View in EDS HTML Full Text PDF Full Text

The Development of Spatial Skills in Elementary School Students

Saved in:
Bibliographic Details
Title: The Development of Spatial Skills in Elementary School Students
Language: English
Authors: Carr, Martha, Alexeev, Natalia, Wang, Lu (ORCID 0000-0002-1049-7255), Barned, Nicole, Horan, Erin, Reed, Adam
Source: Child Development. Mar-Apr 2018 89(2):446-460.
Availability: Wiley-Blackwell. 350 Main Street, Malden, MA 02148. Tel: 800-835-6770; Tel: 781-388-8598; Fax: 781-388-8232; e-mail: cs-journals@wiley.com; Web site: http://www.wiley.com/WileyCDA
Peer Reviewed: Y
Page Count: 15
Publication Date: 2018
Sponsoring Agency: Institute of Education Sciences (ED)
Contract Number: 305A110920
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Descriptors: Spatial Ability, Skill Development, Elementary School Students, Mathematics Achievement, Prediction, Child Development, Profiles, Short Term Memory, Socioeconomic Status, Verbal Ability, Gender Differences, Longitudinal Studies, Tests, Mathematics Tests, Role
DOI: 10.1111/cdev.12753
ISSN: 0009-3920
Abstract: Through five waves of data collection, this longitudinal study investigated the development of spatial skills in 304 elementary school children (M[subscript age] = 7.64 years) as they progressed from the second to fourth grade. The study focused on whether multiple latent classes with different developmental profiles best explain development. Spatial skills were measured by tests featuring two-dimensional figures. Mathematics achievement was measured by the statewide end-of-year test and was included as a distal outcome variable. The role of covariates, including socioeconomic status, verbal working memory, and gender, was also explored. The results indicate a need to view two-dimensional spatial skills development as multidimensional with two developmental profiles predicted by socioeconomic status, verbal working memory, and gender. The developmental profiles predicted differences in mathematics achievement.
Abstractor: As Provided
IES Funded: Yes
Entry Date: 2018
Accession Number: EJ1172410
Database: ERIC
Full text is not displayed to guests.
FullText Links:
  – Type: pdflink
    Url: https://content.ebscohost.com/cds/retrieve?content=AQICAHj0k_4E0hTGH8RJwT4gCJyBsGNe_WN95AvKlDbXJGqwxwGl-ASJFHrCAeWl-_nzom8rAAAA4zCB4AYJKoZIhvcNAQcGoIHSMIHPAgEAMIHJBgkqhkiG9w0BBwEwHgYJYIZIAWUDBAEuMBEEDIfVPw7GPeWTF7-fuQIBEICBm7qX19cPpPqRsZfWTxxGd2r0chwnnSu3pUhEqZ_68cGOuLydCx34iiHML0BIc0XpYgvCJMmHRv9SJpyExg_8o1OT6qpIMS4eI5s3Gok-dKGrC399nUqfVSootbaT1SucelnuHeZ8Ae9w4ser6nNBJa2iyGSJTITXRyYCGJJ3HThxVYSfcIh3CecUKb-tGQbPk9atmY1_gTXIRzhM
Text:
  Availability: 1
  Value: <anid>AN0128440772;cdv01mar.18;2018Mar14.12:40;v2.2.500</anid> <title id="AN0128440772-1">The Development of Spatial Skills in Elementary School Students </title> <p>Through five waves of data collection, this longitudinal study investigated the development of spatial skills in 304 elementary school children (<italic>M</italic><sub>age</sub> = 7.64 years) as they progressed from the second to fourth grade. The study focused on whether multiple latent classes with different developmental profiles best explain development. Spatial skills were measured by tests featuring two‐dimensional figures. Mathematics achievement was measured by the statewide end‐of‐year test and was included as a distal outcome variable. The role of covariates, including socioeconomic status, verbal working memory, and gender, was also explored. The results indicate a need to view two‐dimensional spatial skills development as multidimensional with two developmental profiles predicted by socioeconomic status, verbal working memory, and gender. The developmental profiles predicted differences in mathematics achievement.</p> <p>Evidence for the impact of spatial skills on mathematics achievement comes from correlational data, with studies showing that higher spatial skills are linked to the development of the mental number line (LeFevre et al., [<reflink idref="bib36" id="ref1">36</reflink>] ), and the efficient representation and manipulation of the number (Boonen, van der Schoot, van Wesel, de Vries, & Jolles, [<reflink idref="bib4" id="ref2">4</reflink>] ). Older students with good spatial skills are also more likely to excel in science, technology, engineering, and mathematics (STEM) courses, and they are more likely to be interested in pursuing a STEM‐related career (Achter, Lubinski, Benbow, & Eftekhari‐Sanjani, [<reflink idref="bib1" id="ref3">1</reflink>] ). Aside from the correlational data, a growing number of experimental and quasi‐experimental studies show that interventions designed to improve spatial skills also improve the mathematics skills in elementary school children (Cheng & Mix, [<reflink idref="bib12" id="ref4">12</reflink>] ) and young adults (Sorby, Casey, Veurink, & Dulaney, [<reflink idref="bib61" id="ref5">61</reflink>] ). Although the relation between spatial skills and mathematics achievement is relatively well established, much less is known about the development of spatial skills. In particular, it is not clear whether single or multiple latent classes are needed to explain the development of spatial skills and their impact on mathematics achievement. Given that factors, such as gender, socioeconomic status (SES), and verbal working memory (VWM), have been linked to spatial skills, it is likely that these factors may predict different developmental profiles of spatial skills.</p> <hd id="AN0128440772-2">The Development of Spatial Skills</hd> <p>Although many would agree that spatial skills are not a single, unified construct, it is less clear the most effective ways to categorize and measure different types of spatial skills (Voyer, Voyer, & Bryden, [<reflink idref="bib66" id="ref6">66</reflink>] ). One common approach suggested by Linn and Petersen ([<reflink idref="bib41" id="ref7">41</reflink>] ) is to divide spatial skills into three categories (spatial perception, mental rotation, and spatial visualization) based on cognitive load or task demand. Other work has focused on different systems that are recruited to solve spatial tasks. Specifically, different systems are hypothesized to be engaged when performing egocentric‐based or object‐centered transformations (Zacks & Tversky, [<reflink idref="bib71" id="ref8">71</reflink>] ). Object‐centered transformation encompasses spatial perception, spatial rotation, and spatial visualization. Regardless as to the categorization, all forms of spatial skills require some kind of manipulation or rotation of mental imagery and as such involve the use of visuospatial working memory (VSWM; Loring‐Meier & Halpern, [<reflink idref="bib44" id="ref9">44</reflink>] ).</p> <p>There is surprisingly little research on the development of spatial skills, particularly those utilizing object‐centered transformations, in the elementary school years. We know that spatial skills improve throughout childhood (Harris, Newcombe, & Hirsh‐Pasek, [<reflink idref="bib23" id="ref10">23</reflink>] ; Nardini, Burgess, Breckenridge, & Atkinson, [<reflink idref="bib52" id="ref11">52</reflink>] ). Studies using two‐dimensional mental rotation tasks indicate that such skill can be reliably measured in the preschool years with children showing consistent improvement thereafter (Levine, Huttenlocher, Taylor, & Langrock, [<reflink idref="bib38" id="ref12">38</reflink>] ). Research on spatial transformations has indicated that mental paper folding emerges at 5.5 years of age and improves through early elementary school (Harris et al., [<reflink idref="bib23" id="ref13">23</reflink>] ). Likewise, substantial improvement in the ability to perform the object‐based spatial transformations that require spatial manipulation of mental imagery occurs between 7 and 8 years of age (Crescentini, Fabbro, & Urgesi, [<reflink idref="bib15" id="ref14">15</reflink>] ). Studies have looked at three‐dimensional mental rotation skills, which are typically measured by the Vandenberg and Kuse ([<reflink idref="bib63" id="ref15">63</reflink>] ) Mental Rotation Test, but such skills are difficult to reliably measure using pencil and paper measures until late elementary school (Johnson & Meade, [<reflink idref="bib29" id="ref16">29</reflink>] ). Although it can be assumed that three‐dimensional spatial skills improve in elementary school‐aged children, the dearth of reliable measures in this age group caused us to focus on two‐dimensional spatial measures. In the ensuing paragraphs, we will discuss how the availability of these spatial skills can be conceptualized as supporting emerging quantitative skills in early elementary school.</p> <hd id="AN0128440772-3">The Role of Spatial Skills in Mathematics</hd> <p>There are several theories of quantitative reasoning that explain how spatial skills may support mathematics achievement. One theory by Dehaene and his colleagues (Feigenson, Dehaene, & Spelke, [<reflink idref="bib18" id="ref17">18</reflink>] ; Lemer, Dehaene, Spelke, & Cohen, [<reflink idref="bib37" id="ref18">37</reflink>] ) assumes that quantitative reasoning involves two core systems of number that are grounded in separate neural networks in the brain, one is approximate and nonsymbolic, and the other is precise and symbolic. It is assumed that spatial skills share neural codes with the approximate system of number, whereas exact counting and symbolic math operations recruit primarily the second core system of number (Feigenson et al., [<reflink idref="bib18" id="ref19">18</reflink>] ). Developmentally, as the two core systems of number merge through schooling, spatial skills will increasingly impact mathematics achievement via the second, symbolic system of number (Piazza, Pica, Izard, Spelke, & Dehaene, [<reflink idref="bib57" id="ref20">57</reflink>] ). Thus, existing evidence suggests that good spatial skills in early elementary school will provide a strong foundation for mathematics achievement in elementary school and beyond.</p> <p>Most of the work on the impact of spatial skills on the approximate number system has focused on the mental number line (Gunderson, Ramirez, Beilock, & Levine, [<reflink idref="bib22" id="ref21">22</reflink>] ). There is also evidence that working with place value (Grossberg & Repin, [<reflink idref="bib21" id="ref22">21</reflink>] ) and approximate mental arithmetic (Knops, Viarouge, & Dehaene, [<reflink idref="bib32" id="ref23">32</reflink>] ) involves spatial representations. Research points to the importance of spatial skills for various aspects of mathematics achievement in the early grades. In elementary school populations, spatial skills support the learning of geometry (Clements, Battista, Sarama, & Swaminathan, [<reflink idref="bib13" id="ref24">13</reflink>] ), word problem solving (Carr, Bray, Gerow, & Barned, [<reflink idref="bib8" id="ref25">8</reflink>] ), and the use of more advanced computation strategies in girls (Casey et al., [<reflink idref="bib11" id="ref26">11</reflink>] ; Laski et al., [<reflink idref="bib35" id="ref27">35</reflink>] ). Spatial visualization skill is particularly important for performance on more difficult mathematics problems (Manger & Eikeland, [<reflink idref="bib46" id="ref28">46</reflink>] ). Longitudinal studies have shown that early spatial skills predict later success in mathematics. For example, spatial skills as measured in first‐grade girls are important predictors of fifth‐grade mathematics reasoning (Casey et al., [<reflink idref="bib11" id="ref29">11</reflink>] ), and spatial visualization as measured in kindergarten predicts arithmetic skills in third‐grade boys and girls (Zhang et al., [<reflink idref="bib72" id="ref30">72</reflink>] ).