School mobility and achievement: a meta-analysis

Children and Youth Services Review 26 (2004) 93–119

School mobility and achievement: a meta-analysis Majida Mehanaa, Arthur J. Reynoldsb a

United Arab Emirates University, P.O. Box 17551, Al-Ain, Abu-Dhabi, United Arab Emirates b University of Wisconsin-Madison, USA

Abstract This study evaluated the effects of school mobility on reading and math achievement in the elementary grades (kindergarten to sixth grade) using meta-analysis for studies dated between 1975 and 1994. Mobility was defined as any change in schools. The sample sizes of the 26 studies examined ranged from 62 to 15 000. The statistics were converted into the effect size d. The individual effect sizes were almost all negative except in cases where the sample consisted of military personnel’s dependents. The composite effect size y0.25 for reading and y0.22 for math indicated that the average achievement level of mobile students exceeded that of only 40% of the non-mobile students. This is equivalent to a 3–4 month performance disadvantage in achievement. The major predictors of variation in effect sizes were frequency of mobility, socioeconomic status, and grade. Implications for practice and research are highlighted. 䊚 2003 Elsevier B.V. All rights reserved. Keywords: School mobility; Math achievement; Reading achievement; Childhood risk; Meta analysis; Poverty; Elementary school intervention; Longitudinal research

1. Introduction American children and families have the highest rate of residential and school mobility in the industrialized world. While approximately one fifth of the U.S. households change the location of their residences in any one year, the annual incidence of school mobility is 30% or higher in many urban schools (U.S. General Accounting Office, 1994). Between 1999 and 2000, 13.6 million children aged 1 to 19 moved with a substantial portion of these moves necessitating a change in E-mail address: [email protected] (M. Mehana). 0190-7409/04/$ - see front matter 䊚 2003 Elsevier B.V. All rights reserved. doi: 1 0 . 1 0 1 6 / j . c h i l d y o u t h . 2 0 0 3 . 1 1 . 0 0 4

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schools (U.S. Bureau of the Census, 2001). While mobility is a permanent feature of the social structure, many dislocations may have adverse consequences for young children and schools. Survey findings from the GAO study (1994) indicated that approximately 1 in 6 children in the U.S.—more than half a million children—have attended three or more schools since first grade, and that 1 in 4 have attended two schools. When inner-city third graders were examined separately, one quarter had changed schools three or more times, nearly twice the rate for children from rural or suburban areas or from small cities or towns. Their analysis also revealed that mobility was inversely associated with income. Thirty (30) percent of third graders from lowincome families with yearly earnings below $10 000 changed schools three or more times, compared with only 8% of children from families earning $50 000 or more. Rates of school mobility decrease as children make the transition to middle and high school yet over 3 million youngsters made the transition from elementary to middle school in public schools systems in 1990. Children from migrant families, families in the military, and families whose native language is not English also are more likely to move. Although children change schools for a variety of reasons that span from residential mobility to dissatisfaction with schools, many studies have indicated that school mobility is associated with increased risk for academic difficulties including low academic achievement (Haveman, Wolfe, & Spaulding, 1991; Reynolds, 1991; Astone & McLanahan, 1994; Kerbow, 1996), behavioral problems (Leonard & Elias, 1993; Wood, Halfon, Scarlata, Newacheck, & Nessim, 1993), retention in grade (Wood et al., 1993; GAO, 1994; Reynolds, Mavrogenes, Bezruczko, & Hagemann, 1996), and suspension from school (Simpson & Fowler, 1994). In this study, we conducted a meta-analysis of the effects of school mobility on academic achievement for children in the elementary grades (kindergarten to sixth grade) for studies completed from 1975 to 1994. We address three major questions: 1. Is school mobility associated with children’s reading and mathematics achievement? Does this association vary across studies? 2. What is the magnitude of the association? Is it educationally meaningful? 3. What study characteristics predict variation in effect sizes? We chose the elementary school years because it is during these ages that the foundations for school-based learning take hold and basic skills in reading and math are in their early development. Most theories of child development from personality to ecological perspectives emphasize the importance of regularity and stability in early learning environments in promoting positive development (Cole & Cole, 1993). Thus, the consequences of mobility—positive or negative—would be expected to be greatest during these formative years. 1.1. Research context of mobility studies Research on school mobility is diverse and defies easy description. The published reviews of the effects of mobility are narratives (Turner & McClatchey, 1978;

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Humke & Schaefer, 1995), and there have been few attempts to systematically investigate a representative sample of studies. No meta-analyses of the effects of mobility have been published. The only available research synthesis is a dissertation (Jones, 1990), and it included only studies published up to 1987. Many studies on school mobility do not control for child and family background variables simultaneously and no consensus exists about the demonstrated effects of mobility. The knowledge base for the years of 1975–1994 provides information from a variety of samples, across many disciplines, and for alternative measures of mobility and its consequences. Moreover, it would be difficult for a single study to settle the question of the effects of mobility given the restrictions in sampling and measurement that frequently arise. In addition, there are likely to be many moderator variables at work. Thus, existing published and unpublished studies provide a good approximation to the cumulative knowledge base on the likely impact of school mobility. 1.2. Explaining the link between school mobility and achievement When children change schools they experience an ecological transition. Ecological transitions are changes in the settings, roles, or expectations of an individual (Bronfenbrenner, 1979). School mobility is a change in the educational setting of students. It is believed to be a risk factor because it introduces discontinuity in learning environments that can adversely affect learning, especially if it is frequent or it occurs during children’s formative school years. In ecological systems theory, Bronfenbrenner (1989) indicated that ‘the degree of stability, consistency, and predictability over time in any element of level of the systems constituting an ecology of human development is critical for the effective operation of the system’ (p. 241), in this case children’s learning environment. There are three explanations of why mobility is associated with lower levels of academic achievement. First, school mobility disrupts the instruction of students. Because subject-matter curricula can differ dramatically across schools, children who change schools must adapt to new instructional settings, new textbooks and curricula, and new teachers whose teaching style and expectations may differ substantially from what students are used to. These transitions take time, and in the short-term may adversely affect students’ performance especially if students have other risk factors for low achievement. Interventions that assist children in adapting to new schools and different levels of expectations have been found to counteract negative consequences of mobility and promote successful adjustment (Jason, Johnson, Danner, Taylor & Kurasaki, 1993). Second, school mobility can disrupt relationships with peers in their school and social environments. Given that students spend at least 30 h per week in school, a change in schools can significantly alter the pattern of relationships that students have with other students as well as adults. Super and Harkness (1986) describe these interpersonal settings as developmental niches or the quality of the personenvironment fit of children’s and families’ ecological settings. The instability than results in altering ecological niches can have adverse effects on students, especially if they are not developmentally ready for such changes.

