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The role of goal orientations for adolescent mathematics achievement
Contemporary Educational Psychology 37 (2012) 47–54
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The role of goal orientations for adolescent mathematics achievement Tran D. Keys ⇑, AnneMarie M. Conley, Greg J. Duncan, Thurston Domina Department of Education, University of California, Irvine, USA
a r t i c l e
i n f o
Article history: Available online 17 September 2011 Keywords: Achievement goal theory Goal orientations Mathematics achievement
a b s t r a c t This study examines the association between personal goal orientations and mathematics achievement within the trichotomous goal framework. Participants comprised approximately 2000 seventh and eighth grade White, Hispanic, and Vietnamese students in a low-income urban school district in California. Regression analysis with classroom fixed effects minimized biases arising from non-random assignment of teachers and students to schools and classrooms. While all three achievement goal orientations were correlated with mathematics achievement, only a mastery goal orientation consistently predicted achievement when a full set of prior achievement and demographic controls were included. Performance-approach and performance-avoidance goal orientations did not predict achievement in the full model. Ó 2011 Elsevier Inc. All rights reserved.
1. Introduction Motivation is ‘‘the process whereby goal-directed activity is instigated and sustained’’ and affects whether students engage or disengage in the classroom (Schunk, Pintrich, & Meece, 2007). Once considered a general trait, motivation is now studied multi-dimensionally, for example, through personal goal orientations (students’ reasons for engaging in domain-specific academic tasks), self-efficacy (belief in one’s ability to succeed in a particular situation), and task value (beliefs focus on the general question of ‘‘Why do I want to do this task?’’) constructs. Researchers note the importance of motivation during adolescence because adolescence is a critical period in children’s development when motivation begins to decline (Shim, Ryan, & Anderson, 2008; Wigfield, Byrnes, & Eccles, 2006). The current study examines adolescent mathematics motivation through the lens of personal goal orientations. The research question for the study is: which personal goal orientations—mastery, performance-approach, or performance-avoidance—predicts mathematics achievement among adolescents? Despite an array of methodologies—survey-based questionnaires, interviews, and classroom observations—previous studies have yielded mixed results on the links between goal orientations and achievement (Kaplan & Maehr, 2007; Linnenbrink-Garcia, Tyson, & Patall, 2008; Schunk et al., 2007). This study attempts to clarify this relationship by estimating the relationship between changes in goal orientations and changes in student standardized mathematics test scores for a cohort of middle school student in one California school district. Our analyses address two limitations ⇑ Corresponding author. Address: Department of Education, University of California, Irvine, 3200 Education, Irvine, CA 92697-5500, USA. E-mail address: [email protected] (T.D. Keys). 0361-476X/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.cedpsych.2011.09.002
that have plagued earlier studies of the relationship between goal orientations and achievement: First, we measure achievement directly, using student scores on the California Standards Test (CST) in mathematics. By contrast, earlier studies have relied upon indirect measures of student achievement, such as effort, grades, and GPA. Second, we study the relationship between goal orientations and achievement longitudinally, using three waves of motivation and achievement data gathered over two academic years. In the absence of experimental data, it is impossible to make strong causal claims regarding the effects of goal orientations. However, by measuring how changes in student goal orientations influence student achievement, this study provides estimates of the effects of achievement that are less subject to omitted variable bias than earlier cross-sectional studies. 1.1. Achievement goal theory Several decades of research suggests that goal orientations are one of the primary influences on achievement motivation (Ames, 1992; Atkinson, 1964; Covington, 2000; Dweck, 1986; Nicholls, 1984). A key behavioral outcome of goal orientations is actual achievement or performance, thus ideally goals should link to actual achievement (Schunk et al., 2007). Within the broad achievement goal theory framework there exist both contrasting and complementary perspectives (Maehr & Zusho, 2009). The motivation literature delineates the evolution of different but related achievement goal frameworks. They are (1) mastery versus performance, (2) approach versus avoidance, (3) trichotomous goal framework of mastery-approach, performance-approach, and performance-avoidance; and (4) the addition of mastery-avoidance to create the 2 2 model of achievement goals (Elliot, 1999; Elliot & McGregor, 2001; Maehr & Zusho, 2009).
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Researchers initially distinguished two broad goal orientations toward learning—mastery and performance. A student espousing a mastery goal orientation (also called learning or task goal orientation) focuses on learning, improving or developing new skills, mastering content, and trying to gain understanding or insight. In contrast, a student espousing a performance goal orientation (also called ego-involved, ability-focused, or competitive goal orientation) focuses on the desire to appear competent in the eyes of others by trying to demonstrate one’s competence by outperforming others, by seeking recognition for one’s performance, or by avoiding the appearance of incompetence (Anderman & Wolters, 2006; Elliot, 2005; Pintrich, 2000).
as setting unrealistically high goals, not working hard, procrastinating with homework, and cheating (Urdan, 2004). In summary, mastery goals theoretically have high intrinsic value but are not generally predictive of achievement related outcomes such as test scores and grades. Performance-approach goals can have a positive impact on achievement related outcomes such as grades; however, research has yielded mixed results on the associations between performance-approach goal orientation and achievement (Kaplan & Maehr, 2007). Finally, the association between performance-avoidance goals and achievement is almost always negative (Harackiewicz et al., 1998). 1.3. Two main perspectives: Traditional and multiple goal theory
1.2. Trichotomous goal framework This study examines the widely accepted trichotomous goal framework that includes mastery-approach, performance-approach, and performance-avoidance goal orientations. At the research design phase of our study project, the 2 2 model had much less empirical support whereas the trichotomous model was widely accepted among goal theorists (Linnenbrink-Garcia et al., 2008). The different goal orientations are not necessarily mutually exclusive; in fact, students can simultaneously endorse all three goal orientations. For example, students may want to improve their math skills (mastery) and impress the teacher (performance-approach) and not come across as dumb in math class (performance-avoidance). While a particular goal orientation may dominate, all three goals may be present within the same student (Pintrich, Conley, & Kempler, 2003). The literature on mastery goals is fairly consistent in showing that when students are mastery oriented, they are more highly engaged in learning, use deeper cognitive strategies, and are intrinsically motivated to learn (Anderman & Wolters, 2006; Dweck & Leggett, 1988; Harackiewicz, Barron, & Elliot, 1998; Kaplan & Maehr, 2007; Kaplan & Midgley, 1997; Pintrich, 2000; Utman, 1997). However, some studies have found mastery goals to be unrelated to achievement (Elliot & Church, 1997; Elliot, McGregor, & Gable, 1999; Harackiewicz et al., 1998). For example, Harackiewicz and colleagues (1998) have found that mastery goals are associated with more interest and intrinsic motivation while performance-approach goals are associated with better performance and extrinsic motivation. Exceptions to these general findings are with more recent studies that suggest that the impact of achievement goals depends on how the goals are operationalized (Grant & Dweck, 2003) or whether within-year rather than between-year development of goals and achievement are examined (Shim et al., 2008). The literature on performance goals is less consistent, in part because earlier work in this area did not distinguish between the approach- and avoidance-forms of performance goals (Elliot, 2005). Since earlier studies found mixed results on the relation between performance goals and other motivation, cognitive, and behavior outcomes, researchers further differentiated between performance-approach and performance-avoidance goal orientations (Elliot & Church, 1997; Harackiewicz et al., 1998). Among college students, performance-approach goals are positively associated with performance and other motivation constructs such as academic self-concept and task value, but not associated with interest or intrinsic motivation (Harackiewicz, Barron, Pintrich, Elliot, & Thrash, 2002). Other students are motivated to avoid failure and looking incompetent, reflecting a performance-avoidance goal orientation. Researchers find that performance-avoidance goals have negative consequences for students’ motivation and learning (Elliot & Harackiewicz, 1996; Middleton & Midgley, 1997; Skaalvik, 1997) and are correlated with self-handicapping, or deliberately creating obstacles that reduce one’s probability of success such
According to traditional goal theory (also referred to as normative or mastery goal theory), mastery goals are beneficial while performance goals, under certain conditions, are detrimental to learning. The differentiation of performance-approach and performance-avoidance goals, and the evidence demonstrating that performance-approach goals can relate to positive motivation and achievement outcomes, have led some researchers to call for a revision of goal theory (Harackiewicz et al., 1998; Pintrich, 2000). Traditional and multiple goal perspectives agree on the negative effects of performance-avoidance goals; where they differ is their views of the effects of performance-approach goals. Multiple goal theory (also referred to as revised goal theory) contends that both mastery and performance-approach goals can be beneficial, pointing out that whether goals are adaptive depends on the context. While some advocate for a revision (Harackiewicz et al., 1998; Pintrich, 2000), others (Midgley, Kaplan, & Middleton, 2001) disagree with the call to revise goal theory. Traditionalists argue that the basic assumption that mastery goals are adaptive and performance goals are maladaptive is the best generalization for goal theory. They argue that the findings for the positive associations for performance-approach goal orientation are limited to very particular cases such as when students are high in mastery goals and performance-approach goals (Pintrich, 2000) or in competitive college classrooms where there may be benefits to adopting performance goals (Harackiewicz et al., 1998). Midgley and colleagues (2001) acknowledge that although students with performance-approach goals may have higher grades or test scores than students who have mostly mastery goals, performance oriented students do not learn as deeply. Test scores often reward rote memorization and superficial recall of facts and therefore guide students away from the more important deeper thought processes. Also, they note that performance-approach goals may benefit boys rather than girls and older rather than younger students, thus the multiple goal perspective does not adequately encompass all learners (Midgley et al., 2001). 1.4. Achievement outcome Unlike the vast majority of achievement goal studies, our study used a standardized measure of student achievement in grade-level course content, to investigate the association between goals and achievement. In a recent comprehensive literature review of peer-reviewed journal articles on the achievement effects of mastery and performance-approach goal orientations (LinnenbrinkGarcia et al., 2008), the vast majority of outcome variables examined in the non-experimental studies were students’ course grades. Since individual teachers assign grades independently, often without reference to commonly agreed-upon rubrics, grades are a more subjective outcome measure than an end-of-year standardized assessment. Course grades are often heavily dependent on compliance (e.g. turning in homework), behavior, and other non-academic considerations, rather than more direct measures of
T.D. Keys et al. / Contemporary Educational Psychology 37 (2012) 47–54
student achievement or learning (Randall & Engelhard, 2009). As such, grades correlate weakly with student achievement. In our sample, student grades correlate with student test scores at the 0.20 level, and for some teachers in our sample, grades are entirely uncorrelated with student test scores. Therefore, we argue that standardized test scores – particularly those that are linked to well-known state standards for instruction – measure student achievement far more reliably than do grades. 2. Research questions and hypotheses Our research question is: Which personal goal orientations—mastery, performance-approach, or performance-avoidance—predict mathematics achievement among adolescents? The review of the achievement goal motivation literature reveals a consensus that, generally, a mastery goal orientation is adaptive while a performanceavoidance goal orientation is maladaptive. What still remains debated among goal theorists is the effect of the performance-approach goal orientation. Our hypotheses are as follows: Hypothesis 1. Given the strong theoretical support in the literature, a personal mastery goal orientation is expected to be a significant positive predictor of mathematics achievement. Hypothesis 2. Owing to conflicting findings in the literature, no explicit hypothesis is offered regarding the effects of a performance-approach goal orientation. An exploratory position is taken to examine the association between a performance-approach goal orientation and mathematics achievement for this ethnically diverse sample. Hypothesis 3. Given the strong theoretical support in the literature, a personal performance-avoidance goal orientation is expected to be a significant negative predictor of achievement.
