Ensuring that kindergarten children have a solid foundation in early numerical knowledge is of critical importance for later mathematical achievement. In this study, we targeted improving the numerical knowledge of kindergarteners (n = 81) from primarily low-income backgrounds using two approaches: one targeting their conceptual knowledge, specifically, their understanding of numerical magnitudes; and the other targeting their underlying cognitive system, specifically, their working memory. Both interventions involved playing game-like activities on tablet computers over the course of several sessions. As predicted, both interventions improved children’s numerical magnitude knowledge as compared to a no-contact control group, suggesting that both domain-specific and domain-general interventions facilitate mathematical learning. Individual differences in effort during the working memory game, but not the number knowledge training game predicted children’s improvements in number line estimation. The results demonstrate the potential of using a rapidly growing technology in early childhood classrooms to promote young children’s numerical knowledge.
Providing children with a strong foundation in mathematics is of critical importance since early mathematics performance is highly predictive for later mathematical achievement (
The current study aimed to improve kindergarten children’s numerical knowledge using tablet computer games. We tested the specificity of training activities on either domain-specific or domain-general skills as well as individual factors that may influence children’s learning from these activities. We focused primarily on children from low-income backgrounds since their numerical knowledge tends to trail behind children from middle-income backgrounds, and because they are most at risk for developing mathematical learning difficulties (
According to
The model also specifies that deficits in conceptual and procedural knowledge could be due to deficits in underlying cognitive systems, specifically working memory (WM). WM is an essential system that underlies the performance of virtually all complex cognitive activities including mathematics learning (
Individual differences in underlying cognitive systems, specifically, WM, predict performance in mathematics tasks requiring both, conceptual and procedural knowledge (see
Similarly, WM is critical for children’s procedural knowledge and execution of the action sequences used for solving arithmetic problems (
The mathematical performance of young children from lower-income backgrounds is on average lower than that of children from higher-income backgrounds. This achievement gap can widen over the course of schooling (
Children from low-income backgrounds are also vulnerable to develop deficits in domains that rely on the integrity of frontal brain regions, such as WM and related skills (
Research has shown that playing informal learning activities, specifically linear number board games, can promote children’s numerical magnitude knowledge. Linear number board games are physical representations of the mental number line, which is hypothesized to represent numbers horizontal from left to right in Western cultures (for reviews, see
Empirical work supports this approach and has shown that playing linear numerical board games, but not circular numerical board games, can improve young children’s numerical knowledge. In several studies, preschoolers were randomly assigned to either play a linear numerical board game with squares numbered from 1 to 10 or an identical game, except for the squares varied in color rather than number. After four 20 minute sessions, the children who played the numerical version of the game showed greater improvements in number line estimation, magnitude comparison, counting, numeral identification, and ability to learn novel arithmetic problems (
Promising results have also been found using computer software to improve children’s numerical knowledge. For example, children from lower-SES backgrounds between the ages of 4-6 played an adaptive computer game, “The Number Race,” that focused on performing numerical comparisons using dots, numbers, or arithmetic problems for six 20-min sessions. Playing the mathematics game improved children’s numerical magnitude knowledge, whereas playing a reading game did not (
Based on
Existing interventions, however, have predominantly targeted older children, thus, we have only minimal knowledge concerning the effects of WM training in kindergartners, especially from low-income backgrounds. For example,
An important growing trend in intervention research is to understand for whom and under what conditions training can improve children’s outcomes. One factor that likely influences the benefits of interventions is participants’ initial abilities. For example, playing linear board games is more effective for preschoolers with lower initial numerical knowledge (
Another factor that seems to be important is children’s engagement in activities. Number board games when played in a small group can keep children engaged during a play session (
The present study had three main goals. The first was to examine whether interventions targeting either numerical knowledge (domain-specific skills) or WM (domain-general skills) improved kindergarten children’s numerical knowledge. Both interventions were tablet games that were adapted from previous theoretical and empirical work. The numerical knowledge training game was a 0-100 number board game linearly-arranged in a 10 x 10 array adapted from
The second goal was to examine whether the interventions also improved children’s WM skills. There is a large literature demonstrating an association between children’s WM skills and their mathematics performance, however, since these relations are primarily correlational in nature, the direction and natures of these relations so far is unknown. Domain-general and domain-specific skills likely have a reciprocal relationship with greater developing skills in one can advance skills in the other. Therefore, we hypothesized that both training games would improve children’s WM compared to a control condition.
