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Connecting Math Attitudes With STEM Career Attainment: A Latent Class Analysis Approach


by Myley Dang & Karen Nylund-Gibson - 2017

Background: For many years now, there have been many job vacancies in science, technology, engineering, and mathematics (STEM), but not enough workers to fill these vacancies. Much attention has been given to understanding and changing this situation in our country.

Purpose: The purpose of this study is to address this dilemma by understanding what may be gained by investigating student’s attitudes towards STEM in high school. Specifically, we study the relationship between students’ math attitudes and math self-efficacy beliefs and their career outcomes in STEM. Further, we do this across different English proficiency levels to see if any understanding may be gained by studying these groups differently.

Research Design: This study implemented secondary analysis by using a nationally representative sample of U.S. 10th graders from the Education Longitudinal Study. A latent class analysis was used to classify students’ math attitudes and self-efficacy.

Results: The results from this study provide empirical support suggesting that across all three English proficiency groups, students with high math attitudes and high math self-efficacy were more likely to have a career in STEM. When examining demographic characteristics, female students were more likely to have lower math attitude and lower math self-efficacy, which helps to explain why there is an underrepresentation of female students in STEM fields. We also found that race/ethnicity and socioeconomic status operated differently for each of the English proficiency groups.

Conclusions/Recommendations: This study directly links student math attitudes and self-efficacy to later career choice. This study has implications for researchers and policymakers who are developing interventions, suggesting that fostering positive math attitudes and self-efficacy would help encourage more students to pursue careers in STEM, particularly for non-native English speakers and female students.




Our nation faces an exponentially high demand for science, technology, engineering, and mathematics (STEM) professionals and a scarce supply of individuals who pursue STEM careers. And there are even fewer multilingual individuals interested in STEM. A recent report prepared by the President’s Council of Advisors on Science and Technology (PCAST, 2012), suggests that in order for the United States to remain competitive in the science, technology, engineering, and mathematics (STEM) fields, we must produce approximately one million more STEM professionals than currently projected over the next decade. This is about 34% annually more than current rates (PCAST, 2012). To address this need for more STEM professionals, there is an urgent push to identify and support students’ interest and persistence in STEM fields. Although there is a strong urgency for producing more STEM professionals, there have not been enough STEM career seekers to fill these STEM job vacancies, especially among non-native English speakers, which include English Language Learners (ELLs) (i.e., individuals whose native language is not English) and linguistic minorities (i.e., individuals who speak a language other than English at home and/or have varying English-speaking abilities (Klein, Bugarin, Beltranena, & McArthur, 2004)). These groups are important to study because they bring diversity and multilingualism to STEM fields.


ELLs and linguistic minorities have become one of the largest growing populations in the United States, thus an important group to study. In 2011–2012, there were approximately 4.4 million ELL students, or an estimated 9.1% of the total number of public school students in the United States (Kena et al., 2014). This population is expected to grow at a rapid rate, where it estimated that by the year 2030, there will be approximately 40% of school-aged children will be an ELL (Thomas & Collier, 2002). While they are a quickly growing population in the United States, there has been very little research conducted specifically in ELLs and linguistic minorities pursuing STEM fields. The lack of ELLs and linguistic minorities in the STEM fields is concerning, given the demand for more STEM professionals in the field.


Particularly among students who are non-native English speakers (i.e., English language learners and linguistic minorities), there is little information on what role math attitudes and math self-efficacy play in understanding STEM outcomes. This information is critical to inform educators and policymakers on how to better prepare students and provide them the proper skills to be college and career-ready in STEM careers. Understanding the different roles of math attitudes and math self-efficacy among English proficiency groups may be useful for education policymakers and practitioners to develop specific interventions to improve math attitudes and self-efficacy beliefs that have been linked to successful STEM outcomes. Furthermore, there is a need to identify profiles of students’ attitudes and self-efficacy beliefs to better support their entrance and persistence in STEM careers, as well as build a diverse, multilingual STEM workforce that is representative of the U.S. population in terms of gender, race/ethnicity, and socioeconomic status.


Given the increasing number of ELLs and linguistic minorities in the United States, it is critical for educators and policymakers to be more informed about the academic development of this population. Thus it is important to study this population and gain a better understanding of how the patterns for ELLs and linguistic minorities might be different from native English speakers and how to strengthen the STEM pipeline for these non-native English speaking populations. Although there has been some progress in research on ELLs and linguistic minorities, more research is needed on their outcomes beyond college, such as investigating their career opportunities.


In this current study, we aim to contribute to the literature by using a large, nationally representative sample of 10th grade students from the Education Longitudinal Study of 2002 (ELS:2002) to examine the relationship between math attitudes and math self-efficacy beliefs with STEM career outcomes. More specifically, this study addresses the following research questions: (1) What are the different math attitudes and math self-efficacy beliefs among English Language Learners, linguistic minorities, and native English speakers? (2) How are the selected demographic characteristics (i.e., gender, race/ethnicity, and socioeconomic status) related to students’ math attitudes and math self-efficacy for each English proficiency group? (3) To what extent do students’ math attitude and math self-efficacy contribute to students’ STEM career attainment?


THEORETICAL FRAMEWORK


The theoretical framework that underlies this study comes from Lent, Brown, and Hackett’s (1994) social cognitive career theory (SCCT) and prior literature on factors related to STEM careers. Lent et al. (1994) developed this SCCT framework based on Bandura’s (1986) social cognitive theory to describe three aspects of career development including self-efficacy, expected outcome, and goals. This framework describes the dynamic processes and mechanisms that take place where (a) career and academic interests develop, (b) career-relevant choices are created and enacted, and (c) performance outcomes are achieved (Lent et al., 1994). Through this model, the authors argue that one’s self-efficacy strongly influences the choices people make, the amount of effort they expend, and how long they persevere when they encounter challenges. In this sense, people form interests in activities in which they view themselves to be efficacious and in which they anticipate positive outcomes (Bandura, 1986; Lent et al., 1994). Moreover, Bandura (1986) theorized that people’s behavior can be better predicted by their beliefs rather than their actual capabilities of accomplishing tasks, and that it is these beliefs that help determine what people do with the knowledge and skills that they have.


The theoretical framework used in this study builds from the social cognitive career theory by focusing specifically on math self-efficacy and math attitudes. Hackett and Betz (1989) defined math self-efficacy as “a situational or problem-specific assessment of an individual’s confidence in his or her ability to successfully perform or accomplish a particular [math] task or problem” (p. 262). This study extends SCCT and contributes to the literature by including students’ attitudes toward math, which is generally defined as the positive or negative emotional dispositions toward mathematics (McLeod, 1992). Based on SCCT, learning experiences affect self-efficacy, and self-efficacy expectations affect career outcome expectations (Lent et al, 1994). The self-efficacy and career outcome expectations, in turn, have an effect on career interests, which motivates an individual to set goals and take actions to pursue a career, where both choice goals and actions are affected by contextual influences.


Figure 1 depicts the statistical model that incorporates the SCCT framework of this study. The latent variable, 10th grade math attitudes and math self-efficacy, is measured using three math attitude and five math self-efficacy indicators. Different latent classes were identified by these two constructs of math attitudes and math self-efficacy. Using the SCCT framework, we argue that demographic characteristics of gender, race/ethnicity, and socioeconomic status influence an individual’s math attitudes and math self-efficacy beliefs, which in turn influences whether or not an individual attains a STEM career. To our knowledge, there have been no studies that examine non-native English speakers’ STEM career outcomes using an SCCT framework. Thus this study has potential contributions to the theory by incorporating math attitudes with math self-efficacy and applying the framework to non-native English speakers.


