Teacher Instructional Practices and Language Minority Students: A Longitudinal Model

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Teacher Instructional Practices and Language MinorityStudents: A Longitudinal ModelMido Chang aa Virginia Polytechnic Institute, State University, BlacksburgPublished online: 07 Aug 2010.

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83

ver the past several decades, reformation of U.S. schools to promote the competence of students who are educationally disadvantaged in math-

ematics and science has become a priority for education-al researchers and policymakers. There is a clear need to improve school programs for all students in math achieve-ment and restructure teacher methodology to close the performance gap between mainstream and minority students, especially in the early school years critical for the develop-ment of children’s cognitive and social skills. Providing the best possible learning environment at the beginning of formal schooling would be the most preferable intervention and a cost-effective investment for the future of the United States.

In the present study I investigated the mathematical per-formance of language minority students by using a nationally representative database, the Early Childhood Longitudinal Study Kindergarten Cohort (ECLS-K; National Center for Education Statistics [NCES], 2006). In spite of the dra-matic growth in the language minority population in the United States, there is not yet enough research compiled to provide essential information concerning the relation

between the educational process and school outcomes for language minority students (A. Portes & MacLeod, 1996; Schmid, 2001). Therefore, the first model in this study examined the mathematical performance of language minority students from various ethnic backgrounds, using a longitudinal analysis. The second model of the study used information on academic progress to investigate how the academic achievement of language minority students from diverse ethnic backgrounds is influenced by their social class. In the third model, I analyzed the effects of teacher grouping practices in math classes after controlling for the effect of socioeconomic status (SES).

In particular, the findings of the third portion of this study provide useful information on a wide range of edu-cational processes of various groups in math classroom set-tings. Improving the overall quality of classroom practices is known to result in better cognitive and affective outcomes for language minority groups (Lake & Pappamihiel, 2003), but little research has examined the link between teacher instructional practices and language minority student perfor-mance. The existing body of research on the effectiveness of classroom practices is limited to the general population and excludes subgroup populations. Therefore, the objective of the present study was to facilitate teachers’ understanding of how language minority students from different cultures are likely to respond to a range of teacher instructional-group-ing activities. I hope that the findings of this study will help teachers to prepare culturally responsive practices that will draw language minority students into the classroom environment as active learners, thereby maximizing their learning (Reyes & Fletcher, 2003). In a larger sense, this objective should align with reform efforts in U.S. schools seeking to meet language minority students’ needs and embrace their varied beliefs and values. As the No Child Left Behind Act (Office of the Deputy Secretary, 2004) has

Address correspondence to Mido Chang, Virginia Polytechnic Insti-tute and State University, Educational Research and Evaluation, 304 E. Eggleston Hall (0302), Blacksburg, VA 24061, USA. (E-mail: [email protected])

Copyright © 2008 Heldref Publications

Teacher Instructional Practices and Language Minority Students:

A Longitudinal ModelMIDO CHANGVirginia Polytechnic Institute and State University, Blacksburg

ABSTRACT. The author examined the long-term effects of teacher instructional grouping practices on the early math-ematical achievement of language minority students from various ethnic groups. The study used 3 longitudinal models. In the 1st model, English language learners (ELLs) displayed lower math performance than did English-only students in the Hispanic and Asian groups. The 2nd model confirmed the significance of social class across all groups. The 3rd model focused on 4 grouping practices: (a) teacher-directed whole-class activity, (b) teacher-directed small-group activity, (c) teacher-directed individual activity, and (d) student-selected activity. Significant findings include that (a) Hispanic ELL students displayed low math performance in teacher-directed whole-class activities, (b) Asian ELL students showed low math performance in teacher-directed small-group activi-ties, and (c) Hispanic dual-language students benefited from teacher-directed individual activities.

Keywords: ethnic groups, grouping practices, language minor-ity students, mathematical achievement

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84 The Journal of Educational Research

mandated, schools are now accountable for the progress of all children, including language minority students.

Performance Gap Between Language Minority and English-Speaking Students

U.S. census statistics reveal a dramatic increase of lan-guage minority students in recent years. In 1990, 32 million people over the age of 5 years (i.e., 14% of the population of the United States) spoke languages other than English at home. By 2000, that number had risen to 47 million, a number that represents about 18% of the total U.S. population (NCES, 2004). Among these language minority students, English language learners (ELLs) who need spe-cial support in language learning are more than 6 million individuals and represent approximately 7% of all school-aged children (NCES).

The low performance of these new groups of language minority students in schools is a cause for major concern in the educational establishment. Research has shown that language minority students, and ELL students in particu-lar, exhibit significantly lower academic performance and higher dropout rates than do native-born students (Abedi & Lord, 2001; Capps et al., 2004; Chang & Singh, 2006; Schmid, 2001; Wang & Goldschmidt, 1999, 2003).

Although several theories have been proposed to explain the low achievement of language minority students, in this article I focus on the theoretical approach adopted by socio-linguists. Sociolinguists have substantiated the difficulties that must be overcome when simultaneously learning a new language and a new set of cultural norms. Because of the discontinuities inherent in achieving dual language flu-ency, language minority students need to acquire complex skills to switch languages from home to school. Until these students reach a certain level of bilingualism, code switch-ing between two languages can interfere with their aca-demic success (Krashen & Terrell, 1983; Scarcella, 1990; Teranishi, 2004). According to Krashen and Terrell, second language acquisition for ELL students can take place only when they understand a message in the second language (English). The ability to speak English fluently will emerge by itself after language competence has been reached through a sufficient amount of instructional and social input. There is a silent period during which ELL students do not produce English until they have built up enough competence through active listening. Thus, ELL students are not forced to speak before they are ready, and their speech errors are not corrected. Therefore, it is important for teachers to understand these sociolinguistic theories to prepare classroom practices that will promote the learning among their language minority students.

A hypothesis by Krashen and Terrell (1983) emphasized the importance of teacher support and class activities that encourage ELL students to engage in class learning. They suggested that when ELL students have a positive attitude toward the second language (English), they are more open

to language input. Therefore, teachers should develop a class atmosphere that produces a low anxiety level with regard to language learning, encouraging students to enjoy a good rapport with their teachers and friendly and social relationships with their peers (Lake & Pappamihiel, 2003; Richard-Amato & Snow, 1992). Recent language minori-ties, most of whom are ELL students, need intensive and specialized teacher support to perform at the same level as their English-speaking counterparts. P. R. Portes (1999) demonstrated that the lowest achievers among language minority students are those who receive the least support, encounter language problems in school, and feel most unwelcome by mainstream students and teachers. Clearly, teachers need to be knowledgeable about language minority students’ reactions to instructional practices in classrooms.

