses were performed. Due to the longitudinal nature of the data collection, the criterion of time precedence was met, allowing us to specify the directionality of the presumed effects (as formulated by

To assess the relation between every independent variable and the two dependent variables, arithmetic and number line estimation skills, hierarchical multiple regressions were computed for every dependent variable respectively. To evaluate the predictive value of different abilities and control variables, hierarchical multiple regressions were run in four steps. In a first step the control variables gender, age, school affiliation and occupational level were entered in the model. In a second step the domain-general variables verbal STM and verbal intelligence were entered in the model. In a third step the number-specific predictor variables, namely quantitative knowledge, counting abilities and Arabic numeral knowledge, were entered. In a fourth step, the three spatial measures, namely spatial orientation, spatial visualization and VMI were entered. The focus of the present study is the estimation of the predictive value of the single independent variables and the amount of variance the respective models can explain (^{2}

If one or more aspects were significantly predictive of arithmetic and number line estimation, a mediation analysis with number line estimation as a potential mediator of the relation between spatial skills and arithmetic was performed (in analogy to

Multiple regression and mediation analysis were performed using

Descriptive statistics and correlations between the variables of interest are reported in

Measure | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1. School^{a} |
- | |||||||||||||

2. Age (months) | -.09 | - | ||||||||||||

3. Gender^{b} |
-.00 | .07 | - | |||||||||||

4. Occupational level | .22* | .03 | -.15 | - | ||||||||||

Administered at t1 | ||||||||||||||

5. Spatial orientation | .06 | .50** | .09 | .27** | - | |||||||||

6. Spatial visualization | -.17 | .33** | .03 | .36** | .51** | - | ||||||||

7. Visuo-motor integration | .05 | .52** | .09 | .27** | .56** | .36** | - | |||||||

8. Quantitative knowledge ( |
.11 | -.36** | .03 | -.19* | -.43** | -.28** | -.32** | - | ||||||

9. Counting abilities | -.09 | .55** | -.01 | .32** | .57** | .47** | .53** | -.38** | - | |||||

10. Knowledge of Arabic numerals | .12 | .49** | .02 | .31** | .63** | .42** | .49** | -.28** | .75** | - | ||||

11. Digit span | -.09 | .16 | .06 | .23* | .21* | .26** | .25** | -.32** | .47** | .38** | - | |||

12. Verbal intelligence | .06 | .02 | .03 | .40** | .38** | .30** | .26** | -.09 | .55** | .51** | .31** | - | ||

Administered at t2 | ||||||||||||||

13. Arithmetic | .03 | .38** | -.03 | .30** | .64** | .38** | .59** | -.32** | .62** | .67** | .26** | .44** | ||

14. Number line estimation | -.13 | -.47** | .04 | -.27** | -.60** | -.34** | -.44** | .34** | -.59** | -.65** | -.34** | -.32** | -.58** | |

37.6%^{c} |
65.89 | 48.8^{d} |
50.42 | 5.30 | 5.54 | 4.22 | .35 | 9.67 | 15.75 | 4.5 | .01^{e} |
4.06 | 17.51 | |

7.60 | 15.73 | 2.00 | 2.69 | 2.25 | .35 | 3.81 | 4.15 | 1.88 | .99 | 1.79 | 11.19 | |||

Number of items | - | - | - | - | 8 | 12 | 7 | - | 15 | 20 | 16 | 24 | 6 | 8 |

Mean percentage correct (%) | - | - | - | - | 66.25 | 46.17 | 60.29 | - | 64.47 | 78.75 | 28 | - | 67.67 | - |

Min.-Max. | - | - | - | - | 0-8 | 1-12 | 0-7 | .02-2 | 0-15 | 4-20 | 0-8 | -2.32-2.29 | 0-6 | 3.19–53.25 |

Skewness | .23 | -.18 | -.55 | .34 | -.55 | 3.10 | -.49 | -.98 | -.28 | -.01 | -.79 | 1.23 | ||

Kurtosis | .34 | -1.25 | -.38 | -.79 | -.92 | 11.99 | -.56 | .33 | -.19 | -.69 | -.33 | 1.13 |

^{a}Dummy coded: 1 = Kindergarten A, 0 = Kindergarten B. ^{b}Dummy coded: 1 = female, 0 = male. ^{c}% of children affiliated to kindergarten B. ^{d}% of children who are female. ^{e}Please note that the values of the verbal intelligence score are z-values that have been calculated per age group.