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Finally, the link between school mobility and lower achievement may be a byproduct of economic hardships in the lives of children and families. In this regard, mobility is an indicator of broader economic hardships such as low socioeconomic status, family residential instability, transitions in employment as well as dissatisfaction with children’s school. Indeed, children who move are more likely to come from low-income families, ethnic minority families, and home language that is not English. Nevertheless, school mobility has been found to be independently associated with lower achievement above and beyond a variety of economic hardships or transitions (Haveman et al., 1991; Reynolds & Bezruczko, 1993; Astone & McLanahan, 1994). 1.3. Predictors and correlates of mobility Although studies of mobility and its consequences vary substantially in sample characteristics, research design, the coding of mobility, and measurement of outcomes, several key trends have emerged that help explain variation in effect sizes across studies. First, mobility does not hinder the achievement levels of children from military families as much as children from civilian families (Greene & Daughtry, 1961; Marchant & Medway, 1987; Cramer & Dorsey, 1970). Alternatively, children from low-income families, children who are ethnic minorities, and children who move during the early years of school are more likely to be negatively affected by mobility (Levine, Wesolowski, & Corbett, 1966; Ingersoll, Scamman & Eckerling, 1989; Schuler, 1990; Reynolds, 1991, 1992; Astone & McLanahan, 1994; Hefner, 1994). For the latter factor, the negative impact of mobility diminishes with increasing grade levels. Second, studies that include control variables such as SES, IQ, and prior achievement show more complex effects, among them smaller overall effect sizes but larger ones for low-SES groups (Morris, Pestaner & Nelson, 1967; Alexander, Entwisle & Dauber, 1996; Temple & Reynolds, 1999) controlled studies showed more complex effects of mobility. With the exception of a few studies (e.g. Reynolds & Bezruczko, 1993; Alexander et al., 1996), the effects of mobility over time have not been investigated. Third, there is some evidence that distance of the move is differentially associated with academic achievement such that intracity mobility is associated with lower achievement than intercity mobility (Long, 1975; Straits, 1987; Johnson & Lindblad, 1991). This may be due partially to the fact that children who move within cities are more likely to be from low-income and minority groups. These and other factors will be taken into account in explaining potential variation in the effects of mobility across studies. In the meta-analysis by Jones (1990), only two of 36 studies of reading achievement indicated positive effects of mobility and only one of 21 studies of math achievement showed positive effects but effect sizes varied according to many of the variables discussed above including (a) military vs. civilian status, (b) studies conducted in and outside the U.S., (c) the number of covariates and the inclusion of ability as a covariate, and (d) ethnicity and socioeconomic status. The overall

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unadjusted correlations between mobility status and reading and math achievement were, respectively, y0.31 and y0.17. In this study, we extend on this and other studies to estimate the impact of school mobility on achievement as investigated in the past two decades recognizing the increased attention this relationship has generated. 2. Method For the purposes of this synthesis, school mobility was defined as any change in schools between kindergarten and sixth grade. Mobility included both normative (expected) and non-normative (unexpected) moves. In addition, we observed the following guidelines in selecting eligible studies: 1. Only studies which exclusively included children from kindergarten to sixth grade. Studies including children outside this range and studies that included children in both elementary and high school were excluded. 2. Studies on residential mobility that investigated the relationship between school mobility and achievement were included. 3. Reading and math achievement were included as outcome variables only when measured quantitatively. Standardized test scores and the grade-point average were the most frequently used indicators. 4. Published studies, ERIC documents, reports and dissertations were included. Master’s theses were not. 5. Only studies conducted in the United States were included in the meta-analysis. Our objective was to control for differences in larger social and cultural context that could confound the findings of school mobility effects. 6. Only published or completed since 1975 were included. The decision to exclude studies prior to 1975 was due to the existence of a meta-analysis of school mobility effects on reading and math achievement by Jones (1990) that included studies prior to 1987. Of the 37 studies selected by Jones (1990) for follow-up analyses, 19 studies dated before 1975 included k-6 samples and 10 did so after 1975. The key words used in all the searches were mobility, transition, residential, geographic, elementary, math, reading, and school achievement. The following library databases were used: ERIC, Dissertation Abstracts International (DAI), Social Science Index, and PsychLIT. Early in the process, we checked the references at the back of the articles in order to locate new studies. 2.1. Description of the study variables We coded the studies taking into account the predictors that were included in prior studies or mobility or variables that are believed to explain differences in effect sizes. A copy of the coding form is included in Mehana (1998). A list of these study characteristics follows.

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1. Year of publication or completion. This continuous variable was coded as the reported year of publication or completion. 2. Publication status. Unpublished studies were coded 1 and published studies were coded 0. Journal articles and government reports were coded 0; dissertations and ERIC documents were coded 1. 3. Sex. Studies in which 60% or more of the sample were girls were coded 1 and 0 otherwise. 4. Socio-economic status (SES). Studies, which included samples with low SES, were coded 1 and all others were coded 0. Any study that did not provide a description of the sample’s SES was coded 0. We coded 1 any study that had more than 50% of its sample classified as low-income. 5. Minority status. We coded as 1 any study that had at least 60% of its sample classified as minority. We coded as 0 any study that did not describe the minority status of the study sample. 6. Grade at outcome. This continuous variable was recorded as is. When a study provided results for multiple grades, we coded the median of the grades as the study grade level. For example, a study that had results for grades 3, 4, and 5 was coded as 4. Because few longitudinal studies of mobility have been conducted, this measure was a good proxy for the ages in which mobility occurred. 7. Mobility measure. Studies that provided a non-continuous measure of mobility were coded 1. Those that did not were coded 0. 8. Mobility contrast code. A study was coded 1 when it reported results for more frequent mobility vs. less frequent mobility or more frequent mobility vs. nonmobility. A study that reported results for any move vs. none was coded 0. This is a measure of extent mobility. We also coded as 1 any study that used a correlation coefficient to measure the relationship between mobility and achievement. 9. Civilian status. A study of civilian population was coded 1 while a study of children of parents in the military was coded 0. We coded as 1 any study that had 60% of its sample classified as civilian as well as any study that did not include a description of the sample’ status. The outcome variables were: 1. Effect sizes g and d for reading achievement. The effect size d is the effect size g adjusted for small sample bias. 2. Effect sizes g and d for math achievement. 2.2. Computation of effect sizes The statistical findings of the studies were converted into a common metric, the effect size, in order to be statistically integrated. The effect size represents an estimation of the magnitude of the effect independent of the scale used in the original study. The effect size is ‘the degree to which the phenomenon is present in the population,’ or ‘the degree to which the null hypothesis is false’ (Cohen, 1977, pp. 9–10). An effect size of zero corresponds to a null hypothesis. When comparing

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two groups, the standardized effect size g is equal to the value of the difference between the two group means divided by the pooled standard deviation (Hedges & Olkin, 1985). The formula is as follows: gs