Figure 1. Statistical model using Social Cognitive Career Theory

[39_21781.htm_g/00002.jpg]

JOINTLY MODELING MATH ATTITUDES AND SELF-EFFICACY TO PREDICT STEM CAREER DECISIONS


Some research has shown there is a positive and significant relationship between math self-efficacy and math attitudes, where individuals with stronger math self-efficacy beliefs tend to report lower levels of math anxiety, higher levels of overall confidence and motivation, and a greater tendency to perceive math as useful (Hackett & Betz, 1981). These studies suggest that it is important to study these two constructs together as they are correlated with one another and are worth studying the relationship with STEM career outcomes. Although these two constructs of math attitudes and math self-efficacy are related, they may not be perfectly correlated. For instance, a student may have high math attitudes and low math self-efficacy, or vice versa, and their outcomes may look different based on their patterns of math attitude and math self-efficacy. Furthermore, these patterns may be different for each English proficiency group.


This study contributes to the SCCT theory by applying the framework to examine the heterogeneity in math attitudes and math self-efficacy across English proficiency groups. Much research has shown that math attitudes and math self-efficacy are related to students’ career decisions (Betz & Hackett, 1983; Hackett & Betz, 1981, 1989; Ing & Nylund-Gibson, 2013; Lent & Hackett, 1987; Luzzo, Hasper, Albert, Bibby, & Martinelli, 1999; O’Brien, Martinez-Pons, & Kopala, 1999; Pajares & Miller, 1995; Wang, Eccles, & Kenny, 2013; Zeldin, Britner, & Pajares, 2008). Hackett and Betz (1981) proposed the utility of self-efficacy expectations to career-related behaviors. They hypothesized that having low or weak self-efficacy expectations of one’s career pursuits may limit one’s career options. Additionally, the authors claimed that the level and strength of self-efficacy expectations of individuals choosing a specific career is related to the individual’s degree of persistence and success in that choice.


Other studies have confirmed the predictive power of math self-efficacy expectations on math-related career choices. Hackett and Betz (1989) reported that math self-efficacy expectations were stronger predictors of math-related career choices than actual math performance or past math achievement. Moreover, Luzzo et al., (1999) found statistically significant relationships between math self-efficacy measures of career choice and actions. They concluded that those who have a higher math self-efficacy were more likely to have a greater interest in math/science-related careers. Thus, based on the findings from the reviewed literature, it is evident that math attitudes and math self-efficacy have a strong influence on students’ career decisions.


DEMOGRAPHIC VARIABLES IN RELATION TO MATH ATTITUDES AND SELF-EFFICACY AND STEM CAREER


Much research has shown that multiple demographic factors contribute to students’ career decisions including gender, race/ethnicity, and socioeconomic status. Some research suggests that gender influences the relationship between an individual’s math attitudes and math self-efficacy beliefs with his/her career decisions, where female students tend to have lower math self-efficacy beliefs and as a result, do not pursue careers in STEM (Hackett & Betz, 1981; Ing & Nylund-Gibson, 2013; O’Brien et al., 1999; Wang et al., 2013; Zeldin et al., 2008). Research also suggests that race/ethnicity influences one’s math attitudes and math self-efficacy, as well as one’s decision to pursue a STEM career, where underrepresented minorities tend to have positive attitudes and math self-efficacy beliefs but were less likely to be employed in a STEM field (Ing & Nylund-Gibson, 2013; O’Brien et al., 1999). Another influential factor related to one’s math attitudes and self-efficacy and STEM career outcome is socioeconomic status, where students from higher SES backgrounds tend to have positive math attitudes and math self-efficacy and have positive STEM career interests (O’Brien at al., 1999; Wang et al., 2013). Based on these findings from the literature, it is important to understand how these demographic characteristics influence students’ math attitudes and math self-efficacy as well as students’ STEM career attainment. Examining these factors and identifying profiles of students’ math attitudes and self-efficacy may provide information on how to increase the number of students interested in pursuing STEM careers.


PROFILES OF MATH ATTITUDES AND MATH SELF-EFFICACY


Although there has been much research on examining factors related to STEM career attainment, there has little research on how to empirically identify profiles of math attitudes and math self-efficacy and understand how these profiles differ between English proficiency groups. ELLs and linguistic minorities are a diverse group of students whose varied linguistic, economic, and cultural backgrounds present unique needs and assets for the school community (Kanno & Harklau, 2012). Because non-native English speakers are a diverse group of people, research suggests there are different profiles for ELLs and linguistic minorities (Callahan, Wilkinson, & Muller, 2010; Lewis, Ream, Bocian, Cardullo, & Hammond, 2012). Therefore because of the heterogeneity within each English proficiency group, we are interested in using a clustering technique such as latent class analysis (LCA) to identify groups or classes of individuals who respond similarly to a set of indicators related to math attitudes and self-efficacy.


Understanding and acknowledging that there are different latent classes of math attitudes and math self-efficacy has implications for educators and researchers to target specific interventions for different language proficiency groups to improve attitudes and/or self-efficacy, both of which have been related to STEM outcomes. For example, there might be a group of female ELL students who have low math attitudes and low math self-efficacy beliefs. Intervention programs could encourage ELL female students’ interests in STEM and foster positive math attitudes and math self-efficacy beliefs through inquiry-based STEM programs. Another intervention program could provide opportunities to conduct STEM research with undergraduate students majoring in STEM. Understanding what these profiles of math attitudes and math self-efficacy look like can potentially shed light on why there is a lack of individuals pursuing STEM careers, as well as provide information to develop intervention programs to address the shortage of STEM professionals.


Thus, this study will address this need by examining the profiles of math attitudes and math self-efficacy beliefs among English language learners, linguistic minorities, and native English speakers. Classifying students into distinct classes based on a set of math attitude and math self-efficacy indicators while taking into account differences in gender, race/ethnicity, and SES is important for understanding individual differences in STEM career attainment. This study builds on existing literature by implementing a method to classify 10th grade students’ math attitudes and self-efficacy beliefs and explores differences in students’ attitudes and self-efficacy by gender, race/ethnicity, and socioeconomic status and relates these differences to whether or not these students attain a career in STEM. We hypothesize that students with positive math attitudes and math self-efficacy are more likely to pursue a career in STEM. We also hypothesize that there will be differences in attitudes and self-efficacy based on gender, race/ethnicity, socioeconomic status, and English proficiency.


METHOD

STUDY DESIGN


The data for this study was drawn from the Education Longitudinal Study of 2002 (ELS:2002), which is a nationally representative data set. Over 750 schools were randomly selected across the United States and then 10th graders were randomly selected within the selected schools. The ELS:2002 began its base year data collection in 2002, with the first follow up in 2004, second follow up in 2006, and third follow up in 2012. In 2002, baseline surveys were administered to 10th grade students, their parents, teachers, school principals and librarians. In the first follow up in 2004, most of the students were 12th graders in high school. High school transcripts were collected from the high school last attended by students in 2005. By the second follow up in 2006, many sample members were in their second year of college, while others were employed in the labor force or may not have ever attended college. By the third follow up in 2012, most sample members graduated from college, while others were pursuing their careers.


ANALYTIC SAMPLE


Participants


The ELS:2002 dataset consists of a total sample of over 16,1001 students. At the base year data collection in 2002, there were 15,240 respondents; by the first follow up in 2004, there were 14,930 respondents; at the second follow up in 2006, there were 14,150 respondents; and at the third follow up in 2012, there were 13,250 respondents.