Theories on Grouping Practices

Instructional-grouping practices in class, when organized to support teaching, can produce in-depth learning, coop-erative learning, and collaboration (Kutnick, Blatchford, Clark, MacIntyre, & Baines, 2005). Moreover, class group-ing can contribute substantial gains to educationally dis-advantaged student achievement when the instruction is tailored to student readiness levels, whereas inappropriate grouping practices can hamper students’ academic motiva-tion, disrupt concentration and participation, and inhibit learning (Tieso, 2005).

Although class grouping activities can be classified into various categories, the scope of this study was limited to four grouping practices based on group sizes and instruc-tion orientation: (a) teacher-directed whole-class activity, (b) teacher-directed small-group activity, (c) teacher-directed individual activity, and (d) student-selected activ-ity. Figure 1 shows the four grouping practices.

Teacher-directed whole-class activity. Many previous stud-ies on grouping practices have shown that teacher-directed whole-class activity is linked to high performance in the classroom (Kutnick et al., 2005; Prais, 1997; Zahorik, Hal-bach, & Ehrle, 2003). In teacher-directed whole-class activ-ity, teachers focus on uniformity of instruction, set up single instructional objectives, and deliver core detailed instruc-tion to the whole class. This sequence is often followed by individual assignments. Students are expected to reach the class goal at the same pace, using the same methods and materials. Teacher-directed whole-class instruction is par-ticularly effective when teachers focus on a firm grasp of tar-geted knowledge, authentic tasks, or challenging problems. In this way, teachers can maximize instructional time.

However, teacher-directed whole-class activity poses problems for the instruction of language minority students or underachieving students. When teachers depend mainly on teacher-directed whole-class instruction, students who require special attention may fall behind because individ-ual instructional arrangements for those students become difficult (Lou et al., 1996). For example, Schumm, Moody,

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November/December 2008 [Vol. 102(No. 2)] 85

and Vaughn (2000) found that third-grade low-achieve-ment students showed little academic progress in whole-class instruction, although average- and high-achievement students made moderate academic progress in the same environment.

Teacher-directed small-group activity. Small-group activi-ties offer many advantages for student learning (Lou et al., 1996; Saleh, Lazonder, & De Jong, 2005). Using small-group activities, teachers gain greater flexibility in instruc-tional objectives and the pace of instruction by setting both a single instructional objective for the class as a whole and a wide range of more nuanced instructional objectives for smaller within-class groups based on performance, inter-est, and ability. Students in small groups can exchange ideas and stimulate each other, verbalize their thoughts to clarify and improve understanding, and thus promote cooperative learning. Studies also indicate that teachers have more time to provide either remedial assistance or enrichment activities in this type of setting (Kutnick et al., 2005; Leonard, 2001; Lou et al.).

However, teacher-directed small-group activity can be harmful to language minority students, particularly if their readiness level has not reached that of the rest of the class. For example, they may feel forced to participate in activities in which only a few fast learners tend to dominate group discussions. As shown in several studies, in small-group activities assertive students often tend to dominate the group, shutting out the weaker students (Leonard & McElroy, 2000), and so language minority students may feel incompetent and neglected (Blumenfeld, Marx, Soloway, & Krajcik, 1996).

Teacher-directed individual activity. Teacher-directed indi-vidual activities can be used to compensate for many of the weaker aspects of teacher-directed whole-class activ-ity. With this practice, teachers generally do not alter the

curriculum for individual students but rather expect all their students to acquire the same content. Teachers then identify the learning problems of individual students and provide remedial help (e.g., explanations, analogies, exam-ples, demonstrations, tasks) to students who need it. The major benefit of teacher-directed individual activity is that teachers can assist educationally disadvantaged students via a greater flexibility in adjusting instructional objectives and pace for individual students. Another advantage of this practice may be greater coverage and in-depth treat-ment of content, because the dominant mode of teaching remains direct instruction. This was discussed in more detail by O’Connor, Harty, and Fulmer (2005), who dem-onstrated the benefits of individual instruction. They noted that underachieving students made poor progress during whole-class instruction during kindergarten, but the use of intense, focused individual instruction to supplement the whole-class instruction helped those same students reach average performance by Grade 3. However, although this activity has a strong potential to benefit language minority students, its application requires small class sizes and great-er instructor knowledge of individual students (Zahorik, 1999; Zahorik et al., 2003).

Student-selected activity. Student-centered classroom activities are deeply rooted in the educational philosophy that students should be transformed from passive listen-ers to active performers and partners. In student-selected activity, the teacher plays the role of facilitator rather than instructor, helping students with group discussions and presentations, and students choose their own projects for individual or group learning (Horng, Hong, ChanLin, Chang, & Chu, 2005).

However, this activity requires teacher discretion and student ability and creativity. Teachers should guide stu-dents to enhance the excitement of learning and stimulate

FIGURE 1. Diagram of four grouping activities.

Teacher selected

Student selected

Whole class

Small group

Individual

Teacher-directed whole-class activity

Teacher-directed small-group activity

Teacher-directed individual activity

Student-selected activity

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their intrinsic motivation for learning and at the same time should teach the core curriculum. Nonetheless, this activity may hamper language minority students’ learning. Wang and Goldschmidt (1999) indicated that when learn-ing tasks were given on the basis of student choice, for language minority students in particular, students tended to choose less demanding tasks, thereby limiting their opportunity to acquire the knowledge that they needed to master.

Based on the literature, and using three proposed analy-sis models, in the present study I attempted to answer the following research questions:

Research Question 1: Is the longitudinal growth pattern of mathematical performance of language minority stu-dents different from that of English-speaking students? How does it vary by ethnic group?

Research Question 2: Is the longitudinal growth of math-ematical performance influenced by social class? How does it differ by ethnic group?

Research Question 3: How do teacher instructional-group-ing practices influence the academic achievement of language minority students from diverse ethnic back-grounds after control for the effect of social class?