MeyMc Sp

(1)

where M e is the mean of the experimental (mobile) group, M c is the mean of the control(non-mobile) group, and Sp is the pooled standard deviation of the two means. The g statistic has a small sample bias resulting in an overestimation of the population effect size. Hedges and Olkin (1985) propose that the bias will be removed if g is converted to d defined as: B

dsC1y D

3 E Fg where Nsneqnc 4Ny9 G

(2)

n e is the sample size of the experimental (mobile) group and n c is the sample size of the control (non-mobile) group. 2.3. Analysis plan Once the effect sizes were derived, descriptive information regarding central tendency measures and variability of the mean effect size were obtained. In that case, the mean effect size is unweighed with each study contributing equally regardless of the sample size. Hedges and Olkin (1985) suggested weighting the studies so as to give larger weight to the studies with larger sample sizes. The results were pooled by averaging the d values with each d weighted by the reciprocal of its variance. The answer was a mean weighted effect size or a composite effect size where a greater weight was given to the studies with the larger sample sizes. We used DSTAT (Johnson, 1989) to compute the composite effect size and corresponding confidence interval. The formula for the CI follows: dLsdyCay2 s(d), dUsdqCay2 s(d)

(3)

where Cay2 is the two-tailed critical value of the normal distribution. The 95% composite confidence interval (CI) around the composite mean tests whether there was a relationship between school mobility and achievement in math and reading. If the CI contains zero, we concluded that across all studies there was no relationship between mobility and achievement. If d was negative and the CI did not include zero, we concluded that across all studies, mobility was associated with achievement in math and reading. Once the composite effect size were obtained, the homogeneity of the d was computed to investigate whether the composite effect size adequately summarized

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the studies, that is, whether the studies shared a common effect size. In addition, a homogeneous test implied that the mean and CI were consistent, thus indicating that the individual studies found similar results. 2.4. Interpretation of results We interpreted the composite effect sizes using Glass (1976) and Rosenthal and Rubin (1982). The effect size has been defined as a mean difference expressed in standard deviations units. In other words, the effect size is the standardized z score of the mobile group in the non-mobile group distribution (Glass, 1976). For example, an effect size of ds0.68 is equivalent to a z of 0.68. Looking in the standard normal table, we find that the cumulative probability of having a value of 0.68 or less is 0.75. This implies that the score of the average individual in the experimental group exceeds that of 75% of the individuals in the control group. Cohen (1977) suggested an effect size of 0.20 as small, 0.50 as medium, and 0.80 as a large effect between the groups. These thresholds are arbitrary but are useful in qualitatively defining effect sizes. Rosenthal and Rubin (1982) suggested using the binomial effect size display (BESD) to interpret the results. As applied to this study, BESD displays the change in achievement attributable to mobility using proportions. The effect size is converted into a correlation coefficient and the effect of mobility is computed as 0.50qry2. The non-mobile group achievement is computed as 0.50yry2. The proportions of mobile and non-mobile groups show the change in achievement attributable to mobility. 3. Results 3.1. Description of the studies Twenty-six studies and 19 studies were used to compute effect sizes for reading and math achievement, respectively. We used the coding form included in Mehana (1998) to summarize the studies. Examination of the articles and the dissertations revealed that they rarely studied more than three background variables. Therefore, the following characteristics were coded for each study: (a) year of publication, (b) publication status, (c) SES, (d) grade at outcome, (e) minority status, (f) description of the mobility measure, (g) mobility code, and (h) civilian status. A description of the studies is provided in the Appendix. Although all studies provided codes for mobility and achievement, inclusion of the other background variables was inconsistent. As a consequence, a study that did not include a description of SES was coded as ‘other’. We adopted the same decision for the variable minority. As for the variable civilian, any study that did not specifically mention a military base as the location of the study, was coded as ‘civilian’. Table 1 shows the background characteristics of the studies for reading and math achievement. A percentage was reported for the discrete variables while a median was reported for grade at outcome and year of publication.

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Table 1 Background characteristics of the studies by reading and math achievement Study characteristic

Year of publication Publication status Published Unpublished SES Other Low Grade at outcome Minority status Other Minority Mobility measure Non-continuous Continuous Mobility code Any vs. none Frequency (more vs. less) Civilian status Military Civilian

Reading achievement (Ns26)

Math achievement (Ns19)

Sample size

Percenty median

Sample size

Percenty median

26

1984

19

1985

5 21

19.2 80.8

2 17

10.5 89.5

19 7 26

73.9 26.9 4.8

15 4 19

78.9 21.1 4.5

19 7

73.1 26.9

14 5

73.7 26.3

20 6

76.9 23.1

15 4

78.9 21.1

14

53.8

13

68.4

12

46.2

6

31.6

3 23

11.5 88.5

3 16

15.8 84.2

Note: A median was reported for year of publication and grade at outcome while a percentage was reported for the remainder variables. The mobility code ‘other’ included more frequent mobility vs. less frequent mobility or more frequent mobility vs. non-mobility.

The majority of the studies investigated reading and math achievement simultaneously. Overall, percentages and medians for the background variables were similar for both reading and math achievement with two exceptions. The first was the publication status where five published studies investigated reading while only two investigated math. The second and main difference was the mobility code. Based on a classification developed for this meta-analysis, we categorized mobility into two codes: mobile vs. non-mobile (Ns13) and other (Ns6). The mobility code ‘other’ included studies that investigated more frequent moves vs. less frequent moves or more frequent moves vs. none as well as studies that used a continuous measure for mobility, for example, from 0 to 5. There were more studies that were assigned the mobility code as ‘other’ in the reading dataset (Ns12 out of 26) and thus we expected more variability in the results for reading than for math. 3.2. Estimation of effect sizes The computation of effect sizes was based on (a) means and standard deviations for eleven studies, (b) correlation coefficients for four studies, (c) average of

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Table 2 Intercorrelations, means, and standard deviations of variables in the reading (Ns26) and math (Ns19) achievement models (math achievement is in the upper diagonal) Variable

1

2

3

1. Year of publication 2. Publication status 3. SES 4. Grade at outcome 5. Minority status 6. Mobility code 7. Civilian status 8. Reading d Reading Means S.D. Math Means S.D.

–

y0.44

y0.05 y0.00 y0.30 0.09 0.04 y0.06 y0.12

– y0.14 0.05 0.08 y0.14 y0.18 y0.03

85.04 5.79

0.81 0.40

0.27 0.45

4.81 1.07

85.95 5.25

0.90 0.32

0.21 0.42

40.71 1.28

0.08 y0.24 – y0.30 0.61* y0.04 0.22 y0.08

7

Math d

0.05

y0.00

y0.02

0.23 y0.35 0.25 y0.15 – y0.15 y0.33

0.15 0.22 y0.33 0.26 y0.33 – y0.04

0.21 0.03 0.14 y0.06 y0.37 y0.01 –

0.27 0.45

0.46 0.51

0.88 0.33

0.27 0.29

0.26 0.45

0.32 0.48

0.84 0.38

y0.22 0.26

4

5

6

y0.35

y0.04

0.68* y0.50* – y0.43* 0.06 y0.30 0.02

y0.18 0.57* y0.48* – y0.04 0.22 y0.15

Note: The discrete variables had the following codes: publication status: 0spublished and 1sunpublished; sex: 0sboys and 1sgirls; SES: 0sother and 1slow; minority status: 0sno and 1syes; mobility code: 0sany vs. no moves and 1smore frequent vs. less frequent moves; and civilian status: 0s children of parents in the military and 1scivilian. * P-0.05.