This present study included a sub-sample of 8,790 students, who responded to the base year, first follow up, second follow up, and third follow up surveys and had non-missing responses to items related to math attitudes and math self-efficacy. Using a similar classification system as described by Kanno and Cromley (2013), respondents were classified as English Language Learner if they met any one of the following criteria: (1) respondents indicated that English was not their first language and their complete high school transcripts indicated they took a course with the following labels: “English as a Second Language (ESL),” “English language (EL),” “English Language Learner (ELL),” “English language development (ELD),” “Limited English Proficiency (LEP),” “Sheltered (integration of native language and content instruction),” and “Specially Designed Academic Instruction in English (SDAIE)” (Callahan et al., 2010; Finkelstein, Huang, & Fong, 2009); (2) respondents indicated that English was not their first language and they reported they did not read, speak, write, and/or understand English very well; (3) respondents indicated that English was not their first language and their teacher reported the student was behind in math due to limited English proficiency (LEP).


Respondents were classified as linguistic minority if they reported that English was not their first language and they responded that they read, speak, write, and/or understand English well. Respondents were classified as native English speakers if they indicated they speak English as a first language and they read, speak, write, and understand English well. Using these criteria, among the total 8,790 students, 7,490 (85.2%) were classified as native English speakers, 1,040 (11.8%) were classified as linguistic minority students, and 260 (3.0%) were classified as ELLs.


MEASURES


Math Attitude


On the base-year survey, students were asked a series of questions that aimed to assess their attitudes toward math. Regarding the math attitudes construct, the following variables were analyzed: “Gets totally absorbed in mathematics,” “Thinks math is fun,” and “Mathematics is important.” These math attitude variables were recoded where 1 indicated endorsement on the item and 0 indicated not endorsing the items. Table 1 displays the weighted means and standard deviation for the math attitude items. A complete list of variables included in the study is displayed in Appendix A, Table A1.


Table 1. Descriptive Statistics of the Math Attitude and Math Self-Efficacy Items, Covariates, and Distal Outcome used in the Final Model (Weighted)

 

Variables

M

SD

Math Attitude Items

  

Gets totally absorbed in math

.51

.50

Thinks math is fun

.33

.47

Math is important

.51

.50

Math Self-Efficacy Items

  

Can do excellent job on math tests

.46

.50

Can understand difficult math texts

.41

.49

Can understand difficult math class

.46

.50

Can do excellent job on math assignments

.53

.50

Can master math class skills

.54

.50

Covariates

  

Female

.53

.50

Latino

.14

.35

African American

.14

.34

Asian

.04

.19

White

.63

.48

Other Race

.05

.22

Low Socioeconomic Status

.24

.42

Distal Outcome

  

STEM Career

.07

.25



Math Self-efficacy


Students’ math self-efficacy was measured by five items based on the base-year student survey. The variables that were used to describe the math self-efficacy construct include the following: “Can do excellent job on math tests,” “Can understand difficult math texts,” “Can understand difficult math class,” “Can do excellent job on math assignments,” and “Can master math class skills.” These math attitude and self-efficacy variables were recoded where 1 indicated endorsement on the item and 0 indicated not endorsing the items. Table 1 displays the weighted means and standard deviation for the math self-efficacy items.


COVARIATES


The covariates in the study included students’ gender, race/ethnicity, and socioeconomic status. Table 1 displays the weighted frequencies of the covariates included in the study. Descriptive statistics were weighted by a panel weight for sample members who completed the base year through the third follow up and for whom high school transcript data were collected.


Gender


Gender was represented by students’ self-reported response on the base year survey. A dichotomous variable “Female” was created where 1 indicated female, 0 indicated male.


Race/Ethnicity


Race/ethnicity was represented by students’ self-reported response on the base year survey using the restricted data. Using the race/ethnicity variable, four dichotomous variables were created (i.e., “Latino,” “African American,” “Asian,” and “Other Race”), where 1 indicates the respective race/ethnicity, and 0 otherwise. Due to the small sample size, the “Other Race” category was created to include American Indian/Alaska Native, Native Hawaii/Pacific Islander, and multi-race respondents.


Socioeconomic Status


Students’ socioeconomic status was measured using a composite variable from the parent survey constructed from the following five equally weighted variables: mother’s education, father’s education, mother’s occupation, father’s occupation, and family income (Ingels, Pratt, Rogers, Siegel, & Stutts, 2004). To account for occupational prestige, the 1989 General Social Survey occupational prestige score were used (Nakao & Treas, 1992). Students’ SES was divided into four quartiles, where 1 = lowest quartile, 2 = second lowest quartile, 3 = second highest quartile, 4 = highest quartile. For this study, a dichotomous variable was created where 1 indicates the lowest quartile and 0 otherwise.


Distal Outcome Variable


The distal outcome used in this study was the respondents’ current occupation at the time of the third follow up data collection. Respondents were asked to indicate a job title and describe job duties for each occupation. A dichotomous variable was created where 1 indicated whether the respondent had a STEM-related job, and 0 otherwise. This variable was coded from the two-digit Occupational Information Network (O*NET) variable (Ingels et al., 2014). The complete list of occupations that were coded as STEM is provided in Appendix B.


LATENT CLASS ANALYSIS OF THREE ENGLISH PROFICIENCY GROUPS


For each English proficiency group (i.e., English Language Learner, linguistic minority, and native English speaker), an independent LCA was conducted, for a total of three sets of LCAs. LCA is an exploratory statistical model, a type of mixture modeling technique where it is a hypothesized that there is an underlying categorical latent variable that groups individuals. Traditionally in LCA the indicators of the latent variable are categorical (Collins & Lanza, 2010; Muthén, 2001). Implementing a separate LCA for each English proficiency group allowed for the number and structure of the emergent latent classes to be different.


Class Enumeration


When fitting a latent class model for each English proficiency group, the class enumeration process was conducted separately for each group. Due to the exploratory nature of LCA, it is not known a priori how many classes will emerge. In LCA, determining the number of classes in a final model may be challenging, as there is no one specific method to do so or no specific criterion that identifies the best fitting model (Muthén & Asparouhov, 2006; Nylund, Asparouhov, & Muthén, 2007). Masyn (2013) argues that class enumeration requires a lot of consideration in terms of examining a series of fit indices, applying the parsimony principle, and interpreting the theoretical meaning of the classes. Having different number of classes produces different interpretations. For example, a two-class model (i.e., low and high math attitude) has a different substantive meaning compared to a three-class model (i.e., low, medium, and high math attitude). Therefore it is important to provide careful thought and consideration in the class enumeration process. In this study, we used a number of fit indices to assess absolute fit and relative fit since there is no perfect index that indicates which model fits best (Nylund et al., 2007).


LCA models are fitted by starting with a one-class model and then increasing the number of classes by one, collecting fit statistics for each model. We used the likelihood ratio (LR) chi-square goodness-of-fit to assess how well a latent class model fitted the observed data (Collins & Lanza, 2010). In addition, we included the Bayesian Information Criterion (BIC) (Schwartz, 1978) and adjusted BIC. The BIC is the most common and trusted fit indices used to compare values across a series of models, where lower values indicated better fit (Nylund et al., 2007). The fit of each model is compared to the previous model using the Bootstrap Likelihood Ratio Test (BLRT) and the Lo-Mendell-Rubin-Likelihood Ratio Test (LMR-LRT), which tests neighboring class models, where a statistically significant p-value suggested the model fitted the data significantly better than the model with one less class (Masyn, 2013; Nylund et al., 2007). In addition to assess these fit indices, it is important to use the parsimony principle to compare models, which implies that the model with the fewest number of classes that is statistically and substantively meaningful is selected (Masyn, 2013).