Method

Data Sources and Variables

Early Childhood Longitudinal Study Kindergarten Cohort. The present study used the ECLS-K, a nationwide longi-tudinal data set (NCES, 2006). The ECLS-K provides six waves of assessment of the cognitive growth of children from kindergarten through Grade 5, from 1998 to 2003. For the present study, the data-collection method imple-mented by the ECLS-K involved a multistage probability sample design in which the first-stage units were geograph-ic areas consisting of counties, the second-stage units were schools in sampled counties, and the final-stage units were students in schools (Tourangeau et al., 2006). These data samples should be treated with an appropriate longitudinal weight to adequately represent the target population. The present study used a longitudinal panel weight (C2_6FC0) to encompass the four waves of assessment data and allow representation of the full national population of kinder-garten and elementary-school-aged students. Application of this weight has a practical benefit in avoiding any prob-lems caused by overrepresentation of the minority groups in the ECLS-K. More important, because the longitudinal weight of C2_6FC0 had the highest nonzero weight (98%) among all the available longitudinal weights from kinder-garten to Grade 5 in the ECLS-K (Tourangeau et al.), the ensuing data analyses were based on the largest possible number of observations.

Four waves of data were used to examine longitudinal growth in the academic achievement of students from

diverse backgrounds using the benefit of longitudinal mul-tilevel analysis, which does not require the same intervals of waves and equal measuring points as those needed for indi-viduals. The four waves represented (a) a baseline measure (Spring 1998; kindergarten), (b) a first follow-up (Spring 1999; Grade 1), (c) a second follow-up (Spring 2001; Grade 3), and (d) a third follow-up (Spring 2003; Grade 5). The initial data consisted of 85,596 four-wave observations of 21,399 students. The researchers deleted only cases that lacked values on all four waves of the dependent variable, because longitudinal multilevel analysis is flexible enough to use available cases and does not require complete case data. Therefore, the study was based on a data set of 47,101 observations of 11,776 students.

Taking advantage of the large samples available on the ECLS-K database, the total database was split into four separate ethnic groups in accordance with the methods used in prior studies of ethnic differences (Driessen, 2001; Duncan & Aber, 1997; Keith, 2006). The main purpose of the separate analyses was to examine the differential effects of teacher classroom practices on language minority students within each ethnic group (i.e., Caucasian, Afri-can American, Hispanic, and Asian). Another statistical benefit of applying separate analyses was the alleviation of collinearity, because the variables for the ethnic groups became a constant, thereby reducing the number of predic-tor variables within the model. More important, interpre-tation became straightforward because it did not depend on an indirect interpretation that compared the results for each ethnic group with those of another ethnic group (i.e., the reference group).

The main analysis in the study was performed using longitudinal multilevel model and general linear model-ing (GLM) methods. The present study was designed to examine the average growth trajectory of various language and ethnic groups following the approaches demonstrated by Singer and Willett (2003) and Nagin (2005). The three models used in the present study therefore depicted the average change trajectory for the groups on the basis of individual trajectories in those groups.

I focused on language minority students speaking lan-guages other than English as their primary language. Three language groups were created using ECLS-K databases from kindergarten to Grade 5. Students speaking languages other than English were identified by combining informa-tion regarding multiple variables: (a) home language of the child, (b) primary language at home, and (c) language other than English that was spoken at home. The three language groups were named English only (ENGLISH), dual language (DUAL), and English language learner (ELL). The English-only group included students speaking English at home as their primary language. The dual-language group indicated students speaking languages other than English at home, although with no difficulty speaking English. The ELL group included students speaking languages other than English at home who had been referred to either pull-out

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or in-class English as a second language programs at least once during kindergarten or Grades 1, 3, or 5. In this study, the ELL group comprised language minority students who showed trouble with English or who had recently overcome a language barrier.

On the basis of the three language groups, two dummy variables of DUAL and ELL were created. DUAL was coded as 1 for the dual-language group and 0 for the other two groups (ENGLISH and ELL). In the same manner, for the variable of ELL, 1 indicated the ELL group, and 0 indicated the other groups (ENGLISH and DUAL). The results of the two language groups were compared with those of the reference group (ENGLISH). The percentages and frequencies of the three language groups by ethnic group are presented in Table 1.

Item response theory (IRT). The IRT scale score among three available math scores (IRT scale score, raw score, and T score) was chosen for the present study. The IRT scale scores in the ECLS-K database represent estimates of the number of items students would have answered cor-rectly if they had answered all questions. IRT scale scores are known to offer major advantages in working with growth models. For example, they ensure that scores at different time points are measured on a comparable scale, thus enabling researchers to compare the results of all four waves without the need to apply an equating process. The IRT scale scores also separate each student’s ability and test characteristics (i.e., difficulty and discrimination). Conse-quently, the IRT scores represent a comparatively genuine measure of student ability uncontaminated by test char-acteristics (Hambleton, Swaminathan, & Rogers, 1991; McDonald, 1999; Tourangeau et al., 2006).

Contextual variable. An important contextual vari-able for student academic performance—the student’s SES—was controlled for in this study. Considering that the status of language minority families in the United States often changes, the continuous SES variable was centered to have an average of zero and was specified as a time-varying variable.

Predictor variables. The main predictor variables for the study were four grouping activities based on group size and instruction orientation: (a) teacher-directed whole-class activity (WHLCLS), (b) teacher-directed small-group activity (SMLGRP), (c) teacher-directed individual activ-ity (INDVDL), and student-selected activity (CHCLDS). The measures of the four class practices were self-reports by teachers that were indicated by frequencies of in-class grouping activities. The frequencies were measured on a 5-point scale ranging from 1 (no time) to 5 (3 hr or more). The grouping variables in this study were specified as time-varying predictors. The values of these variables were allowed to change at each time point, and the relation between math performance and teacher practices appeared as an outcome at each time point. Descriptive statistics of the four grouping practices and mathematics performance by grade are presented in Table 2.

Model Specification

The present study used three models to address the research questions: (a) Model 1 (the baseline model) compared the growth patterns of student performance from various language and ethnic groups, (b) Model 2 (the SES model) examined the differential effects of SES on the performance of those students, and (c) Model 3 (the math grouping model) focused on the differential effects of teacher grouping practice on student performance after controlling for the effect of SES.

Baseline model. Model specification began with the base-line model to provide information about the variations in student performance. The baseline model is often useful as a preliminary step in a hierarchical data analysis (Raudenbush & Bryk, 2002). The present study includes the time vari-able in Level 1 of the baseline model, as suggested by Hox (2002). According to Hox, without the time variable, the model would overestimate the variance at Level 1 (growth) and underestimate the variance at Level 2 (student).

Level l of Model 1 was specified as

Yti = π0i + π1i(time)ti + eti,

where Yti is a dependent variable; time is a time point cod-ing for linear growth from spring semester of the kinder-garten year to spring semester of Grade 5; π0i is the initial value of the dependent variable (a math score at spring semester of kindergarten); and π1i is a linear growth param-eter, indicating the growth rate math scores.