The third goal was to examine how individual differences predicted children’s outcomes. We examined whether pre-existing ability (i.e. children’s existing numerical magnitude knowledge) predicted their learning from the training. We also tested whether children’s engagement during the training activities predicted children’s outcomes on the numerical knowledge and WM measures. Self-reports of engagement have been important predictors of older children’s and adults’ learning from training (
Participants were 81 kindergarteners, ranging in age from 5 years 4 months to 7 years 3 months (
Characteristic | Participants ( |
---|---|
Age in months, |
72.11 (4.31) |
Gender (%) | |
Female | 44 |
Male | 56 |
Race and Ethnicity of Children (%)^{a} | |
Hispanic or Latino | 46 |
Caucasian/White | 18 |
Mixed Race | 12 |
African American or Black | 11 |
Asian or Pacific Islander | 11 |
Maternal Education (%) | |
Some high school | 11 |
High school diploma/GED | 32 |
Some college/vocational training or a 2-year college degree | 21 |
College degree or post-graduate degree | 30 |
Unreported | 6 |
Paternal Education (%) | |
Some high school | 16 |
High school diploma/GED | 30 |
Some college/vocational training or a 2-year college degree | 25 |
College degree or post-graduate degree | 23 |
Unreported | 6 |
Household Income (%) ^{b} | |
Less than $15,000 | 12 |
$15,000 - $30,000 | 28 |
$31,000 - $45,000 | 16 |
$46,000 - $59,000 | 11 |
$60,000 - $75,000 | 10 |
$76,000 - $100,000 | 5 |
$101,000 or greater | 9 |
Household Languages (%) | |
Monolingual English speakers | 67 |
Exposed to more than one language | 33 |
^{a}Race and ethnicity were unreported for 2% of the children. ^{b}Household income was unreported for 9% of the families.
The study consisted of 14 sessions conducted over the course of one to two months in the children’s classrooms. During sessions 1-2 and 13-14, an experimenter assessed children’s numerical knowledge and WM with three measures for each construct. Children were randomly assigned within classrooms to one of three conditions (
The games used in both training conditions were designed to be engaging by incorporating video game-like features and artistic graphics (
In this tablet game, children were presented with a 10 x 10 matrix numbered 1-100 with numbers in each row increasing from left to right (
Domain-specific condition: Numerical magnitude knowledge training a) Example of a turn; b) Example of a character magnitude comparison question.
This tablet game was modeled after previous work (
Domain-general condition: Working memory training. Example for set size 2, along with feedback screens shown at the end of each trial.
After each training session, children answered three questions to assess their enjoyment, self-efficacy, and effort during the session. These questions have been validated in previous work (
The first question was “How much did you enjoy this game?” with responses ranging from
Children assigned to this condition participated in their standard kindergarten curriculum and only completed pre- and post-testing. Children were given the opportunity to play the tablet games for a session after completing the post-testing.
Children were given three assessments of numerical knowledge and three assessments of WM during the pretest and posttest sessions. The measures were administered in the same order.
To assess children’s numerical magnitude knowledge, children were administered a 0-100 number line estimation task. Children were presented with 20 cm lines on a tablet computer one at a time. On each line, there was a “0” just below the left end of the line, and a “100” just below the right end. A number between 0 and 100 was displayed approximately 4 cm above the center of the line. The experimenter told the children that they would be playing a game in which they needed to mark the location of a number on a line. On each trial, the experimenter asked, “If this is where 0 goes (pointing) and this is where 100 goes (pointing), where does N go?” There were 26 trials of the following numbers 3, 4, 6, 8, 12, 14, 17, 18, 21, 24, 25, 29, 33, 39, 42, 48, 52, 57, 61, 64, 72, 79, 81, 84, 90, and 96 (
Children were presented with 35 different Arabic numerals presented randomly one at a time on cards (adapted from
Children were asked to complete five simple arithmetic problems all with addends less than 10. The problems were written on paper, as well as presented orally by the experimenter. Children were encouraged to use their fingers or the paper to solve the problems. Two sets of problems were counterbalanced at pretest and posttest. The problems given across the two sets were 1+7, 2+3, 3+3, 5+2, 5+3, 1+4, 4+3, 5+4, and 6+3. The dependent measure was the total number of problems correctly solved.