</p> <p>To our knowledge, no studies have determined whether multiple developmental profiles are needed to explain the development of spatial skills. Studies showing that gender differences in spatial skills differ as a function of SES indicate a need for more complex models to explain the development of spatial skills. Furthermore, verbal ability appears to complement spatial skills to improve the development of arithmetic skill in this age group (Zhang et al., [<reflink idref="bib72" id="ref31">72</reflink>] ), indicating that it may affect how spatial skills predict mathematics achievement. These findings point to potential multiple profiles as a result of differences in these variables.</p> <hd id="AN0128440772-4">Gender, SES, and VWM</hd> <p>Gender differences favoring boys have been observed for spatial skills and, to a lesser extent, mathematics skills. Gender differences in spatial perception and two‐dimensional mental rotation tasks are evident before children enter elementary school (Levine et al., [<reflink idref="bib38" id="ref32">38</reflink>] ) and during elementary school, as measured by Thurstone's ([<reflink idref="bib62" id="ref33">62</reflink>] ) measure of primary mental abilities (PMA) test (Levine, Vasilyeva, Lourenco, Newcombe, & Huttenlocher, [<reflink idref="bib39" id="ref34">39</reflink>] ). Gender differences were not found in the developmental trajectory of spatial visualization tasks that involved embedded figures, but this task did not involve mental manipulation of those figures (Lachance & Mazzocco, [<reflink idref="bib34" id="ref35">34</reflink>] ). In older populations, gender differences are more common in tasks that require three‐dimensional mental rotation (Voyer et al., [<reflink idref="bib66" id="ref36">66</reflink>] ). In general, the more cognitively demanding in regard to mental manipulation, the more likely gender differences are to emerge (Vecchi & Girelli, [<reflink idref="bib64" id="ref37">64</reflink>] ).</p> <p>Likewise, research examining the developmental trajectories of mathematics skills, as measured by performance on computation, word problem solving, and number knowledge tasks, indicates that boys are more likely to be in a higher performing latent class and that gender predicts growth within this higher performing class (Aunola, Leskinen, Lerkkanen, & Nurmi, [<reflink idref="bib2" id="ref38">2</reflink>] ). Gender differences in mathematics achievement, although decreasing over time, continue to be evident for tasks involving more spatial processing (Penner, [<reflink idref="bib54" id="ref39">54</reflink>] ). Given this, we hypothesized that gender would affect mathematics competency through its impact on the developmental profile of spatial skills.</p> <p>There is considerable evidence that SES influences the developmental trajectories of mathematics competencies as well. Jordan, Kaplan, Olah, and Locuniak ([<reflink idref="bib30" id="ref40">30</reflink>] ), for example, found that low‐income status was linked to a low initial performance and a flat developmental trajectory of number sense, and this trajectory was linked to poorer performance on an array of math assessments at the end of kindergarten. The relation between SES and spatial skills is much less understood. A study of preschool‐age children found that low‐SES children tend to do more poorly than middle‐income children on a three‐dimensional spatial assembly task before they enter school (Verdine et al., [<reflink idref="bib65" id="ref41">65</reflink>] ), and low‐SES elementary fourth‐grade children have been found to possess poorer two‐dimensional spatial skills, as measured by mental rotation and visualization tasks, in comparison to their middle‐class counterparts (Casey, Dearing, Vasilyeva, Ganley, & Tine, [<reflink idref="bib10" id="ref42">10</reflink>] ). In addition, the association between spatial skills and performance on tests of measurement skills is moderated by socioeconomic status with a stronger association existing for higher income students (Casey et al., [<reflink idref="bib10" id="ref43">10</reflink>] ).</p> <p>SES and gender have been found to interact in predicting spatial skills and mathematics achievement with boys coming from higher income homes having an advantage over girls. Gender differences are less evident in low‐income families. A study by Levine et al. ([<reflink idref="bib39" id="ref44">39</reflink>] ) indicated gender differences favoring boys in middle‐class second and third grades but not in low‐income second and third graders. A similar pattern is evident in mathematics with gender differences in favor of boys being more pronounced in higher income families than lower income families (Penner & Paret, [<reflink idref="bib55" id="ref45">55</reflink>] ). Given this, we expected multiple latent classes with different developmental profiles as a function of gender and SES.</p> <p>In addition to spatial skills, VWM has also been found to predict mathematics achievement and specifically mathematics problem solving and computation (Healy & Nairne, [<reflink idref="bib24" id="ref46">24</reflink>] ); see Bull and Johnston ([<reflink idref="bib6" id="ref47">6</reflink>] ) for evidence to the contrary. VWM is hypothesized to be utilized more in solving mathematics problems during elementary school as children shift from visuospatial processing during counting to symbolic representation of number (Holmes & Adams, [<reflink idref="bib25" id="ref48">25</reflink>] ). The relation between VWM and spatial skills is more tenuous. VWM may be a predictor of spatial skills for individuals who prefer to use strategies that utilize VWM, instead of spatial processing, when solving spatial tasks (Geiser, Lehmann, Corth, & Eid, [<reflink idref="bib19" id="ref49">19</reflink>] ; Janssen & Geiser, [<reflink idref="bib27" id="ref50">27</reflink>] ). There is some evidence for this; girls’ verbal ability predicts performance on spatial measures even when spatial activities (e.g., spatially focused toys) are controlled for in the analysis (Dearing et al., [<reflink idref="bib17" id="ref51">17</reflink>] ). Given this, VWM needs to be controlled for when assessing the relation between spatial skills and mathematics achievement.</p> <hd id="AN0128440772-5">Growth Mixture Modeling</hd> <p>As our goal is to learn more about the development of spatial skills, in particular whether multiple developmental profiles are needed to explain its development and impact on mathematics achievement, we first utilized the traditional (single‐class) latent curve growth model to test whether a single‐group model would fit the data. We followed this with a growth mixture model when it was evident that multiple latent groups were needed to explain the data.</p> <p>In the traditional latent curve growth model, the repeated measurements of observed variables are used to estimate the latent variables (random coefficients) that measure the participant's change over time. One random coefficient, an intercept, represents the initial value of outcome at time zero and the other coefficient, a slope, shows the rate of change in the outcome over time. In this model, the assumption is that the population is homogeneous in the shape of the growth and that individual trajectories are accounted for through random variation in their intercepts and slopes: A single growth trajectory explains all variation. In addition to the linear growth, higher order growth can be examined (e.g., quadratic growth).</p> <p>Growth mixture modeling (GMM) allows us to test whether there are multiple developmental trajectories: There is no assumption that the population is homogeneous. To the contrary, it is assumed that a population is a mixture of several populations, and these populations are not manifest but latent (e.g., Muthén, [<reflink idref="bib49" id="ref52">49</reflink>] ; Muthén & Shedden, [<reflink idref="bib51" id="ref53">51</reflink>] ). The GMM classifies individuals in terms of the similarities in the patterns of the data. For each individual, membership in a latent class is based on their maximum posterior probability. The intercept and the slope can vary between the classes as well as within the classes. As such, with multiple classes, it is important to attend to differences in the intercept and slope that discriminate classes, and differences in the intercept and slope within classes that define that class. The word trajectory when used in this context refers to class differences in the intercept and slope, the impact of covariates, and the impact on achievement, not just the slope.</p> <p>GMM allows researchers to examine the impact of covariates, in this case, SES, gender, and VWM, on the intercept and slope of the latent classes as well as the impact of class membership on an outcome variable. The technique is ideal for dealing with complex systems that might involve a number of variables that could influence an outcome.</p> <hd id="AN0128440772-6">The Present Study</hd> <p>This study used GMM to examine the developmental trajectory of spatial skills, determine whether there are latent groups with different trajectories, and estimate the effect of SES, gender, and VWM covariates on these trajectories as they predict mathematics achievement. Given the evidence of SES × Gender and Gender × VWM interactions in other studies, we hypothesized multiple developmental trajectories as opposed to a single‐class linear growth trajectory. SES and gender, in particular, were expected to affect the developmental profiles of spatial skills as predictors of mathematics achievement. We hypothesized that girls and students from low‐income homes would have lower and less steep developmental trajectories of spatial skills, and this would result in poorer mathematics achievement at the end of fourth grade. Regarding VWM, there is some evidence that in combination with spatial skills, it supports mathematics achievement. However, it could also be argued that a strong VWM suppresses the emergence of spatial skills as children, particularly girls, use analytic strategies that draw on VWM resources.</p> <hd id="AN0128440772-7">Method</hd> <hd id="AN0128440772-8">Participants</hd> <p>The results reported here are from a longitudinal study in which other research questions were addressed in addition to the one we discuss in this article. In the study, 304 children in four schools in two counties in Georgia were recruited in the second grade. The mean age of the children (53.3% male) at the beginning of the study was 7.64 (SD = .41). The percentage breakdown of ethnicity was 16.5% African American, 2.3% Asian, 72.3% Caucasian, 7.9% Hispanic, and 1.0% unknown. Data collection took place between 2011 and 2014. The children were English speaking and came from either low‐income or middle‐class homes. Most parents in the participating counties have a high school degree (82%), but only 18% of the families in the counties have a bachelor's degree or higher. The counties in which the participants reside can be considered rural or suburban.</p> <p>SES was quantified based on students’ free or reduced lunch status that was collected from the school records. The children were classified into three levels: 0 = free lunch, 1 = reduced lunch, 2 = full price lunch. Children are eligible for free or reduced lunch if their families receive SNAP (supplemental nutrition assistance program) or TANF (temporary assistance for needy families) benefits or the family income is within the Federal Income Eligibility Guidelines. Although this classification allowed us to discriminate between low‐income and middle‐class children, it did not allow us to tease apart the effects of higher incomes. The percentage of children who had free lunch, reduced price lunch, and full lunch status were 49.3%, 7.9%, and 42.8%, respectively.