Level 2 of Model 1 was designed to show the interaction effects of student language status with the growth of math performance and was specified as follows:

π0i = β00 + β01(DUAL) + β02(ELL) + r0i and

π1i = β10 + β11(DUAL) + β12(ELL) + r1i,

where β00 is the intercept that indicates the initial score of English-only students; β10is the average growth rate of English-only students; β01, β02, β11, and β12 represent the effects of DUAL and ELL on π0i and π1i; r0i is the random error of the initial scores; and r1i is the random error of the growth rate.

SES model. The SES model was used to examine the performance levels of language minority students and their progress in early schooling associated with the effect of SES. Level 1 of Model 2 contained the variables time and SES. The SES variable of the study was a time-varying covariate because the SES of language minority families tends to change frequently. Therefore, the outcomes repre-sent the association of the changing SES status with math achievement for each wave.

Level 1 of Model 2 was specified as follows:

Yti = π0i + π1i(time) + π2i(SES) ti + eti,

where π2i is a linear growth parameter of the SES variable. Level 2 of Model 2 was designed to show the interac-

tion effects of student language status associated with the

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TA

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86.5

13

1317

5 58

63

86.0

31

3249

11

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27.3

14

4128

71

8 25

.5

2098

5 19

6 71

.9

1791

537

7928

Dua

l 12

.9

1958

60

806

13.5

48

970

185

40.2

21

2493

55

9 49

.0

4048

9 30

3 19

.9

4978

12

1853

ELL

0.6

8735

55

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5 18

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32.5

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96

5 25

.5

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9 8.

1 20

2866

13

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tal

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0 15

1777

0 67

24

100.

0 36

4083

13

52

100.

0 52

7562

22

42

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0 82

800

818

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0 24

9221

5 11

136

Not

e. E

LL =

Eng

lish

lang

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; W =

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W =

unw

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Eng

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= En

glis

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ly; D

ual =

dua

l lan

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SES effect and the growth of student performance. In the second level, the English-only group was the comparison group. Thus, the outcomes of the dual-language and ELL groups were compared with the outcomes of the English-only group. Level 2 of Model 2 was specified as the fol-lowing:

π0i = β00 + β01(DUAL) + β02(ELL) + r0i,

π1i = β10 + β11(DUAL) + β12(ELL) + r1i, and

π2i = β20 + β21(DUAL) + β22(ELL),

where β22 represents the effect of DUAL and ELL on π0i, π1i, and π2i.

Math grouping model. The math grouping model focused on the effects of math classroom practices on the math achievement of students by specifying them at Level 1 as time-varying covariates. (Level 1 of Model 2 included four grouping practices in Level 1 of Model 1) (a) WHLCLS, (b) SMLGRP, (c) INDVDL, and (d) CHCLDS. Level 1 of Model 2 was specified as the following:

Yti = π0i + π1i(time) + π2i (SES) + π3i(WHCLS) + π4i(SMLGRP) + π5i(INDVDL) + π6i(CHCLD) + eti,

where π3i, π4i, π5i, and π6i are the parameters for WHLCLS, SMLGRP, INDVDL, and CHCLDS, respectively.

Level 2 of Model 3 was designed to show the interaction effects of student language status with the growth of math performance and teacher classroom practices. To determine the significance of random components, the deviance sta-tistics of the full model with random components and the reduced model with restricted random components were tested. I found that the random components were signifi-cant only in the intercept and the growth slope. Level 2 of Model 3 was specified as the following:

π0i = β00 + β01(DUAL) + β02(ELL) + r0i,

π1i = β10 + β11(DUAL) + β12(ELL) + r1i,

π2i = β20 + β21(DUAL) + β22(ELL),

π3i = β30 + β31(DUAL) + β32(ELL),

π4i = β40 + β41 (DUAL) + β42 (ELL),

π5i = β50 + β51(DUAL) + β52(ELL), and

π6i = β60 + β61(DUAL) + β62(ELL),

where β30, β31, . . . , and β62 represent the effects of DUAL and ELL on π3i, π4i, π5i, and π6i.

All models were applied to the data for students from four ethnic groups. All variables at the second level were grand mean centered to avoid collinearity and to facilitate clear interpretation of the intercepts and the slopes (Hox, 2002; Raudenbush & Bryk, 2002).

Results

The major analytical tool of the study was longitudinal multilevel analysis, which provided unbiased estimates of the effects. Graphical presentations of the GLM were also used to aid clear understanding by comparing the average values of achievement scores of the various groups. The presentation of results below follows the specifications of Model 1, Model 2, and Model 3.

Model 1: Performance Gap Between English-Speaking and Language Minority Students

The first set of analyses focused on comparisons of the growth trajectory of math performance of English-only, dual-language, and ELL students by ethnic group. The results for the English-only group were used as the reference for comparison and presented as actual scores, whereas those of dual-language and ELL groups appeared as difference scores from the English-only group. Results from the analysis for each ethnic group using Model 1 are shown in Table 3.

The first set of analyses demonstrated that the math scores of dual-language students in initial scores and growth rates did not differ significantly from those of English-only students in three ethnic groups: Caucasian, African American, and Asian. However, comparing Hispanic dual-language students with Hispanic English-only students revealed them to have significantly lower initial scores (β01 = –2.068, p < .05) and a slower increment rate, although this rate was not significant (β11 = –0.869, p > .05). In other words, Hispanic dual-language students began with

TABLE 2. Descriptive Statistics of Math Scores and Instructional Practices Based on All Students

Spring Kindergarten Spring Grade 1 Spring Grade 3 Spring Grade 5

Variable M SD M SD M SD M SD

Math item response theory score 33.529 11.416 57.883 16.502 92.099 21.573 110.941 22.472Teacher-directed whole-class activity 3.330 1.613 4.356 1.545 4.337 1.554 1.725 1.344Teacher-directed small-group activity 2.217 1.334 2.752 1.436 2.192 1.225 1.095 0.784Teacher-directed individual activity 1.383 0.935 1.792 1.151 1.681 1.156 1.073 0.782Child-selected activity 1.718 1.014 1.415 0.833 1.142 0.683 0.532 0.596

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math scores that were 2.068 points lower in the spring semester of kindergarten and were not able to catch up to the performance level of their English-speaking counter-parts until the spring semester of Grade 5.

Another important finding of the baseline model is that ELL students displayed significantly lower perfor-mance than English-only students. This tendency was manifested more noticeably in minority groups than in the Caucasian group.