3. Method 3.1. Model The conceptual model of achievement that guides our empirical analysis views mathematics achievement as a product of past levels of student motivation and other determinants. Suppose we have two schooling periods (1 and 2). Suppose further that the achievement of student i at the end of period 1 can be expressed as:
Ach1i ¼ a1 þ b1 RMotivation1i þ c1 Z i þ e1i
ð1Þ
In (1), RMotivation1 is the average level of motivation across period 1 and Z are other determinants of achievement. Estimating (1) with cross-sectional data is problematic because of the potential biases in b1 arising from difficult-to-measure components of Z – such as classroom dynamics, peer effects, and family approaches to education – that are correlated with both motivation and achievement. But now suppose that the determinants of achievement measured later in school, at the end of period 2, have a similar structure:
Ach2i ¼ a2 þ b1 ½RMotivation1i þ RMotivation2i þ c1 Z i þ e2i
ð2Þ
In this case, later achievement is the product of both recent and more distant levels of motivation. Using ‘‘D’’ to denote changes, subtracting (1) from (2) gives:
DAchi ¼ Da þ b1 RMotivation2i þ De2i
ð3Þ
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In this equation, changes in achievement between the ends of periods 1 and 2 are a product of the average level of motivation across period 2. The possible influences of time-invariant Z characteristics (both measureable and not) are differenced out of (3), which is likely to produce an estimate of the effect of motivation on achievement that is less biased than would be the case in the cross-sectional estimation of Eq. (1). Eq. (3) is the basis for our empirical work. We estimate (3) as a ‘‘residualized change’’ model by using time 2 achievement as the dependent variable and time 1 achievement as a predictor, but interpret b1 as relating average motivational levels during period 2 to achievement changes between the ends of periods 1 and 2. We also ran a simple change model (by subtracting time 1 achievement from time 2 achievement) and the association between goal orientations and mathematics achievement were nearly identical to the results in our residualized change model. 3.2. Procedure The data for the study came from the California Motivation Project—Mathematics (CAMP-Math). CAMP-Math is part of the larger National Science Foundation-funded Math and Science Partnership – Motivation Assessment Program (MSP–MAP) that studies the role of motivation-related beliefs in students’ achievement in mathematics and science (Conley, 2011). Although the program provided professional development for teachers, for the current study, student motivation data were collected before this development occurred. Passive consent was received by letters to parents. Less than one percent of the larger study sample chose not to participate in the survey. Researchers informed the students that the purpose of the survey was to get their confidential opinions about mathematics in general and their current mathematics class in particular. Students took approximately 30 minutes to complete the paper-and-pencil survey. Student motivation surveys were administered roughly 4 weeks after the beginning of the school year and roughly 4 weeks before the end of the school year in both the 2004–2005 and 2005–2006 academic years. Student achievement and demographic data were obtained from district annual testing records. Consistent with model (3), above, the analysis presented in this paper relates levels of motivation (using the average of three waves of motivation surveys that were measured prior to the achievement outcome) in these two school years to achievement changes from the beginning to the end of the 2-year period. 3.3. Sample The analyses presented in this study were on 2231 students (1185 in 7th grade and 1046 in 8th grade) from four middle schools in an urban school district in California in 2004–2006. The sample was fairly evenly split by gender (1104 males and 1127 females) with the average age of 12.5 years (SD = 0.16). Only White (6%), Hispanic (73%), and Vietnamese (20%) students were included in the analysis as the other ethnic groups (1%) were too small numerically to include in subgroup comparisons. We controlled for White, Hispanics and Vietnamese students separately (that is, letting the intercept differ between the groups) by including race/ethnicity dummies to account for achievement differences. The subgroup analyses suggest that the relationship between motivation and achievement does not differ across these groups, so our models, in fact, are capturing reality. Students from these three racial/ethnic backgrounds were included in the analysis if they met all of the following criteria: (1) student had valid mathematics test scores in both Spring of 2004 and 2006, (2) student had at least one valid score on each of the three motivation measures on personal goal orientations—mastery, performance-approach, and performance-avoidance and (3) student took the General Math,
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Table 1 Descriptive statistics for study sample (N = 2231 students). # Valid obs.
Mean/%
SD
Gender Male
1104
49%
0.50
Race/ethnicity White Hispanic Vietnamese
143 1639 449
6% 73% 20%
0.24 0.44 0.40
Free/reduced lunch status
1691
76%
0.43
English learner status
1149
52%
0.50
Grade-level Grade 7 Grade 8
1185 1046
53% 47%
0.50 0.50
954 914 363
43% 41% 16%
0.49 0.49 0.37
Goal orientation Mastery Performance-approach Performance-avoidance
3.68 2.54 2.22
Math achievement Math achievement – 2004 Math achievement – 2006
342.79 335.25
Math test taken General Math Algebra 1 Geometry
Min.
Max.
0.83 0.93 0.83
1 1 1
5 5 5
57.06 54.34
202 185
600 569
Notes: Motivation scales = 1–5; Math scale score range = 150–600, 350 = Proficient.
Algebra I, or Geometry test in 2006. Approximately 11% of the sample was missing achievement data for Spring 2004 and 12% of the sample was missing data for Spring 2006. According to the California Department of Education (2009), the school district in the study is a large urban unified school district with over 50,000 K-12 students enrolled during 2004–2005. More than half of the students in the district are Hispanic (52%) and it is clear from discussions with district and county officials that the overwhelming majority of Hispanic students are of Mexican descent. Regardless, the broader Hispanic label is used throughout the paper since that is how the demographic data are reported. About one third of students in the district are of Asian/Pacific Islander/Filipino (31%) descent, nearly all of whom are of Vietnamese descent. Whites are a minority in this district (16%). Approximately 47% of the district is composed of English learners with Spanish and Vietnamese as the primary non-English languages spoken in the home. Approximately 61% of the district student body participates in the National School Lunch Program (NSLP) where low income students receive free or reduced-priced meals. Lacking an actual socioeconomic status (SES) measure such as income, the current study follows suit with other studies that use students’ participation status in the NSLP as a proxy for SES. A detailed summary description of the study sample can be found in Table 1. 3.4. Measures The outcome variable in the study was the student’s 2006 mathematics achievement. The predictors were the three personal goal orientations—mastery, performance-approach, and performance-avoidance. Controls included prior mathematics achievement, gender, race/ethnicity, free/reduced lunch status, English Learner status, grade-level, and mathematics class taken in 2006. Importantly, we also control for both measurable and unmeasurable differences across classrooms by including dummy variables, one per classroom in our most complete regression models. This so-called classroom fixed effects adjustment is explained in greater detail below.