Children were read a list of numbers and asked to repeat the list in the same order presented (
Similar to the forward digit span, children were read a list of numbers and asked to repeat the list in reverse order (
Children were seated in front of an array of familiar items (pencils, erasers, folders, boxes, rulers) in varying colors (blue, yellow, red) (
Preliminary analyses revealed no age, gender, parent education, or classroom differences between groups (all
For the number training game, the children played one game per session.
Training performance while playing the numerical magnitude game: a) the percentage of the magnitude comparison questions answered correctly (i.e., Who is leading?), b) the number of times feedback was given in response to an error.
As for the WM game, the children completed 29 trials (
Training performance for the WM game: a) maximum set size recalled for each training session, b) average reaction time (RT) during the recall part of the game, c) average accuracy during the recall part of the game.
Descriptive data as well as re-test reliabilities and effect sizes are reported in
Group, Measure | Pre-Test |
Post-Test |
Pre vs. Post |
||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Mean | Min | Max | Mean | Min | Max | ES | |||||
Number Game Group ( |
|||||||||||
Mathematics Measures | |||||||||||
Number line (% Absolute Error) | 23.82 | 7.71 | 7.85 | 36.69 | 17.80 | 6.57 | 6.41 | 31.86 | *** | .85 | -1.48 |
Numeral Identification (% Correct) | 84.66 | 17.79 | 22.86 | 100.00 | 91.75 | 12.64 | 54.29 | 100.00 | ** | .82 | 0.68 |
Arithmetic (% Correct) | 74.81 | 34.46 | 0.00 | 100.00 | 85.93 | 22.06 | 20.00 | 100.00 | .12 | 0.29 | |
Working Memory Measures | |||||||||||
Following instructions | 2.33 | 0.53 | 1.33 | 3.66 | 2.29 | 0.55 | 1.33 | 3.66 | .09 | -0.05 | |
Digit Span: Forward | 8.52 | 1.70 | 5.00 | 12.00 | 8.85 | 2.30 | 4.00 | 14.00 | .41 | 0.15 | |
Digit Span: Backward | 2.85 | 1.63 | 0.00 | 6.00 | 3.52 | 1.34 | 0.00 | 6.00 | * | .46 | 0.43 |
Working Memory Game Group ( |
|||||||||||
Mathematics Measures | |||||||||||
Number line (% Absolute Error) | 24.78 | 8.68 | 10.34 | 44.11 | 21.76 | 8.69 | 7.04 | 38.84 | *** | .87 | -0.68 |
Numeral Identification (% Correct) | 77.14 | 24.24 | 20.00 | 100.00 | 85.40 | 20.88 | 28.57 | 100.00 | *** | .88 | 0.72 |
Arithmetic (% Correct) | 76.30 | 32.83 | 0.00 | 100.00 | 80.00 | 27.74 | 0.00 | 100.00 | .39 | 0.11 | |
Working Memory Measures | |||||||||||
Following instructions | 2.31 | 0.58 | 1.00 | 3.66 | 2.16 | 0.69 | 0.00 | 3.66 | .12 | -0.18 | |
Digit Span: Forward | 8.70 | 2.16 | 5.00 | 12.00 | 8.33 | 2.50 | 0.00 | 13.00 | .61 | -0.18 | |
Digit Span: Backward | 2.81 | 1.97 | 0.00 | 7.00 | 3.44 | 1.97 | 0.00 | 6.00 | 0.08 | .58 | 0.35 |
Control Group ( |
|||||||||||
Mathematics Measures | |||||||||||
Number line (% Absolute Error) | 24.39 | 8.64 | 7.95 | 43.03 | 22.80 | 8.87 | 11.09 | 40.46 | .79 | -0.28 | |
Numeral Identification (% Correct) | 86.56 | 21.58 | 37.14 | 100.00 | 90.58 | 14.99 | 37.14 | 100.00 | .82 | 0.32 | |
Arithmetic (% Correct) | 80.00 | 31.87 | 0.00 | 100.00 | 84.44 | 18.67 | 20.00 | 100.00 | .34 | 0.14 | |
Working Memory Measures | |||||||||||
Following instructions | 2.38 | 0.69 | 1.33 | 4.00 | 2.34 | 0.54 | 1.33 | 3.66 | .26 | -0.05 | |
Digit Span: Forward | 9.00 | 2.11 | 6.00 | 16.00 | 8.93 | 2.06 | 6.00 | 16.00 | .75 | -0.05 | |
Digit Span: Backward | 3.30 | 1.77 | 0.00 | 8.00 | 3.59 | 1.62 | 0.00 | 7.00 | .36 | 0.15 |
*