Specifically, Caucasian ELL students demonstrated sig-nificantly lower performance than Caucasian English-only students (β02 = –9.191, p < .01) during the spring semester of kindergarten. By Grade 5 the Caucasian ELL students were able to narrow the performance gap that separated them from English-only Caucasian students, demonstrat-ing a significant growth rate (β12 = 2.191, p < .05). Com-pared with Caucasian English-speaking students, Cauca-sian ELL students had math scores that were 9.191 points lower in kindergarten but had narrowed this gap dramati-cally by Grade 5, displaying a growth rate that was 2.191 points faster at each time point. This pattern is clearly illustrated in Figure 2. Although African American ELL students demonstrated significantly lower performance than their English-only counterparts, the interpretation of the analysis results for this group was deferred in this article because of the small number of these students in the ELL group (n = 26).

A conspicuous gap divided the Hispanic ELL group from the English-only group, which was much greater than the gap between the Hispanic dual-language group and the Hispanic English-only group. When compared with the English-only group, the Hispanic ELL group began with a significantly lower math score (β02 = –6.760, p < .01) and increased their math scores at a significantly slower pace (β12 = –1.541, p < .05). The Hispanic ELL students showed math performance that was 6.760 points lower in kindergarten and fell further behind by about 1.541 points at each time point com-

pared with their English-only counterparts. These results are shown in Figure 3.

As illustrated in Figure 4, the performance lag of Asian ELL students also attracted attention. When compared with their English-only counterparts, the Asian ELL stu-dents began with a significantly lower performance level (β02 = –10.083, p < .01) and continued to display a lower growth rate, although the effect was not significant (β12 = –1.418, p > .05). The Asian ELL students began with a math score that was 10.083 points lower in kindergarten and showed about a 1.418-point lower increment rate com-pared with the Asian English-speaking students.

In addition to the outcomes on math performance levels of various language and ethnic groups, the baseline model also provides information on random components, reliabil-ity statistics, and correlation coefficients between initial scores and growth rates of the parameters, as presented in Table 4. This model produced a medium range of reliability statistics of initial scores and growth rates (.335–.670). Correlations between initial scores and growth rates ranged from .689 to .975, indicating that high initial scores tended to be associated with high growth rates.

Model 2: Differential SES Effects on Student Performance

As presented in Table 5, the analyses using Model 2 con-firmed the significance of SES for mathematics achieve-ment, with SES having significant coefficients in all four ethnic groups: β20 = 3.740, p < .01 in the Caucasian group; β20 = 1.741, p < .01 in the African American group; β20 = 2.732, p < .01 in the Hispanic group; and β20 = 5.095, p < .01 in the Asian group. In particular, the high SES status of English-only students in all four groups tended to be associ-ated with a higher performance level in math.

As indicated in Table 4, the fit statistics of Model 2 improved significantly as compared with those of Model 1. Significant differences of deviance statistics ranged from 431.63 to 36.09 in the four ethnic groups.

TABLE 3. Model 1: Hierarchical Linear Model Results of Baseline Model

Caucasian African American Hispanic Asian

Level Coefficient SE Coefficient SE Coefficient SE Coefficient SE

Initial status (π0i) Intercept (β00) 35.569** 0.349 26.947** 0.451 27.529** 0.351 34.170** 0.993 Dual language (β01) –0.419 1.141 –0.599 1.453 –2.068* 1.052 –0.075 3.347 ELL (β02) –9.191** 2.154 –8.714** 1.709 –6.760** 0.863 –10.083** 3.148Growth rate (π1i) Intercept (β10) 27.941** 0.149 24.033** 0.313 26.763** 0.220 29.122** 0.366 Dual language (β11) 0.124 0.470 –0.304 0.922 –0.869 0.664 –0.295 0.954 ELL (β12) 2.191* 1.053 –0.048 2.191 –1.541** 0.479 –1.418 0.970

Note. ELL = English language learner.*p < .05. **p < .01.

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Model 3: Effect of Grouping Practices on the Math Performance of Language Minority Students

The set of teacher practices was based on four models of grouping: (a) WHLCLS, (b) SMLGRP, (c) INDVDL,

and (d) CHCLDS. Results regarding these activities are presented in Table 6. As first illustrated by the descrip-tive statistics in Table 2, WHLCLS was the most popular instructional mode in math classrooms among the four practices, in agreement with reports by previous researchers (Kutnick et al., 2005; Prais, 1997; Rathbun, Walston, & Hausken, 2000; Zahorik et al., 2003).

Teacher-directed whole-class activity. In WHLCLS, Cauca-sian and African American English-only students demon-strated increased achievement scores: β30 = 0.448, p < .01, and β30 = 0.335, p < .05, respectively. This indicates that when teachers increased whole-class activity by one unit (about 30–45 min), Caucasian and African American stu-dents tended to improve their math scores by about 0.448 and 0.335 points, respectively. In contrast, Hispanic ELL students experienced a negative effect from this pedagogi-cal method, β32 = –0.477, p < .05. Caucasian and African American English-only students were able to increase their math scores when they had more teacher instruction and examples, but Hispanic ELL students fell behind Hispanic English-only students under the same conditions.

Teacher-directed small-group activity. Contradicting the common positive perception of the effectiveness of small-group activities in classrooms, this research found that SMLGRP did not result in significant posi-tive influences for all groups, with the sole exception being Caucasian dual-language students, β41 = 0.671, p < .05. Most important, this activity had a negative influence on the performance of Asian ELL students

FIGURE 2. Comparison of math performance of English-only, dual-language, and English language learner students from the Caucasian group.

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FIGURE 4. Comparison of math performance of English-only, dual-language, and English language learner students from the Asian group.

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FIGURE 3. Comparison of math performance of English-only, dual-language, and English language learner students from the Hispanic group.

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(β42 = –2.076, p < .05). Consequently, when teachers increased small-group activities by one unit, Caucasian dual-language students increased their math scores by 0.671 points more than did Caucasian English-speak-ing students, but Asian ELL student math scores rose at a rate that was 2.076 points lower than that of their English-speaking counterparts.

Teacher-directed individual activity. INDVDL showed a sig-nificant positive result for the math performance of the His-panic dual-language group (β51 = 1.213, p < .05) when com-pared with the Hispanic English-only group. When teachers increased their individual instruction by one unit, the Hispanic dual-language student math ability levels rose by 1.213 points more than did those of their English-speaking counterparts.