*

Several correlations are worth noting. The eight variables measured at t1 were significantly correlated. Quantitative knowledge was related to spatial skills, Arabic number knowledge, counting abilities and verbal STM but not to verbal intelligence. Measures of spatial skills were all interrelated with correlation coefficients ranging from

The effects of different predictor combinations (described earlier in the methods section) on arithmetic and number line estimation were studied by four different multiple regression models.

The standardized parameter estimates are summarized in

Model | Estimate | ||
---|---|---|---|

Model 1 | |||

Intercept | -1.89 | .87 | .04 |

Gender^{a} |
.01 | .08 | .91 |

Age | .37 | .09 | < .01 |

School^{b} |
-.01 | .08 | .91 |

Occupational level | .29 | .07 | < .01 |

^{2} |
.07 | < .01 | |

Model 2 | |||

Intercept | -1.62 | .78 | .04 |

Gender | -.05 | .07 | .52 |

Age | .36 | .07 | < .01 |

School | .01 | .07 | .85 |

Occupational level | .13 | .08 | .10 |

Verbal STM | .07 | .07 | .34 |

Verbal Intelligence | .35 | .08 | < .01 |

^{2} |
.07 | < .01 | |

Model 3 | |||

Intercept | -.05 | .75 | .95 |

Gender | -.03 | .07 | .96 |

Age | .03 | .09 | .71 |

School | -.03 | .07 | .61 |

Occupational level | .09 | .07 | .19 |

Verbal STM | -.08 | .07 | .22 |

Verbal Intelligence | .10 | .09 | .28 |

Quantitative knowledge ( |
-.11 | .07 | .11 |

Counting abilities | .16 | .13 | .25 |

Arabic numeral knowledge | .47 | .11 | < .01 |

^{2} |
.07 | < .01 | |

Model 4 | |||

Intercept | .57 | .74 | .44 |

Gender | -.05 | .06 | .41 |

Age | -.12 | .09 | .18 |

School | -.08 | .07 | .25 |

Occupational level | .05 | .07 | .42 |

Verbal STM | -.05 | .06 | .41 |

Verbal Intelligence | .03 | .08 | .66 |

Quantitative knowledge ( |
-.02 | .08 | .83 |

Counting abilities | .10 | .12 | .36 |

Arabic numeral knowledge | .36 | .12 | < .01 |

Spatial orientation | .26 | .09 | < .01 |

Spatial visualization | -.04 | .07 | .52 |

VMI | .29 | .08 | < .01 |

^{2} |
.06 | < .01 |

^{a}Dummy coded: 1 = female, 0 = male. ^{b}Dummy coded: 1 = Kindergarten A, 0 = Kindergarten B.