We then investigated transfer by calculating two multivariate analyses of variance (MANOVA) with group (domain-general, domain-specific, or control) as the between factor and the differences between post- and pretest scores (from now on termed gain scores) as dependent variables using the three outcome measures for each domain separately (mathematics: number line PAE, numeral identification, and arithmetic performance; WM: following directions, forward and backward digit span).^{i} We report Pillai’s V as an
The MANOVA using the three mathematics tasks as dependent variables was significant (
Observed net effect sizes (Cohen’s d) of performance gains from pre-test to post-test for the Math and WM outcome measures. Bars show net effect sizes (standardized changes in the trained group minus standardized changes in the control group), separately for the participants who completed the math intervention (dark bars) and those who completed the WM intervention (light bars).
The MANOVA using the three WM tasks as dependent variables was not significant (
Next we examined whether children’s training performance and engagement ratings during the games related to children’s numerical knowledge and WM skills. First, we compared children’s engagement between the two training conditions using a Mann-Whitney U comparison for each of the measures (
Measure | Number Game |
WM Game |
||
---|---|---|---|---|
Enjoyment | 2.02 | .88 | 1.80 | .63 |
Self-efficacy | 2.11 | .90 | 1.89 | .76 |
Effort | 1.98 | .92 | 2.02 | .83 |
Second, we examined whether children’s improvements in the two groups varied by children’s initial numerical magnitude knowledge. The correlations between initial numerical knowledge and improvement in the number line task were
To further illustrate this point, we conducted a median split of all of the children based on their pretest performance on the number line task (median PAE score = 24%, range = 8% to 44%). Paired samples t-tests of children in the number condition showed that both children with lower and higher initial numerical knowledge improved from pretest to posttest. Specifically, children who played the number game with lower initial knowledge improved from their PAE from 29% to 21% (
Next we calculated correlations between the engagement measures, training measures, and each of the outcome measures at pretest and posttest separately for the two training conditions. Since lower scores for the number line estimation task indicate higher accuracy, we reversed this score for the subsequent analyses to be consistent with the other measures to ease interpretability. As shown in
Measure | Pretest |
Posttest |
||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Number Line PAE^{a} | No Id | Arithmetic | Follow Instructions | Digit Span: Forward | Digit Span: Backward | Number Line PAE^{a} | No Id | Arithmetic | Follow Instructions | Digit Span: Forward | Digit Span: Backward | |
Enjoyment | -.08 | -.11 | -.29 | .18 | .05 | .01 | .17 | .01 | .04 | -.34 | .00 | -.15 |
Self-efficacy | -.31 | -.34 | -.20 | .13 | .02 | -.15 | -.11 | -.20 | -.17 | -.34 | .10 | -.33 |
Effort | .12 | -.18 | -.12 | -.13 | -.15 | -.24 | .13 | -.12 | -.38* | -.30 | .07 | -.31 |
Character Mag Compare | .48* | .63** | .17 | -.10 | .04 | .05 | .49* | .48** | .32 | -.12 | .33 | .13 |
Feedback | -.49** | -.59** | -.27 | .35 | -.13 | -.39* | -.42* | -.51** | -.39* | .06 | -.07 | -.47* |
^{a}Percent absolute error (PAE) scores from the number line task are reversed to be consistent with the other measures with higher scores indicating greater accuracy.