TABLE 5. Model 2: Hierarchical Linear Model Results of SES Model



For initial status (π0i) Intercept (β00) 35.859** 0.333 26.900** 0.439 27.447** 0.380 33.744** 1.011 Dual language (β01) 0.051 1.041 –0.361 1.455 –1.915 1.078 1.943 3.297 ELL (β02) –7.652** 1.885 –8.574** 1.648 –5.304** 0.926 –4.833 3.093For growth rate (π1i) Intercept (β10) 28.033** 0.148 24.090** 0.309 26.820** 0.218 29.411** 0.337 Dual language (β11) 0.152 0.457 –0.416 0.906 –0.810 0.646 –0.681 0.814 ELL (β12) 2.137* 1.010 –0.150 2.199 –1.573** 0.486 –1.774* 0.815For SES (π2i) Intercept (β20) 3.740** 0.477 1.741** 0.547 2.732** 0.487 5.095** 1.014 Dual language (β21) 1.846 1.106 –0.627 1.297 1.633 1.263 –1.878 3.267 ELL (β22) 2.676 2.668 –2.335 1.542 –0.602 1.155 –1.500 3.174

Note. ELL = English language learner.*p < .05. **p < .01.

TABLE 4. Random Components and Deviance Statistics


Model Coefficient df N χ2 Coefficient df N χ2 Coefficient df N χ2 Coefficient df N χ2

1 Level 2 intercept variance (r0i) 114.795** 6183 6186 18447.84 40.305** 1148 1151 2563.38 52.198** 1883 1886 3871.03 147.692** 652 655 1670.62 Level 2 Slope variance (τ1i) 14.060** 6183 6186 10110.14 23.918** 1148 1151 3175.79 20.684** 1883 1886 4403.19 10.471** 652 655 846.89 Level 1 (σ0i) 75.332 57.760 69.139 83.941 Reliability of π0i 0.670 0.468 0.498 0.652 Reliability of π1i 0.460 0.611 0.566 0.335 Correlation between π0i and π1i 0.759 0.975 0.969 0.689 Deviance 188632.84 32090.58 54519.83 18899.22 Estimated parameter 4 4 4 42 Level 2 intercept (r0i) 98.120** 6183 6186 16612.62 36.036** 1148 1151 2428.30 46.536** 1883 1886 3605.71 127.704** 652 655 1549.42 Level 2 slope (τ1i) 13.651** 6183 6186 9977.56 23.312** 1148 1151 3133.25 20.326** 1883 1886 4382.01 9.491** 652 655 832.81 Level 1 (σ0i) 76.465 58.451 69.564 84.846 Deviance 188201.21 32054.49 54436.78 18815.02 Estimated parameter 4 4 4 43 Level 2 intercept (r0i) 89.671** 5780 5783 14230.58 34.154** 973 976 2114.37 39.726** 1598 1601 2774.79 109.916** 539 542 1255.70 Level 2 slope (τ1i) 16.370** 5780 5783 9489.77 26.976** 973 976 2382.17 24.083** 1598 1601 3281.95 14.495** 539 542 700.15 Level 1 (σ0i) 65.493 47.427 60.341 71.939 Deviance 140271.75 21579.65 36283.16 13087.59 Estimated parameter 4 4 4

*p < .05. **p < .01.

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Student-selected activity. Although CHCLDS had a nega-tive effect for African American ELL students (β62 = –1.877, p < .05), this finding was not interpreted because of the small sample size of this group and its consequently large standard error.

The analyses using Model 3 also provided important information about model specification. As indicated in Table 4, a large amount of variance at the higher level was accounted for by teacher grouping practices in all ethnic groups. Moreover, Model 3 showed improved fit statistics compared with Model 2, with the differences of deviance statistics ranging from 5727.43 to 479929.46—all levels were significant. The findings of this study therefore support the significance of the teacher instruc-tional-grouping model.

To summarize the results of the Model 3 analyses, the association of four grouping practices with performance level displayed a great deal of variability among the four ethnic and three language groups. The significant results for the ethnic groups can be summarized as follows. (a) In the Caucasian group, English-only students exhibited a benefit from increased WHLCLS, and dual-language students showed a positive outcome from SMLGRP; (b) African American English-only students displayed high performance in WHLCLS; (c) in the Hispanic group, ELL students showed a significantly slower growth rate of performance during WHLCLS, and dual-language students benefited from INDVDL; and (d) Asian ELL students dis-

played a significantly low growth rate of performance when teachers increased activities in SMLGRP.

Discussion

In the present study, I explored an important but under-researched policy-relevant issue: the differential longi-tudinal effects of math instructional practices on early math achievement by four ethnic (Caucasian, African American, Hispanic, and Asian) and three language groups (English only, dual language, and ELL). Math achievement of students is of critical importance because it not only pre-pares students for future employment but also helps them to become productive citizens of a technological society.

In this study, English-only students were defined as native-born students who spoke only English at home; dual-lan-guage students were defined as those who did not show difficulty in English, although they spoke languages other than English at home; and ELL students were language minority students who had trouble using English and spoke languages other than English at home. The main objec-tive of the study was to suggest practical implementation of research-identified practices in classroom instruction by identifying classroom practices that are potentially benefi-cial or harmful to each of these groups of students.

In an initial step, I examined the growth patterns of math performance and the performance gap among the three language groups by employing a baseline model. The

TABLE 4. Random Components and Deviance Statistics


Model Coefficient df N χ2 Coefficient df N χ2 Coefficient df N χ2 Coefficient df N χ2

1 Level 2 intercept variance (r0i) 114.795** 6183 6186 18447.84 40.305** 1148 1151 2563.38 52.198** 1883 1886 3871.03 147.692** 652 655 1670.62 Level 2 Slope variance (τ1i) 14.060** 6183 6186 10110.14 23.918** 1148 1151 3175.79 20.684** 1883 1886 4403.19 10.471** 652 655 846.89 Level 1 (σ0i) 75.332 57.760 69.139 83.941 Reliability of π0i 0.670 0.468 0.498 0.652 Reliability of π1i 0.460 0.611 0.566 0.335 Correlation between π0i and π1i 0.759 0.975 0.969 0.689 Deviance 188632.84 32090.58 54519.83 18899.22 Estimated parameter 4 4 4 42 Level 2 intercept (r0i) 98.120** 6183 6186 16612.62 36.036** 1148 1151 2428.30 46.536** 1883 1886 3605.71 127.704** 652 655 1549.42 Level 2 slope (τ1i) 13.651** 6183 6186 9977.56 23.312** 1148 1151 3133.25 20.326** 1883 1886 4382.01 9.491** 652 655 832.81 Level 1 (σ0i) 76.465 58.451 69.564 84.846 Deviance 188201.21 32054.49 54436.78 18815.02 Estimated parameter 4 4 4 43 Level 2 intercept (r0i) 89.671** 5780 5783 14230.58 34.154** 973 976 2114.37 39.726** 1598 1601 2774.79 109.916** 539 542 1255.70 Level 2 slope (τ1i) 16.370** 5780 5783 9489.77 26.976** 973 976 2382.17 24.083** 1598 1601 3281.95 14.495** 539 542 700.15 Level 1 (σ0i) 65.493 47.427 60.341 71.939 Deviance 140271.75 21579.65 36283.16 13087.59 Estimated parameter 4 4 4

*p < .05. **p < .01.