3.4.1. Outcome variable—student achievement Academic achievement was assessed with the mathematics scaled score on the California Standards Tests (CSTs). The CSTs are annual state-mandated tests for students in grades 2–11 in all California public schools and measures student performance on California’s content standards by identifying students who achieve at each performance level: advanced, proficient, basic, below basic, or far below basic (California Department of Education, 2009). The state’s target is for all students to score at or above the proficient performance level. The CSTs are high-stakes at the school and district level because the results are used in both state and federal accountability calculations (California Department of Education, 2009). Scale scores range from a low of 150 to a high of 600 with 350 as the cutoff for proficiency or meeting state standards. The 2006 mathematics scale score was the dependent variable measuring achievement outcome. The 2004 mathematics scale score served as the student’s prior mathematics achievement score. This lagged achievement helps to control for omitted variable bias (NICHD ECCRN & Duncan, 2003). With prior achievement controlled the analysis amounts to a study of changes in achievement across the 2-year period. Beginning in eighth grade, the CST mathematics tests are mathcourse specific. Only students who took grade-level mathematics in 2004 and the General Math, Algebra I, or Geometry CST exam in 2006 were included in the analysis. These students were considered to be progressing normally through the district’s middle school mathematics sequence. As such, this study focuses on achievement for students with normative mathematics course trajectories. The 89 students who took a more advanced Algebra II exam in 2006 represented approximately 3% of the sample. As a proxy for test difficulty, CST math test taken in 2006 (whether General Math, Algebra I, or Geometry) was included as a series of dummy variables in the regressions. 3.4.2. Predictor variables—student motivation scores The three achievement goal scales were adapted for the domain of mathematics from Midgley and colleagues’ (2000) widely-used Patterns of Adaptive Learning Survey (PALS) instrument and measures mastery, performance-approach, and performance-avoidance goal orientations. All three goal orientation constructs were scored on a 5-point Likert scale ranging from 1 (not at all true for me) to 5 (very true for me). Items included ‘‘really understanding my math work is important to me’’ (mastery), ‘‘it’s important to me that others think I am good at doing math’’ (performance-approach), and ‘‘it’s important to me that I don’t look stupid in math class’’ (performance-avoidance). Individual items in the specific goal constructs were averaged and a final score from 1 to 5 was created. The relatively high alpha coefficients (.78–.88) on all three scales suggest that the items in each of the goal orientation scales are measuring the same construct. Next, an average of each of the goal orientation variables was computed across the first three of the four data collection periods (i.e. waves) that were collected at baseline and before the outcome. The fourth wave was excluded because it coincided with the time when the outcome variable (2006 math achievement) was measured. It was these three-wave average scores that were used in the analysis. A complete listing of the items measuring the three goals and their reliabilities can be found in Table 2. 3.4.3. Control variables Besides prior achievement, several other student-level covariates were included in the study. Gender was a dummy variable, coded 1 for male and 0 for female. Race/ethnicity categories were Hispanic, White, and Vietnamese. Participation in the National School Lunch Program (NSLP) served as a proxy for SES. The NSLP variable was coded 1 for yes and 0 for no. English learner (EL)
T.D. Keys et al. / Contemporary Educational Psychology 37 (2012) 47–54 Table 2 Motivation survey items and cronbach’s alpha for personal goal orientations. Scale and items
Reliability
Personal goal orientation: Mastery approach Learning a lot of new things is what is important to me in math One of my main goals in math is to improve my skills My main goal in math is to learn as much as I can Really understanding my math work is important to me Learning new skills in math is one of my goals
a = .86–.88
Personal goal orientation: Performance-approach In math, doing better than other students is important to me My goal in math is to look smarter than other students One of my goals is to show others that math is easy for me It’s important to me that others think I am good at doing math My goal in math is to do better than other students
a = .82–.86
Personal goal orientation: Performance-avoidance My goal is to keep others from thinking I’m not smart in math It’s important to me that I don’t look stupid in math class An important reason I do my math work is so that I don’t embarrass myself I do my math work so that my teacher doesn’t think I know less than others My goal in math is to avoid looking like I can’t do my work
a = .78–.82
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estimated links between motivation and achievement are based solely on within-classroom variation in dependent and independent variables. Their focus on within-classroom variation also obviates the need for multi-level modeling. 4. Results
Notes: The range for scale reliability is reported given the multiple waves (totaling 4) of motivation surveys in the study. Source: Midgley et al. (2000).
status was a dummy variable coded 1 for EL and 0 for non-EL. Approximately half of the sample was made up of English learners. The grade-level variable identifies whether the student was in seventh or eighth grade in the 2004–2005 school year. Finally, math test taken identified whether the student took the General Math, Algebra I, or Geometry test in 2006. Each was coded 1 or 0 depending on whether or not the student took the particular mathematics test. 3.5. Analysis In terms of our model (3), we consider the end of the 2004– 2005 and 2005–2006 academic years as period 2 and the prior school years to be period 1. This led us to regress a student’s spring, 2006 mathematics achievement on 3-wave averages of middle school (across the 2004–2005 and 2005–2006 academic years) achievement goal orientations (mastery, performance-approach, and performance-avoidance), baseline (spring, 2004) mathematics achievement, a set of demographic controls, and type math test taken. Consistent with model (3), we use the averages of the three motivation scores rather than growth across the three waves of these motivation data as our key independent variables. To allow for comparability across the different units of measurement of different variables, the regression analysis was based on standardized achievement and motivation variables. The individual goal scales were standardized before taking the average of the three waves. In a lagged dependent variable model such as ours, the later outcome assessment is used as the dependent variable while the early assessment becomes an explanatory variable. This analysis approach has been used by other researchers to adjust for observed and unobserved selection factors (NICHD & Duncan, 2003). Finally, time-invariant classroom characteristics were controlled in the analysis with classroom fixed effects, which amounts to including dummy variables for all but one classroom (using Stata’s xtreg command). Adjusting for classroom fixed effects is a powerful method for minimizing biases arising from non-random assignment of teachers and students to schools and classrooms (Schneider, Carnoy, Kilpatrick, Schmidt, & Shavelson, 2007). In effect, the fixed effects adjustment ensures that the
The means, standard deviations, and score ranges for the three goal orientation variables and two achievement variables measured in the study are reported in Table 1. Of the three goal orientations, mastery had the highest 3-wave average compared to performance-approach and performance-avoidance for the overall sample. Table 3 presents correlations among variables of interest in our study. Correlations among variables for the total sample showed that mastery orientation was positively and moderately correlated with performance-approach (r = .39) and performance-avoidance (r = .17) goal orientations. Also, performance-approach and performance-avoidance goal orientations were strongly positively correlated to each other (r = .56). All three correlations were significant at p < 0.001 level. The significant correlations among the three goal measures are not surprising, given the range of correlations found in previous research using similar scales such as with Murayama and Elliot’s (2009) Japanese version of the Achievement Goal Questionnaire (mastery and performance approach, r = .40; mastery and performance-avoidance, r = .21; performance-approach and performance-avoidance, r = .61). The correlations between mathematics achievement in 2006 (the dependent variable) and the individual goal orientations generally conformed to the study hypotheses. That is, mastery had a mild positive correlation with achievement, there was no correlation between performance-approach and achievement, and performance-avoidance had a very slight negative correlation with achievement. Table 4 presents the regression results for goal orientations predicting mathematics achievement. Models 1, 2, and 3 report the bivariate regressions or the effect of each goal orientation on achievement. With all the variables standardized, these coefficients represent a measure of effect size. A one standard deviation increase in mastery goal orientation was associated with a 0.13 standard deviation increase in achievement (p < 0.001). A one standard deviation increase in performance-approach was associated with a 0.05 standard deviation increase in achievement (p < 0.05) whereas a one standard deviation increase in performance-avoidance yielded a 0.05 standard deviation decrease in achievement (p < 0.05). Model 4 included all three goal orientations in the same regression but no covariates. In Model 4 performance-avoidance had a larger regression coefficient (0.11, p < 0.001). In fact, the performance-avoidance coefficient and standard error were very similar with mastery in this model, but predicting achievement in opposite directions. Along with all three goal orientations, Model 5 included prior mathematics achievement, the full set of demographic (gender, race/ethnicity, free/reduced lunch status, English learner status, grade level), and math test taken controls. The reference categories were female, Hispanic, Grade 7, and General Math. The size of the coefficient for mastery fell to 0.09 but remained statistically significant at the most conservative level (p < 0.001). Performance-approach and performance-avoidance were no longer predictive of achievement in Model 5. 5. Discussion 5.1. Mastery goal orientation Study results suggest that mastery was the only goal orientation that consistently predicted mathematics achievement. That is,
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Table 3 Correlations among variables for total sample (N = 2231).
1. 2. 3. 4. 5. 6. 7. 8. 9. * ***
Mastery Performance-approach Performance-avoidance Male Hispanic Vietnamese White Math achievement in 2004 Math achievement in 2006
1
2
3
4
5
6
7
8
9
1 0.39*** 0.17*** 0.12*** 0.04 0.09*** 0.07*** 0.09*** 0.15***
1 0.56*** 0.03 0.05* 0.03 0.13*** 0.03 0.02
1 0.09*** 0.07*** 0.05* 0.04 0.14*** 0.08***
1 0.01 0.02 0.05* 0.02 0.00
1 0.84*** 0.44*** 0.33*** 0.31***
1 0.13*** 0.34*** 0.34***
1 0.04 0.00
1 0.67***
1
p < 0.05. p < 0.01. p < 0.001.