The standardized parameter estimates are summarized in

Model | Estimate | SE | |
---|---|---|---|

Model 1 | |||

Intercept | 6.97 | .61 | < .01 |

Gender^{a} |
.04 | .08 | .62 |

Age | -.48 | .06 | < .01 |

School^{b} |
-.12 | .08 | .11 |

Occupational level | -.22 | .07 | < .01 |

^{2} |
.07 | < .01 | |

Model 2 | |||

Intercept | 6.98 | .53 | < .01 |

Gender | .08 | .07 | .30 |

Age | -.45 | .06 | < .01 |

School | -.16 | .07 | .02 |

Occupational level | -.07 | .08 | .33 |

Verbal STM | -.20 | .08 | .01 |

Verbal Intelligence | -.22 | .08 | .01 |

^{2} |
.06 | < .01 | |

Model 3 | |||

Intercept | 5.62 | .64 | < .01 |

Gender | .04 | .07 | .53 |

Age | -.18 | .08 | .03 |

School | -.12 | .07 | .07 |

Occupational level | -.04 | .07 | .61 |

Verbal STM | -.08 | .07 | .27 |

Verbal Intelligence | -.01 | .10 | .92 |

Quantitative knowledge ( |
.09 | .08 | .22 |

Counting abilities | -.14 | .16 | .40 |

Arabic numeral knowledge | -.37 | .14 | .01 |

^{2} |
.06 | < .01 | |

Model 4 | |||

Intercept | 5.62 | .70 | .00 |

Gender | .07 | .07 | .30 |

Age | -.12 | .10 | .20 |

School | -.11 | .07 | .11 |

Occupational level | -.03 | .08 | .68 |

Verbal STM | -.12 | .07 | .09 |

Verbal Intelligence | .04 | .10 | .71 |

Quantitative knowledge ( |
.02 | .08 | .80 |

Counting abilities | -.13 | .17 | .42 |

Arabic numeral knowledge | -.27 | .14 | .06 |

Spatial orientation | -.29 | .10 | .01 |

Spatial visualization | .04 | .07 | .60 |

VMI | .00 | .09 | .98 |

^{2} |
.05 | < .01 |

^{a}Dummy coded: 1 = female, 0 = male. ^{b}Dummy coded: 1 = Kindergarten A, 0 = Kindergarten B.

To further study the respective role of the spatial measures, hierarchical regression including the three measures of spatial skills in three different steps was performed. The regression analysis was run for arithmetic and number line estimation separately. In a first step, spatial visualization was entered, in a second step the VMI was entered and in a third step spatial orientation was entered as a predictor. The order of predictors was based on the correlation coefficients between the predictors and the dependent variables. Spatial visualization showed the lowest correlation with the dependent variables, VMI showed higher correlation with the dependent variables than spatial visualization and spatial orientation exhibited the highest correlation with the dependent variables.

Spatial visualization is a significant predictor of

Spatial visualization is a significant predictor of

Mediation analysis was performed by computing total, direct and indirect effects of the model depicted in

Mediation Model with Spatial Orientation as Independent Variable (x), Number Line Estimation as Mediator (m) and Arithmetic as Dependent Variable (y).

Results of the analysis reveal a partial mediation of the relation between spatial orientation and arithmetic through number line estimation. The standardized total effect from spatial orientation to arithmetic is 0.64 (_{1} × β_{2}

The purpose of the present study was to study the predictive power of spatial skills on mathematical learning in young children prior formal schooling. Regression models, including indicators of number-specific and domain-general abilities for mathematical learning, highlight the importance of different spatial measures for children’s arithmetic performance and number line estimation.

Performance on the arithmetic task was predicted by spatial orientation, VMI and Arabic numeral knowledge in the final model. Performance on the number line estimation task was predicted by spatial orientation only in the final model. These findings highlight the predictive power of spatial skills for early mathematics in children prior formal schooling. Furthermore, our results show, that different measures of spatial skills are not equally important for the prediction of early mathematics. One spatial measure, spatial visualization, did not significantly predict any of the outcome measures when controlling for other aspects. In contrast, spatial orientation predicted arithmetic and number line estimation. In addition to spatial orientation, VMI predicted arithmetic when being considered with number-specific and control variables concurrently.

To interpret these findings, a closer look at the spatial tasks is necessary. The spatial orientation task requires orientation discrimination of the same object. The target item and distractor items are mirrored or rotated versions of the same object. In contrast, the spatial visualization task used in the present study is more object-based and it requires mental transformation. Children have to identify the target shape out of four different shapes that they get when two separate pieces are put together. As the four shapes (one target shape and three distractor shapes) presented to the child differ as objects, focusing on one aspect of the target shape might be sufficient to solve this task. The key aspect of the spatial orientation task might thus be orientation discrimination (e.g. left-right orientation) of specific features within series of shapes that are otherwise identical (see e.g.

The administered task of VMI taps into children’s ability to coordinate spatial processing and fine-motor control. VMI significantly predicted performance in arithmetic, but not in number line estimation, when considered concurrently with other measures. The latter seems to be in conflict with the assumption of

In the final regression model, the task of spatial visualization did not predict any of our outcome measures. This is most likely explained by the additional consideration of spatial orientation in our model. Spatial orientation might be the more relevant aspect of spatial skills in the context of mathematical development. This assumption is confirmed by results of the additional regression analysis with arithmetic and number line estimation as dependent variables respectively. Spatial visualization is a significant predictor of arithmetic and number line estimation, until spatial orientation is added to the model. Both measures of spatial skills appear to be overlapping (underpinned by their correlation). When considered isolatedly from other spatial measures, the measure of spatial visualization seems to carry significant information, but the measure of spatial orientation may contain the only relevant information. These findings are in line with

The predictive power of three different number-specific abilities on arithmetic and number line estimation was studied. In the hierarchical regression analyses, number-specific predictors were added in model 3 to more general predictors. Adding number-specific predictors to the regression models, predicting arithmetic and number line estimation respectively, yielded the importance of Arabic numeral knowledge for both dependent variables. Arabic numeral knowledge was the only significant predictor of arithmetic in Model 3; Arabic numeral knowledge and age were both two significant predictors for number line estimation in Model 3.