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analyses used a nationally representative database, ECLS-K, to provide an involved figure of academic performance patterns that ranged from kindergarten to Grade 5. The math performance of English-only and dual-language stu-dents in three ethnic groups (Caucasian, African Ameri-can, and Asian) showed no significant differences from each other. However, in the Hispanic group dual-language students began with significantly lower math performance than their English-only counterparts and were not able to catch up until Grade 5. This result is particularly important because of the high proportion of dual-language students (40.2%) in the Hispanic group, as shown in Table 1. This finding implies that about 40% of Hispanic students are at increased risk of low math achievement.

Another critical finding of the baseline model is that ELL students displayed significantly lower performance than English-only students, as prior studies have also noted (Abedi & Lord, 2001; Capps et al., 2004; Chang & Singh, 2006; Schmid, 2001; Wang & Goldschmidt, 1999, 2003). This tendency was especially pronounced in the Hispanic and Asian groups. The performance of Hispanic

ELL students was significantly low in kindergarten and then fell significantly further behind when compared with the performance of their English-only counterparts. This result also suggests important implications for policy. This language minority group makes up about one third (32.5%) of all the Hispanic students in the ECLS-K database. Moreover, recent statistics indicate that the Hispanic group makes up 43% of all recent immigrant students (Capps et al., 2006). Therefore, if educators fail to identify and sup-port systematic efforts to boost their academic performance during their early schooling, there is a high chance that Hispanic immigrant students will fall behind the standards of mainstream education. These two Hispanic language groups (dual language and ELL) make up about 72.7% of all the Hispanic students in U.S. schools. The finding that these students displayed significantly lower performance than the Hispanic English-only students highlights the importance of implementing efficient school programs early to ease the language transition and bridge the per-formance gap, consequently enhancing the long-range prospects of these language minority students.

TABLE 6. Model 3: Hierarchical Linear Model Results of Math Grouping Model



Initial status (π0i) Intercept (β00) 35.641** 0.323 26.348** 0.451 27.666** 0.373 34.766** 1.117 Dual language (β01) –0.163 1.101 –0.897 1.150 –1.421 1.041 3.075 3.475 ELL (β02) –6.141** 1.747 –8.873** 3.158 –5.358** 0.872 –1.742 3.271Growth rate (π0i) Intercept (β10) 28.717** 0.187 24.540** 0.384 26.808** 0.278 29.423** 0.460 Dual language (β11) 0.394 0.546 –0.009 1.057 –1.251 0.856 –0.226 1.140 ELL (β12) 0.604 1.226 –0.470 1.463 –1.978** 0.560 –2.955** 1.085SES (π0i) Intercept (β20) 4.361** 0.541 3.157** 0.527 2.879** 0.482 5.551** 1.067 Dual language (β21) 0.851 1.142 1.867 1.403 1.505 1.224 –3.092 3.244 ELL (β22) 1.194 2.252 –4.367* 1.717 –0.886 1.078 –2.739 3.184WHLCLS (π0i) Intercept (β30) 0.448** 0.077 0.335* 0.147 0.156 0.092 0.140 0.222 Dual language (β31) –0.223 0.228 –0.010 0.341 –0.255 0.268 0.234 0.627 ELL (β32) 0.548 0.675 –1.847 1.266 –0.477* 0.217 0.310 0.528SMLGRP (π0i) Intercept (β40) –0.192 0.111 0.005 0.192 0.063 0.144 –0.269 0.314 Dual language (β41) 0.671* 0.336 0.051 0.363 0.067 0.430 –1.126 0.930 ELL (β42) –0.906 0.610 –0.868 0.627 0.283 0.360 –2.076* 0.902INDVDL (π0i) Intercept (β50) 0.041 0.136 –0.246 0.209 0.024 0.160 0.384 0.451 Dual language (β51) –0.626 0.447 –0.631 0.457 1.213* 0.479 –0.396 1.279 ELL (β52) –0.441 0.902 2.809 2.244 0.158 0.357 –0.233 1.141CHCLDS (π0i) Intercept (β60) 0.085 0.187 0.084 0.249 0.008 0.188 –0.606 0.499 Dual language (β61) –0.283 0.334 –0.800 0.429 –0.065 0.553 1.303 1.253 ELL (β62) –1.532 0.798 –1.877* 0.936 –0.049 0.432 0.931 1.177

Note. WHCLS = teacher-directed whole-class activity; SMLGRP = teacher-directed small-group activity; INDVDL = teacher-directed individual activity; CHCLDS = child-selected activity.*p < .05. **p < .01.

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The study’s findings also indicate that Asian ELL stu-dents who began their formal schooling with a language barrier were not able to catch up with Asian English-only students by the time they reached Grade 5. Again, statistics indicate that Asian immigrants make up 32% of all recent immigrant students (Capps et al., 2006). It is significant to note that these recent Asian immigrant students do not fall into the high-achievement group, thus contradicting the positive perceptions of Asian performance in math classes (Sy & Schulenberg, 2005).

Having a school environment that is conducive to learn-ing is not a luxury but a necessity for recent-immigrant lan-guage minority students, who often do not have adequate language support or an ideal educational environment at home. Teacher practices should therefore be culturally and socially relevant to provide more opportunities for narrow-ing the performance gap between language minority stu-dents and native-born students. Developing the potential of language minority students in school will be cost effec-tive in the long run by making schools more responsive to the needs of diverse students; diminishing the inequalities of school systems; and reducing the probability of later academic failure, dropout, and delinquency of language minority students.