Table 4 Standardized regression results for goal orientations predicting mathematics achievement. Dependent variable = 2006 math achievement (1) Goal orientation Mastery
(2)
(3)
(4)
(5)
0.05* (0.02)
0.12*** (0.02) 0.07* (0.03) 0.11*** (0.03)
0.09*** (0.02) 0.02 (0.02) 0.02 (0.02)
0.13*** (0.02) 0.05* (0.02)
Performance-approach Performance-avoidance Controls Prior math achievement (2004)
Constant
0.02 (0.02)
0.02 (0.02)
0.02 (0.02)
0.02 (0.02)
0.68*** (0.02) 0.04 (0.03) – – 0.08 (0.07) 0.39*** (0.04) 0.07 (0.04) 0.06 (0.04) – – 0.04 (0.05) – – 0.07 (0.04) 0.51*** (0.11) 0.01 (0.06)
N R2
1985 0.018
1985 0.003
1985 0.003
1985 0.027
1985 0.454
Male Race/ethnicity (Reference category = Hispanic) White Vietnamese Free/reduced lunch status (1 = yes, 0 = no) English Learner Status (1 = yes, 0 = no) Grade level (Reference category = Grade 7) Grade 8 Math test taken (Reference category = General Math) Algebra 1 Geometry
Notes: Standard errors in parentheses; time-invariant classroom characteristics are controlled in the analysis with classroom ‘‘fixed effects’’, which amounts to including dummy variables for all but one classroom (using Stata’s xtreg command). Fixed effects estimates are based solely on within-classroom variation in dependent and independent variables. * p < 0.05. p < 0.01. *** p < 0.001.
students who maintain higher levels of mastery goals had the largest gains in achievement in this sample. This finding was expected given the strong theoretical support on the positive effects of mastery goals in the achievement motivation literature. This finding, however, is not completely consistent with results from other studies (e.g., Maehr & Zusho, 2009) suggesting that mastery goals
do not always predict achievement. That the current study found a positive association of mastery on achievement while other studies did not may speak to the distinctiveness of our methods or sample. Most previous studies focused on White students, whereas the current study was composed of predominantly Hispanic and Vietnamese students. In addition, we used a measure of mathe-
T.D. Keys et al. / Contemporary Educational Psychology 37 (2012) 47–54
matics achievement that was aligned with course content standards and available across multiple years. 5.2. Performance-approach goal orientation No significant associations for performance-approach goal orientation were found. The null result for performance-approach was not surprising. There are inconsistent findings in the literature, with some studies finding positive associations, other studies finding negative associations, and still other studies finding no associations (Harackiewicz et al., 2002; Linnenbrink-Garcia et al., 2008; Urdan, 2004). The ongoing debate over traditional and multiple goal theory perspectives centers on the potential positive potential of performance-approach goals for some individuals in certain types of situations (Harackiewicz et al., 1998; Middleton, Kaplan, & Midgley, 2004; Midgley et al., 2001; Pintrich, 2000). Given that this study sampled widely in all normative mathematics classes and across the entire range of students, the null finding is in line with the debates in the literature. 5.3. Performance-avoidance goal orientation We hypothesized that performance-avoidance goal orientation would be a significant negative predictor of achievement. Study results suggest that students’ performance-avoidance goal orientation was not predictive of their mathematics achievement. This finding was unexpected, given the consistent findings in the literature on the negative effects of espousing a performance-avoidance goal orientation. It is important to note that the literature has focused mostly on White students whereas our sample is composed of mostly Hispanic and Vietnamese students. Several studies have documented that Asian Americans adopt more performanceavoidance goals than non-Asian Americans, although with Asian Americans, these goals are not always predictive of achievement outcomes (Elliot, Chirkov, Kim, & Sheldon, 2001; Murdock, 2009; Witkow & Fuligni, 2007; Zusho, Pintrich, & Cortina, 2005). Researchers offer the explanation that the Asian (and to a lesser degree, Asian American) cultures have a high degree of familial obligation, which in turn triggers fear of failure thoughts that are characteristic of performance-avoidance goals (Chen & Stevenson, 1995; Witkow & Fuligni, 2007). A strong sense of familial obligation is also true of the Hispanic culture (Feliciano & Rumbaut, 2005; Kao & Tienda, 1995; Urdan & Giancarlo, 2001); however, performance-avoidance goals are not as strong with Hispanics as with Asian groups (Witkow & Fuligni, 2007). A possible explanation for our unexpected findings is that validation studies of the widely-used PALS instrument (Midgley et al., 2000) have not, to date, included Hispanic or Asian samples. The ethnically diverse sample in the validation studies conducted by the PALS instrument creators were primarily on African American students. It is our conjecture that our predominantly Hispanic and Asian sample, specifically of Mexican and Vietnamese descent are quite different from other achievement motivation studies that are on Whites and African American students.
53
achievement, net of the potentially confounding influence of omitted student characteristics. Our analyses, which investigate the relationship between changes in student goal orientations and changes in student achievement, therefore provide relatively unbiased estimates of the consequences of goal orientations for student learning. In addition, our data provide relatively precise estimates of the relationship between goal orientations and achievement and in a more ethnically and socio-economically diverse setting than earlier studies. While the majority of studies are limited by small sample sizes (Barron & Harackiewicz, 2001), this study included approximately 2000 participants. Larger sample size translates to smaller sampling error and estimates that are less likely to be influenced by a few unusual cases or missing values (Allison, 1999). This study also has several limitations and suggestions for future research. First, our sample was made up of seventh and eighth graders from four middle schools from a single urban California school district. More studies on districts with similar demographic characteristics need to be conducted to see if results are replicable. Second, we know little about how motivation matters for non-Whites since the vast majority of motivation research is conducted on middle class White students (Urdan & Giancarlo, 2001); therefore, more research is needed on minority groups. We suggest that PALS validation studies be performed on Hispanic and Asian samples to determine if goal orientations relate the same way with different population subgroups. Finally, the study did not focus on the role of SES because our study was only able to use a proxy for SES (i.e. the free/reduced lunch measure). There are plans to collect more accurate and sophisticated SES measures for future analysis.
6. Conclusion In summary, the current study examined the association between students’ personal goal orientations and mathematics achievement. While all three achievement goal orientations were correlated with mathematics achievement, only a mastery goal orientation consistently predicted achievement when a full set of prior achievement and demographic controls were included. Performance-approach and performance-avoidance goal orientations did not predict achievement in the full model. Achievement goal theory provides a useful explanatory framework that assumes that goals are not just stable personal traits, but rather that goals can be shaped by the teacher and learning environment (Schunk et al., 2007). The relation between the different personal goal orientations and positive academic outcomes remains a contested issue. Our results suggest that (1) a full complement of demographic controls, and (2) achievement measures that precede and follow the motivation assessments are important for demonstrating the theoretically-predicted relations between achievement goals and mathematics achievement.
5.4. Study contributions, limitations, and future research
Acknowledgments
The present study contributes to the literature in two important ways. First, unlike most other achievement goal studies, this study used standardized scores of student achievement (rather than teacher-assigned grades) to investigate the association between goals and achievement. Doing so allows us to directly investigate the relationship between student goal orientations and student achievement, without the subjective and behavioral biases that exist in teacher-assigned grades. Second, our longitudinal data provides a look at the relationship between goal orientation and
The California Motivation Project (CAMP-Math) data collection was supported in part by a grant to the Math Science Partnership–Motivation Assessment Program (PIs Stuart Karabenick and Martin Maehr) from the National Science Foundation (No. EHR0335369). The findings and views reported in this manuscript are the authors’ and do not necessarily reflect the views of the National Science Foundation. The authors would like to thank the editor and three anonymous reviewers for their helpful comments on earlier drafts of this article.
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References Allison, P. D. (1999). Multiple regression: A primer. CA: Pine Forge Press, Thousand Oaks. Ames, C. (1992). Classrooms: Goals, structures, and student motivation. Journal of Educational Psychology, 84, 261–271. Anderman, E. M., & Wolters, C. A. (2006). Goals, values, and affect: Influences on student motivation. In P. Alexander & P. Winne (Eds.), Handbook of educational psychology (2nd ed., pp. 369–389). Mahwah, NJ: Erlbaum. Atkinson, J. W. (1964). An introduction to motivation. Princeton, NJ: Van Nostrand. Barron, K., & Harackiewicz, J. (2001). Achievement goals and optimal motivation: Testing multiple goal models. Journal of Personality and Social Psychology, 80, 706–722. California Department of Education (2009). DataQuest.