correlation coefficients for two studies, (d) contrast analysis using unweighed means approach for three studies, (e) average of two effect sizes using the intercorrelation between the findings for one study, (f) pooled effect sizes using DSTAT for two studies, (g) F value for analysis of variance for one study, (h) comparison of two means from analysis of variance results for one study, and (i) means and mean square error from the one way analysis of variance model for one study. A description of the process that was involved in the computation of the effect sizes for the individual studies is provided in Mehana (1998). The sample sizes of the studies that measured reading achievement ranged from 62 to 15 000. The mean and the median effect sizes were y0.27 and y0.22, respectively. As for math, the sample sizes of the studies ranged from 72 to 15 000. The mean and the median effect sizes were y0.22 and y0.19, respectively. Overall, the effect sizes were small. It is interesting to note the disparity between the mean and the median for both reading (437 and 1283) and math (474 and 1606) sample sizes due to the presence of two studies that had large sample sizes. The GAO report (1994) had a national sample of 15 000 third-graders and Chandler-Goddard (1985) had 5527 third, fourth and fifth graders. Correlation coefficients among the variables in the reading and math achievement models are presented in Table 2. The background variables year of publication, publication status, SES, grade at outcome, minority status and civilian status had small correlations with reading achievement. The range was from y0.15 to 0.02. Mobility code had a higher correlation with reading effect size y0.33, Ps0.10.

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This relationship was negative, i.e. increased student mobility was associated with a decrease in reading achievement. One of the interesting characteristics of the studies was that the minority and SES had a correlation of 0.61, Ps0.001. A minority status was associated with low SES. For 23 out of the 26 studies, minority status and SES were identical. Therefore, it was reasonable to include only one of the variables in multiple regression analyses and we chose SES. Finally, grade at outcome had a negative correlation of y0.43, Ps0.03 with minority status. Generally, studies that involved earlier grades had more minority children than studies at later grades. The correlation coefficients between the background variables and math followed a similar pattern. Mobility was negatively associated with math achievement, rsy 0.37, Ps0.12. The variable minority status was positively related to SES and negatively related to grade at outcome. Both published studies that included math were conducted at earlier grades, Grade 3 and Grade 1.5, and so unpublished studies were associated with later grades. Finally, the four studies that included a majority of low SES samples were conducted in earlier grades (by Grade 4.5) and so the correlation between low SES and higher grades was negative, rsy0.50, Ps0.03. All other correlations were relatively small. For both reading and math models, publication status and year of publication were not significantly associated with achievement at the 0.05 level and so they were not utilized in multiple regression models. Mobility code, SES, grade and civilian status were plausible predictors of reading and math achievement and thus were included in the multiple regression models. 3.3. Homogeneity test Hedges and Olkin (1985) recommended weighting the studies by the reciprocal of the variance. The weighted mean effect size for reading was y0.25 with 95% CI between y0.27 and y0.23. The interval did not include zero; thus, the hypothesis that the population composite effect size was equal zero at the 95% significance level was rejected. An examination of statistic Q revealed that though the overall d was significant, the individual effect sizes were heterogeneous, implying inconsistencies in the direction and magnitude of the effect of mobility on reading. The value of Q(25) was 102.08, P-0.001. As for math, the weighted mean effect size was y0.24 with 95% CI between y 0.27 and y0.22. The interval did not include zero; thus, the hypothesis that the population composite effect size was equal to zero at the 95% significance level was rejected. The value of Q(18) was 110.96, P-0.001; consequently, we rejected the null hypothesis and concluded that the composite effect size for math did not adequately describe the individual studies. Individual effect sizes and corresponding confidence intervals are displayed in Figs. 1 and 2. Due to the heterogeneity of the effect sizes, two alternatives were applied in an attempt to understand the source of heterogeneity. The first was removal of effect

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Fig. 1. Reading results: plot of the individual studies’ effect sizes and corresponding confidence intervals. The study authors listed from 1 to 26 were as follows: Abercrombie, 1980; Benson et al., 1979; Black and Bargar, 1975; Brigham, 1994; Carrier, 1982; Chandler-Goddard, 1985; Cope, 1984; Corr, 1982; Dovell, 1987; GAO report, 1994; Hefner, 1994; Hersh, 1988; Hummel, 1987; Jones, 1990; Kaplan, 1978; Kirkland-Lyles, 1995; Liechty, 1996; Lindblad and Johnson, 1988; McClanahan, 1988; Moyers, 1986; Paulikens, 1983; Posa, 1976; Average of Reynolds, 1991 and Reynolds & Bezruczko, 1993; Sorensen, 1986; Taylor, 1980; and Yim, 1983.

sizes that were heterogeneous in magnitude until homogeneity was achieved1 and the second was model testing using continuous models. 3.4. Continuous models 3.4.1. Bivariate regression Bivariate regression was used to test differences among the studies. Minority status, mobility measure and mobility code significantly predicted reading achieve1 We removed the effect sizes that were inconsistent with the composite effect size and reanalyzed the data. The removal of the effect sizes identified as outliers resulted in a large reduction to Qw. For reading, the removal of Carrier (1982), Chandler-Goddard (1985), Hefner (1994), Liechty (1996), Moyers (1986) and Yim (1983) yielded a homogeneous test with an overall effect size of y0.22: The Q(19) was 29.40, Ps0.06. For math, the removal of Chandler-Goddard (1985), the GAO report (1994), Liechty (1996), Lindblad (1987), Reynolds (1991) and Yim (1983) resulted in an overall effect size of y0.16 that is homogeneous. The Q(12) was 20.97, Ps0.05.

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Fig. 2. Math results: plot of the individual studies’ effect sizes and corresponding confidence intervals. The study authors listed from 1 to 19 were as follows: Brigham, 1994; Carrier, 1982; Chandler-Goddard, 1985; Corr, 1982; GAO report, 1994; Hersh, 1988; Hummel, 1987; Jones, 1990; Kirkland-Lyles, 1995; Liechty, 1996; Lindblad, 1987; McClanahan, 1988; Moyers, 1986; Paulikens, 1983; Posa, 1976; Reynolds, 1991; Sorensen, 1986; Taylor, 1980; and Yim, 1983.

ment at the 0.05 level. A minority status was associated with a decrease of 0.06 in the average reading effect size. Frequent moves were associated with a decrease of 0.12 in the average reading effect size. Math effect size was significantly predicted by grade at outcome, minority status and mobility code at the 0.05 level. On average, the math effect size increased by 0.04 in the higher grades, and decreased by 0.08 and 0.13 with minority status and frequent mobility, respectively. 3.4.2. Multiple regression models Three multiple regression models using ordinary2 and weighted least squares were tested. The first multiple included the predictors mobility and grade; the second included the predictors mobility, civilian, and SES; and the third model included mobility, civilian, grade and SES. The choice of the variables was based on previous literature that suggested these variables were most likely to affect reading and math outcomes. The inclusion of grade at outcome in the regression equation along with mobility did not significantly change the regression estimates of mobility found in the 2

The OLS results are shown for comparative purposes.