The Three-Step Procedure for Estimating LCA Models


The three-step LCA approach was implemented in this study, which is a relatively new method that is used when including covariates and/or distal outcomes into LCA models (Asparouhov & Muthén, 2013; Nylund-Gibson, Grimm, Quirk, & Furlong, 2014; Vermunt, 2010). The goal of this three-step approach is to build a measurement model based on a set of categorical indicators and then relate the class membership to auxiliary variables (i.e., covariates and distal outcomes). The LCA with covariates uses the observed variable (i.e., covariate) as a predictor of the latent class variable and the distal outcomes as an outcome of the latent class variable. Both methods involve estimating logistic regression models for the latent classes.


As the name suggests, the three-step approach involves three steps. In the first step, the latent class model is estimated without any covariates (i.e., unconditional model). In the second step, individuals are assigned to latent classes using modal class assignment and a measurement error is determined for the most likely class variable. The final step involves estimating a model with auxiliary variables, where the latent class variable is measured by the most likely class, and the measurement error in the class assignment is fixed to a specific value found in the second step. For more details on the three-step model including sample syntax, see Nylund et al. (2014) and Asparouhov and Muthén (2013).


The following section presents the modeling results of the three English proficiency groups broken up by specific research questions. The first research question relates to the number of latent classes in each group (e.g., the class enumeration process for each language proficiency group). The second research question relates to the inclusion of covariates (i.e., gender, races, and SES), and lastly, the third research question relates to how the emergent classes differentiate in terms of the distal outcome (i.e., STEM career or not). We present results by research question, rather than proficiency group, to highlight differences that emerged across groups. Our research questions and models tested are displayed in Appendix A, Table A2.


RESULTS


RESEARCH QUESTION 1: What are the different math attitudes and math self-efficacy beliefs among English Language Learners, linguistic minorities, and native English speakers?


CLASS ENUMERATION: ENGLISH LANGUAGE LEARNERS


Table 2 presents a summary of the latent class analysis fit indices with 1 to 5 classes for ELLs, linguistic minorities, and native English speakers. Bolded values indicate the best model given the fit index. After examining the fit indices, the model with the lowest BIC value was the two-class model. In addition, applying the parsimony principle confirmed the decision to select a two-class model. The item probability plot presented in Figure 2 was used to identify two emerging classes for English Language Learners. The first class was labeled Medium math attitude, Low self-efficacy (ML), which represented 57.1% of the sample; the second class was labeled High math attitudes, High math self-efficacy (HH), which represented 42.9% of the sample.


Table 2. Latent Class Analysis Fit Indices for ELLs, Linguistic Minorities and Native English Speakers


English Proficiency Group

Number of classes

Log likelihood

BIC

ABIC

p value of BLRT

p value of LMRT

ELL (n = 260)

1

-1189.25

2422.83

2397.47

-

-

 

2

-995.26

2084.73

2030.83

< .001

< .001

 

3

-971.82

2087.72

2005.29

< .001

0.005

 

4

-955.02

2103.98

1993.02

< .001

0.21

 

5

-944.33

2132.47

1992.98

.14

0.22

Linguistic

1

-5258.43

10572.48

10547.07

-

-

Minority

2

-4155.17

8428.50

8374.50

< .001

< .001

(n = 1,040)

3

-4050.71

8282.13

8199.55

< .001

< .001

 

4

-3960.83

8164.93

8053.76

< .001

< .001

 

5

-3913.69

8133.22

7993.47

< .001

0.109

Native English

1

-38488.25

77047.86

77022.44

-

-

Speaker

2

-29338.43

58828.53

58774.51

< .001

< .001

(n = 7,490)

3

-28508.73

57249.43

57166.81

< .001

< .001

 

4

-27804.46

55921.18

55809.96

< .001

< .001

 

5

-27497.77

55388.10

55248.28

< .001

< .001

 

6

-27369.35

55211.56

55043.14

< .001

< .001

Note. BIC = Bayesian Information Criterion; ABIC = Adjusted BIC; BLRT = Bootstrap Likelihood Ratio Test; LMRT = Lo-Mendell-Rubin Likelihood Ratio Test


Figure 2. Item Probability Plot for English Language Learners (n = 260)

[39_21781.htm_g/00004.jpg]


CLASS ENUMERATION: LINGUISTIC MINORITIES


From Table 2, taking into consideration the fit indices and interpreting the theoretical meaning of the classes, a four-class model was identified for linguistic minorities. The non-significant p value of the Lo-Mendell-Rubin Likelihood Ratio Test (LMRT) suggested that a five-class model does not significantly improve the model fit, and therefore a four-class model fits better. The item probability plot presented in Figure 3 illustrates the four emerging classes for linguistic minorities. The first class was labeled High math attitudes, Low math self-efficacy (HL), which represented 23.4% of the sample; the second class was labeled Low math attitude, High self-efficacy (LH), which represented 17.6% of the sample; the third class was labeled Low math attitudes, Low math self-efficacy (LL), which represented 29.4% of the sample; and the fourth class was labeled High math attitudes, High math self-efficacy (HH), which represented 29.6% of the sample.


Figure 3. Item Probability Plot for Linguistic Minorities (n = 1,040)

[39_21781.htm_g/00006.jpg]


CLASS ENUMERATION: NATIVE ENGLISH SPEAKERS


To aid in identifying the number of classes, the BIC values were examined. From Table 2, it is evident the BIC never reached a minimum; however, an “elbow,” or the largest decrease in the BIC value (Nylund et al., 2007) occurred with the five-class model. Considering substantive reasons and the “elbow” in BIC value suggested that a five-class model was preferable. The item probability plot presented in Figure 4 displays the five emerging classes for native English speakers. The first class was labeled High math attitudes, High math self-efficacy (HH), which represented 25.6% of the sample; the second class was labeled Low math attitude, High self-efficacy (LH), which represented 11.2% of the sample; the third class was labeled High math attitudes, Low math self-efficacy (HL), which represented 11.8% of the sample; the fourth class was labeled Medium math attitudes, Medium math self-efficacy (MM), which represented 17.7% of the sample; and the fifth class was labeled Low math attitudes, Low math self-efficacy (LL), which represented 33.6% of the sample.


Figure 4. Item Probability Plot for Native English Speakers (n = 7,490) [39_21781.htm_g/00008.jpg]


RESEARCH QUESTION 2: How are the selected demographic characteristics (i.e., gender, race/ethnicity, and socioeconomic status) related to students’ math attitudes and math self-efficacy for each English proficiency group?


The demographic characteristics included in this analysis were students’ gender (whether or not the student is female); race/ethnicity (i.e., whether or not the student is Latino, African American, Asian, or other race/ethnicity); and socioeconomic status (i.e., whether or not students were from low socioeconomic backgrounds). When comparing the emergent latent classes with and without these covariates, there were no large shifts in the emergent latent classes, which suggested that these latent classes were stable and the relative class size remained the same. In interpreting the logit coefficients, a negative logit indicates that individuals who are coded 1 on the covariate were more likely to be in the reference class than the comparison class, whereas a positive logit indicates that individuals who are coded 1 are more likely to be in the comparison class than the reference class. The following sections present the relationship of the covariates and students’ class membership for each of the English proficiency groups, where only significant values are presented.


COVARIATES: ENGLISH LANGUAGE LEARNERS


Including covariates for ELLs reduced the sample from 260 to 240 due to missing variables on the covariates. For ELLs, only two covariates proved to be significant predictors of class assignment: gender and race/ethnicity. More specifically, the positive logit coefficient presented in Table 3 suggests that female ELL students were significantly more likely to be in the Medium math attitude, Low math self-efficacy (ML) class compared to the High math attitude, High math self-efficacy (HH) class relative to males. Similarly, there were racial/ethnic differences, where Latino and Asian ELLs were significantly more likely to be in the HH class compared to the ML class, relative to their White ELL counterparts.