effects and moderating factors. International Review of Social Psychology, 21, 19–70. Maehr, M. L., & Zusho, A. (2009). Achievement goal theory: The past, present, and future. In K. R. Wentzel & A. Wigfield (Eds.), Handbook of motivation at school (pp. 77–104). New York: Taylor Francis. Middleton, M. J., Kaplan, A., & Midgley, C. (2004). The change in middle school students’ achievement goals in mathematics over time. Social Psychology of Education, 7, 289–311. Middleton, M. J., & Midgley, C. (1997). Avoiding the demonstration of lack of ability: An under-explored aspect of goal theory. Journal of Educational Psychology, 89, 710–718. Midgley, C., Kaplan, A., & Middleton, M. (2001). Performance-approach goals: Good for what, for whom, under what circumstances, and at what cost? Journal of Educational Psychology, 93, 77–86. Midgley, C., Maehr, M. L., Hruda, L. Z., Anderman, E. M., Anderman, L., Freeman, K. E., et al. (2000). Manual for the patterns of adaptive learning scales (PALS). Ann Arbor, MI: University of Michigan. Murayama, K., & Elliot, A. J. (2009). The joint influence of personal achievement goals and classroom goal structures on achievement-relevant outcomes. Journal of Educational Psychology, 101, 432–447. Murdock, T. B. (2009). Achievement motivation in racial and ethnic context. In K. R. Wentzel & A. Wigfield (Eds.), Handbook of motivation at school (pp. 433–461). New York: Taylor Francis. NICHD Early Child Care Research Network & Duncan, G. J. (2003). Modeling the impacts of child care quality on children’s preschool cognitive development. Child Development, 74, 1454–1475. Nicholls, J. G. (1984). Achievement motivation: Conceptions of ability, subjective experience, task choice, and performance. Psychological Review, 91, 328–346. Pintrich, P. R. (2000). Multiple goals, multiple pathways: The role of goal orientation in learning and performance. Journal of Educational Psychology, 92, 544–555. Pintrich, P. R., Conley, A. M., & Kempler, T. (2003). Current issues in achievement goal theory and research. International Journal of Educational Research, 319, 337. Randall, J., & Engelhard, G. (2009). Examining teacher grades using rasch measurement theory. Journal of Educational Measurement, 46, 1–18. Schneider, B., Carnoy, M., Kilpatrick, J., Schmidt, W. H., & Shavelson, R. J. (2007). Estimating causal effects using experimental and observational designs (report from the Governing Board of the American Educational Research Association Grants Program). Washington, DC: American Educational Research Association. Schunk, D. H., Pintrich, P. R., & Meece, J. (2007). Motivation in education: Theory, research and applications (3rd ed.). Upper Saddle River, NJ: Merrill Prentice-Hall. Shim, S., Ryan, A., & Anderson, C. (2008). Achievement goals and achievement during early adolescence. Examining time-varying predictor and outcome variables in growth-curve analysis. Journal of Educational Psychology, 100, 655–671. Skaalvik, E. M. (1997). Self-enhancing and self-defeating ego orientation: Relations with task and avoidance orientation, achievement, self-perceptions, and anxiety. Journal of Educational Psychology, 89, 1–11. Urdan, T. (2004). Predictors of self-handicapping and achievement: Examining achievement goals, classroom goal structures, and culture. Journal of Educational Psychology, 96, 251–254. Urdan, T., & Giancarlo, C. (2001). A comparison of motivational and critical thinking orientations across ethnic groups. In D. M. McInerney & S. V. Etten (Eds.). Research on sociocultural influences on motivation and learning (Vol. 1, pp. 37–60). Greenwich, CT: Information Age Publishing. Utman, C. H. (1997). Performance effects of motivational state: A metaanalysis. Personality and Social Psychology Review, 1, 170–182. Wigfield, A., Byrnes, J. P., & Eccles, J. S. (2006). Development during early and middle adolescence. In P. Alexander & P. Winne (Eds.), Handbook of educational psychology (2nd ed., pp. 369–389). Mahwah, NJ: Erlbaum. Witkow, M., & Fuligni, A. (2007). Achievement goals and daily school experiences among adolescents with Asian, Latino, and European American backgrounds. Journal of Educational Psychology, 99, 584–596. Zusho, A., Pintrich, P. R., & Cortina, K. S. (2005). Motives, goals, and adaptive patterns of performance in Asian American and Anglo American students. Learning and Individual Differences, 15, 141–158.
Contents lists available at SciVerse ScienceDirect
Contemporary Educational Psychology journal homepage: www.elsevier.com/locate/cedpsych
The role of goal orientations for adolescent mathematics achievement Tran D. Keys ⇑, AnneMarie M. Conley, Greg J. Duncan, Thurston Domina Department of Education, University of California, Irvine, USA
a r t i c l e
i n f o
Article history: Available online 17 September 2011 Keywords: Achievement goal theory Goal orientations Mathematics achievement
a b s t r a c t This study examines the association between personal goal orientations and mathematics achievement within the trichotomous goal framework. Participants comprised approximately 2000 seventh and eighth grade White, Hispanic, and Vietnamese students in a low-income urban school district in California. Regression analysis with classroom fixed effects minimized biases arising from non-random assignment of teachers and students to schools and classrooms. While all three achievement goal orientations were correlated with mathematics achievement, only a mastery goal orientation consistently predicted achievement when a full set of prior achievement and demographic controls were included. Performance-approach and performance-avoidance goal orientations did not predict achievement in the full model. Ó 2011 Elsevier Inc. All rights reserved.
1. Introduction Motivation is ‘‘the process whereby goal-directed activity is instigated and sustained’’ and affects whether students engage or disengage in the classroom (Schunk, Pintrich, & Meece, 2007). Once considered a general trait, motivation is now studied multi-dimensionally, for example, through personal goal orientations (students’ reasons for engaging in domain-specific academic tasks), self-efficacy (belief in one’s ability to succeed in a particular situation), and task value (beliefs focus on the general question of ‘‘Why do I want to do this task?’’) constructs. Researchers note the importance of motivation during adolescence because adolescence is a critical period in children’s development when motivation begins to decline (Shim, Ryan, & Anderson, 2008; Wigfield, Byrnes, & Eccles, 2006). The current study examines adolescent mathematics motivation through the lens of personal goal orientations. The research question for the study is: which personal goal orientations—mastery, performance-approach, or performance-avoidance—predicts mathematics achievement among adolescents? Despite an array of methodologies—survey-based questionnaires, interviews, and classroom observations—previous studies have yielded mixed results on the links between goal orientations and achievement (Kaplan & Maehr, 2007; Linnenbrink-Garcia, Tyson, & Patall, 2008; Schunk et al., 2007). This study attempts to clarify this relationship by estimating the relationship between changes in goal orientations and changes in student standardized mathematics test scores for a cohort of middle school student in one California school district. Our analyses address two limitations ⇑ Corresponding author. Address: Department of Education, University of California, Irvine, 3200 Education, Irvine, CA 92697-5500, USA. E-mail address: [email protected] (T.D. Keys). 0361-476X/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.cedpsych.2011.09.002
that have plagued earlier studies of the relationship between goal orientations and achievement: First, we measure achievement directly, using student scores on the California Standards Test (CST) in mathematics. By contrast, earlier studies have relied upon indirect measures of student achievement, such as effort, grades, and GPA. Second, we study the relationship between goal orientations and achievement longitudinally, using three waves of motivation and achievement data gathered over two academic years. In the absence of experimental data, it is impossible to make strong causal claims regarding the effects of goal orientations. However, by measuring how changes in student goal orientations influence student achievement, this study provides estimates of the effects of achievement that are less subject to omitted variable bias than earlier cross-sectional studies. 1.1. Achievement goal theory Several decades of research suggests that goal orientations are one of the primary influences on achievement motivation (Ames, 1992; Atkinson, 1964; Covington, 2000; Dweck, 1986; Nicholls, 1984). A key behavioral outcome of goal orientations is actual achievement or performance, thus ideally goals should link to actual achievement (Schunk et al., 2007). Within the broad achievement goal theory framework there exist both contrasting and complementary perspectives (Maehr & Zusho, 2009). The motivation literature delineates the evolution of different but related achievement goal frameworks. They are (1) mastery versus performance, (2) approach versus avoidance, (3) trichotomous goal framework of mastery-approach, performance-approach, and performance-avoidance; and (4) the addition of mastery-avoidance to create the 2 2 model of achievement goals (Elliot, 1999; Elliot & McGregor, 2001; Maehr & Zusho, 2009).
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Researchers initially distinguished two broad goal orientations toward learning—mastery and performance. A student espousing a mastery goal orientation (also called learning or task goal orientation) focuses on learning, improving or developing new skills, mastering content, and trying to gain understanding or insight. In contrast, a student espousing a performance goal orientation (also called ego-involved, ability-focused, or competitive goal orientation) focuses on the desire to appear competent in the eyes of others by trying to demonstrate one’s competence by outperforming others, by seeking recognition for one’s performance, or by avoiding the appearance of incompetence (Anderman & Wolters, 2006; Elliot, 2005; Pintrich, 2000).