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Table 3 Regression analysis predictors of reading achievement (Ns26) Predictor

1. Mobility 2. Mobility Grade 3. Mobility Civilian SES 4. Mobility Civilian Grade SES

OLS model

WLS model 2

Metric coefficient

Probability values for t

R

y0.18 y0.18 0.06 y0.19 y0.07 y0.05 y0.19 y0.07 y0.00 y0.05

0.10 0.12 0.57 0.11 0.71 0.70 0.11 0.71 0.95 0.70

0.11 0.12 0.12

0.12

Metric coefficient

Probability values for z

R2

y0.12* y0.12* 0.03 y0.12* y0.08 0.05 y0.13* y0.07 0.01 0.05

0.00 0.00 0.24 0.00 0.42 0.17 0.00 0.50 0.45 0.17

0.24 0.25 0.26

0.27

Note: Grade was dichotomized into early grades (ky4) and later grades (4.5–6). Mobility was coded 0 for none vs. any move and 1 for more frequent moves as well as other definitions. * P-0.001.

bivariate regressions. On average, reading and math effect sizes were associated with a decrease of 0.12 as the frequency of mobility increased. The regression coefficients were significant at the 0.001 level. As children moved from earlier to later grades, there was, on average, a change of 0.03 for reading and 0.12 for math. However, the results were significant at the 0.001 level for math but not for reading. In the second and third models, frequent mobility was associated with a decrease of about 0.12 in reading achievement. Results were significant at the 0.001 level as shown in Table 3. Table 4 Regression analysis predictors of math achievement (Ns19) Predictor

1. Mobility 2. Mobility Grade 3. Mobility Civilian SES 4. Mobility Civilian Grade SES

OLS model

WLS model 2

Metric coefficient

Probability values for t

R

y0.20 y0.21 0.09 y0.24 y0.09 y0.06 y0.24 y0.05 0.05 0.00

0.12 0.11 0.46 0.11 0.61 0.71 0.11 0.76 0.43 0.98

0.14 0.17 0.16

0.20

Metric coefficient

Probability values for z

R2

y0.13* y0.12* 0.12* y0.14* 0.10 y0.05 y0.19* y0.00 0.07* y0.02

0.00 0.00 0.00 0.00 0.36 0.22 0.00 0.97 0.00 0.58

0.20 0.36 0.22

0.52

Note: Grade was dichotomized into early grades (ky4) and later grades (4.5–6). Mobility was coded 0 for any vs. no moves and 1 for more frequent vs. less frequent moves. * P-0.001.

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As for math results shown in Table 4, frequent mobility was associated with a decrease of about 0.14 in math achievement for the mobility-SES-civilian-math model and of 0.19 for the mobility-civilian-grade-SES-math model. The results were significant at the 0.001 level.3 3.5. Sensitivity analyses So far, studies were analyzed using the full reading and math datasets. In an effort to address the disparity in sample sizes without losing studies, Durlak and Lipsey (1991) suggest replacing the studies with the largest sample sizes by some specific limiting value. In this meta-analysis, there were two studies that had large sample sizes: The GAO (1994) report with 15 000 children and Chandler-Goddard (1985) with sample sizes of 5527 for reading and 5481 for math. The third largest study had 1686 children and so we chose to substitute the two largest sample sizes by 1995 and reanalyze the studies. For reading, frequently mobile were more impacted by mobility than less frequently mobile children. The mean effect size of the mobile vs. the non-mobile children was y0.20 while the mean effect size of the frequently mobile vs. the less frequently mobile children was y0.32. As for math, we found that published studies had more negative effect sizes than unpublished studies. However, there were only two published studies. In addition, frequently mobile children who were in low SES, below or in grade 4, and minorities were more impacted than the other groups. The means for reading and math are displayed in Table 5. The regression analyses, shown in Tables 6 and 7 revealed that the relationship between mobility and reading achievement was consistent regardless of the model used. Grade at outcome, SES and civilian status did not significantly predict reading achievement at the 0.05 level whereas mobility did. The mobility regression coefficient y0.12 was significant at the 0.001 level. Increased mobility was associated with a decrease in reading achievement. The relationship between mobility and math was significantly negative at the 0.001 level with or without additional predictors in the model. The mobility regression coefficients ranged from y0.13 to y0.19 depending on the number of predictors added to the model. However, the predictors SES and grade at the outcome showed mixed effects. In the mobility-grade-math model, the grade regression coefficient 0.13 counterbalanced the mobility regression coefficient y 0.13. In the mobility-civilian-SES-math model, the mobility regression coefficient 3 The visual inspection of the residuals against the predictors revealed that two studies, ChandlerGoddard (1985) and the GAO report (1994), were outliers primarily because of their large sample sizes. The removal of the two studies with the largest sample sizes did not change the mobility regression coefficient for reading. As for math, the removal of the two studies changed the mobility regression coefficients to approximately y0.23. As for the other variables, low SES was associated with a decrease of 0.13 in math effect size in the mobility-civilian-SES-math model. Grade was associated with an increase of 0.10 in math effect size for the mobility-civilian-grade-SES-math model. Both grade at outcome and SES were significant at P-0.01.

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Table 5 Mean reading and math effect sizes of mobile and non-mobile groups by study characteristic Study characteristic

Na

Overall Year of publication 1975–1984 1985–1994 Publication status Published Unpublished SES Other Low Grade at outcome Below or in grade 4 Beyond grade 4 Minority status Other Minority Mobility measure Non-continuous Continuous Mobility code Any vs. none Frequency (more vs. less) Civilian status Military Civilian

26y19

y0.27

y0.25

14y9 12y10

y0.26 y0.28

5y2 21y17

Reading achievement

Wc

Wd

y0.25

y0.22

y0.24

y0.22

y0.29 y0.23

y0.26 y0.24

y0.23 y0.21

y0.27 y0.23

y0.23 y0.22

y0.25 y0.27

y0.23 y0.27

y0.25 y0.25

y0.37 y0.20

y0.25 y0.23

y0.33 y0.19

19y15 7y4

y0.26 y0.31

y0.25 y0.22

y0.26 y0.22

y0.22 y0.20

y0.24 y0.26

y0.22 y0.26

10y8 16y11

y0.32 y0.24

y0.26 y0.22

y0.28 y0.22

y0.25 y0.19

y0.27 y0.14

y0.30 y0.14

19y14 7y5

y0.24 y0.34

y0.23 y0.29

y0.24 y0.26

y0.21 y0.24

y0.22 y0.29

y0.19 y0.27

20y15 6y4

y0.23 y0.40

y0.22 y0.36

y0.20 y0.36

y0.17 y0.40

y0.21 y0.36

y0.19 y0.37

14y13

y0.19

y0.21

y0.20

y0.16

y0.21

y0.18

12y6

y0.37

y0.33

y0.32

y0.35

y0.34

y0.34

3y3 23y16

y0.24 y0.28

y0.24 y0.25

y0.24 y0.25

y0.21 y0.22

y0.23 y0.24

y0.23 y0.22

W

c

Math achievement Ub

U

b

W

d

a

Ns are displayed for reading and math, respectively. Unweighed. c Weighed. d Weighed after substitution of the two largest sample sizes for 1995. b