The analyses using Model 2 confirmed the significance of SES for mathematics achievement as a coefficient of SES. Although no differential effects of SES on the perfor-mance of language minority students were noticed, overall SES effects were significant across all four ethnic groups. These results confirmed the findings of prior research on student achievement, in which family SES has consis-tently been one of the most powerful predictors of student academic achievement, directly and indirectly, across dif-ferent school contexts and various ethnic backgrounds. In particular, early poverty has been associated with low levels of school readiness, lower achievement test scores, and lower rates of high school completion (Alderman-Swain & Battle, 2000; Duncan, 1994; Fuligni, Brooks-Gunn, & Berlin, 2003; Krashen, 2005; A. Portes & MacLeod, 1996). The improvement of familial income takes a comparatively long time, so language minority students inevitably go through their critical periods of learning in educationally disadvantaged conditions. In this regard, a renewed empha-sis must be placed on supporting the efforts of schools and classroom teachers. Teachers must also find effective ways to maximize learning when students are at school.

In Model 3, teacher instructional-grouping practices were examined after being controlled for the SES effect. Among four grouping practices differentiated by size and orienta-tion, teacher-directed whole-class activity had a positive significant association with the math performance of Cau-casian and African American English-only students. How-ever, the same practice resulted in a significant negative association with the academic performance of Hispanic ELL students. These results suggest the need for special atten-tiveness on the part of teachers who serve Hispanic ELL

students, who may be neglected in whole-group activities. As the descriptive statistics of the study showed, the most frequent mode of instructional grouping was the whole-class activity. Because teachers in math classes inevitably spend some whole-class instructional time in providing important concepts and examples, they should make an extra effort to provide help for their Hispanic ELL students.

The second instructional-grouping practice in Model 3, teacher-directed small-group activity, did not result in sig-nificant positive influences for all the groups in this study, with one exception: Caucasian dual-language students. Importantly, this practice actually had a negative influence on the performance of Asian ELL students. These results did not integrate with previous findings on the effects of small-group activities for the general student population, which indicated that such activities allow teachers to have greater flexibility in instruction and provide enough reme-dial and enrichment activities (Kutnick et al., 2005; Leon-ard, 2001; Lou et al., 1996). This instance of a negative outcome on the performance of Asian ELL students can be interpreted in the theoretical framework of sociolinguists. When the language proficiency level of Asian ELL students has not reached the level at which they are able to discuss their reasoning, they may feel forced to participate in small-group activities with their peers, which causes them to feel inferior (Blumenfeld et al., 1996). This effect can be especially significant for many recent Asian immigrant students who are not assertive in class.

The next grouping practice, teacher-directed individ-ual activity, had a significant effect on the math perfor-mance of the Hispanic dual-language group. When teach-ers increased the amount of their individual instruction, the Hispanic dual-language students improved their math ability levels. This result highlights the importance of teachers’ individual help for the Hispanic dual-language students who make up more than one third of the Hispanic population (40.2%). Moreover, considering that teacher-directed individual activity requires a large amount of time and effort from teachers, this result reinforces educational policy initiatives that provide extra support for teachers who work with this language group of students.

The results of teacher-directed individual activities for ELL students in all ethnic groups contradicted the gen-erally held belief that most ELL students benefit from teachers’ individualized support. Although the Hispanic ELL group and the African American ELL group demon-strated slightly improved achievement scores when they participated in increased teacher-directed individual activi-ties, the results were not significant. These results can be explained by Krashen and Terrell’s (1983) theory, which holds that ELL students need to be exposed to enough mathematical lessons and language instruction to build their ability to respond to individual guidance from teach-ers. Teacher-directed individual activities may force ELL students to participate in class activities even when they have not reached their language competence level. As

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research findings suggest, teachers need to provide a silent period for these students, during which they can actively listen and receive sufficient instructions. It is also suggested that the classroom atmosphere must be supportive and that teachers should appear approachable to language minority students, especially because such students may already feel marginalized in an uncomfortable language setting.

The effect of student-selected activity was not noted in this study. Although it had a negative effect for African American ELL students, it was not interpreted because of the small sample size of this group and its large standard error. According to prior research for the general popu-lation, student-selected activity has a positive effect for student groups of comparatively high ability (Horng et al., 2005). As in a previous study (Wang & Goldschmidt, 1999), many language minority students in the present study who demonstrated low ability levels did not benefit from student-selected activities or classes. It is possible that teachers supervising student-selected activities may not provide enough instructional examples, and thus these activities may actually reduce these students’ opportunities to acquire the knowledge that they need.

The present findings of the effects of four teacher instruc-tional-grouping practices on the performance of students from various ethnic groups lead to a series of practical suggestions for classroom teachers. First, teacher-directed whole-class activity was associated with the increased math performance of Caucasian and African American English-only students but had a negative association with the math performance of Hispanic ELL students. Thus, prudent spe-cial arrangements are required for Hispanic ELL students when teachers provide instructions for the whole group. Second, teacher-directed small-group activity had a posi-tive effect on the performance of Caucasian dual-language students but a negative association with the performance of the Asian ELL students. Therefore, teachers need to take special care when arranging small groups for these Asian ELL students. Last, teacher-directed individual activity displayed a beneficial effect for the Hispanic dual-language group, who significantly lagged behind the Hispanic Eng-lish-only group. Teacher-directed individual activity is therefore strongly recommended for teachers who have been struggling to improve the math performance of their Hispanic dual-language students.

In reporting these findings, it is important to acknowl-edge some limitations of the study. Although I found that differential effects of classroom grouping practices are associated with the achievements of language minor-ity students, these types of practices are not the only factors that can influence student performance. Future researchers should examine how the present findings on grouping practices can best be combined with quality of instruction and curricula using grouping activities. More important, because this study was not an experiment, in which random assignment makes plausible a cause–effect association, the direct cause–effect link between teacher

instructional practice and student achievement levels should be deferred. In that sense, the objective of this study was to provide a better understanding of the effects of different dynamics of class activities for diverse ethnic language minority groups.

Another limitation of this study was the availability of data values. Although this research did enjoy solid benefits as a result of its use of a well-organized, nationally repre-sentative database, the database suffered from a limitation due to weighting issues. In particular, the lack of weights for teachers and school levels for longitudinal data analy-sis limited the study’s scope. Future research on teaching practices should involve analysis at the school or classroom level and use proper weights.

The present research points to the need for improved classroom instruction, in which social and cultural factors can be more effectively used to encourage the full academic engagement of language minority students. In particular, the study results support the efficacy of classroom practices in reinforcing language minority student success in math-ematics, which provides the foundation for future learn-ing in math, science, and other technological subjects. I hope that this article will stimulate further research on issues related to identifying the instructional practices most appropriate for language minority students and provide a foundation for a better understanding of the effects of dif-ferent grouping practices for math learning. The long-term goal of this research is to lower the barriers for language minority students that prevent these students from suc-ceeding in school and living up to their full potential.

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Teacher Instructional Practices and Language Minority Students: A Longitudinal Model

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