as setting unrealistically high goals, not working hard, procrastinating with homework, and cheating (Urdan, 2004). In summary, mastery goals theoretically have high intrinsic value but are not generally predictive of achievement related outcomes such as test scores and grades. Performance-approach goals can have a positive impact on achievement related outcomes such as grades; however, research has yielded mixed results on the associations between performance-approach goal orientation and achievement (Kaplan & Maehr, 2007). Finally, the association between performance-avoidance goals and achievement is almost always negative (Harackiewicz et al., 1998). 1.3. Two main perspectives: Traditional and multiple goal theory
1.2. Trichotomous goal framework This study examines the widely accepted trichotomous goal framework that includes mastery-approach, performance-approach, and performance-avoidance goal orientations. At the research design phase of our study project, the 2 2 model had much less empirical support whereas the trichotomous model was widely accepted among goal theorists (Linnenbrink-Garcia et al., 2008). The different goal orientations are not necessarily mutually exclusive; in fact, students can simultaneously endorse all three goal orientations. For example, students may want to improve their math skills (mastery) and impress the teacher (performance-approach) and not come across as dumb in math class (performance-avoidance). While a particular goal orientation may dominate, all three goals may be present within the same student (Pintrich, Conley, & Kempler, 2003). The literature on mastery goals is fairly consistent in showing that when students are mastery oriented, they are more highly engaged in learning, use deeper cognitive strategies, and are intrinsically motivated to learn (Anderman & Wolters, 2006; Dweck & Leggett, 1988; Harackiewicz, Barron, & Elliot, 1998; Kaplan & Maehr, 2007; Kaplan & Midgley, 1997; Pintrich, 2000; Utman, 1997). However, some studies have found mastery goals to be unrelated to achievement (Elliot & Church, 1997; Elliot, McGregor, & Gable, 1999; Harackiewicz et al., 1998). For example, Harackiewicz and colleagues (1998) have found that mastery goals are associated with more interest and intrinsic motivation while performance-approach goals are associated with better performance and extrinsic motivation. Exceptions to these general findings are with more recent studies that suggest that the impact of achievement goals depends on how the goals are operationalized (Grant & Dweck, 2003) or whether within-year rather than between-year development of goals and achievement are examined (Shim et al., 2008). The literature on performance goals is less consistent, in part because earlier work in this area did not distinguish between the approach- and avoidance-forms of performance goals (Elliot, 2005). Since earlier studies found mixed results on the relation between performance goals and other motivation, cognitive, and behavior outcomes, researchers further differentiated between performance-approach and performance-avoidance goal orientations (Elliot & Church, 1997; Harackiewicz et al., 1998). Among college students, performance-approach goals are positively associated with performance and other motivation constructs such as academic self-concept and task value, but not associated with interest or intrinsic motivation (Harackiewicz, Barron, Pintrich, Elliot, & Thrash, 2002). Other students are motivated to avoid failure and looking incompetent, reflecting a performance-avoidance goal orientation. Researchers find that performance-avoidance goals have negative consequences for students’ motivation and learning (Elliot & Harackiewicz, 1996; Middleton & Midgley, 1997; Skaalvik, 1997) and are correlated with self-handicapping, or deliberately creating obstacles that reduce one’s probability of success such
According to traditional goal theory (also referred to as normative or mastery goal theory), mastery goals are beneficial while performance goals, under certain conditions, are detrimental to learning. The differentiation of performance-approach and performance-avoidance goals, and the evidence demonstrating that performance-approach goals can relate to positive motivation and achievement outcomes, have led some researchers to call for a revision of goal theory (Harackiewicz et al., 1998; Pintrich, 2000). Traditional and multiple goal perspectives agree on the negative effects of performance-avoidance goals; where they differ is their views of the effects of performance-approach goals. Multiple goal theory (also referred to as revised goal theory) contends that both mastery and performance-approach goals can be beneficial, pointing out that whether goals are adaptive depends on the context. While some advocate for a revision (Harackiewicz et al., 1998; Pintrich, 2000), others (Midgley, Kaplan, & Middleton, 2001) disagree with the call to revise goal theory. Traditionalists argue that the basic assumption that mastery goals are adaptive and performance goals are maladaptive is the best generalization for goal theory. They argue that the findings for the positive associations for performance-approach goal orientation are limited to very particular cases such as when students are high in mastery goals and performance-approach goals (Pintrich, 2000) or in competitive college classrooms where there may be benefits to adopting performance goals (Harackiewicz et al., 1998). Midgley and colleagues (2001) acknowledge that although students with performance-approach goals may have higher grades or test scores than students who have mostly mastery goals, performance oriented students do not learn as deeply. Test scores often reward rote memorization and superficial recall of facts and therefore guide students away from the more important deeper thought processes. Also, they note that performance-approach goals may benefit boys rather than girls and older rather than younger students, thus the multiple goal perspective does not adequately encompass all learners (Midgley et al., 2001). 1.4. Achievement outcome Unlike the vast majority of achievement goal studies, our study used a standardized measure of student achievement in grade-level course content, to investigate the association between goals and achievement. In a recent comprehensive literature review of peer-reviewed journal articles on the achievement effects of mastery and performance-approach goal orientations (LinnenbrinkGarcia et al., 2008), the vast majority of outcome variables examined in the non-experimental studies were students’ course grades. Since individual teachers assign grades independently, often without reference to commonly agreed-upon rubrics, grades are a more subjective outcome measure than an end-of-year standardized assessment. Course grades are often heavily dependent on compliance (e.g. turning in homework), behavior, and other non-academic considerations, rather than more direct measures of
T.D. Keys et al. / Contemporary Educational Psychology 37 (2012) 47–54
student achievement or learning (Randall & Engelhard, 2009). As such, grades correlate weakly with student achievement. In our sample, student grades correlate with student test scores at the 0.20 level, and for some teachers in our sample, grades are entirely uncorrelated with student test scores. Therefore, we argue that standardized test scores – particularly those that are linked to well-known state standards for instruction – measure student achievement far more reliably than do grades. 2. Research questions and hypotheses Our research question is: Which personal goal orientations—mastery, performance-approach, or performance-avoidance—predict mathematics achievement among adolescents? The review of the achievement goal motivation literature reveals a consensus that, generally, a mastery goal orientation is adaptive while a performanceavoidance goal orientation is maladaptive. What still remains debated among goal theorists is the effect of the performance-approach goal orientation. Our hypotheses are as follows: Hypothesis 1. Given the strong theoretical support in the literature, a personal mastery goal orientation is expected to be a significant positive predictor of mathematics achievement. Hypothesis 2. Owing to conflicting findings in the literature, no explicit hypothesis is offered regarding the effects of a performance-approach goal orientation. An exploratory position is taken to examine the association between a performance-approach goal orientation and mathematics achievement for this ethnically diverse sample. Hypothesis 3. Given the strong theoretical support in the literature, a personal performance-avoidance goal orientation is expected to be a significant negative predictor of achievement.
3. Method 3.1. Model The conceptual model of achievement that guides our empirical analysis views mathematics achievement as a product of past levels of student motivation and other determinants. Suppose we have two schooling periods (1 and 2). Suppose further that the achievement of student i at the end of period 1 can be expressed as:
Ach1i ¼ a1 þ b1 RMotivation1i þ c1 Z i þ e1i
ð1Þ
In (1), RMotivation1 is the average level of motivation across period 1 and Z are other determinants of achievement. Estimating (1) with cross-sectional data is problematic because of the potential biases in b1 arising from difficult-to-measure components of Z – such as classroom dynamics, peer effects, and family approaches to education – that are correlated with both motivation and achievement. But now suppose that the determinants of achievement measured later in school, at the end of period 2, have a similar structure:
Ach2i ¼ a2 þ b1 ½RMotivation1i þ RMotivation2i þ c1 Z i þ e2i
ð2Þ
In this case, later achievement is the product of both recent and more distant levels of motivation. Using ‘‘D’’ to denote changes, subtracting (1) from (2) gives:
DAchi ¼ Da þ b1 RMotivation2i þ De2i
ð3Þ
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In this equation, changes in achievement between the ends of periods 1 and 2 are a product of the average level of motivation across period 2. The possible influences of time-invariant Z characteristics (both measureable and not) are differenced out of (3), which is likely to produce an estimate of the effect of motivation on achievement that is less biased than would be the case in the cross-sectional estimation of Eq. (1). Eq. (3) is the basis for our empirical work. We estimate (3) as a ‘‘residualized change’’ model by using time 2 achievement as the dependent variable and time 1 achievement as a predictor, but interpret b1 as relating average motivational levels during period 2 to achievement changes between the ends of periods 1 and 2. We also ran a simple change model (by subtracting time 1 achievement from time 2 achievement) and the association between goal orientations and mathematics achievement were nearly identical to the results in our residualized change model. 3.2. Procedure The data for the study came from the California Motivation Project—Mathematics (CAMP-Math). CAMP-Math is part of the larger National Science Foundation-funded Math and Science Partnership – Motivation Assessment Program (MSP–MAP) that studies the role of motivation-related beliefs in students’ achievement in mathematics and science (Conley, 2011). Although the program provided professional development for teachers, for the current study, student motivation data were collected before this development occurred. Passive consent was received by letters to parents. Less than one percent of the larger study sample chose not to participate in the survey. Researchers informed the students that the purpose of the survey was to get their confidential opinions about mathematics in general and their current mathematics class in particular. Students took approximately 30 minutes to complete the paper-and-pencil survey. Student motivation surveys were administered roughly 4 weeks after the beginning of the school year and roughly 4 weeks before the end of the school year in both the 2004–2005 and 2005–2006 academic years. Student achievement and demographic data were obtained from district annual testing records. Consistent with model (3), above, the analysis presented in this paper relates levels of motivation (using the average of three waves of motivation surveys that were measured prior to the achievement outcome) in these two school years to achievement changes from the beginning to the end of the 2-year period. 3.3. Sample The analyses presented in this study were on 2231 students (1185 in 7th grade and 1046 in 8th grade) from four middle schools in an urban school district in California in 2004–2006. The sample was fairly evenly split by gender (1104 males and 1127 females) with the average age of 12.5 years (SD = 0.16). Only White (6%), Hispanic (73%), and Vietnamese (20%) students were included in the analysis as the other ethnic groups (1%) were too small numerically to include in subgroup comparisons. We controlled for White, Hispanics and Vietnamese students separately (that is, letting the intercept differ between the groups) by including race/ethnicity dummies to account for achievement differences. The subgroup analyses suggest that the relationship between motivation and achievement does not differ across these groups, so our models, in fact, are capturing reality. Students from these three racial/ethnic backgrounds were included in the analysis if they met all of the following criteria: (1) student had valid mathematics test scores in both Spring of 2004 and 2006, (2) student had at least one valid score on each of the three motivation measures on personal goal orientations—mastery, performance-approach, and performance-avoidance and (3) student took the General Math,
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Table 1 Descriptive statistics for study sample (N = 2231 students). # Valid obs.
Mean/%
SD
Gender Male
1104
49%
0.50
Race/ethnicity White Hispanic Vietnamese
143 1639 449
6% 73% 20%
0.24 0.44 0.40
Free/reduced lunch status
1691
76%
0.43
English learner status
1149
52%
0.50
Grade-level Grade 7 Grade 8
1185 1046
53% 47%
0.50 0.50
954 914 363
43% 41% 16%
0.49 0.49 0.37
Goal orientation Mastery Performance-approach Performance-avoidance
3.68 2.54 2.22
Math achievement Math achievement – 2004 Math achievement – 2006
342.79 335.25
Math test taken General Math Algebra 1 Geometry
Min.
Max.