</p> <p>The researchers made every effort to minimize participant attrition by following children who moved in each wave of data collection. Despite these efforts, 40 children (13% of the original sample) moved sometime during the study, and we were unable to follow them to their new schools. A comparison of the scores of these children to those who did not move indicated that they did not differ significantly on any of the measures.</p> <hd id="AN0128440772-9">Materials and Procedures</hd> <p>Data on spatial skills were collected over a 3‐year period in five waves: fall and spring of second and third grades, and fall of the fourth grade. Scores for the end‐of‐year mathematics tests were collected in the spring of the fourth grade. VWM was assessed once in the first wave of data collection at the beginning of the second grade. The spatial skills assessments and verbal working memory test were randomly interspersed among the other measures that were a part of the larger project and not reported here. Given the large number of tests being administered, counterbalancing of assessments was not feasible.</p> <p>All data collection was done individually outside of the classroom, typically in a conference room, during regular school hours. Data collection took about an hour and took place in a single session. Aside from parental consent, verbal assent to participate was obtained from the children. A description of each task and administration procedures are presented below.</p> <hd id="AN0128440772-10">Verbal Working Memory</hd> <p>We gave the participants the Backward Digit Span (Wechsler, [<reflink idref="bib70" id="ref54">70</reflink>] ) to assess VWM at the first time point. To ensure consistency in the presentation of the number strings, the number strings were prerecorded and were played back to students. Testing was halted after a student incorrectly repeated two strings in a row as per administrator's manual. Scores were determined by the number of correctly repeated strings.</p> <hd id="AN0128440772-11">Primary Mental Abilities Subtest</hd> <p>We used the PMA subtest (Two‐Dimensional Mental Rotation Task) developed by Thurstone ([<reflink idref="bib62" id="ref55">62</reflink>] ) that has been successfully used with this age group in previous studies (e.g., Levine et al., [<reflink idref="bib39" id="ref56">39</reflink>] ). For this measure, children are given a square that has a missing part. They are asked to select a shape from a group of four shapes that completes a square or rectangle. These pieces may be turned to make them fit. The percentage correct out of 16 items was initially scored, however, for the purposes of the general GMM using the Mplus program, these scores were rescaled to a 0 to 10 range to improve the computational capability of the Mplus program; that is, a score of 80% correct was rescaled to an 8. Reliability for this measure is .98 (Johnson & Meade, [<reflink idref="bib29" id="ref57">29</reflink>] ).</p> <hd id="AN0128440772-12">Spatial Relations (Matching Parts)</hd> <p>We also used a spatial relations task taken from Levy and Levy ([<reflink idref="bib40" id="ref58">40</reflink>] ). This test required that the children mentally rotate and match two shapes to form the target shape, as such, it involved the mental manipulation of images characteristic of object‐centered transformation. Specifically, children were given a target shape on the left side of the page. The children were then required to select from five‐lettered shapes the two shapes that when combined matched the target shape. There were 15 items on this test, and the scores ranged from 0 to 15. As with the PMA subtest, the percent correct out of 15 was rescaled to a 0 to 10 scale to make it easier for the Mplus program to estimate the model. Cohen's alpha for this measure was .66. Although this alpha level is lower than .70, this measure significantly correlated with the PMA subtest at each time point with correlations ranging from r = .37 at the first time point to r = .50 at the fifth time point. These correlations were close to the correlations among the Thurstone PMA measures, which ranged from r = .49 to r = .59.</p> <hd id="AN0128440772-13">Mathematics Competency</hd> <p>To assess mathematics competency, students’ scores on the mathematics portion of the Criterion Referenced Competency Test were obtained at the end of the fourth grade. The test is designed to assess how well students have acquired knowledge and skills mandated by the state's performance standards, and it assessed several mathematics competencies that have been linked to spatial skills (number and operations, measurement, word problem solving, statistics, and geometry). The test is in a multiple choice format in which children must select from one of the three answer choices. Possible scores for the regular form of the test ranged from 650 to 990, with scores falling between 800 and 850 indicating that the student meets the state standard for the test. A score below 800 indicates that the child does not meet the standard, and a score above 850 indicates that the child exceeds the standard. For the analyses, we used the state‐established cutoffs to create three categories: meets expectations, exceeds expectations, and does not meet expectations. Our decision on converting the scores into a categorical variable was based on several considerations. First, there were two forms of the test, regular and modified (for children with disabilities), and their scoring was different. Second, some scores were reported to us only by the level of competency. Third, by using state‐established levels of competence, we achieved a better picture of the composition of the latent class; that is, placement in a category had significant implications for students with regard to promotion and placement. A mean score for that latent class would not have provided information about the probability of children meeting, exceeding, or not exceeding expectations.</p> <hd id="AN0128440772-14">Results</hd> <hd id="AN0128440772-15">Preliminary Analysis and Analytic Plan</hd> <p>Given the significant correlations between the two spatial measures, we collapsed across the two spatial measures to create a variable that was the average percent correct. That score was transformed to a 1 to 10 range to improve the performance of the Mplus program. In addition, for the preliminary analyses, we collapsed across free‐lunch and reduced lunch categories because of the small percentage of children in the reduced lunch category. We first examined the spatial data for differences in gender and SES. A repeated measures analysis of variance (ANOVA) with gender and SES as the independent variables and the combined spatial measures at each time point as the dependent measures indicated significant linear, F(<reflink idref="bib1" id="ref59">1</reflink>, 259) = 463.79, p < .001, , and quadratic, F(<reflink idref="bib1" id="ref60">1</reflink>, 259) = 40.66, p < .001, , effects of time with spatial skills improving over time and a decrease in the rate of improvement over time. The main effect for SES was significant with children who receive free or reduced lunch scoring lower on the combined spatial measure, F(<reflink idref="bib1" id="ref61">1</reflink>, 259) = 10.29, p = .002, . The gender effect was marginal (p = .07) but not significant, nor was the Gender × SES interaction significant. The means and standard deviations for the composite spatial measure are reported as the number correct out of 10 and can be found in Table .</p> <p>Means and Standard Deviations for the Spatial Measures by Gender and SES</p> <p> <ephtml> <table border="1" cellpadding="6"><tr><th /><th>Gender</th><th>SES</th><th>M</th><th>SD</th><th>N</th></tr><tr><td>Spatial 1</td><td>0</td><td>0</td><td>5.00</td><td>1.40</td><td>82</td></tr><tr><td>1</td><td>5.15</td><td>1.26</td><td>57</td></tr><tr><td>1</td><td>0</td><td>4.64</td><td>1.45</td><td>67</td></tr><tr><td>1</td><td>5.28</td><td>1.57</td><td>57</td></tr><tr><td>Total</td><td /><td>4.98</td><td>1.44</td><td>263</td></tr><tr><td>Spatial 2</td><td>0</td><td>0</td><td>5.69</td><td>1.46</td><td>82</td></tr><tr><td>1</td><td>6.10</td><td>1.38</td><td>57</td></tr><tr><td>1</td><td>0</td><td>5.67</td><td>1.61</td><td>67</td></tr><tr><td>1</td><td>5.89</td><td>1.43</td><td>57</td></tr><tr><td>Total</td><td /><td>5.82</td><td>1.48</td><td>263</td></tr><tr><td>Spatial 3</td><td>0</td><td>0</td><td>6.15</td><td>1.32</td><td>82</td></tr><tr><td>1</td><td>6.69</td><td>1.15</td><td>57</td></tr><tr><td>1</td><td>0</td><td>5.56</td><td>1.40</td><td>67</td></tr><tr><td>1</td><td>6.23</td><td>1.40</td><td>57</td></tr><tr><td>Total</td><td /><td>6.13</td><td>1.38</td><td>263</td></tr><tr><td>Spatial 4</td><td>0</td><td>0</td><td>6.46</td><td>1.22</td><td>82</td></tr><tr><td>1</td><td>6.94</td><td>1.27</td><td>57</td></tr><tr><td>1</td><td>0</td><td>6.22</td><td>1.38</td><td>67</td></tr><tr><td>1</td><td>6.71</td><td>1.14</td><td>57</td></tr><tr><td>Total</td><td /><td>6.57</td><td>1.28</td><td>263</td></tr><tr><td>Spatial 5</td><td>0</td><td>0</td><td>6.69</td><td>1.26</td><td>82</td></tr><tr><td>1</td><td>7.34</td><td>1.13</td><td>57</td></tr><tr><td>1</td><td>0</td><td>6.29</td><td>1.43</td><td>67</td></tr><tr><td>1</td><td>6.92</td><td>1.17</td><td>57</td></tr><tr><td>Total</td><td /><td>6.71</td><td>1.29</td><td>263</td></tr><tr><td>Verbal working memory</td><td>0</td><td>0</td><td>5.28</td><td>1.34</td><td>78</td></tr><tr><td>1</td><td>5.62</td><td>0.86</td><td>58</td></tr><tr><td>1</td><td>0</td><td>5.52</td><td>1.19</td><td>71</td></tr><tr><td>1</td><td>5.75</td><td>1.49</td><td>56</td></tr><tr><td>Total</td><td /><td>5.52</td><td>1.25</td><td>263</td></tr><tr><td>Mathematics competency</td><td>0</td><td>0</td><td>2.09</td><td>0.69</td><td>78</td></tr><tr><td>1</td><td>2.48</td><td>0.60</td><td>58</td></tr><tr><td>1</td><td>0</td><td>2.15</td><td>0.65</td><td>71</td></tr><tr><td>1</td><td>2.52</td><td>0.63</td><td>56</td></tr><tr><td>Total</td><td /><td>2.29</td><td>0.67</td><td>263</td></tr></table> </ephtml> </p> <p>Note 2 SES = socioeconomic status; SD = standard deviation.</p> <p>An ANOVA to assess gender and SES differences on the mathematics competency test indicated clear SES differences in children's mathematics competency test scores, F(<reflink idref="bib1" id="ref62">1</reflink>, 259) = 22.08, p < .001, , with children from lower income homes having lower scores on the mathematics competency test. No gender or SES differences were evident in the VWM measure, although the SES effect was marginal, F(<reflink idref="bib1" id="ref63">1</reflink>, 259) = 3.35, p = .07. See Table  for the means and standard deviations of the VWM, with a possible range between 0 and 9, and mathematics competency scores that range between 1 and 3. The correlations among the variables are in Table .</p> <p>Correlations Among the Variables</p> <p> <ephtml> <table border="1" cellpadding="8"><tr><th /><th>Math test</th><th>SP1</th><th>SP2</th><th>SP3</th><th>SP4</th><th>SP5</th><th>VWM</th></tr><tr><td>Math test</td><td>1</td><td /><td /><td /><td /><td /><td /></tr><tr><td>SP<sub>1</sub></td><td>.348</td><td>1</td><td /><td /><td /><td /><td /></tr><tr><td>SP<sub>2</sub></td><td>.409</td><td>.591</td><td>1</td><td /><td /><td /><td /></tr><tr><td>SP<sub>3</sub></td><td>.405</td><td>.579</td><td>.621</td><td>1</td><td /><td /><td /></tr><tr><td>SP<sub>4</sub></td><td>.444</td><td>.553</td><td>.642</td><td>.729</td><td>1</td><td /><td /></tr><tr><td>SP<sub>5</sub></td><td>.384</td><td>.502</td><td>.616</td><td>.694</td><td>.693</td><td>1</td><td /></tr><tr><td>VWM</td><td>.296</td><td>.209</td><td>.145</td><td>.131</td><td>.141</td><td>.125</td><td>1</td></tr></table> </ephtml> </p> <p>Note 3 VWM = verbal working memory.