Quantitative knowledge did not predict any of our two outcome measures. In prior research, findings about the importance of the ANS in mathematical development remained inconclusive (

Counting abilities did not predict arithmetic and number line estimation. This finding is particularly surprising with regard to arithmetic. It contrasts with findings suggesting that arithmetic builds up on counting abilities (

The finding that Arabic numeral knowledge, but not counting abilities, is predictive of arithmetic performance, could indicate that a more mature understanding of numbers is needed to solve this task. Simple counting strategies might be insufficient. Knowledge of the number symbol and the cardinality, especially the understanding of relations between numerical quantities (as described by

Results of the mediation analysis reveal that number line estimation partially mediates the relation between spatial orientation and arithmetic. A complete mediation of the latter relation by number line estimation could have accounted for the assumption that better spatial skills go along with a more refined representation of the mental number line, which in turn leads to better performance in arithmetic (

In a previous study,

In the introduction, the non-consensus with regard to the classification of spatial skills as either domain-specific or domain-general abilities for mathematical development was discussed. In our study we considered number-specific abilities (i.e. quantitative knowledge, counting abilities and Arabic numeral knowledge), domain-general abilities (i.e. verbal STM and verbal intelligence) and three measures of spatial skills (i.e. spatial orientation, spatial visualization and VMI) concurrently. The concurrent consideration of these different variables allows us to gain a clearer view of their relation with early mathematics.

Two major findings can be retained. First, we observed that different measures of spatial skills were not equally predictive of early mathematics. Spatial orientation predicted arithmetic and number line estimation, VMI predicted arithmetic only and spatial visualization predicted neither arithmetic nor number line estimation when controlling for other spatial skills. Second, the specific role of spatial orientation is highlighted by its prediction of arithmetic

Two measures of domain-general abilities that could potentially predict early mathematics were included, but neither verbal intelligence nor verbal STM significantly predicted arithmetic or number line estimation in the final model. In the model predicting number line estimation, verbal STM and verbal intelligence lose their predictive value as soon as number-specific variables are added. In the model predicting arithmetic, verbal intelligence loses its predictive value when numerical precursor variables are added.

Taking these findings together, we can conclude that in the present study, spatial skills, and notably the spatial orientation task, predict performance on two early math measures. Whereas domain-general abilities, such as verbal STM and verbal intelligence, are not significantly predictive of early mathematics when number-specific variables are considered, spatial measures significantly predict early mathematics even when considered concurrently with domain-general and number-specific abilities. These findings suggest that spatial skills might indeed be domain-specific abilities rather than domain-general abilities. To investigate this further, a follow-up of children’s school achievement in mathematics, and another school domain such as reading, should be envisaged to assess whether spatial skills do predict children’s achievement in mathematics but not in reading. If the latter were true, this would allow us to conclude that the predictive value of spatial skills is specific to mathematics and does not generalize to other domains.

A further point of discussion is the choice of the early mathematics outcome measures. We chose two measures we considered as tapping into children’s more mature understanding of mathematics: arithmetic and number line estimation.

When assessing arithmetic performance in children, it is crucially important to choose an age-appropriate task. In kindergarten formal mathematics instruction has not yet begun. Thus, we cannot expect children to be familiar with written arithmetic (e.g. ”3 + 5 = _“) nor with the verbal presentation of a simple arithmetic problem (e.g. “one plus three makes…?“). The administration of word problems goes along with a comparably high load in verbal working memory and proficiency in the language of test administration is required. We used an arithmetic task with visual support and verbal instruction to address these issues. We do acknowledge that the presence of visual support throughout the arithmetic task could have affected the results. The additional visual presentation of the arithmetic problem could have led some children to use simple counting strategies rather than mental arithmetic operations. If this were the case, it would be possible that the task would rather be a task of basic counting abilities than a task of early arithmetic. Nevertheless, two arguments can be put forward suggesting that the task does indeed assess early mental arithmetic operations. First, our results suggest that the arithmetic task is “more” than a simple counting task: counting abilities do not predict children’s performance on the arithmetic task. If the arithmetic task would solely assess children’s counting abilities, counting abilities would significantly predict performance on that task. Second, the nature of the visual support for subtraction items does not fit with the assumption that performance on the arithmetic task is assessing children’s counting abilities solely. Here a counting strategy would be insufficient to solve the item: if children would only count the visually presented items, their answer would correspond to the first operand, no subtraction operation would be performed.