*
Measure | Pretest |
Posttest |
||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Number Line PAE^{a} | No Id | Arithmetic | Follow Instructions | Digit Span: Forward | Digit Span: Backward | Number Line PAE^{a} | No Id | Arithmetic | Follow Instructions | Digit Span: Forward | Digit Span: Backward | |
Enjoyment | -.14 | -.06 | -.39* | -.14 | -.17 | -.24 | -.14 | -.08 | -.28 | -.26 | -.40* | -.31 |
Self-efficacy | -.21 | -.05 | -.17 | -.13 | -.17 | -.43* | -.30 | -.08 | -.26 | -.09 | -.32 | -.21 |
Effort | -.27 | -.09 | -.33 | -.25 | -.36 | -.41* | -.44* | -.22 | -.38* | -.22 | -.38* | -.31 |
Average Set Size | -.02 | .22 | .11 | .33 | .32 | .32 | .06 | .39* | .30 | .25 | .11 | .04 |
Max Set Size | .11 | .37 | .30 | .35 | .28 | .10 | .22 | .53** | .42* | .02 | -.01 | .05 |
^{a}Percent absolute error (PAE) scores from the number line task are reversed to be consistent with the other measures with higher scores indicating greater accuracy.
*
As shown in
Overall, there were stronger associations between the training measures for children who played the number game than for children who played the WM game. However, child engagement was more strongly correlated with the outcome measures in those children who played the WM game as compared with those who played the number game.
Finally, to examine whether measures of engagement and training performance predicted children’s posttest performance on the number line estimation, we conducted two hierarchical linear regression analyses. Regressions were only conducted for the number line estimation task since this was the only measure showing significant group effects and yielded the largest improvements for both training groups. Given the two interventions required different amounts of engagement, we conducted the regressions separately for the two training groups. For both analyses, we first controlled for pretest scores, then entered the three measures of engagement as a block followed by the two measures of training performance for each of the two training groups (i.e., magnitude comparison and feedback for the number training group; average set size and maximum set size for the WM training group).
As shown in
Parameter estimate (standardized) |
|||
---|---|---|---|
Predictors | Model 1 | Model 2 | Model 3 |
Pretest Number Line PAE | .85*** | .90*** | .87*** |
Engagement Measures | |||
Enjoyment | .31 | .32 | |
Self-efficacy | .00 | .00 | |
Effort | -.14 | -.15 | |
Training Performance | |||
Character Magnitude Comparison | .14 | ||
Feedback | .08 | ||
73 | 80 | 81 | |
66.94*** | 21.94*** | 14.22*** | |
Degrees of freedom for |
1, 25 | 4, 22 | 6, 20 |
*
Parameter estimate (standardized) |
|||
---|---|---|---|
Predictors | Model 1 | Model 2 | Model 3 |
Pretest Number Line PAE | .87*** | .81*** | .79*** |
Engagement Measures | |||
Enjoyment | .12 | .13 | |
Self-efficacy | .19 | .20 | |
Effort | -.45* | -.51* | |
Training Performance | |||
Average Set Size | -.28 | ||
Maximum Set Size | .22 | ||
76 | 83 | 84 | |
80.21*** | 26.00*** | 16.94*** | |
Degrees of freedom for |
1, 25 | 4, 22 | 6, 20 |
*
As shown in
This study tested whether playing tablet games that focused on domain-specific and domain-general training is an efficacious means for improving the numerical knowledge and WM of kindergarten children primarily from lower-income backgrounds. Playing both the number game and the WM game for 10 sessions on the computer tablet led to improvements in children’s numerical knowledge, particularly in the area of numerical magnitude understanding. These improvements were greatest for children who had lower pre-existing numerical magnitude knowledge, and furthermore, their self-reported effort predicted the learning outcome.