Table 3. Covariate Table for the Final Two-Class Model (English Language Learners)

       

 Latent Classes

Effect

Logit

SE

Logit/SE

p value

OR

Med MA, Low MSE

Female

  0.95**

0.34

2.82

.01

2.59

(57.1%)

Latino

-1.75*

0.88

-2.00

.05

0.17

 

African American

  -2.03

1.20

-1.68

.09

0.13

 

Asian

  -2.13*

0.88

-2.43

.02

0.12

 

Other Race

   1.22

4.06

0.30

.76

3.40

 

Low SES

   0.43

0.32

1.35

.18

1.54

Note. n = 240; Class percentages are noted in parentheses. Reference class is High Math Attitude, High Math Self-Efficacy (42.9%); Med MA, Low MSE = Medium Math Attitudes, Low Math Self-Efficacy; OR = odds ratio

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


COVARIATES: LINGUISTIC MINORITIES


For linguistic minorities, including covariates reduced the sample from 1,040 to 1,010. There were two significant covariates, which include gender and SES. Results from Table 4 suggest that there was a consistent gender effect, where female linguistic minorities were significantly more likely to be in classes that were not the High math attitude, High math self-efficacy (HH) class relative to males. Another significant comparison was linguistic minorities from low socioeconomic (SES) backgrounds were more likely to be in the HL or the LL class when compared to the HH class, relative to linguistic minorities from higher SES backgrounds. This suggests that low SES linguistic minorities tend to have low self-efficacy compared to higher SES linguistic minorities.


Table 4. Covariate Table for the Final Four-Class Model (Linguistic Minorities)

       

 Latent Classes

Effect

Logit

SE

Logit/SE

p value

OR

High MA, Low MSE

Female

     0.57**

0.22

2.64

.01

1.77

(23.4%)

Latino

 -0.41

0.38

-1.07

.28

0.67

 

African American

0.09

0.59

0.15

.89

1.09

 

Asian

-0.58

0.36

-1.60

.11

0.56

 

Other Race

0.62

0.58

1.07

.28

1.86

 

Low SES

0.84***

0.23

3.57

 < .001

2.31

  

 

    

Low MA, High MSE

Female

0.74**

0.25

2.97

 < .01

2.10

(17.6%)

Latino

0.04

0.44

0.09

.93

1.04

 

African American

-0.41

0.83

-0.50

.62

0.66

 

Asian

-0.06

0.43

-0.14

.89

0.94

 

Other Race

-0.72

1.05

-0.69

.49

0.48

 

Low SES

-0.24

0.27

-0.88

.38

0.79

  


    

Low MA, Low MSE

Female

0.53**

0.18

2.90

 < .01

1.70

(29.4%)

Latino

0.13

0.34

0.39

.70

1.14

 

African American

0.24

0.55

0.43

.67

1.26

 

Asian

-0.31

0.34

-0.93

.35

0.73

 

Other Race

0.96

0.53

1.82

.07

2.60

 

Low SES

0.60**

0.20

3.01

 < .01

1.82

Note. n = 1,010; Class percentages are noted in parentheses. Reference class is High Math Attitude, High Math Self-Efficacy (29.6%); Low MA, High MSE = Low Math Attitudes, High Math Self-Efficacy; High MA, Low MSE = High Math Attitude, Low Math Self-Efficacy; Low MA, Low MSE = Low Math Attitude, Low Math Self-Efficacy; OR = odds ratio
* p < .05, ** p < .01, *** p < .001


COVARIATES: NATIVE ENGLISH SPEAKERS


For native English speakers, including covariates reduced the sample from 7,490 to 7,390. Results from Table 5 suggest that when compared to male native English speakers, female native English speakers were more likely to be in the HL, MM, or LL class relative to the HH class. This suggests that female native English speakers tended to have lower math self-efficacy beliefs than their male counterparts. In examining racial/ethnic comparisons, Latino native English speakers were more likely to be in the HH class compared to the LH class, relative to their White counterparts. African Americans native English speakers were more likely to be in the HL class compared to the HH class, but were also more likely to be in the HH class compared to the LL or LH classes. This suggests that Latino and African American native English speakers were more likely to have positive math attitudes compared to White native English speakers.


Table 5. Covariate Table for the Final Five-Class Model

    

 Latent Classes

Effect

 Logit

SE

 Logit/SE

  p value

OR

Low MA, High MSE

Female

-0.16

0.10

-1.51

.13

0.85

(11.2%)

Latino

-0.44*

0.22

-1.97

.05

0.65

 

African American

-0.53**

0.19

-2.82

.01

0.59

 

Asian

-0.31

0.27

-1.12

.26

0.74

 

Other Race

-0.23

0.22

-1.06

.29

0.79

 

Low SES

-0.08

0.16

-0.51

.61

0.92

     

 

 

High MA, Low MSE

Female

 0.30**

0.11

2.78

.01

1.35

(11.8%)

Latino

 0.07

0.21

0.35

.72

1.08

 

African American

 0.72***

0.14

5.21

< .001

2.06

 

Asian

 0.13

0.26

0.50

.62

1.14

 

Other Race

-0.11

0.24

-0.48

.63

0.89

 

Low SES

 0.65***

0.14

4.71

< .001

1.91

     

 

 

Med MA, Med MSE

Female

 0.34***

0.09

3.66

< .001

1.40

(17.7%)

Latino

-0.12

0.18

-0.69

.49

0.89

 

African American

-0.23

0.15

-1.56

.12

0.79

 

Asian

-0.07

0.23

-0.31

.76

0.93

 

Other Race

-0.41

0.21

-1.91

.06

0.67

 

Low SES

0.29*

0.13

2.23

.03

1.34

     

 

 

Low MA, Low MSE

Female

 0.76***

0.07

10.85

< .001

2.13

(33.6%)

Latino

-0.05

0.13

-0.40

.69

0.95

 

African American

-0.41***

0.12

-3.52

< .001

0.67

 

Asian

-0.47**

0.19

-2.50

.01

0.62

 

Other Race

-0.12

0.14

-0.89

.37

0.88

 

Low SES

 0.35***

0.10

3.50

 < .001

1.41

Note. n = 7,390; Class percentages are noted in parentheses. Reference class is High Math Attitude, High Math Self-Efficacy (25.6%); Low MA, High MSE = Low Math Attitudes, High Math Self-Efficacy; High MA, Low MSE = High Math Attitude, Low Math Self-Efficacy; Med MA, Med MSE = Medium Math Attitudes, Medium Math Self-Efficacy; Low MA, Low MSE = Low Math Attitude, Low Math Self-Efficacy; OR = odds ratio

* p < .05, ** p < .01, *** p < .001

      


Similarly to linguistic minorities, native English speakers from low SES backgrounds were more likely to be in the HL, MM, or LL class compared to the HH class, relative to those from high SES backgrounds. This suggests that native English speakers from low SES backgrounds tend to have lower math self-efficacy compared to their counterparts with high SES backgrounds.


RESEARCH QUESTION 3: To what extent do students’ math attitude and math self-efficacy contribute to students’ STEM career attainment?


The distal outcome used in this analysis was a dichotomous variable indicating whether or not the respondents’ job as of 2012 was STEM-related. The following sections present the relationship of the students’ class membership and STEM career attainment for each of the English proficiency groups with results displayed in Figure 5.