was y0.19 and the SES regression coefficient was y0.10 (P-0.01). Both frequent mobility and low SES decreased math achievement. Finally, in the mobility-civiliangrade-SES-math model, it appeared as though grade and SES canceled each other out with both regression coefficients being approximately 0.01. The mobility regression coefficient y0.19 was significant at the 0.001 level. It was interesting to note that SES was significant in predicting math achievement in the absence of the variable ‘grade at outcome’. Unfortunately, the number of studies was not large enough to measure the interaction between grade and SES. 3.6. Interpretation of results The reading effect size y0.25 was similar for weighting with or without replacement of the largest sample sizes by a common sample size of 1995.

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Table 6 Regression analysis predictors of reading achievement after replacing the sample sizes of the two largest studies in the WLS model by 1995 (Ns26) Predictor

1. Mobility 2. Mobility Grade 2. Mobility Civilian SES 3. Mobility Civilian Grade SES

OLS model

WLS model 2

Metric coefficient

Probability Values for t

R

y0.18 y0.18 0.06 y0.19 y0.07 y0.05 y0.19 y0.07 y0.00 y0.05

0.10 0.12 0.57 0.11 0.71 0.70 0.11 0.71 0.95 0.70

0.11 0.12 0.12

0.12

Metric coefficient

Probability values for z

R2

y0.12* y0.12* 0.02 y0.13* y0.08 0.04 y0.12* y0.07 0.01 0.05

0.00 0.00 0.51 0.00 0.47 0.29 0.00 0.53 0.55 0.24

0.16 0.16 0.17

0.18

Note: In the second model, Grade at outcome was dichotomized into 0sbelow and in Grade 4 and 1sbeyond Grade 4. * P-0.001.

Interpreting the reading results using Glass’s (1976) method, the composite effect size y0.25 of the 26 available studies corresponded to a z of 0.40. The reading score of an average individual in the mobile group exceeded that of only 40% in the non-mobile group. The math effect size was y0.24 for weighting the studies by the reciprocal of the variance and y0.22 for weighting the studies after Table 7 Regression analysis predictors of math achievement after replacing the sample sizes of the two largest studies in the WLS model by 1995 (Ns19) Predictor

1. Mobility 2. Mobility Grade 3. Mobility Civilian SES 4. Mobility Civilian Grade SES

OLS model

WLS model

Metric coefficient

Probability values for t

R2

Metric coefficient

Probability values for z

R2

y0.20 y0.21 0.09 y0.24 y0.09 y0.06 y0.24 y0.05 0.05 0.00

0.12 0.11 0.46 0.11 0.61 0.71 0.11 0.76 0.43 0.98

0.14 0.17

y0.16** y0.13** 0.13** y0.19** y0.09 y0.10* y0.19** y0.01 0.08** 0.00

0.00 0.00 0.00 0.00 0.42 0.02 0.00 0.91 0.00 0.92

0.16 0.30

0.16

0.20

0.22

0.48

Note: In the second model, Grade at outcome was dichotomized into 0sbelow and in Grade 4 and 1sbeyond Grade 4. * P-0.01. ** P-0.001.

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replacement of the two largest sample sizes by 1995. The math composite effect size y0.24 of the 19 available studies corresponded to a z of 0.41. The math score of an average individual in the mobile group exceeded that of only 41% in the nonmobile group. The result was similar for the effect size y0.22. Other methods to interpret the effect size included (a) converting the effect size into a correlation coefficient, (b) using the binomial effect size display (BESD), and (c) translating the effect size into an academic achievement metric such as months of performance. The effect sizes y0.25 for reading (with and without replacement of the two largest sample sizes by 1995), and y0.24 for math without and y0.22 for math with replacement of the two largest sample sizes by 1995 corresponded to a correlation coefficient of approximately y0.12. We used the formula 0.50qry2 to obtain the proportion in achievement attributable to mobility. This resulted in a value of 0.44. Conversely, the non-mobile children had a proportion of 0.56. Mobility was associated with a reduction in achievement from 56 to 44%. A more applied interpretation was obtained after translating the effect size into growth score points. We took the Iowa Tests of Basic Skills (ITBS), which is a widely used test of achievement, as an example to illustrate the growth score points method. We first obtained the month value of one standard deviation of ITBS, which is equivalent to 16 months. Next, we converted the effect sizes y0.25 for reading and y0.24 for math into their value in months. Standard deviations of 0.25 and 0.24 corresponded to approximately 4 months of performance. Thus, mobile children are approximately 4 months behind the non-mobile children in reading and in math. This corresponds to a reduction in percentile rank from the 51st to 41st percentile or alternatively from the 41st to 32nd percentile in reading achievement on the ITBS. We interpret this as a practically significant difference. 3.7. Fail-safe N Computation of a fail-safe N was necessary in order to compensate for the difficulty in locating all eligible studies. In addition, unpublished studies often show non-significant results and thus could differ systematically from published studies. In an attempt to obtain all unpublished studies, we placed an interlibrary borrowing request of all dissertations that appeared to fit the inclusion criteria. There were more unpublished than published studies and so the risk of publication bias due to the scarcity of unpublished studies was not applicable to this meta-analysis. However, there were six dissertations that were either not on shelf or non-circulating at the time we placed the interlibrary borrowing request. The list of studies is included in Mehana (1998). In addition, there were some studies that were located but had to be discarded. A selected list of discarded studies and related reasons is also included in Mehana (1998). We computed the fail-safe N as proposed by Orwin (1983) to obtain the number of studies needed to bring the unweighed effect sizes for reading and math to a much lower value. The unweighed effect sizes were y0.27 and y0.22 for reading and math, respectively. Since the effects were already around y0.20, we applied