</p> <ulist> <item>4 *Correlation is significant at the .05 level (two‐tailed).</item> <item>5 **Correlation is significant at the .01 level (two‐tailed).</item> </ulist> <p>Following the preliminary analyses, growth modeling was utilized to examine the developmental trajectory of spatial skills. We compared the results of conventional growth modeling, which assumes that a single model accounts for all variations in the individual trajectories to the results of GMM that assumes that there are several subgroups in the population and explores qualitative differences in growth trajectories. Because GMM allows for latent classes that have different developmental trajectories and allows researchers to examine the impact of covariates on the intercept and slope of individual classes as well as the impact of class membership on an outcome variable, the technique is ideal for dealing with complex systems that have multiple covariates.</p> <p>For these analyses, we first explored basic, single‐group growth models to get a better understanding of the data and to be certain that we did not make the model more complex than necessary. This is common practice in the growth modeling (Berlin, Parra, & Williams, [<reflink idref="bib3" id="ref64">3</reflink>] ). The next step was to explore the data with GMM. All of the models were estimated using Mplus version 7 (Muthén & Muthén, [<reflink idref="bib50" id="ref65">50</reflink>] ), under missing data theory using all available data and full information maximum likelihood estimation, which is considered to be an appropriate method of modeling with missing data (Little, Jorgensen, Lang, & Moore, [<reflink idref="bib42" id="ref66">42</reflink>] ).</p> <hd id="AN0128440772-16">Does a Single Developmental Trajectory Fit the Data?</hd> <p>To determine whether single‐group growth models adequately explained the data, we tested two models, a linear growth model and a quadratic growth model. The quadratic growth model including estimates of the intercept (I), slope (S), and quadratic growth (Q) can be seen in Figure . In this model, SP<subs>1</subs>…SP<subs>5</subs> represent the spatial skills variables as measured at five time points. For the linear growth model, the quadratic term (Q) was removed. Gender, income status (SES), and VWM were entered as covariates.</p> <p>The results on the fit of the models are in Table . For a model to be a good fit, the comparative fix index and the Tucker–Lewis index should be more than .95, and the root mean square error of approximation and standardized root mean square residual should be less than .05. As we can see, the linear model is the worst fit of these two models and does not meet the criteria for good model fit. Although the quadratic model is a good fit, there were problems with convergence of the model. The model converged only when it was modified to fix the residual variance of Q to zero. In sum, neither model fit the data well, indicating that we needed to assess the fit of two or more latent classes.</p> <p>Fit Indices, Statistics, Intercepts, Slopes, Quadratic Term, SES, and VWM Effects on the Intercept for the Single‐Group Growth Models</p> <p> <ephtml> <table border="1" cellpadding="11"><tr><th>Growth model</th><th>CFI</th><th>TLI</th><th>RMSEA</th><th>SRMR</th><th>BIC</th><th>Intercept</th><th>Slope</th><th>Quadratic term</th><th>SES</th><th>VWM</th></tr><tr><td>Linear</td><td>.941</td><td>.922</td><td>.090</td><td>.041</td><td>6,534</td><td>3.94 (.35)</td><td>1.10 (.17)</td><td>—</td><td>.18 (.08)</td><td>.23 (.06)</td></tr><tr><td>Quadratic</td><td>.987</td><td>.978</td><td>.048</td><td>.046</td><td>6,516</td><td>3.66 (.38)</td><td>2.14 (.53)</td><td>−.5 (.24)</td><td>.18 (.09)</td><td>.23 (.07)</td></tr></table> </ephtml> </p> <p>Note 6 CFI = comparative fix index; TLI = Tucker–Lewis index; RMSEA = root mean square error of approximation; SRMR = standardized root mean square residual; BIC = Bayesian information criterion; SES = socioeconomic status; VWM = verbal working memory.</p> <p>7 SEs are in parentheses. *p < .05.</p> <p>Regardless of the model chosen, the impact of SES, gender, and VWM was approximately the same. The covariates, SES and VWM, had a significant effect on the intercept (p < .05 for SES and p < .05 for VWM) for both the linear and quadratic models. For the linear growth model, the rate of change (slope) was constant at 1.10 (SE = .17). For the quadratic growth model, the rate of change was dependent on the time point so that the rate of growth is initially slightly higher for the quadratic model in comparison to the linear model (which is constant) at the beginning of the study, but that rate decreases over time. See Table  for the values of the intercepts, slopes, quadratic term, and SES and VWM effects.</p> <hd id="AN0128440772-17">Growth Mixture Modeling: Are Multiple Trajectories Necessary to Explain Development?</hd> <p>The GMM, shown in Figure , is similar to the single‐group growth model with two exceptions. A distal categorical outcome variable, the performance on the fourth‐grade mathematics competency test, was included in the model. In addition, a class variable (C) was included to determine whether there were multiple latent classes with different developmental trajectories. The model included a quadratic term, but issues similar to those found with the single‐group model emerged. As a result of the poor convergence of the quadratic model, the linear model was our main focus for the GMM.</p> <p>There is still no consensus on the best method for determining the number of classes for GMM or whether to use a one‐step or two‐step procedure. In the two‐step procedure, the decision on the number of classes is made in the unconditional mixture model before the covariates and the distal outcome variable are included in the equation. After the classes are identified, the covariates and distal outcome are analyzed using multinomial logistic regression or other appropriate analyses. In the one‐step procedure, the covariates and the distal outcome variable are included from the beginning and are estimated as a unified model. Both approaches are used in practice, but there is no clear evidence regarding which one is better, and many issues are involved in the decision (Huang, Brech, Hara, & Haer, [<reflink idref="bib26" id="ref67">26</reflink>] ). Given that several studies have shown that including covariates improves membership classification (e.g., Lubke & Muthén, [<reflink idref="bib45" id="ref68">45</reflink>] ) and given our interest in the effect of the covariates on the class membership, we opted for the one‐step analysis in this study.</p> <p>To decide on the number of classes, the model was assessed using the information‐based criteria index, the reliability of classification into classes, the entropy index, and the likelihood ratio test for the optimal number of classes, which are all available in Mplus. The Bayesian information criterion (BIC) is used to compare model fit between non‐nested models, with smaller values of the index indicating a better model fit. The reliability of the classification was assessed by examining the average posterior probability for students to be in the particular class. The entropy index shows the possibility of the prediction of class membership given the observed variables with values ranging from 0 to 1, and the higher values indicating that the latent classes are more discriminative. We used the Vuong–Lo–Mendel–Rubin likelihood ratio test (Lo, Mendell, & Rubin, [<reflink idref="bib43" id="ref69">43</reflink>] ; Vuong, [<reflink idref="bib67" id="ref70">67</reflink>] ) to assess the model and the optimal number of classes by comparing a k versus k − 1 class model. For this test, a low p value indicates that the k − 1 class model is rejected in favor of the k class model.</p> <p>Table  shows the fit indices for both the linear and quadratic growth mixture models. As mentioned previously, the quadratic model had too many constraints to be accepted; therefore, only linear models are discussed below. In comparing the 1‐, 2‐ and 3‐class linear models, the 2‐class model was the best fit to the data. As can be seen in Table , the Akaike's information criterion (AIC), BIC, and sample size‐adjusted BIC were larger for the 3‐class model. Also, the Vuong–Lo–Mendel–Rubin likelihood ratio test for one versus two classes and two versus three classes confirmed that the 2‐class model is the better fit (p < .05 and p > .05, respectively). Furthermore, the 3‐class model required constraints in order for the model to converge; specifically, we had to set the residual variances for the slope to be small and equal across classes and set the correlation between the intercept and the slope to be 0.</p> <p>Fit Indices for Mixture Growth Models</p> <p> <ephtml> <table border="1" cellpadding="6"><tr><th /><th>AIC</th><th>BIC</th><th>Sample size‐adjusted BIC</th><th>Entropy</th><th>VLMR p value</th></tr><tr><td>Linear GMM</td></tr><tr><td>1‐class</td><td>4,766</td><td>4,833</td><td>4,776</td><td>—</td><td>—</td></tr><tr><td>2‐class</td><td>4,703</td><td>4,826</td><td>4,721</td><td>.66</td><td>< .01</td></tr><tr><td>3‐class</td><td>4,891</td><td>5,062</td><td>4,917</td><td>.72</td><td>= .10</td></tr><tr><td>Quadratic GMM</td></tr><tr><td>1‐class</td><td>4,733</td><td>4,815</td><td>4,745</td><td>—</td><td>—</td></tr><tr><td>2‐class</td><td>4,664</td><td>4,816</td><td>4,686</td><td>.65</td><td>< .05</td></tr><tr><td>3‐class</td><td>4,644</td><td>4,867</td><td>4,677</td><td>.73</td><td>= .29</td></tr></table> </ephtml> </p> <p>Note 8 AIC = Akaike's information criterion; BIC = Bayesian information criterion; VLMR = Vuong–Lo–Mendel–Rubin likelihood ratio test; GMM = growth mixture modeling.</p> <p>9 *Model has constraints.</p> <p>The resulting 2‐class growth mixture model included two classes of about equal size. Class 1 with 143 students (63 girls and 80 boys) had an intercept of 4.13 (SE = .63) and a slope of 1.06 (SE = .43), whereas Class 2 with 161 students (79 girls and 82 boys) had an intercept of 5.36 (SE = .48) and a slope of 1.07 (SE = .29). The children in Class 2, the higher performing class, began the second grade with stronger spatial skills and maintained that strength over the 3 years of the study. The children in Class 1, the poorer performing class, began the study with poorer spatial scores, and that pattern was maintained over 3 years.