The second outcome measure was a number line estimation task, more precisely a number-to-position task. We chose a number line between 0 to 20, because this should reflect the number range children are familiar with in kindergarten (see ^{2}_{lin}^{2}_{lin}_{.} This conclusion informed our choice to use PAE rather than ^{2}_{lin}

One limitation of the present study is that only single measures were used to assess each aspect of spatial skills. Ideally, method triangulation should be used to measure the different spatial aspects more reliably and reduce potential measurement errors (see discussion in

A further limitation is the choice of statistical analysis and modelling as we did only consider observed variables. Working with latent variables that are operationalized through at least two different measures, would have allowed to integrate variables that are free of measurement error and it would have provided a more coherent representation of the underlying construct than a single measure (see argumentation of

The delay between the two testing waves was comparably short (e.g.

Even though our model included number-specific abilities, as well as measures of spatial skills, verbal STM, verbal intelligence and children’s social and cultural background, we do not claim it to be exhaustive. We consider it especially important to specify that we did not include any specific measures of children’s language ability and executive functions. Language skills and executive functions are related to mathematical development, as pointed out in the introduction section. Future research should take into account further aspects of language, executive functions and spatial skills concurrently when studying their role as precursors for mathematical development

The present findings highlight the role of spatial skills for mathematical development prior formal schooling when controlling for number-specific and domain-general abilities. They emphasize the importance of differentiating between different aspects of spatial skills, as they tend to relate to early mathematics differentially. From a more practical point view, they also yield fruitful information for instruction in the kindergarten classroom as they support initiatives that aim to foster pre-schoolers’ spatial skills, most notably spatial orientation and visuo-motor integration, as important prerequisites for optimal learning in mathematics.

The authors confirm that the present empirical work has been carried out in accordance with relevant ethical principles and standards. Ethical approval has been obtained by the Ethics Review Panel (ERP) of the University of Luxembourg.

Socio-economic status was assessed by a parental questionnaire. Not all the parents returned the questionnaire fully completed. Information on the occupational level was missing for 10 children. Children were from diverse socioeconomic background: 0.8% of mothers and 0.8% of fathers have never carried out remunerated work, 6.4% of mothers and 8.8% of fathers are company managers or executive employees, 27.2% of mothers and 22.4 of fathers work in a scientific or related profession, 5.6% of mothers and 6.4% of fathers work as technicians, 23.2% of mothers and 10.4% of fathers are office workers, 12% of mothers 6.4% of fathers are employed in the services and sales domain, 14.4% of mothers and 10.4% of fathers are semi-skilled workers, 3.2% of fathers are qualified agricultural workers, 15.2% of fathers are craftsmen and 5.6% of fathers are motorists, machine operators or assembly workers.

The test was administered on a 13-inch Apple MacBook Pro. Each trial consisted of red and yellow dots that were presented within two rectangles. A picture of a sesame street character (Big Bird and Elmo) was associated with each rectangle. For each trial, dots appeared simultaneously in each rectangle and children had to judge in which rectangles more dots were presented. The number of dots within each set varied between 5 and 21. The ratio of the sets per trial and the time of presentation were adapted to children’s age according to the recommended settings by the authors of the test (

To further study the association between the number-specific and spatial measures, we conducted a regression analysis with the spatial measures as independent variables and each number-specific measure as dependent variable (DV) respectively. In the table below, the standardized estimates are reported. The measure of spatial orientation is significantly associated with the three number-specific measures. VMI is significantly associated with counting abilities and Arabic numeral knowledge. Spatial visualization is significantly associated with counting abilities. Overall, strong associations between spatial measures and measures of symbolic number knowledge (counting abilities and Arabic numeral knowledge) are observed.