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Orwin’s (1983) formula to criterion values of y0.15 and y0.10. Approximately 21 and 44 studies were needed to bring the average reading effect size from y0.27 to y0.15 and y0.10, respectively. As for math, we found that approximately 12 and 31 studies were needed to bring the average effect size from y0.22 to y0.15 and y0.10, respectively. We also note that findings from two available studies published since 1995 (Alexander et al., 1996; Temple & Reynolds, 1999) are consistent with the findings of the meta-analysis. 4. Discussion This study evaluated the effects of school mobility on reading and math achievement in the elementary grades using meta-analysis. Our objective was (a) to estimate the direction and magnitude of the association between school mobility and achievement in reading and math and (b) to investigate study characteristics that explain variation in effect sizes across studies. Mobility was defined as any change in schools. After setting the sample sizes of the two largest studies to a limiting value of 1995, the composite reading effect size for the 26 studies remained approximately y0.25 and the composite math effect size of the 19 studies decreased slightly from y0.24 to y0.22. The relationship between mobility and reading achievement was significant regardless of the number of predictors used. Grade at outcome, SES and civilian status did not significantly predict reading achievement at the 0.05 level. The relationship between mobility and math was significantly negative at the 0.001 level with or without additional predictors in the model. The mobility regression coefficient ranged from y0.13 to y0.19 depending on the number of predictors added to the model. This is the first meta-analysis of school mobility using contemporary studies. The key contribution of this study was that mobility was associated with lower levels of reading and math achievement regardless of the number of predictors included. Specifically, frequently mobile groups were more impacted than the less frequently or non-mobile groups. For reading, the mean effect size of the mobile vs. the nonmobile children was y0.20 while the mean effect size of the frequently mobile vs. the less frequently mobile children was y0.32. As for math, frequently mobile children with low SES and enrolled in earlier grades were more impacted than the other groups. The mean effect sizes for math were y0.18 for the mobility code ‘any vs. no moves’ and y0.34 for the mobility code ‘more frequent vs. less frequent mobility’. 4.1. Comparison with previous studies The findings of this study confirmed the negative association between mobility and reported by Jones (1990) and many other primary studies (e.g. Haveman et al., 1991; Astone & McLanahan, 1994; U.S. General Accounting Office, 1994; Alexander et al., 1996). Jones (1990), for example, analyzed a select sample of 37 studies appearing in the literature as early as 1938 and found that the composite correlation was y0.31 for reading and y0.17 for math. In this meta-analysis, we

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computed the weighted effect size d first and then converted the result to a correlation coefficient. We found a correlation coefficient of y0.12 between mobility and achievement in reading and math. Possible reasons for the discrepancy in the magnitude of the correlation coefficient are that (a) we defined mobility to include only individual level mobility and not both individual and school level mobility, (b) we included studies between kindergarten and sixth grade, (c) Jones (1990) and we examined studies dated between 1975 and 1987 but the rest of the studies were from different years, and (d) we derived the correlation coefficient after computing d first. It has been our observation that studies using correlation coefficients to measure the mobility-achievement relationship yielded higher effect sizes d than studies that used a non-continuous measure of mobility. In this study, the means were y0.36 and y0.37 for effect sizes derived from a continuous mobility measure and y0.20 and y0.19 for effect sizes derived from a non-continuous mobility measure, for reading and math, respectively. Confirmation and reasons for that observation need further investigation. In this study, we used the meta-analysis methodology as suggested by Hedges and Olkin (1985). We investigated both categorical and continuous models to assess the influence of the other background variables on the mobility-achievement relationship. Jones (1990) did not test the homogeneity of the effect sizes nor did he use continuous models. Although our study revealed effects sizes of slightly lower magnitude than Jones (1990), both studies point to the complex nature of the consequences of mobility. 4.2. Limitations of the study Despite the fact that we analyzed studies over a 20-year period, it is notable that mobility was consistently associated with lower levels of achievement in almost all studies regardless of model specification. Nevertheless, our findings would have been more informative had the studies used a common definition for mobility and accounted for more background variables. SES was significant in predicting math achievement in the absence of grade at outcome. Unfortunately, one limitation of this meta-analysis was that the number of studies was not large enough to measure the interaction between SES and grade at outcome. In addition, the codes of the SES variable were not mutually exclusive. The variable SES was coded 0 for ‘Other’ and 1 for ‘low SES.’ A study was coded 1 if more than 50% of the sample was classified as low income. Consequently, the code 0 included samples with up to 50% low SES as well as middle and upper SES samples. The results might have underestimated the effects of poverty. Moreover, hardly any of the studies included in our meta-analysis controlled for prior achievement in estimating the impact of school mobility. Thus, effect sizes adjusted for prior achievement could not be estimated. Consequently, we interpret this link between school mobility and achievement as correlational and predictive rather than causal. Notably, the studies that did include prior achievement also found negative associations between mobility and achievement.

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We further note that some studies could not be located and it is possible that other studies were missed during the search process. However, it is unlikely that these missing studies would have changed the overall findings of the study. Indeed, more recent studies of mobility largely confirm the findings reported here. 4.3. Sensitivity analyses in context We performed a variety of tests to determine if our findings were affected by our analytic methods and data analysis procedures. In summary, our findings were consistent under a variety of analytic assumptions and methods. First, to control heterogeneity, we tested whether differences in the criteria and definitions of mobility were associated with the results. We also tested the homogeneity of effect sizes. Second, to control quality of the studies’ research designs, we examined estimated effects sizes in relation to indicators of the quality of studies’ research designs (e.g. measurement reliability and validity; controls for confounding variables). The pattern of findings was similar across studies. One variable we would have liked to investigate further was the quality variable. It was difficult to define high vs. low quality studies without creating redundant information with the rest of the predictors. We had already defined the mobility code in terms of the studies’ definition of mobility. Studies that did not include a non-mobile group were instead coded as having a frequent vs. less frequent mobile group. We felt that group comparability was inherent in the mobility definition code. We also coded the background characteristics of the studies and tried to extract common information from all of them. Moreover, to control for publication bias, we reviewed results in books, unpublished dissertations and documents. We also computed the number of studies needed to reverse findings. In this study, there were more unpublished than published studies. Most of the findings were in the range of y0.20 standard deviations, which is a solid indication that the effects found reflect the status quo. One question that might arise is why there were not more published studies. One answer could be that studies found small effects and were likely to be unpublished. The effects would have been stronger if more studies had been published. Another answer could be that published studies had stronger methodological rigor than unpublished studies. However, we have no reason to believe that all the unpublished studies were of lesser quality due the wide variability among the unpublished studies. 4.4. Implications for school practices At a minimum, the findings of this study indicate that school mobility increases the risk of lower levels of reading and math achievement during the elementary grades. They also indicate that the magnitude of association, equivalent to 4 months of performance, is within the range of practical significance. A variety of interventions may help in reducing the potentially negative effects of school mobility on children’s school performance. Fernandez (1987) suggested some steps to ease child’s transition after a move. At the administrative level, the school should