Figure 5. STEM Job Attainment for ELLs (n = 240), Linguistic Minorities (n = 1,010), and Native English Speakers (n = 7,390). MA = Math Attitudes, MSE = Math Self-Efficacy



[39_21781.htm_g/00010.jpg]



STEM CAREER ATTAINMENT: ENGLISH LANGUAGE LEARNERS


For ELLs, a significantly higher proportion of individuals in the High math attitudes, High math self-efficacy pursued a STEM career (13%), compared to 3% of individuals in the Medium math attitudes, Low math self-efficacy class.


STEM CAREER ATTAINMENT: LINGUISTIC MINORITIES


For linguistic minorities, there were 16% of linguistic minorities in the HH class who pursued a STEM career and this was statistically significant compared to the 6% of linguistic minorities in the HL class and the 7% of linguistic minorities in the LL class. There were 9% of linguistic minorities in the LH class who pursued a STEM career, but this was not significantly different from the other classes.


STEM CAREER ATTAINMENT: NATIVE ENGLISH SPEAKERS


For native English speakers, a significantly higher proportion of native English speakers in the HH class (12%) pursued a STEM career compared to the other classes. In addition, compared to the LL class, where there were only 4% of students in a STEM career, the LH, HL, and MM have significantly higher proportions of students in a STEM career at 8%, 7%, and 7%, respectively.


DISCUSSION


The results from this study extend the social cognitive career theory to English language learners, linguistic minorities, and native English speakers, and also provide information on how math attitudes and math self-efficacy beliefs differ between each English proficiency group. Our finding supports the logical basis of SCCT that there are complex factors involved in students’ STEM career attainment. The result of fitting three independent LCAs on each of the English proficiency group revealed that there were different patterns of math attitudes and math self-efficacy for each group. These latent classes in the language groups could have been the same, but the results from the analysis revealed there were different latent classes for each group. Combining the English proficiency groups into one group masks these differences. Thus, had we not done the analysis by English proficiency subgroup, this interesting result would have been overlooked and we would not know that there were differences in math attitudes and math self-efficacy beliefs among these English proficiency groups. The findings from this study stress the importance to not make the assumption that all linguistic minorities or all ELLs are the same, but that they have different profiles and experiences and should be treated differently instead of aggregated together.


In summary, across the English proficiency groups, there were common and unique themes. What was common among the ELLs, linguistic minorities, and native English speakers was that regardless of English proficiency, female students tended to be in classes that were not High math attitudes, High math self-efficacy (HH), suggesting they have less positive math attitudes and math self-efficacy compared to their male counterparts. This finding is consistent with research that suggest female students perceive to have more negative attitudes and have lower math self-efficacy compared to males (Betz & Hackett, 1983; Hackett & Betz, 1981; Ing & Nylund-Gibson, 2013; Luzzo et al., 1999; O’Brien et al., 1999; Wang et al., 2013; Zeldin et al., 2008). Female students with low math attitudes and math self-efficacy may be one of the reasons why there is an underrepresentation of female individuals in STEM fields (NSF, 2013). Future research should develop interventions to improve female students’ math attitudes and self-efficacy beliefs and promote positive attitudes, while also encouraging female students to pursue STEM careers. One recommendation is having more discussions within classrooms to describe the types of jobs available in STEM and have students interact with representatives from STEM organizations to increase STEM career awareness as well as improve attitudes and self-efficacy beliefs about STEM jobs. More interventions such as the Mother Daughter program, developed by the University of Texas at El Paso, are necessary to promote Latino female students’ attitudes and self-efficacy and promoting awareness of different career opportunities (Excellencia in Education, 2010).


In terms of STEM career attainment, another commonality across all three English proficiency groups was students with high math attitudes and high math self-efficacy beliefs had a higher proportion of students in STEM careers compared to the other classes. This finding is in congruence with social cognitive theory that suggests self-efficacy strongly influences the choices people make, the amount of effort they expend, and how long they persevere when they encounter challenges (Bandura, 1977; Lent et al., 1994; Pajares & Miller, 1994, 1995). What is interesting to note is the linguistic minority and native English speaking students with low math attitudes and high math self-efficacy had the next highest proportion of students in STEM careers, where there were 9% in the LH class compared to the 16% in the HH class for the linguistic minorities, and 8% in LH compared to the 12% in HH for native English speakers. This suggests that math self-efficacy is important in STEM career attainment regardless of math attitudes. This has implications to focus on improving students’ math self-efficacy in the high school years, if not earlier, to increase the likelihood of going into a STEM career. Implementing an LCA contributes to our understanding on how to develop specific interventions for different language proficiency groups. For example, an intervention for students with high math attitudes and low math self-efficacy can focus specifically on improving students’ math self-efficacy, while an intervention for students with low math attitudes and high math self-efficacy may focus on improving students’ math attitudes. Thus, using LCA improves our understanding of how to design different interventions for different latent classes.


Another common finding between the linguistic minority and native English speaking students was the relationship between students’ socioeconomic backgrounds and math attitudes and math self-efficacy beliefs. Linguistic minority and native English speaking students with low SES backgrounds were more likely to be in the HL class compared to the HH class, which suggests that they share similar positive math attitudes, but have lower math self-efficacy beliefs compared to their peers with higher SES backgrounds. The low SES covariate was not significant for ELLs. This finding confirms what has been found in the literature, where students from higher SES background tend to have higher math attitudes and higher math self-efficacy (Wang et al., 2013).


A unique finding among the English proficiency groups was how race/ethnicity functions differently, where Latino and Asians ELLs were more likely to be in the HH class compared to the ML class. This is interesting to note since it provides evidence against some literature that suggests Latino ELLs have low self-efficacy beliefs that may be due to the cognitive (Campbell, Davis, & Adams, 2007) and linguistic demands in math (Spanos, Rhodes, Dale, & Crandall, 1988; Wolf & Leon, 2009). This finding would not have emerged if we treated the classes as one homogeneous group. By conducting an LCA for each English proficiency group, we could make inferences and draw conclusions for that particular group, and thereby develop specific interventions for each group. This finding suggests that ELL students, who are traditionally seen as the underachieving group, do in fact have positive math attitudes and positive math self-efficacy, which can lead to positive STEM outcomes.


However ELLs face a host of inequitable schooling conditions (Gándara, Rumberger, Maxwell-Jolly, & Callahan, 2003) that prevent them from achieving successful STEM outcomes. Thus even though ELL students may have positive math attitudes and math self-efficacy beliefs, there may be certain schooling policies in place that prevent students from persisting in STEM such as tracking (Callahan, 2005; Mosqueda, 2010, 2012; Oakes, 2005) and access to advanced coursetaking (Mosqueda & Maldonado, 2013). Koelsch (2011) suggest that ELL students have a better chance to succeed at high levels when barriers are removed. This has implications for policymakers to remove programs that hinder students’ success and instead offer support and guidance to maximize students’ potential to succeed. In addition, this finding has implications for policymakers and administrators to review inequitable conditions in schools to ensure that every student has equal educational opportunities. Furthermore, this finding that Latino and Asian ELLs have positive math attitudes and math self-efficacy suggest that intervention programs need to continue to foster these positive attitudes and keep these ELL students interested in pursuing a STEM career.