</p> <p>The role of the covariates in the 2‐class model is best understood in light of their role in the 1‐class model. Similar to the single‐group growth model, the 1‐class growth mixture model indicated that SES and VWM had a significant effect on the intercept, .18 (SE = .08; p < .05) for SES and .23 (SE = .06, p < .01) for VWM. In contrast, in the 2‐class mixture model the effect of these covariates on the intercept was not significant in either class. The explanation is that the effect of these covariates on the intercept in the 1‐class model is transformed into a significant effect on class membership in the 2‐class mixture model, both of which were significant at the .01 level. Specifically, the data indicated that a student with a free‐lunch status (SES = 0) was more than four times more likely to be in Class 1 (with a lower intercept and slope) than a student with full price lunch status (SES = 2; see Figure ) and that two classes, suggesting two underlying populations, are needed to best explain the role of SES in the development of spatial skills. Likewise, a student with a VWM score of 4, indicating that student scored in the lowest 30% on the VWM task, was more than three times more likely to be in Class 1 than a student with a score of 7, which places students in the top 30% of the VWM scores. In addition, performing ANOVA on the means indicated no significant differences in the intercepts in either class as a function of VWM, F(<reflink idref="bib5" id="ref71">5</reflink>, 137) = 2.16, p = .06; F(<reflink idref="bib6" id="ref72">6</reflink>, 154) = 0.80, p = .58 for Class 1 and Class 2, respectively, and SES, F(<reflink idref="bib2" id="ref73">2</reflink>, 140) = 2.43, p = .09; F(<reflink idref="bib2" id="ref74">2</reflink>, 158) = 0.86, p = .42 for Class 1 and Class 2, respectively, indicating homogeneity within class. The means of the intercepts by SES for each class are given in Table . These results, however, do not mean that the covariates perfectly predicted membership. Although a student with free‐lunch status has a much higher chance to be in Class 1 than Class 2, approximately a third of the students with low SES were in the higher performing Class 2 and a fourth of students with full priced lunch were in the lower performing Class 1.</p> <p>Mean Intercept Scores for Spatial Skills by SES in the Two‐Class Mixture Model</p> <p> <ephtml> <table border="1" cellpadding="4"><tr><th>SES</th><th>M</th><th>N</th><th>SD</th></tr><tr><td>Class 1</td></tr><tr><td>0</td><td>4.54</td><td>101</td><td>0.86</td></tr><tr><td>1</td><td>4.67</td><td>11</td><td>0.71</td></tr><tr><td>2</td><td>4.18</td><td>31</td><td>0.87</td></tr><tr><td>Class 2</td></tr><tr><td>0</td><td>5.96</td><td>49</td><td>0.59</td></tr><tr><td>1</td><td>5.89</td><td>13</td><td>0.88</td></tr><tr><td>2</td><td>5.81</td><td>99</td><td>0.75</td></tr><tr><td>Overall</td></tr><tr><td>0</td><td>5.01</td><td>150</td><td>1.03</td></tr><tr><td>1</td><td>5.33</td><td>24</td><td>1.01</td></tr><tr><td>2</td><td>5.42</td><td>130</td><td>1.04</td></tr></table> </ephtml> </p> <p>Note 10 SES = socioeconomic status; SD = standard deviation.</p> <p>Gender had no impact on class membership and its influence on the intercept emerged only in the 2‐class model. In the 1‐class model, gender did not have a significant effect on either the intercept or the slope. In the growth mixture 2‐class model, gender had a significant effect on the intercept in the lower performing Class 1 (−.69, p < .01). The effect was confirmed by the t test in the post hoc analysis. The mean of the intercept for boys in Class 1 was 4.78 and for girls the mean was 4.08, and this difference was significant (p < .01). In Class 2, the means for the intercept were not different: 5.84 for boys and 5.89 for girls. The effect of gender on the intercept would be missed in a single‐class model.</p> <p>Class membership had a significant impact on children's performance on the fourth‐grade mathematics competency test, the distal outcome variable. The probability distributions for competency test performance indicated that most of the children (70%) in the low‐performing Class 1 would meet the standards set for mathematics competency and the probability of children in this class not meeting the standards was 30%. The probability of children in Class 1 exceeding the standards was 0. In contrast, children in Class 2 had a very high probability of exceeding the standards for mathematics competency (.72), whereas the probability of meeting the standards was .28. The probability of not meeting the competency standards for this group was 0. Thus, beginning the second grade with better spatial skills had long‐term consequences for mathematics achievement.</p> <hd id="AN0128440772-18">Discussion</hd> <p>We know little about the development of spatial skills, particularly the skills that are linked to better performance in mathematics. In particular, there is a dearth of longitudinal research in this area, specifically research that examines whether different developmental profiles emerge as a function of key variables, such as gender, SES, and VWM. In this study, in comparing models that assumed a single latent class versus a model that assumed two latent classes, we found that a 2‐class model, indicating two underlying populations, best fit the data. Although these latent classes were similar in their slope and in the roles of SES and VWM, they differed substantially in their intercepts, in the role of gender, and how they predicted mathematics achievement. The strength of the 2‐class model was also evident when we examined the classes. In neither class did SES and VWM predict the intercept or growth, indicating homogeneity within class. The 2‐class model also allowed us to observe how gender predicted spatial skills in the lower performing class but not the higher performing class. Our data confirmed our hypothesis that multiple latent classes are needed to explain spatial skills development as a predictor of mathematics achievement; however, we did not find these classes to be a function of gender differences. Instead, VWM and SES appeared to have the only influence on the latent classes.</p> <p>At least with regard to two‐dimensional mental rotation skills, the data indicate early emerging and consistent differences in spatial skills that should be considered when making decisions about remediation in mathematics. Children from low‐income homes, or who have poor VWM and are female, are likely to be candidates for interventions designed to improve spatial skills. It should be noted that this is a correlational study; therefore, we cannot conclude that these variables cause differences in spatial skills and subsequent math achievement. However, these characteristics are linked to poorer spatial skills development. It may be that another variable, such as exposure to activities that support the development of spatial skills, may explain the link among SES, working memory, gender, and spatial skill development.</p> <p>Although class membership was not entirely determined by SES, lower income children were substantially more likely to be in the latent class that began the study with poorer spatial skills and to maintain this pattern over the 3‐year period of the study. Most of the children in this group met the standards for mathematics competency; however, over a third of the children in the class scored below standards, and none exceeded the standards. In contrast, the higher performing class was more likely to include children from higher income homes. These children were much more likely to begin the second grade with a higher initial level of spatial skills and to maintain that advantage over the 3‐year period of the study. The outcome for these children was much better than the other group, with close to 70% of the children in this class exceeding the standards. These results are consistent with earlier work on the environmental effects on spatial skills indicating that children who grow up in low‐SES environments have poorer spatial skills (Jirout & Newcombe, [<reflink idref="bib28" id="ref75">28</reflink>] ; Levine et al., [<reflink idref="bib39" id="ref76">39</reflink>] ). The results are also consistent with research showing that in general children living in poverty are significantly less likely to be involved in experiences that support academic achievement (Bradley, Corwyn, Burchinal, Pipes McAdoo, & García Coll, [<reflink idref="bib5" id="ref77">5</reflink>] ; Davis‐Kean, [<reflink idref="bib16" id="ref78">16</reflink>] ). One such experience may be parent–child interactions that involve spatial language; parental spatial language use predicts children's spatial language that, in turn, predicts their spatial skills (Pruden, Levine, & Huttenlocher, [<reflink idref="bib58" id="ref79">58</reflink>] ). The present study extends prior work on the environmental effects on spatial skills by showing that a consistent pattern of poor spatial skills is linked to low‐SES environments, which in turn predicts later poorer mathematics competency. It points to the need to improve the spatial skills in those at‐risk children through remediation.</p> <p>We hypothesized that gender would affect the intercept and slope of spatial skills, but that was the case only in the low‐performing class in which girls’ intercept was lower than boys. The expectation that girls, overall, would have a lower intercept and slope was not found to be the case. This finding was surprising given the long history of research indicating gender differences in spatial skills (Burnett, Lane, & Dratt, [<reflink idref="bib7" id="ref80">7</reflink>] ; Levine et al., [<reflink idref="bib38" id="ref81">38</reflink>] ) and previous research showing gender differences on a similar task in preschoolers (Levine et al., [<reflink idref="bib38" id="ref82">38</reflink>] ) and with older children using the Thurstone PMA (Levine et al., [<reflink idref="bib39" id="ref83">39</reflink>] ). However, gender differences are more pronounced in older children and adults and more pronounced on three‐dimensional tasks than two‐dimensional tasks with this age group (Johnson & Meade, [<reflink idref="bib29" id="ref84">29</reflink>] ; Voyer et al., [<reflink idref="bib66" id="ref85">66</reflink>] ). The current study differs from the two studies by Levine et al. ([<reflink idref="bib38" id="ref86">38</reflink>] , [<reflink idref="bib39" id="ref87">39</reflink>] ), in that we used a composite spatial skill score including both the Thurstone PMA and Matching Parts measures. We do not believe using a composite spatial skills score dampened the potential gender effect, because when we examined the individual spatial measures, we found no indication of gender differences in either measure.</p> <p>The model with two latent classes allowed us to observe how the combination of low SES, poor VWM, and gender characterize poorer development of spatial skills as they predict mathematics achievement. Our results are different with previous work finding gender differences to be more pronounced in higher SES children (e.g., Waber, Carlson, & Mann, [<reflink idref="bib68" id="ref88">68</reflink>] ) but consistent with the work of Casey et al. ([<reflink idref="bib10" id="ref89">10</reflink>] ). This may be a function of the longitudinal design and analytic technique that included mathematics achievement as a distal outcome. The results of the current study are better compared to that of Casey et al. ([<reflink idref="bib10" id="ref90">10</reflink>] ), who found gender differences in children from low‐income homes, in that both studies focused on how spatial skills predict mathematics achievement. Levine et al. ([<reflink idref="bib39" id="ref91">39</reflink>] ), in contrast, examined gender and SES differences in spatial skills alone. The inclusion of mathematics achievement as an outcome measure may account for the discrepancy. Alternatively, our results could be a function of recent efforts made in the last 10 years to improve mathematics achievement and spatial skills of girls. The home life of children certainly impacts their academic achievement (Bradley et al., [<reflink idref="bib5" id="ref92">5</reflink>] ; Davis‐Kean, [<reflink idref="bib16" id="ref93">16</reflink>] ), and with regard to girls, Casey, Dearing, Dulaney, Heyman, and Springer ([<reflink idref="bib9" id="ref94">9</reflink>] ) found that maternal supportive interactions to be related to their daughters’ spatial problem solving. Our results may reflect middle‐class parents’ higher investment in their daughters’ early mathematics and science education through participation in STEM‐themed summer camps (e.g., GirlStart, Girls Inc, CTY, Duke TIP) or computer activities that emphasize spatial processing skills.