0.83 0.93 0.83
1 1 1
5 5 5
57.06 54.34
202 185
600 569
Notes: Motivation scales = 1–5; Math scale score range = 150–600, 350 = Proficient.
Algebra I, or Geometry test in 2006. Approximately 11% of the sample was missing achievement data for Spring 2004 and 12% of the sample was missing data for Spring 2006. According to the California Department of Education (2009), the school district in the study is a large urban unified school district with over 50,000 K-12 students enrolled during 2004–2005. More than half of the students in the district are Hispanic (52%) and it is clear from discussions with district and county officials that the overwhelming majority of Hispanic students are of Mexican descent. Regardless, the broader Hispanic label is used throughout the paper since that is how the demographic data are reported. About one third of students in the district are of Asian/Pacific Islander/Filipino (31%) descent, nearly all of whom are of Vietnamese descent. Whites are a minority in this district (16%). Approximately 47% of the district is composed of English learners with Spanish and Vietnamese as the primary non-English languages spoken in the home. Approximately 61% of the district student body participates in the National School Lunch Program (NSLP) where low income students receive free or reduced-priced meals. Lacking an actual socioeconomic status (SES) measure such as income, the current study follows suit with other studies that use students’ participation status in the NSLP as a proxy for SES. A detailed summary description of the study sample can be found in Table 1. 3.4. Measures The outcome variable in the study was the student’s 2006 mathematics achievement. The predictors were the three personal goal orientations—mastery, performance-approach, and performance-avoidance. Controls included prior mathematics achievement, gender, race/ethnicity, free/reduced lunch status, English Learner status, grade-level, and mathematics class taken in 2006. Importantly, we also control for both measurable and unmeasurable differences across classrooms by including dummy variables, one per classroom in our most complete regression models. This so-called classroom fixed effects adjustment is explained in greater detail below.
3.4.1. Outcome variable—student achievement Academic achievement was assessed with the mathematics scaled score on the California Standards Tests (CSTs). The CSTs are annual state-mandated tests for students in grades 2–11 in all California public schools and measures student performance on California’s content standards by identifying students who achieve at each performance level: advanced, proficient, basic, below basic, or far below basic (California Department of Education, 2009). The state’s target is for all students to score at or above the proficient performance level. The CSTs are high-stakes at the school and district level because the results are used in both state and federal accountability calculations (California Department of Education, 2009). Scale scores range from a low of 150 to a high of 600 with 350 as the cutoff for proficiency or meeting state standards. The 2006 mathematics scale score was the dependent variable measuring achievement outcome. The 2004 mathematics scale score served as the student’s prior mathematics achievement score. This lagged achievement helps to control for omitted variable bias (NICHD ECCRN & Duncan, 2003). With prior achievement controlled the analysis amounts to a study of changes in achievement across the 2-year period. Beginning in eighth grade, the CST mathematics tests are mathcourse specific. Only students who took grade-level mathematics in 2004 and the General Math, Algebra I, or Geometry CST exam in 2006 were included in the analysis. These students were considered to be progressing normally through the district’s middle school mathematics sequence. As such, this study focuses on achievement for students with normative mathematics course trajectories. The 89 students who took a more advanced Algebra II exam in 2006 represented approximately 3% of the sample. As a proxy for test difficulty, CST math test taken in 2006 (whether General Math, Algebra I, or Geometry) was included as a series of dummy variables in the regressions. 3.4.2. Predictor variables—student motivation scores The three achievement goal scales were adapted for the domain of mathematics from Midgley and colleagues’ (2000) widely-used Patterns of Adaptive Learning Survey (PALS) instrument and measures mastery, performance-approach, and performance-avoidance goal orientations. All three goal orientation constructs were scored on a 5-point Likert scale ranging from 1 (not at all true for me) to 5 (very true for me). Items included ‘‘really understanding my math work is important to me’’ (mastery), ‘‘it’s important to me that others think I am good at doing math’’ (performance-approach), and ‘‘it’s important to me that I don’t look stupid in math class’’ (performance-avoidance). Individual items in the specific goal constructs were averaged and a final score from 1 to 5 was created. The relatively high alpha coefficients (.78–.88) on all three scales suggest that the items in each of the goal orientation scales are measuring the same construct. Next, an average of each of the goal orientation variables was computed across the first three of the four data collection periods (i.e. waves) that were collected at baseline and before the outcome. The fourth wave was excluded because it coincided with the time when the outcome variable (2006 math achievement) was measured. It was these three-wave average scores that were used in the analysis. A complete listing of the items measuring the three goals and their reliabilities can be found in Table 2. 3.4.3. Control variables Besides prior achievement, several other student-level covariates were included in the study. Gender was a dummy variable, coded 1 for male and 0 for female. Race/ethnicity categories were Hispanic, White, and Vietnamese. Participation in the National School Lunch Program (NSLP) served as a proxy for SES. The NSLP variable was coded 1 for yes and 0 for no. English learner (EL)
T.D. Keys et al. / Contemporary Educational Psychology 37 (2012) 47–54 Table 2 Motivation survey items and cronbach’s alpha for personal goal orientations. Scale and items
Reliability
Personal goal orientation: Mastery approach Learning a lot of new things is what is important to me in math One of my main goals in math is to improve my skills My main goal in math is to learn as much as I can Really understanding my math work is important to me Learning new skills in math is one of my goals
a = .86–.88
Personal goal orientation: Performance-approach In math, doing better than other students is important to me My goal in math is to look smarter than other students One of my goals is to show others that math is easy for me It’s important to me that others think I am good at doing math My goal in math is to do better than other students
a = .82–.86
Personal goal orientation: Performance-avoidance My goal is to keep others from thinking I’m not smart in math It’s important to me that I don’t look stupid in math class An important reason I do my math work is so that I don’t embarrass myself I do my math work so that my teacher doesn’t think I know less than others My goal in math is to avoid looking like I can’t do my work
a = .78–.82
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estimated links between motivation and achievement are based solely on within-classroom variation in dependent and independent variables. Their focus on within-classroom variation also obviates the need for multi-level modeling. 4. Results
Notes: The range for scale reliability is reported given the multiple waves (totaling 4) of motivation surveys in the study. Source: Midgley et al. (2000).
status was a dummy variable coded 1 for EL and 0 for non-EL. Approximately half of the sample was made up of English learners. The grade-level variable identifies whether the student was in seventh or eighth grade in the 2004–2005 school year. Finally, math test taken identified whether the student took the General Math, Algebra I, or Geometry test in 2006. Each was coded 1 or 0 depending on whether or not the student took the particular mathematics test. 3.5. Analysis In terms of our model (3), we consider the end of the 2004– 2005 and 2005–2006 academic years as period 2 and the prior school years to be period 1. This led us to regress a student’s spring, 2006 mathematics achievement on 3-wave averages of middle school (across the 2004–2005 and 2005–2006 academic years) achievement goal orientations (mastery, performance-approach, and performance-avoidance), baseline (spring, 2004) mathematics achievement, a set of demographic controls, and type math test taken. Consistent with model (3), we use the averages of the three motivation scores rather than growth across the three waves of these motivation data as our key independent variables. To allow for comparability across the different units of measurement of different variables, the regression analysis was based on standardized achievement and motivation variables. The individual goal scales were standardized before taking the average of the three waves. In a lagged dependent variable model such as ours, the later outcome assessment is used as the dependent variable while the early assessment becomes an explanatory variable. This analysis approach has been used by other researchers to adjust for observed and unobserved selection factors (NICHD & Duncan, 2003). Finally, time-invariant classroom characteristics were controlled in the analysis with classroom fixed effects, which amounts to including dummy variables for all but one classroom (using Stata’s xtreg command). Adjusting for classroom fixed effects is a powerful method for minimizing biases arising from non-random assignment of teachers and students to schools and classrooms (Schneider, Carnoy, Kilpatrick, Schmidt, & Shavelson, 2007). In effect, the fixed effects adjustment ensures that the
The means, standard deviations, and score ranges for the three goal orientation variables and two achievement variables measured in the study are reported in Table 1. Of the three goal orientations, mastery had the highest 3-wave average compared to performance-approach and performance-avoidance for the overall sample. Table 3 presents correlations among variables of interest in our study. Correlations among variables for the total sample showed that mastery orientation was positively and moderately correlated with performance-approach (r = .39) and performance-avoidance (r = .17) goal orientations. Also, performance-approach and performance-avoidance goal orientations were strongly positively correlated to each other (r = .56). All three correlations were significant at p < 0.001 level. The significant correlations among the three goal measures are not surprising, given the range of correlations found in previous research using similar scales such as with Murayama and Elliot’s (2009) Japanese version of the Achievement Goal Questionnaire (mastery and performance approach, r = .40; mastery and performance-avoidance, r = .21; performance-approach and performance-avoidance, r = .61). The correlations between mathematics achievement in 2006 (the dependent variable) and the individual goal orientations generally conformed to the study hypotheses. That is, mastery had a mild positive correlation with achievement, there was no correlation between performance-approach and achievement, and performance-avoidance had a very slight negative correlation with achievement. Table 4 presents the regression results for goal orientations predicting mathematics achievement. Models 1, 2, and 3 report the bivariate regressions or the effect of each goal orientation on achievement. With all the variables standardized, these coefficients represent a measure of effect size. A one standard deviation increase in mastery goal orientation was associated with a 0.13 standard deviation increase in achievement (p < 0.001). A one standard deviation increase in performance-approach was associated with a 0.05 standard deviation increase in achievement (p < 0.05) whereas a one standard deviation increase in performance-avoidance yielded a 0.05 standard deviation decrease in achievement (p < 0.05). Model 4 included all three goal orientations in the same regression but no covariates. In Model 4 performance-avoidance had a larger regression coefficient (0.11, p < 0.001). In fact, the performance-avoidance coefficient and standard error were very similar with mastery in this model, but predicting achievement in opposite directions. Along with all three goal orientations, Model 5 included prior mathematics achievement, the full set of demographic (gender, race/ethnicity, free/reduced lunch status, English learner status, grade level), and math test taken controls. The reference categories were female, Hispanic, Grade 7, and General Math. The size of the coefficient for mastery fell to 0.09 but remained statistically significant at the most conservative level (p < 0.001). Performance-approach and performance-avoidance were no longer predictive of achievement in Model 5. 5. Discussion 5.1. Mastery goal orientation Study results suggest that mastery was the only goal orientation that consistently predicted mathematics achievement. That is,
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T.D. Keys et al. / Contemporary Educational Psychology 37 (2012) 47–54
Table 3 Correlations among variables for total sample (N = 2231).