Another unique result was Latino native English speakers were more likely to be in the HH class compared to the LH or LL class, while African Americans were more likely to be in high attitudinal classes compared to their White counterparts. These results confirm findings from previous research that suggests Latinos and African Americans tend to have higher math attitudes and math self-efficacy compared to their White counterparts (Else-Quest, Mineo, & Higgins, 2013; Stevens, Olivarez, Lan, & Tallent-Runnels, 2004; Thomas, 2000). Although the results from the study suggest that Latinos and African Americans have higher math attitudes and math self-efficacy beliefs, this does not necessarily translate to higher math achievement as demonstrated in the 2013 Mathematics Assessment from the National Assessment of Educational Progress (NAEP, 2013) results. The NAEP (2013) results revealed that 12th grade Latino and African Americans performed significantly lower on the math assessments compared to their White counterparts. Perhaps there are other factors that impact Latinos’ and African Americans’ mathematical performance, which may include poor academic preparation (Ma, 2009), lack of exposure to advanced math or science coursetaking (Wang, 2013), or lack of positive role models (Lent, Lopez, Brown, & Gore, 1996). Future research is needed to investigate the complex relationship of Latinos and African American students’ positive math attitudes and math self-efficacy beliefs, and low math achievement. Nevertheless, what is important is for parents and educators to continue to promote these positive attitudes and beliefs that will keep these underrepresented populations interested in STEM and motivated to pursue STEM fields.


LIMITATIONS


There are a few limitations that the reader should be aware when interpreting the results. First, this study only used data from respondents who participated in all four data collection waves (i.e., base year, first follow up, second follow up, and third follow up). Students who respond to multiple data collection waves and persist through a longitudinal study are likely to persist through their educational and career goals (Kanno & Cromley, 2013). Thus, limiting the sample to those who participated in all data collection waves may show a more optimistic perspective than if all the respondents in the base year completed all waves of data collection.


Second, the sample excludes students with extremely low English proficiency skills who were unable to read or respond to the base year survey. Thus, the ELLs and linguistic minorities in the sample may not be truly representative of the ELL and linguistic minority population in the United States as a whole. Furthermore, those ELLs and linguistic minorities who persist in the longitudinal data collection are likely to persist in attaining their educational and career goals compared to those who did not respond to all four data collection waves. Nevertheless, this study is one of the few studies to examine ELL and linguistic minority students’ outcomes beyond high school. Third, the ELS:2002 data relies on students’ self-reported measures, where fields can be blank or filled in with false information. For example, respondents’ English proficiency status was classified on one critical question that asks students whether English is their native language. Students may choose “Yes” even if English was not their native language. This may underestimate the number of ELLs and linguistic minorities in the sample. Therefore, some underestimation should be assumed in the study.


Fourth, data examined in this study relied on a secondary data, thus, some critical variables for the analysis were unavailable. For example, self-efficacy beliefs are central to the SCCT, which serves as the guiding theoretical framework for this study. Although the ELS:2002 data contains items measuring math attitudes and math self-efficacy, it does not include any variables on science attitudes or science self-efficacy beliefs. This study assumes that math attitudes and math self-efficacy beliefs influence STEM outcomes. Having the combination of math and science attitudes and self-efficacy may provide a better profile of students’ STEM attitudinal and self-efficacy beliefs and would help researchers understand the complex nature of STEM outcomes.


Despite these limitations, the results from this study are important due to the fast-growing population of ELLs and linguistic minorities and the lack of research conducted on this population. Through this study, we contribute to the field by bridging the gap in knowledge of ELL and linguistic minority students’ career opportunities beyond secondary and postsecondary education. Findings from this study will contribute to the emerging body of literature of ELLs and linguistic minorities in STEM. This study suggests that ELLs and linguistic minorities have different educational needs and thus more research should focus on how to best support this at-risk population as well as improve their math self-efficacy. More professional development is needed for educators to be able to provide differentiated instruction for ELLs (Gamoran, 2009) and offer care and support to improve students’ math attitudes and math self-efficacy, which in turn positively impact students’ math achievement (Lewis et al., 2012).


There are many facets to understanding what contributes to students’ STEM outcomes; this study serves as a stepping stone to one of many future studies that examines ELLs’ and linguistic minority students’ STEM outcomes beyond high school. Such research is needed to inform policy and practice to ensure the future success of non-native English speakers in STEM fields. In doing so, educators, researchers, and policymakers have a real opportunity to prepare one of the fastest growing U.S. population and create the next generation of scientific talent to fill the STEM job vacancies.


Notes


1. Following the restricted data security policy of the National Center for Education Statistics (NCES), which collected the ELS:2002 data, unweighted sample sizes were rounded to the nearest 10.


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APPENDIX A


Table A1. Variables included in Study with Recoded Values

Construct

ELS:2002 variable name

Description

Original coding

New Coding

Math attitudes

BYS87A

When I do mathematics, I sometimes get totally absorbed

1=Strongly Agree, 2=Agree, 3= Disagree, 4= Strongly Disagree

1 & 2=1;
3 & 4=0

Math attitudes

BYS87C

Because doing mathematics is fun, I wouldn’t want to give it up

1=Strongly Agree, 2=Agree, 3= Disagree, 4= Strongly Disagree

1 & 2=1;
3 & 4=0

Math attitudes

BYS87F

Mathematics is important to me personally

1=Strongly Agree, 2=Agree, 3= Disagree, 4= Strongly Disagree

1 & 2=1;
3 & 4=0

Math self-efficacy

BYS89A

I’m confident that I can do an excellent job on my math tests

1=Almost never, 2=Sometimes, 3= Often, 4=Almost always

1 & 2=0;
3 & 4=1

Math self-efficacy

BYS89B

I’m certain I can understand the most difficult material presented in math texts

1=Almost never, 2=Sometimes, 3= Often, 4=Almost always

1 & 2=0;
3 & 4=1

Math self-efficacy

BYS89L

I’m confident I can understand the most complex material presented by my math teacher

1=Almost never, 2=Sometimes, 3= Often, 4=Almost always

1 & 2=0;
3 & 4=1

Math self-efficacy

BYS89R

I’m confident I can do excellent job on my math assignments

1=Almost never, 2=Sometimes, 3= Often, 4=Almost always

1 & 2=0;
3 & 4=1

Math self-efficacy

BYS89U

I’m certain I can master the skills being taught in my math class

1=Almost never, 2=Sometimes, 3= Often, 4=Almost always

1 & 2=0;
3 & 4=1

English Proficiency

BYS70A

How well 10th grader understands spoken English

1=Very well, 2=Well, 3=Not well, 4=Not at all

1 & 2=1;
3 & 4=0

English Proficiency

BYS70B

How well 10th grader speaks English

1=Very well, 2=Well, 3=Not well, 4=Not at all

1 & 2=1;
3 & 4=0

English Proficiency

BYS70C

How well 10th grader reads English

1=Very well, 2=Well, 3=Not well, 4=Not at all

1 & 2=1;
3 & 4=0

English Proficiency

BYS70D

How well 10th grader writes English

1=Very well, 2=Well, 3=Not well, 4=Not at all

1 & 2=1;
3 & 4=0

English Proficiency

BYSTLANG

Whether English is student's native language - composite. Missing values were imputed

0=No; 1=Yes

N/A

English Proficiency

BYTM12B

Student behind due to limited proficiency in English language (math)

0=No; 1=Yes

N/A

Gender (covariate)

BYSEX

Gender

1=male, 2=female

Female: 0=male, 1=female

Race (restricted) (covariate)

BYRACE_R

Race

1=American Indian/Alaska Native, 2=Asian, 3=African American, 4=Hispanic (no race specified), 5=Hispanic (race specified), 6=More than one race (non-Hispanic), 7=Native Hawaiian/Pacific Islander, 8=White

Latino: 0=non-Hispanic; 1=Hispanic (4,5)

African American: 0=non-African American; 1=African American (3)

Asian: 0=non-Asian; 1=Asian (2); Other Race: 1= other (1,6,7); 0 otherwise

Students’ socioeconomic status (covariate)

BYSES2QU

SES composite variable based on the 1989 GSS occupational prestige scores used instead of the SES1, which used the 1961 Duncan SEI values

1=lowest quartile, 2=second lowest quartile, 3=second high quartile, 4=highest quartile

Low_SES:

1=1;

2, 3, 4 = 0

Occupation (outcome)

F3ONET2CURR

2-digit ONET code for current/most recent job

 

stem_job: 0=non-STEM job; 1=STEM job

Occupation (outcome)

F3ONET6CURR

6-digit ONET code for current/most recent job

 

stem_job: 0=non-STEM job; 1=STEM job

Weighting variable

F3BYTSCWT

Panel weight, BY and F3 (2002 and 2012) HS transcript respondent weight

  



Table A2. Summary of Research Questions and Hypotheses

Research Questions

DVs

IVs

Covariates

Hypothesis

1.