</p> <p>We included VWM as one of the covariates to control for its influence on mathematics achievement and also because it might impact spatial skill development through the strategies children use on the spatial tasks. We hypothesized that VWM either would be negatively related to spatial skills, in the case of competing strategies, or be positively related to spatial skills. The latter hypothesis was supported. Given that there is evidence that VWM in combination with VSWM predicts spatial ability (Kaufman, [<reflink idref="bib31" id="ref95">31</reflink>] ), there was reason to believe that it would predict performance on spatial tasks, albeit indirectly, via strategy use. Prior research has suggested that children with poorer VSWM might use analytic strategies that are supported by VWM when solving spatial tasks (Coluccia & Louse, [<reflink idref="bib14" id="ref96">14</reflink>] ; Pezaris & Casey, [<reflink idref="bib56" id="ref97">56</reflink>] ). We found that VWM predicted latent class membership and mathematics achievement as a function of class membership. Children with poorer VWM were more likely to be in the class with poorer spatial skills. The results of the current study are consistent with those of Kaufman ([<reflink idref="bib31" id="ref98">31</reflink>] ) and provide evidence that VWM supports the emergence of spatial skills at this age. However, because we did not assess strategy use, we do not know whether VWM predicted spatial skills through strategy use. It could be that VWM allowed children with poor VSWM to use analytic strategies while solving the spatial skills tasks (for a discussion of this possibility, see Wang & Carr, [<reflink idref="bib69" id="ref99">69</reflink>] ). Future research needs to explicitly assess the strategies spontaneously used by children during spatial tasks.</p> <hd id="AN0128440772-19">Limitations</hd> <p>The current study has several strengths, for example, the use of a large and diverse sample allows for the generalizability of the results, but it has several limitations. One limitation of the study was that in describing the participants in the sample, information was not collected about whether children were diagnosed with learning disabilities. Most of the research on children with mathematics learning disabilities has focused on deficits in spatial working memory as opposed to spatial skills (e.g., Passolunghi & Mammarella, [<reflink idref="bib53" id="ref100">53</reflink>] ). Nevertheless, given the relation between VSWM and spatial skills (Reuhkala, [<reflink idref="bib59" id="ref101">59</reflink>] ), it is likely that children with learning disabilities also have deficits in spatial skills. The identification of these children would have allowed for a better understanding of the developmental profiles of these and typically developing children.</p> <p>Another possible limitation is the repeated use of the same measures across the five time points. Some of the gains in the scores on these measures could be attributed to a practice effect. To avoid this issue, we could have alternated between several measures, but there are very few spatial skills measures available for this age group. Furthermore, the use of a different measure would have introduced the possibility that any change might be due to the change in measure and not change in spatial skills. As such, the practice effect was the lesser of the two evils. However, in interpreting these results we need to keep in mind the potential practice effects.</p> <p>Another variable that was not assessed in this study and that could have potential implications for mathematics achievement is the strategies the children use while doing the spatial tasks. There are differences in the ways individuals solve the same spatial task (Glueck & Fitting, [<reflink idref="bib20" id="ref102">20</reflink>] ). Some students, particularly girls, use verbal and analytic strategies more often than spatial strategies (Coluccia & Louse, [<reflink idref="bib14" id="ref103">14</reflink>] ). Differences in strategy use have been suggested to explain the more pronounced gender differences on tasks that require more intensive spatial processing (Masters & Sanders, [<reflink idref="bib47" id="ref104">47</reflink>] ). Although beyond the scope of this study, this needs to be done to better understand how spatial skills influence mathematics achievement.</p> <p>We did not include a measure of visuo‐spatial working memory in this study. Measures of VSWM and spatial skills are often highly correlated (e.g., Kaufman, [<reflink idref="bib31" id="ref105">31</reflink>] ; Miyake, Friedman, Rettinger, Shah, & Hegarty, [<reflink idref="bib48" id="ref106">48</reflink>] ) and are often used interchangeably (e.g., Kyttälä & Lehto, [<reflink idref="bib33" id="ref107">33</reflink>] ; Miyake et al., [<reflink idref="bib48" id="ref108">48</reflink>] ; Reuhkala, [<reflink idref="bib59" id="ref109">59</reflink>] ). Although we would expect that VSWM, as a covariate, would predict the development of spatial skills, we did not include it as a covariate because we were concerned that the two constructs would overlap significantly and that the inclusion of both would complicate the model interpretation.</p> <p>Although not necessarily a limitation, it should be made clear that the results of this study, particularly regarding gender, may not be generalized to three‐dimensional spatial skills. Gender differences are more prevalent in three‐dimensional tasks, possibly due to the greater demand of VSWM resources entailed by spatial tasks using three‐dimensional stimuli (Wang & Carr, [<reflink idref="bib69" id="ref110">69</reflink>] ). Future research needs to determine whether these results extend to three‐dimensional spatial skills.</p> <p>Finally, these results are correlational in nature. These data point to possible causal links between SES, gender, and VWM and two‐dimensional spatial skill development, but a causal relation cannot be assumed. Although SES and gender cannot be manipulated via experimental work we can look at their impact of instructional programs designed to improve spatial skills. Research by Sorby ([<reflink idref="bib60" id="ref111">60</reflink>] ) suggests that spatial interventions are particularly effective for girls, suggesting that gender differences can decrease in response to treatment. As such, gender differences in spatial task performance may reflect differences in experience, more so than biology. Future research should look at other factors, such as exposure to spatial games and tasks that might explain both SES and gender differences in spatial skills.</p> <ref id="AN0128440772-20"> <title>Notes</title> <blist> <bibl id="bib1" idref="ref3" type="bt">1</bibl> <bibtext>This research was supported by the Institute for Educational Sciences Grant #305A110920. </bibtext> </blist> </ref> <ref id="AN0128440772-21"> <title>References</title> <blist> <bibtext>Achter, J. A., Lubinski, D., Benbow, C. P., & Eftekhari‐Sanjani, H. (1999). Assessing vocational preferences among gifted adolescents adds incremental validity to abilities: A discriminant analysis of educational outcomes over a 10‐year interval. Journal of Educational Psychology, 91, 777–786. doi:10.1037/0022‐0663.91.4.777 </bibtext> </blist> <blist> <bibl id="bib2" idref="ref38" type="bt">2</bibl> <bibtext>Aunola, K., Leskinen, E., Lerkkanen, M.‐K., & Nurmi, J.‐E. (2004). Developmental dynamics of math performance from preschool to grade 2. Journal of Educational Psychology, 96, 699–713. doi:10.1348/000709905X51608 </bibtext> </blist> <blist> <bibl id="bib3" idref="ref64" type="bt">3</bibl> <bibtext>Berlin, K. S., Parra, G. R., & Williams, N. A. (2013). An introduction to latent variable mixture modeling (part 2): Longitudinal latent class growth analysis and growth mixture models. Journal of Pediatric Psychology, 39, 188–203. doi:10.1093/jpepsy/jst085 </bibtext> </blist> <blist> <bibl id="bib4" idref="ref2" type="bt">4</bibl> <bibtext>Boonen, A. J. H., van der Schoot, M., van Wesel, F., de Vries, M. H., & Jolles, J. (2013). What underlies successful word problem solving? A path analysis in sixth grade students. Contemporary Educational Psychology, 38, 271–279. doi:10.1016/j.cedpsych.2013.05.001 </bibtext> </blist> <blist> <bibl id="bib5" idref="ref71" type="bt">5</bibl> <bibtext>Bradley, R. H., Corwyn, R. F., Burchinal, M., Pipes McAdoo, H., & García Coll, C. (2001). The home environments of children in the United States Part II: Relations with behavioral development through age thirteen. Child Development, 72, 1868–1886. doi:10.1111/1467‐8624.t01‐1‐00383 </bibtext> </blist> <blist> <bibl id="bib6" idref="ref47" type="bt">6</bibl> <bibtext>Bull, R., & Johnston, R. S. (1997). Children's arithmetical difficulties: Contributions from processing speed, item identification, and short‐term memory. Journal of Experimental Child Psychology, 65, 1–24. <ulink href="http://dx.doi.org/10.1006/jecp.1996.2358">http://dx.doi.org/10.1006/jecp.1996.2358</ulink></bibtext> </blist> <blist> <bibl id="bib7" idref="ref80" type="bt">7</bibl> <bibtext>Burnett, S. A., Lane, D. M., & Dratt, L. M. (1979). Spatial visualization and sex differences in quantitative ability. Intelligence, 3, 345–354. doi:10.1016/0160‐2896(79)90003‐5 </bibtext> </blist> <blist> <bibl id="bib8" idref="ref25" type="bt">8</bibl> <bibtext>Carr, M., Bray, B., Gerow, K., & Barned, N. (2010). Spatial skills and elementary school mathematics. Paper presented at the Spatial Learning Conference, Boston, MA. </bibtext> </blist> <blist> <bibl id="bib9" idref="ref94" type="bt">9</bibl> <bibtext>Casey, B. M., Dearing, E., Dulaney, A., Heyman, M., & Springer, R. (2014). Young girls’ spatial and arithmetic performance: The mediating role of maternal supportive interactions during joint spatial problem solving. Early Childhood Research Quarterly, 29, 636–648. doi:10.1016/j.ecresq.2014.07.005 </bibtext> </blist> <blist> <bibl id="bib10" idref="ref42" type="bt">10</bibl> <bibtext>Casey, B. M., Dearing, E., Vasilyeva, M., Ganley, C. M., & Tine, M. (2011). Spatial and numerical predictors of measurement performance: The moderating effects of community income and gender. Journal of Educational Psychology, 103, 296–311. doi:10.1037/a0022516 </bibtext> </blist> <blist> <bibl id="bib11" idref="ref26" type="bt">11</bibl> <bibtext>Casey, B., Lombardi, C., Pollock, A., Fineman, B., Pezaris, E., & Dearing, E. (2015, March). Girls’ spatial skills and arithmetic strategies in first grade as predictors of fifth grade analytical math reasoning. Paper presented at biennial meeting of the Society for Research in Child Development, Philadelphia, PA. </bibtext> </blist> <blist> <bibl id="bib12" idref="ref4" type="bt">12</bibl> <bibtext>Cheng, Y.