1. 2. 3. 4. 5. 6. 7. 8. 9. * ***
Mastery Performance-approach Performance-avoidance Male Hispanic Vietnamese White Math achievement in 2004 Math achievement in 2006
1
2
3
4
5
6
7
8
9
1 0.39*** 0.17*** 0.12*** 0.04 0.09*** 0.07*** 0.09*** 0.15***
1 0.56*** 0.03 0.05* 0.03 0.13*** 0.03 0.02
1 0.09*** 0.07*** 0.05* 0.04 0.14*** 0.08***
1 0.01 0.02 0.05* 0.02 0.00
1 0.84*** 0.44*** 0.33*** 0.31***
1 0.13*** 0.34*** 0.34***
1 0.04 0.00
1 0.67***
1
p < 0.05. p < 0.01. p < 0.001.
Table 4 Standardized regression results for goal orientations predicting mathematics achievement. Dependent variable = 2006 math achievement (1) Goal orientation Mastery
(2)
(3)
(4)
(5)
0.05* (0.02)
0.12*** (0.02) 0.07* (0.03) 0.11*** (0.03)
0.09*** (0.02) 0.02 (0.02) 0.02 (0.02)
0.13*** (0.02) 0.05* (0.02)
Performance-approach Performance-avoidance Controls Prior math achievement (2004)
Constant
0.02 (0.02)
0.02 (0.02)
0.02 (0.02)
0.02 (0.02)
0.68*** (0.02) 0.04 (0.03) – – 0.08 (0.07) 0.39*** (0.04) 0.07 (0.04) 0.06 (0.04) – – 0.04 (0.05) – – 0.07 (0.04) 0.51*** (0.11) 0.01 (0.06)
N R2
1985 0.018
1985 0.003
1985 0.003
1985 0.027
1985 0.454
Male Race/ethnicity (Reference category = Hispanic) White Vietnamese Free/reduced lunch status (1 = yes, 0 = no) English Learner Status (1 = yes, 0 = no) Grade level (Reference category = Grade 7) Grade 8 Math test taken (Reference category = General Math) Algebra 1 Geometry
Notes: Standard errors in parentheses; time-invariant classroom characteristics are controlled in the analysis with classroom ‘‘fixed effects’’, which amounts to including dummy variables for all but one classroom (using Stata’s xtreg command). Fixed effects estimates are based solely on within-classroom variation in dependent and independent variables. * p < 0.05. p < 0.01. *** p < 0.001.
students who maintain higher levels of mastery goals had the largest gains in achievement in this sample. This finding was expected given the strong theoretical support on the positive effects of mastery goals in the achievement motivation literature. This finding, however, is not completely consistent with results from other studies (e.g., Maehr & Zusho, 2009) suggesting that mastery goals
do not always predict achievement. That the current study found a positive association of mastery on achievement while other studies did not may speak to the distinctiveness of our methods or sample. Most previous studies focused on White students, whereas the current study was composed of predominantly Hispanic and Vietnamese students. In addition, we used a measure of mathe-
T.D. Keys et al. / Contemporary Educational Psychology 37 (2012) 47–54
matics achievement that was aligned with course content standards and available across multiple years. 5.2. Performance-approach goal orientation No significant associations for performance-approach goal orientation were found. The null result for performance-approach was not surprising. There are inconsistent findings in the literature, with some studies finding positive associations, other studies finding negative associations, and still other studies finding no associations (Harackiewicz et al., 2002; Linnenbrink-Garcia et al., 2008; Urdan, 2004). The ongoing debate over traditional and multiple goal theory perspectives centers on the potential positive potential of performance-approach goals for some individuals in certain types of situations (Harackiewicz et al., 1998; Middleton, Kaplan, & Midgley, 2004; Midgley et al., 2001; Pintrich, 2000). Given that this study sampled widely in all normative mathematics classes and across the entire range of students, the null finding is in line with the debates in the literature. 5.3. Performance-avoidance goal orientation We hypothesized that performance-avoidance goal orientation would be a significant negative predictor of achievement. Study results suggest that students’ performance-avoidance goal orientation was not predictive of their mathematics achievement. This finding was unexpected, given the consistent findings in the literature on the negative effects of espousing a performance-avoidance goal orientation. It is important to note that the literature has focused mostly on White students whereas our sample is composed of mostly Hispanic and Vietnamese students. Several studies have documented that Asian Americans adopt more performanceavoidance goals than non-Asian Americans, although with Asian Americans, these goals are not always predictive of achievement outcomes (Elliot, Chirkov, Kim, & Sheldon, 2001; Murdock, 2009; Witkow & Fuligni, 2007; Zusho, Pintrich, & Cortina, 2005). Researchers offer the explanation that the Asian (and to a lesser degree, Asian American) cultures have a high degree of familial obligation, which in turn triggers fear of failure thoughts that are characteristic of performance-avoidance goals (Chen & Stevenson, 1995; Witkow & Fuligni, 2007). A strong sense of familial obligation is also true of the Hispanic culture (Feliciano & Rumbaut, 2005; Kao & Tienda, 1995; Urdan & Giancarlo, 2001); however, performance-avoidance goals are not as strong with Hispanics as with Asian groups (Witkow & Fuligni, 2007). A possible explanation for our unexpected findings is that validation studies of the widely-used PALS instrument (Midgley et al., 2000) have not, to date, included Hispanic or Asian samples. The ethnically diverse sample in the validation studies conducted by the PALS instrument creators were primarily on African American students. It is our conjecture that our predominantly Hispanic and Asian sample, specifically of Mexican and Vietnamese descent are quite different from other achievement motivation studies that are on Whites and African American students.
53
achievement, net of the potentially confounding influence of omitted student characteristics. Our analyses, which investigate the relationship between changes in student goal orientations and changes in student achievement, therefore provide relatively unbiased estimates of the consequences of goal orientations for student learning. In addition, our data provide relatively precise estimates of the relationship between goal orientations and achievement and in a more ethnically and socio-economically diverse setting than earlier studies. While the majority of studies are limited by small sample sizes (Barron & Harackiewicz, 2001), this study included approximately 2000 participants. Larger sample size translates to smaller sampling error and estimates that are less likely to be influenced by a few unusual cases or missing values (Allison, 1999). This study also has several limitations and suggestions for future research. First, our sample was made up of seventh and eighth graders from four middle schools from a single urban California school district. More studies on districts with similar demographic characteristics need to be conducted to see if results are replicable. Second, we know little about how motivation matters for non-Whites since the vast majority of motivation research is conducted on middle class White students (Urdan & Giancarlo, 2001); therefore, more research is needed on minority groups. We suggest that PALS validation studies be performed on Hispanic and Asian samples to determine if goal orientations relate the same way with different population subgroups. Finally, the study did not focus on the role of SES because our study was only able to use a proxy for SES (i.e. the free/reduced lunch measure). There are plans to collect more accurate and sophisticated SES measures for future analysis.
6. Conclusion In summary, the current study examined the association between students’ personal goal orientations and mathematics achievement. While all three achievement goal orientations were correlated with mathematics achievement, only a mastery goal orientation consistently predicted achievement when a full set of prior achievement and demographic controls were included. Performance-approach and performance-avoidance goal orientations did not predict achievement in the full model. Achievement goal theory provides a useful explanatory framework that assumes that goals are not just stable personal traits, but rather that goals can be shaped by the teacher and learning environment (Schunk et al., 2007). The relation between the different personal goal orientations and positive academic outcomes remains a contested issue. Our results suggest that (1) a full complement of demographic controls, and (2) achievement measures that precede and follow the motivation assessments are important for demonstrating the theoretically-predicted relations between achievement goals and mathematics achievement.
5.4. Study contributions, limitations, and future research
Acknowledgments
The present study contributes to the literature in two important ways. First, unlike most other achievement goal studies, this study used standardized scores of student achievement (rather than teacher-assigned grades) to investigate the association between goals and achievement. Doing so allows us to directly investigate the relationship between student goal orientations and student achievement, without the subjective and behavioral biases that exist in teacher-assigned grades. Second, our longitudinal data provides a look at the relationship between goal orientation and
The California Motivation Project (CAMP-Math) data collection was supported in part by a grant to the Math Science Partnership–Motivation Assessment Program (PIs Stuart Karabenick and Martin Maehr) from the National Science Foundation (No. EHR0335369). The findings and views reported in this manuscript are the authors’ and do not necessarily reflect the views of the National Science Foundation. The authors would like to thank the editor and three anonymous reviewers for their helpful comments on earlier drafts of this article.
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