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accurately document school turnover rates so that schools have greater levels of awareness about mobility. Smardo (1987) recommended interpersonal and academic counseling for mobile children. At the policy level, more efforts could be invested in maintaining computerized records on students so that the child is quickly placed at the appropriate level in the new school. If possible, policy makers could push for voluntary standards for academic achievement so there is compatibility between the curricula among the schools. More proactive intervention is needed prior to an actual move. Elias, Gara and Ubriaco (1985) found that before a move, there is a need to enhance the children’s problem solving skills and to enhance the teachers’ conflict resolution skills as preventive measures in a normative transition. Also, Smardo (1987) suggested enhancing parent–school relationships so that the school could be notified in the case of a transfer to facilitate the forwarding of records. Some schools have recognized mobility as a disruptive event in the migrant children’s lives and introduced programs that have been successful in alleviating the effects of mobility. Other orientation programs for children, parents and teachers, buddy system, monitoring home programs and individualized interventions have been implemented in the case of a systemic transfer. Jason, Johnson, Danner, Taylor and Kurasaki (1993) emphasized the importance of including families in the school’s efforts to alleviate mobility effects. School organization differs for systemic and for individualized transfer (Bayer, 1982). Although the school cannot remedy familial situations that result in a school move, it could alleviate mobility effects related to academic and social adjustment at school. Unfortunately, students who move unexpectedly do not routinely receive special educational programs (Cornille, Boyer & Smyth, 1983). The absence of established standard interventions for individualized mobility places the primary responsibility of working with mobile children on the teachers. Interviews with teachers in an urban elementary school that serves diverse populations revealed that only four teachers out of 21 received training for mobility. Teachers also reported that mobility affects instruction, classroom management, and learning of the class (Lash & Kirkpatrick, 1990). Therefore, it is recommended that teachers should be given more training on how to deal with the mobile child. Community-based approaches that involve social service agencies and landlords also may be helpful. Schuler (1990) provides an interesting account of how agencies such as the Department of Social Services can reduce the rates of mobility by coordinating rentals for housing within the academic calender year. Nevertheless, many school and residential moves will remain outside the control of schools and communities. It is recommended that schools document their programs for mobile children and evaluate the effectiveness of the steps taken to ease children’s move. 4.5. Implications for future research This study investigated a few moderator variables that may help explain variation in effect sizes across studies. These variables were SES, civilian status and grade level. It is highly recommended that studies investigating mobility in the future

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continue to include those moderator variables. However, there were other variables that were mentioned in the literature but could not be included in the meta-analysis due to the insufficient number of studies that researched those variables in relation to achievement. Parental attitudes, reason for the move, school mobility index, and prior achievement are examples of such variables. Future studies should attempt to include these factors, as there are evidences from the existing literature that they act as moderator variables between mobility and achievement. Indeed, the findings from this study, in particular the heterogeneity of the test statistic, suggest that other influential variables may be present (see Marchant & Medway, 1987; Stroh, 1990; Warren-Sohlberg & Jason, 1992; Audette, Algozzine, & Warden, 1993). Achievement prior to the move was found to be an important predictor for achievement after the move (Mehana & Reynolds, 1995; Alexander et al., 1996; Temple & Reynolds, 1999). The variable was not included in the meta-analysis due to the insufficient number of studies that researched it. It is also recommended that studies be conducted in a longitudinal manner to track changes in the achievement over time and to investigate the presence of critical periods in school attendance. Kaplan (1978) and Jones (1990) studied children over more than one academic year but the sample of children kept changing. It was not clear that the second or third year samples had similar characteristics as the original sample. Putting the section ‘Implications for future research’ into practice, it is recommended that an ideal study specify variables from each of the following five categories: 1. Sample definition: Specify how the mobile groups were chosen and provide comparison between all the mobile groups. The sample size should be as large as possible in order to maximize the internal validity of the study and its predictive power. Stevens (1992) recommended having 15 subjects per variable. 2. Mobility measures: It is recommended that as many as the following elements are specified: the type of mobility (systemicyindividualized; within districtyout of district; privateypublic; geographical direction of mobility), the number of school and residential moves, and the number of uninterrupted years in the school. 3. Ecological factors accounting for both home and school variables: Home variables should include reason for the move, SES, parental attitude toward the move, parental marital status, parent education and language spoken at home. School variables should include school SES, school turnover rate, curriculum compatibility, and availability of programs for mobile children. 4. Developmental factors: These factors are specific to each child and include measures of self-concept, attendance data, behavior data, prior achievement, and student socio-emotional adjustment to the new school environment. 5. Achievement measures: Both quantitative and qualitative measures are recommended. Children’s parents’, and teachers’ reactions to the move are examples of qualitative indices that might help school counselors deal successfully with the impact of mobility.

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As for an appropriate analytical method, predictive multivariate models are recommended as well as longitudinal studies to assess linear effects with measurements taken at different times after the move. It is only when these issues are investigated fully that a more complete understanding of school mobility and its consequences will emerge. Acknowledgments Preparation of this article was supported in part by grants from the Office of Educational Research and Improvement in the U.S. Department of Education (No. R306F960055) and the National Institute of Child Health and Human Development (No. R01HD34294). References Abercrombie, V. M. (1980). The relationship between reading achievement, self concept, and academic ability of mobile and non-mobile elementary school students. Dissertation Abstracts International, 40(07) 3758A. (University Microfilms No. AAC80-01082). Alexander, K. L., Entwisle, D. R., & Dauber, S. L. (1996). Children in motion: school transfers and elementary school performance. Journal of Educational Research, 90(1), 3 –12. Astone, N. M., & McLanahan, S. S. (1994). Family structure, residential mobility, and school dropout: a research note. Demography, 31(4), 575 –584. Audette, R., Algozzine, R., & Warden, M. (1993). Mobility and school achievement. Psychological Reports, 72, 701 –702. Bayer, A. E. (1982, March). A school transfer typology: Implications for new theory, revised research design, and refocused school policy and practice. New York: Paper presented at the American Educational Research Association. (ERIC Document Reproduction Service No. ED 214 241). Benson, G. P., Haycraft, J. R., Steyaert, J. P., & Weigel, D. J. (1979). Mobility in sixth graders as related to achievement, adjustment and socioeconomic status. Psychology in the Schools, 16, 444 – 447. Black, F. S., & Bargar, R. R. (1975). Relating pupil mobility and reading achievement. The Reading Teacher, 28(4), 370 –374. Brigham, M. F. (1994). The effects of mobility, intelligence, and the interaction of these two variables on sixth-graders’ achievement test scores. Dissertation Abstracts International, 54 (09). (University Microfilms No. AAC94-05129). Bronfenbrenner, U. (1979). The ecology of human development. Cambridge, MA: Harvard University Press. Bronfenbrenner, U. (1989). Ecological systems theory. In: Vasta, R. (Ed). Annals of child development: six theories of child development: revised formulations and current issues, vol. 6. Greenwich, CT: Jai Press. Carrier, R. J. (1982). The relationship of non-school factors to achievement in reading and mathematics. Dissertation Abstracts International, 42(09), 3863A. (University Microfilms No. AAC82-04615). Chandler-Goddard, B. (1985). Student mobility and achievement test results. Dissertation Abstracts International, 46(01), 70A. (University Microfilms No. 85-05356). Cohen, J. (1977). Statistical power analysis for the behavioral sciences (Revised ed). New York: Academic Press. Cole, M., & Cole, S. R. (1993). The development of children (2nd ed). New York: Scientific American Books. Cope, C. L. (1984). The effect of student mobility, aptitude, and military status on student reading scores. Dissertation Abstracts International, 45(06), 1636A. (University Microfilms No. AAC8418771).

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