Independent variable | DV: Quantitative knowledge |
DV: Counting abilities |
DV: Arabic numeral knowledge |
||||||
---|---|---|---|---|---|---|---|---|---|

Estimate | SE | Estimate | SE | Estimate | SE | ||||

Spatial orientation | -.34 | .11 | <.01 | .30 | .11 | <.01 | .46 | .10 | <.01 |

Spatial visualization | -.06 | .09 | .45 | .22 | .09 | .01 | .12 | .08 | .15 |

VMI | -.11 | .11 | .30 | .29 | .09 | <.01 | .20 | .09 | .02 |

^{2} |
.20 | .07 | <.01 | .43 | .07 | <.01 | .43 | .07 | <.01 |

Additional 7% of variance in arithmetic are explained by adding number-specific measures to the model.

Model | Estimate | SE | |
---|---|---|---|

Model 1 | |||

Intercept | .32 | .75 | .67 |

Gender^{a} |
-.09 | .06 | .15 |

Age | .03 | .08 | .71 |

School^{b} |
-.04 | .06 | .57 |

Occupational level | .04 | .07 | .52 |

Verbal STM | .04 | .06 | .53 |

Verbal Intelligence | .18 | .08 | .02 |

Spatial orientation | .37 | .09 | < .01 |

Spatial visualization | -.01 | .07 | .88 |

VMI | .32 | .08 | < .01 |

^{2} |
.06 | < .01 | |

Model 2 | |||

Intercept | .58 | .74 | .43 |

Gender | -.05 | .06 | .41 |

Age | -.11 | .08 | .18 |

School | -.08 | .07 | .25 |

Occupational level | .05 | .07 | .42 |

Verbal STM | -.05 | .06 | .41 |

Verbal Intelligence | .03 | .08 | .66 |

Spatial orientation | .26 | .09 | < .01 |

Spatial visualization | -.04 | .07 | .52 |

VMI | .29 | .08 | < .01 |

Quantitative knowledge ( |
-.02 | .08 | .83 |

Counting abilities | .10 | .12 | .36 |

Arabic numeral knowledge | .36 | .12 | < .01 |

^{2} |
.06 | < .01 |

^{a}Dummy coded: 1 = female, 0 = male. ^{b}Dummy coded: 1 = Kindergarten A, 0 = Kindergarten B.

Additional 3% of variance in number line estimation are explained by adding number-specific measures to the model.

Model | Estimate | SE | |
---|---|---|---|

Model 1 | |||

Intercept | 5.54 | .62 | < .01 |

Gender^{a} |
.10 | .07 | .13 |

Age | -.26 | .09 | < .01 |

School^{b} |
-.13 | .06 | .03 |

Occupational level | -.03 | .08 | .65 |

Verbal STM | -.20 | .07 | <. 01 |

Verbal Intelligence | -.10 | .08 | .23 |

Spatial orientation | -.38 | .10 | < .01 |

Spatial visualization | .01 | .07 | .90 |

VMI | -.02 | .09 | .81 |

^{2} |
.06 | < .01 | |

Model 2 | |||

Intercept | 5.12 | .66 | < .01 |

Gender | .07 | .07 | .30 |

Age | -.12 | .10 | .21 |

School | -.11 | .07 | .10 |

Occupational level | -.03 | .08 | .67 |

Verbal STM | -.12 | .07 | .09 |

Verbal Intelligence | .04 | .10 | .70 |

Spatial orientation | -.29 | .10 | < .01 |

Spatial visualization | .04 | .07 | .60 |

VMI | .00 | .09 | .98 |

Quantitative knowledge ( |
.02 | .08 | .83 |

Counting abilities | -.14 | .17 | .40 |

Arabic numeral knowledge | -.26 | .15 | .07 |

^{2} |
.05 | < .01 |

^{a}Dummy coded: 1 = female, 0 = male. ^{b}Dummy coded: 1 = Kindergarten A, 0 = Kindergarten B.

The authors have no funding to report.

The authors would like to thank all the children, their parents and the concerned teachers who kindly agreed to participate in the present study. The authors are grateful to Yanica Reichel and Nuno de Matos for their assistance during data collection. Furthermore, the authors would like to thank Ulrich Keller, University of Luxembourg (LUCET), for providing statistical advice.

The authors have declared that no competing interests exist.