‐L., & Mix, K. S. (2014). Spatial training improves children's mathematics ability. Journal of Cognition and Development, 15, 2–11. doi:10.1080/15248372.2012.725186 </bibtext> </blist> <blist> <bibl id="bib13" idref="ref24" type="bt">13</bibl> <bibtext>Clements, D. H., Battista, M. T., Sarama, J., & Swaminathan, S. (1997). Development of students’ spatial thinking in a unit on geometric motions and area. The Elementary School Journal, 98, 171–186. doi:10.1086/461890 </bibtext> </blist> <blist> <bibl id="bib14" idref="ref96" type="bt">14</bibl> <bibtext>Coluccia, E., & Louse, G. (2004). Gender differences in spatial orientation: A review. Journal of Environmental Psychology, 24, 329–340. doi:10.1016/j.jenvp.2004.08.006 </bibtext> </blist> <blist> <bibl id="bib15" idref="ref14" type="bt">15</bibl> <bibtext>Crescentini, C., Fabbro, F., & Urgesi, C. (2014). Mental spatial transformations of objects and bodies: Different developmental trajectories in children from 7 to 11 years of age. Developmental Psychology, 50, 370–383. doi:10.1037/a0033627.supp </bibtext> </blist> <blist> <bibl id="bib16" idref="ref78" type="bt">16</bibl> <bibtext>Davis‐Kean, P. E. (2005). The influence of parent education and family income on child achievement: The indirect role of parental expectations and the home environment. Journal of Family Psychology, 19, 294–304. doi:10.1037/0893‐3200.19.2.294 </bibtext> </blist> <blist> <bibl id="bib17" idref="ref51" type="bt">17</bibl> <bibtext>Dearing, E., Casey, B. M., Ganley, C. M., Tillinger, M., Laski, E., & Montecillo, C. (2012). Young girls’ arithmetic and spatial skills: The distal and proximal roles of family socioeconomics and home learning experiences. Early Childhood Research Quarterly, 27, 458–470. doi:10.1016/j.ecresq.2012.01.002 </bibtext> </blist> <blist> <bibl id="bib18" idref="ref17" type="bt">18</bibl> <bibtext>Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8, 307–314. </bibtext> </blist> <blist> <bibl id="bib19" idref="ref49" type="bt">19</bibl> <bibtext>Geiser, C., Lehmann, W., Corth, M., & Eid, M. (2008). Quantitative and qualitative change in children's mental rotation performance. Learning and Individual Differences, 18, 419–429. doi:10.1016/j.lindif.2007.09.001 </bibtext> </blist> <blist> <bibl id="bib20" idref="ref102" type="bt">20</bibl> <bibtext>Glueck, J., & Fitting, S. (2003). Spatial strategy selection: Interesting incremental information. International Journal of Testing, 3, 293–308. doi:10.1207/S15327574IJT0303_7 </bibtext> </blist> <blist> <bibl id="bib21" idref="ref22" type="bt">21</bibl> <bibtext>Grossberg, S., & Repin, D. V. (2003). A neural model of how the brain represents and compares multi‐digit numbers: Spatial and categorical processes. Neural Networks: The Official Journal of the International Neural Network Society, 16, 1107–1140. 10.1016/S0893‐6080(03)00193‐X </bibtext> </blist> <blist> <bibl id="bib22" idref="ref21" type="bt">22</bibl> <bibtext>Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). “The relation between spatial skill and early number knowledge: The role of the linear number line”: Correction to Gunderson et al. (2012). Developmental Psychology, 48, 1229–1241. doi: 10.1037/a0028593 </bibtext> </blist> <blist> <bibl id="bib23" idref="ref10" type="bt">23</bibl> <bibtext>Harris, J., Newcombe, N. S., & Hirsh‐Pasek, K. (2013). A new twist on studying the development of dynamic spatial transformations: Mental paper folding in young children. Mind, Brain, and Education, 7, 49–55. doi:10.1111/mbe.12007 </bibtext> </blist> <blist> <bibl id="bib24" idref="ref46" type="bt">24</bibl> <bibtext>Healy, A. F., & Nairne, J. S. (1985). Short‐term memory processes in counting. Cognitive Psychology, 17, 417–444. doi:10.1016/0010‐0285(85)90015‐5 </bibtext> </blist> <blist> <bibl id="bib25" idref="ref48" type="bt">25</bibl> <bibtext>Holmes, J., & Adams, J. W. (2006). Working memory and children's mathematical skills: Implications for mathematical development and mathematics curricula. Educational Psychology, 26, 339–366. doi:10.1080/01443410500341056 </bibtext> </blist> <blist> <bibl id="bib26" idref="ref67" type="bt">26</bibl> <bibtext>Huang, D., Brech, M. L., Hara, M., & Haer, Y. I. (2010). Influences of a covariate on growth mixture modeling. Journal of Drug Issues, 40, 173–194. doi:10.1177/002204261004000110 </bibtext> </blist> <blist> <bibl id="bib27" idref="ref50" type="bt">27</bibl> <bibtext>Janssen, A. B., & Geiser, C. (2010). On the relationship between solution strategies in two mental rotation tasks. Learning and Individual Differences, 20, 473–478. doi:10.1016/j.lindif.2010.03.002 </bibtext> </blist> <blist> <bibl id="bib28" idref="ref75" type="bt">28</bibl> <bibtext>Jirout, J. J., & Newcombe, N. S. (2015). Building blocks for developing spatial skills: Evidence from a large, representative U.S. sample. Psychological Science, 26, 302–310. doi:10.1177/0956797614563338 </bibtext> </blist> <blist> <bibl id="bib29" idref="ref16" type="bt">29</bibl> <bibtext>Johnson, E. S., & Meade, A. C. (1987). Developmental patterns of spatial ability: An early sex difference. Child Development, 58, 725–740. doi:10.2307/1130210 </bibtext> </blist> <blist> <bibl id="bib30" idref="ref40" type="bt">30</bibl> <bibtext>Jordan, N. C., Kaplan, D., Olah, L. N., & Locuniak, M. N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153–175. doi:10.1111/j.1467‐8624.2006.00862.x </bibtext> </blist> <blist> <bibl id="bib31" idref="ref95" type="bt">31</bibl> <bibtext>Kaufman, S. B. (2007). Sex differences in mental rotation and spatial visualization ability: Can they be accounted for by differences in working memory capacity? Intelligence, 35, 211–223. doi:10.1016/j.intell.2006.07.00 </bibtext> </blist> <blist> <bibl id="bib32" idref="ref23" type="bt">32</bibl> <bibtext>Knops, A., Viarouge, A., & Dehaene, S. (2009). Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from the operational momentum effect. Attention, Perception & Psychophysics, 71, 803–821. doi:10.3758/APP.71.4.803 </bibtext> </blist> <blist> <bibl id="bib33" idref="ref107" type="bt">33</bibl> <bibtext>Kyttälä, M., & Lehto, J. E. (2008). Some factors underlying mathematical performance: The role of visuospatial working memory and non‐verbal intelligence. European Journal of Psychology of Education, 23, 77–94. doi:10.1007/BF03173141 </bibtext> </blist> <blist> <bibl id="bib34" idref="ref35" type="bt">34</bibl> <bibtext>Lachance, J. A., & Mazzocco, M. M. M. (2006). A longitudinal analysis of sex differences in math and spatial skills in primary school age children. Learning and Individual Differences, 16, 195–216. doi:10.1016/j.lindif.2005.12.001 </bibtext> </blist> <blist> <bibl id="bib35" idref="ref27" type="bt">35</bibl> <bibtext>Laski, E. V., Casey, B. M., Yu, Q., Dulaney, A., Heyman, M., & Dearing, E. (2013). Spatial skills as a predictor of first grade girls’ use of higher level arithmetic strategies. Learning and Individual Differences, 23, 123–130. doi:10.1016/j.lindif.2012.08.001 </bibtext> </blist> <blist> <bibl id="bib36" idref="ref1" type="bt">36</bibl> <bibtext>LeFevre, J. A., Jimenez, L. C., Sowinski, C., Cankaya, O., Kamawar, D., & Skwarchuk, S. L. (2013). Charting the role of the number line in mathematical development. Frontiers in Psychology, 4, 1–9. doi:10.3389/fpsyg.2013.00641 </bibtext> </blist> <blist> <bibl id="bib37" idref="ref18" type="bt">37</bibl> <bibtext>Lemer, C., Dehaene, S., Spelke, E., & Cohen, L. (2003). Approximate quantities and exact number words: Dissociable systems. Neuropsychologia, 41, 1942–1958. doi:10.1016/S0028‐3932(03)00123‐4 </bibtext> </blist> <blist> <bibl id="bib38" idref="ref12" type="bt">38</bibl> <bibtext>Levine, S. C., Huttenlocher, J., Taylor, A., & Langrock, A. (1999). Early sex differences in spatial skill. Developmental Psychology, 35, 940–949. doi:10.1037/0012‐1649.35.4.940 </bibtext> </blist> <blist> <bibl id="bib39" idref="ref34" type="bt">39</bibl> <bibtext>Levine, S. C., Vasilyeva, M., Lourenco, S. F., Newcombe, N. S., & Huttenlocher, J. (2005). Socioeconomic status modifies the sex difference in spatial skill. Psychological Science, 16, 841–845. doi:10.1111/j.1467‐9280.2005.01623.x </bibtext> </blist> <blist> <bibl id="bib40" idref="ref58" type="bt">40</bibl> <bibtext>Levy, J. U., & Levy, N. (2002). Mechanical aptitude and spatial relations tests. Princeton, NJ: Thomson/Arco. </bibtext> </blist> <blist> <bibl id="bib41" idref="ref7" type="bt">41</bibl> <bibtext>Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta‐analysis. Child Development, 56, 1479–1498. doi:10.2307/1130467 </bibtext> </blist> <blist> <bibl id="bib42" idref="ref66" type="bt">42</bibl> <bibtext>Little, T. D., Jorgensen, T. D., Lang, K. M., & Moore, W. G. (2013). On the joys of missing data. Journal of Pediatric Psychology, 39, 151–162. doi:10.1093/jpepsy/jst048 </bibtext> </blist> <blist> <bibl id="bib43" idref="ref69" type="bt">43</bibl> <bibtext>Lo, Y., Mendell, N. R., & Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika, 88, 767–778. doi:10.1093/biomet/88.3.767 </bibtext> </blist> <blist> <bibl id="bib44" idref="ref9" type="bt">44</bibl> <bibtext>Loring‐Meier, S., & Halpern, D. F. (1999). Sex differences in visuospatial working memory: Components of cognitive processing. Psychonomic Bulletin & Review, 6, 464. doi:10.3758/BF03210836 </bibtext> </blist> <blist> <bibl id="bib45" idref="ref68" type="bt">45</bibl> <bibtext>Lubke, G., & Muthén, B. (2007). Performance of factor mixture models as a function of model size, covariate effects, and class‐specific parameters. Structural Equation Modeling, 14, 26–47. doi:10.1207/s15328007sem1401_2 </bibtext> </blist> <blist> <bibl id="bib46" idref="ref28" type="bt">46</bibl> <bibtext>Manger, T., & Eikeland, O.‐J. (1998). The effects of spatial visualization and students’ sex on mathematical achievement. British Journal of Psychology, 89, 17–25. doi:10.1111/j.2044‐8295.1998.tb02670.x </bibtext> </blist> <blist> <bibl id="bib47" idref="ref104" type="bt">47</bibl> <bibtext>Masters, M. S., & Sanders, B. (1993). Is the gender difference in mental rotation disappearing? Behavior Genetics, 23, 337–341. doi:10.1007/BF01067434 </bibtext> </blist> <blist> <bibl id="bib48" idref="ref106" type="bt">48</bibl> <bibtext>Miyake, A., Friedman, N. P., Rettinger, D. A., Shah, P., & Hegarty, M. (2001). How are visuospatial working memory, executive functioning, and spatial abilities related? A latent‐variable analysis. Journal of Experimental Psychology: General, 130, 621–640. doi:10.1037/0096‐3445.130.4.621 </bibtext> </blist> <blist> <bibl id="bib49" idref="ref52" type="bt">49</bibl> <bibtext>Muthén, B. (2006). The potential of growth mixture modeling. Infant and Child Development, 15, 623–625. doi:10.1002/icd.482 </bibtext> </blist> <blist> <bibl id="bib50" idref="ref65" type="bt">50</bibl> <bibtext>Muthén, L. K., & Muthén, B. O. (1998–2015). Mplus user's guide (7th ed.). Los Angeles, CA: Author. </bibtext> </blist> <blist> <bibl id="bib51" idref="ref53" type="bt">51</bibl> <bibtext>Muthén, B. O., & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55, 463–469. doi:10.1111/j.0006‐341x.1999.00463.x </bibtext> </blist> <blist> <bibl id="bib52" idref="ref11" type="bt">52</bibl> <bibtext>Nardini, M., Burgess, N., Breckenridge, K., & Atkinson, J. (2006). Differential developmental trajectories for egocentric, environmental and intrinsic frames of reference in spatial memory. Cognition, 101, 153–172. doi:10.1016/j.cognition.2005.09.005 </bibtext> </blist> <blist> <bibl id="bib53" idref="ref100" type="bt">53</bibl> <bibtext>Passolunghi, M. C., & Mammarella, I. C. (2010). Spatial and visual working memory ability in children with difficulties in arithmetic word problem solving. European Journal of Cognitive Psychology, 22, 944–963. doi:10.1080/09541440903091127 </bibtext> </blist> <blist> <bibl id="bib54" idref="ref39" type="bt">54</bibl> <bibtext>Penner, A. M. (2003). International gender x item difficulty interactions in mathematics and science achievement tests. Journal of Educational Psychology, 95, 650–655. doi:10.1037/0022‐0663.95.3.650 </bibtext> </blist> <blist> <bibl id="bib55" idref="ref45" type="bt">55</bibl> <bibtext>Penner, A., & Paret, M. (2008). Gender differences in mathematics achievement: Exploring the early grades