Our study provides evidence that both domain-specific knowledge and domain-general processes are critical for children’s numerical knowledge. Our study has tested an established conceptual framework of mathematics development (
Several of the findings from the numerical magnitude and WM training games used in the present study replicate previous research in important ways. Specifically, consistent with
However, it is also important to note that the findings of the present study extend this previous research in several important ways. First, consistent with the cognitive alignment framework (
Second, our findings show that tablets are a promising technological tool that could be utilized to improve children’s numerical knowledge. Although previous studies have found that non-tablet computer games targeting either mathematical skills (
Third, our findings provide evidence that experimentally tested tablet games can produce improvements in young children’s numerical knowledge. Parents and teachers of young children appear to value the use of technology, and specifically tablets, such as iPads, to promote learning (
The present study adds to a growing area of intervention research which seeks to better understand for whom and under what conditions training activities are most beneficial to children’s learning. We found that self-reports of greater effort put into the WM game predicted children’s number line estimation accuracy after playing the games, even after controlling for their initial number line performance. This suggests that level of engagement during the WM game played a critical role in its influence on children’s number line estimation performance. These findings are consistent with previous WM training that has shown that children’s self-perceptions about the games are related to their improvements during the game. Specifically, children who felt the WM trainings game was challenging, but not overwhelming improved more from the training. Further, greater gains in the WM training game were associated with improvements in transfer tasks (
We also examined how initial ability impacted children’s improvements in number line estimation. We found that playing the number game improved numerical magnitude knowledge for children with lower initial ability as well as for children with higher initial ability. In contrast, only children with lower initial numerical magnitude knowledge improved from playing the WM training game. It is likely that higher numerical magnitude knowledge indicates that children have a higher skill level and therefore they rely less on their WM. However, children with lower initial ability likely rely more on their domain-general skills to do those (non-automatic) tasks, then improving WM might be the right approach. This suggests that for children with more advanced numerical knowledge providing greater training with games that target their domain-specific skills may be more beneficial than training that targets their domain-general skills.
There are several limitations of this present study. First, although we observed improvements in children’s numerical knowledge, we did not find improvements in children’s arithmetic performance and only limited improvements in WM. For the arithmetic problems this was likely due to ceiling effects with 73% of the children answering 4 or 5 of the problems correctly at pretest. For the WM measures, it is likely that these measures relied too heavily on children’s language skills, making the tasks difficult given that 33% of parents in our diverse sample reported that their children are exposed to more than one language at home. Thus, this reliance on language skills likely limited the reliability of the measures (see
Second, the training data indicate that children only minimally improved their performance in the training tasks (
Third, our control condition received their standard classroom instruction during the study. It is possible that playing a tablet game regardless of the content could have improved children’s numerical knowledge; however, the differential effects and individual differences analyses provide some evidence that the effects are likely tied to the specific tasks and not due to placebo effects (
To conclude, this study replicates and extends previous research showing that playing number board games can improve children’s numerical magnitude knowledge. Further, our data provide some evidence that playing games that require domain-general skills (i.e., WM) can improve children’s numerical magnitude knowledge as well. Finally, these games can be implemented and played on a rapidly growing and easy-to use technology, tablets. Future research has to demonstrate whether combining the two training approaches will result in enhanced effects compared to the outcome of each training approach on its own. Individual differences should be considered in future interventions, including assessments of sustained attention and engagement (particularly for WM games).
The changing technological landscape offers fresh opportunities to capitalize on popular, intuitive platforms such as the tablet computer (
This research was supported by a grant from the University of Maryland NSF-ADVANCE Interdisciplinary and Engaged Research Seed Grant Program.
Martin Buschkuehl is employed at the MIND Research Institute, whose interest is related to this work and Susanne M. Jaeggi has an indirect financial interest in MIND Research Institute.
The results of the outcome measures did not change when age was included as a co-variate. The MANCOVA for the three mathematics task remained significant for condition,
When univariate ANCOVAs with pretest scores as covariate were conducted to follow-up the MANOVA, the results are consistent to the results presented. Specifically, there were significant group differences on the number line estimation task, (
We would like to thank the administrators, parents, and children who supported and participated in this research.