What are the different math attitudes and math self-efficacy beliefs among English Language Learners, linguistic minorities, and native English speakers?

Within latent classes

1. Math attitudes:
a. Gets totally absorbed in mathematics (BYS87A)
b. Thinks math is fun (BYS87C)
c. Mathematics is important (BYS87F)
2. Math self-efficacy:
a. Can do excellent job on math tests (BYS89A)
b. Can understand difficult math texts (BYS89B)
c. Can understand difficult math class (BYS89L)
d. Can do excellent job on math assignments (BYS89R)
e. Can master math class skills (BYS89U)

None

It is hypothesized that there will be different levels of math attitudes and math self-efficacy for each English proficiency group.

2.

How are the selected demographic characteristics (i.e., gender, race/ethnicity, and socioeconomic status) related to students’ math attitudes and math self-efficacy for each English proficiency group?

Within latent classes

1. Math attitudes:
a. Gets totally absorbed in mathematics (BYS87A)
b. Thinks math is fun (BYS87C)
c. Mathematics is important (BYS87F)
2. Math self-efficacy:
a. Can do excellent job on math tests (BYS89A)
b. Can understand difficult math texts (BYS89B)
c. Can understand difficult math class (BYS89L)
d. Can do excellent job on math assignments (BYS89R)
e. Can master math class skills (BYS89U)

1. Gender (BYSEX)
2. Race (BYRACE_R)
3. SES (BYSES2QU)

It is hypothesized that these covariates influence an individual’s decision to pursue a STEM career, where female individuals, underrepresented minorities, and/or individuals from low SES backgrounds are less likely to pursue STEM, while those on the college prep track and/or take a math course beyond Algebra II are more likely to pursue a STEM career.

3.

To what extent do students’ math attitude and math self-efficacy contribute to students’ STEM career attainment?

Dichotomous variable: STEM Career (F3ONET6CURR)

Latent class membership

1. Gender (BYSEX)
2. Race (BYRACE_R)
3. SES (BYSES2QU)

It is hypothesized that individuals with high math attitudes and high math self-efficacy will be more likely to attain a STEM career.

Note. BY = Base year (2002) of study; F1 = First follow-up (2004) of study; F2 = Second follow up (2006); F3 = Third follow up (2012)


APPENDIX B


Table B1. Classification of STEM Occupations in ELS:2002

O*NET Code

STEM Occupation Description

11

Management Occupations

113021

Computer and info systems managers

113051

Industrial production managers

119041

Engineering managers

119121

Natural sciences managers

15

Computer and Mathematical Occupations

151111

Computer and Information Research Scientists

151121

Computer Systems Analysts

151122

Information Security Analysts

151131

Computer Programmers

151132

Software Developers, Applications

151133

Software Developers, Systems Software

151134

Web Developers

151141

Database Administrators

151142

Network and Computer Systems Administrators

151143

Computer Network Architects

151151

Computer User Support Specialists

151152

Computer Network Support Specialists

151199

Computer Occupations, All Other

152011

Actuaries

152021

Mathematicians

152031

Operations research analysts

152041

Statisticians

152099

Mathematical Science Occupations, All Other

17

Architecture and Engineering Occupations

172011

Aerospace engineers

172021

Agricultural engineers

172031

Biomedical engineers

172041

Chemical engineers

172051

Civil engineers

172061

Computer hardware engineers

172071

Electrical engineers

172072

Electronics engineers, except computer

172081

Environmental engineers

172111

Health/safety engineer, except mining

172112

Industrial engineers

172121

Marine engineers and naval architects

172131

Materials engineers

172141

Mechanical engineers

172161

Nuclear engineers

172171

Petroleum engineers

172199

Engineers, all other

173011

Architectural and civil drafters

173012

Electrical and electronics drafters

173013

Mechanical drafters

173019

Drafters, all other

173022

Civil engineering technicians

173023

Electrical engineering technicians

173025

Environmental engineering technicians

173026

Industrial engineering technicians

173027

Mechanical engineering technicians

173029

Engineering tech, other (except drafter)

173031

Surveying and mapping technicians

19

Life, Physical, and Social Science Occupations

191012

Food Scientists and Technologists

191013

Soil and plant scientists

191021

Biochemists and biophysicists

191022

Microbiologists

191023

Zoologists and wildlife biologists

191029

Biological scientists, all other

191031

Conservation scientists

191032

Foresters

191041

Epidemiologists

191042

Medical scientist, except epidemiologist

191099

Life scientists, all other

192011

Astronomers

192012

Physicists

192021

Atmospheric and space scientists

192031

Chemists

192032

Materials scientists

192041

Environmental scientist, includes health

192042

Geoscientist, except hydrologists

192099

Physical scientists, all other

194021

Biological technicians

194031

Chemical technicians

194041

Geological and petroleum technicians

194051

Nuclear technicians

194091

Environmental/protection science tech

194092

Forensic science technicians

194093

Forest and conservation technicians

194099

Life/physical technician, other

25

Education, Training, and Library Occupations

251022

Mathematical science, postsecondary

251042

Biological science, postsecondary

251051

Atmospheric science, postsecondary

251052

Chemistry teachers, postsecondary

45

Farming, Fishing, and Forestry Occupations

451011

First-line manager, farming/fishing/etc

452041

Grader/sorter, agricultural products

452091

Agricultural equipment operators

452092

Farm worker/laborer: crop, nursery, etc

452093

Farm workers, farm and ranch animals

452099

Agricultural workers, all other

453011

Fishers and related fishing workers

454022

Logging equipment operators

454023

Log Graders and Scalers

51

Production Occupations

518011

Nuclear power reactor operators

518091

Chemical plant and system operators

519011

Chemical equipment operators and tenders

Note. O*NET = Occupational Information Network






Cite This Article as: Teachers College Record Volume 119 Number 6, 2017, p. 1-38
https://www.tcrecord.org ID Number: 21781, Date Accessed: 10/27/2021 6:03:20 PM

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About the Author
  • Myley Dang
    Mathematica Policy Research
    E-mail Author
    MYLEY DANG is a survey researcher at Mathematica Policy Research. Her research interests include science, technology, engineering, and mathematics (STEM); secondary and post-secondary education; underrepresented populations; math attitudes; math self-efficacy; college and career readiness; survey methodology; longitudinal data; large-scale data; and quantitative data analysis.
  • Karen Nylund-Gibson
    University of California, Santa Barbara
    E-mail Author
    KAREN NYLUND-GIBSON is an associate professor in the Gevirtz School at the University of California, Santa Barbara. Her research helps to bridge the gap between advanced statistical literature and application of these models to substantive issues. Her publications have appeared in numerous peer-reviewed publications including Structural Equation Modeling, Journal of Educational Psychology, and Child Development.
 
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