and the extremes. Social Science Research, 37, 239–253. doi:10.1016/j.ssresearch.2007.06.012 </bibtext> </blist> <blist> <bibl id="bib56" idref="ref97" type="bt">56</bibl> <bibtext>Pezaris, E., & Casey, M. B. (1991). Girls who use “Masculine” problem‐solving strategies on a spatial task: Proposed genetic and environmental factors. Brain and Cognition, 17, 1–22. doi:10.1016/0278‐2626(91)90062‐D </bibtext> </blist> <blist> <bibl id="bib57" idref="ref20" type="bt">57</bibl> <bibtext>Piazza, M., Pica, P., Izard, V., Spelke, E. S., & Dehaene, S. (2013). Education enhances the acuity of the nonverbal approximate number system. Psychological Science, 24, 1037. doi:10.1177/0956797612464057 </bibtext> </blist> <blist> <bibl id="bib58" idref="ref79" type="bt">58</bibl> <bibtext>Pruden, S. M., Levine, S. C., & Huttenlocher, J. (2011). Children's spatial thinking: Does talk about the spatial world matter? Developmental Science, 14, 1417–1430. doi:10.1111/j.1467‐7687.2011.01088.x </bibtext> </blist> <blist> <bibl id="bib59" idref="ref101" type="bt">59</bibl> <bibtext>Reuhkala, M. (2001). Mathematical skills in ninth‐graders: Relationship with visuo‐spatial abilities and working memory. Educational Psychology, 21, 387–399. doi:10.1080/01443410120090786 </bibtext> </blist> <blist> <bibl id="bib60" idref="ref111" type="bt">60</bibl> <bibtext>Sorby, S. (2009). Developing spatial cognitive skills among middle school students. Cognitive Processing, 10, 312–315. doi:10.1007/s10339‐009‐0310‐y </bibtext> </blist> <blist> <bibl id="bib61" idref="ref5" type="bt">61</bibl> <bibtext>Sorby, S., Casey, B., Veurink, N., & Dulaney, A. (2013). The role of spatial training in improving spatial and calculus performance in engineering students. Learning and Individual Differences, 26, 20–29. doi:10.1016/j.lindif.2013.03.010 </bibtext> </blist> <blist> <bibl id="bib62" idref="ref33" type="bt">62</bibl> <bibtext>Thurstone, T. G. (1974). PMA readiness level. Chicago, IL: Science Research. </bibtext> </blist> <blist> <bibl id="bib63" idref="ref15" type="bt">63</bibl> <bibtext>Vandenberg, S. G., & Kuse, A. R. (1978). Mental rotations, a group test of three‐dimensional spatial visualization. Perceptual & Motor Skills, 47, 599. doi:10.2466/pms.1978.47.2.599 </bibtext> </blist> <blist> <bibl id="bib64" idref="ref37" type="bt">64</bibl> <bibtext>Vecchi, T., & Girelli, L. (1998). Gender differences in visuo‐spatial processing: The importance of distinguishing between passive storage and active manipulation. Acta Psychologica, 99, 1–16. doi:10.1016/S0001‐6918(97)00052‐8 </bibtext> </blist> <blist> <bibl id="bib65" idref="ref41" type="bt">65</bibl> <bibtext>Verdine, B. N., Golinkoff, R. M., Hirsh‐Pasek, K., Newcombe, N. S., Filipowicz, A. T., & Chang, A. (2014). Deconstructing building blocks: Preschoolers’ spatial assembly performance relates to early mathematical skills. Child Development, 85, 1062–1076. doi:10.1111/cdev.12165 </bibtext> </blist> <blist> <bibl id="bib66" idref="ref6" type="bt">66</bibl> <bibtext>Voyer, D., Voyer, S., & Bryden, M. P. (1995). Magnitude of sex differences in spatial abilities: A meta‐analysis and consideration of critical variables. Psychological Bulletin, 117, 250–270. doi:10.1037/0033‐2909.117.2.250 </bibtext> </blist> <blist> <bibl id="bib67" idref="ref70" type="bt">67</bibl> <bibtext>Vuong, Q. (1989). Likelihood ratio test for model selection and non‐nested hypotheses. Econometrica: Journal of the Econometric Society, 57, 307–333. doi:10.2307/1912557 </bibtext> </blist> <blist> <bibl id="bib68" idref="ref88" type="bt">68</bibl> <bibtext>Waber, D. P., Carlson, D., & Mann, M. (1982). Developmental and differential aspects of mental rotation in early adolescence. Child Development, 53, 1614–1621. doi:10.2307/1130089 </bibtext> </blist> <blist> <bibl id="bib69" idref="ref99" type="bt">69</bibl> <bibtext>Wang, L., & Carr, M. (2014). Working memory and strategy use contribute to gender differences in spatial ability. Educational Psychologist, 49, 261–282. doi:10.1080/00461520.2014.960568 </bibtext> </blist> <blist> <bibl id="bib70" idref="ref54" type="bt">70</bibl> <bibtext>Wechsler, D. (1974). WISC‐R: Wechsler Intelligence Scale for Children‐Revised. New York, NY: The Psychological Corporation. </bibtext> </blist> <blist> <bibl id="bib71" idref="ref8" type="bt">71</bibl> <bibtext>Zacks, J. M., & Tversky, B. (2005). Multiple systems for spatial imagery: Transformations of objects and bodies. Spatial Cognition and Computation, 5, 271–306. doi:10.1207/s15427633scc0504_1 </bibtext> </blist> <blist> <bibl id="bib72" idref="ref30" type="bt">72</bibl> <bibtext>Zhang, X., Koponen, T., Räsänen, P., Aunola, K., Lerkkanen, M. K., & Nurmi, J. E. (2014). Linguistic and spatial skills predict early arithmetic development via counting sequence knowledge. Child Development, 85, 1091–1107. doi:10.1111/cdev.12173 </bibtext> </blist> </ref> <p>PHOTO (COLOR): Latent growth model (top) and path diagram for growth mixture model (bottom). Note. In these models, SP1…SP5 represent the spatial skills variables as measured at five time points. I refers to the intercept, S refers to the slope, and Q refers to quadratic growth. In the second model, C refers to the latent class.</p> <p>PHOTO (COLOR): Estimated means for girls and boys in Class 1 and Class 2 (top), probability of class membership as a function of socioeconomic status (SES; middle), and verbal working memory (VWM; bottom).</p> <aug> <p>By Martha Carr; Natalia Alexeev; Lu Wang; Nicole Barned; Erin Horan and Adam Reed</p> </aug>
Header DbId: eric
DbLabel: ERIC
An: EJ1172410
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: The Development of Spatial Skills in Elementary School Students
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Carr%2C+Martha%22">Carr, Martha</searchLink><br /><searchLink fieldCode="AR" term="%22Alexeev%2C+Natalia%22">Alexeev, Natalia</searchLink><br /><searchLink fieldCode="AR" term="%22Wang%2C+Lu%22">Wang, Lu</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-1049-7255">0000-0002-1049-7255</externalLink>)<br /><searchLink fieldCode="AR" term="%22Barned%2C+Nicole%22">Barned, Nicole</searchLink><br /><searchLink fieldCode="AR" term="%22Horan%2C+Erin%22">Horan, Erin</searchLink><br /><searchLink fieldCode="AR" term="%22Reed%2C+Adam%22">Reed, Adam</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Child+Development%22"><i>Child Development</i></searchLink>. Mar-Apr 2018 89(2):446-460.
– Name: Avail
  Label: Availability
  Group: Avail
  Data: Wiley-Blackwell. 350 Main Street, Malden, MA 02148. Tel: 800-835-6770; Tel: 781-388-8598; Fax: 781-388-8232; e-mail: cs-journals@wiley.com; Web site: http://www.wiley.com/WileyCDA
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 15
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2018
– Name: SourceSuprt
  Label: Sponsoring Agency
  Group: SrcSuprt
  Data: Institute of Education Sciences (ED)
– Name: NumberContract
  Label: Contract Number
  Group: NumCntrct
  Data: 305A110920
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Audience
  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Spatial+Ability%22">Spatial Ability</searchLink><br /><searchLink fieldCode="DE" term="%22Skill+Development%22">Skill Development</searchLink><br /><searchLink fieldCode="DE" term="%22Elementary+School+Students%22">Elementary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Achievement%22">Mathematics Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Prediction%22">Prediction</searchLink><br /><searchLink fieldCode="DE" term="%22Child+Development%22">Child Development</searchLink><br /><searchLink fieldCode="DE" term="%22Profiles%22">Profiles</searchLink><br /><searchLink fieldCode="DE" term="%22Short+Term+Memory%22">Short Term Memory</searchLink><br /><searchLink fieldCode="DE" term="%22Socioeconomic+Status%22">Socioeconomic Status</searchLink><br /><searchLink fieldCode="DE" term="%22Verbal+Ability%22">Verbal Ability</searchLink><br /><searchLink fieldCode="DE" term="%22Gender+Differences%22">Gender Differences</searchLink><br /><searchLink fieldCode="DE" term="%22Longitudinal+Studies%22">Longitudinal Studies</searchLink><br /><searchLink fieldCode="DE" term="%22Tests%22">Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Tests%22">Mathematics Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Role%22">Role</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1111/cdev.12753
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0009-3920
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Through five waves of data collection, this longitudinal study investigated the development of spatial skills in 304 elementary school children (M[subscript age] = 7.64 years) as they progressed from the second to fourth grade. The study focused on whether multiple latent classes with different developmental profiles best explain development. Spatial skills were measured by tests featuring two-dimensional figures. Mathematics achievement was measured by the statewide end-of-year test and was included as a distal outcome variable. The role of covariates, including socioeconomic status, verbal working memory, and gender, was also explored. The results indicate a need to view two-dimensional spatial skills development as multidimensional with two developmental profiles predicted by socioeconomic status, verbal working memory, and gender. The developmental profiles predicted differences in mathematics achievement.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: CodeSource
  Label: IES Funded
  Group: SrcInfo
  Data: Yes
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2018
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1172410
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1172410
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1111/cdev.12753
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
        StartPage: 446
    Subjects:
      – SubjectFull: Spatial Ability
        Type: general
      – SubjectFull: Skill Development
        Type: general
      – SubjectFull: Elementary School Students
        Type: general
      – SubjectFull: Mathematics Achievement
        Type: general
      – SubjectFull: Prediction
        Type: general
      – SubjectFull: Child Development
        Type: general
      – SubjectFull: Profiles
        Type: general
      – SubjectFull: Short Term Memory
        Type: general
      – SubjectFull: Socioeconomic Status
        Type: general
      – SubjectFull: Verbal Ability
        Type: general
      – SubjectFull: Gender Differences
        Type: general
      – SubjectFull: Longitudinal Studies
        Type: general
      – SubjectFull: Tests
        Type: general
      – SubjectFull: Mathematics Tests
        Type: general
      – SubjectFull: Role
        Type: general
    Titles:
      – TitleFull: The Development of Spatial Skills in Elementary School Students
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Carr, Martha
      – PersonEntity:
          Name:
            NameFull: Alexeev, Natalia
      – PersonEntity:
          Name:
            NameFull: Wang, Lu
      – PersonEntity:
          Name:
            NameFull: Barned, Nicole
      – PersonEntity:
          Name:
            NameFull: Horan, Erin
      – PersonEntity:
          Name:
            NameFull: Reed, Adam
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2018
          Identifiers:
            – Type: issn-print
              Value: 0009-3920
          Numbering:
            – Type: volume
              Value: 89
            – Type: issue
              Value: 2
          Titles:
            – TitleFull: Child Development
              Type: main
ResultId 1