Reducing Racial and Gender Gaps in Mathematics Attitudes: Investigating the Use of Instructional Strategies in Inclusive STEM High Schools
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Abstract
Inclusive STEM (science, technology, engineering, and mathematics) schools operate with a mission to increase and broaden participation in STEM among all students, particularly girls and students from under-represented ethnic groups (e.g., ethnic/racial minorities). As such, inclusive STEM schools promote various instructional strategies, such as risk-taking, autonomy, and technology use, to help peak diverse students’ interests and achievement in STEM subjects. However, little research has investigated how these instructional strategies are implemented in inclusive STEM school settings, and whether these strategies reduce racial and gender gaps in students’ mathematics attitudes. The current study uses hierarchical linear regression analyses to investigate associations between such strategies (i.e., student autonomy, cooperation and teamwork, technology use, risk taking, and cognitively-demanding work) and students’ attitudes toward mathematics. Results indicate that higher levels of risk-taking in mathematics classes were associated with more positive mathematics attitudes for all students. Girls and African American students reported more positive mathematics attitudes compared to boys and White students when they experienced higher levels of autonomy in their mathematics classes. These findings suggest that some instructional strategies should be examined further for their potential to reduce persistent gaps seen in mathematics attitudes.
Keywords
STEM education Mathematics attitudes Inclusive STEM schools Instructional strategiesIntroduction
Substantial efforts have been made to broaden participation in STEM education and career paths (LaForce et al. 2016; Hernandez et al. 2013). The current STEM workforce; however, does not reflect the diversity of the U.S. Population (Economics and Statistics Administration [ESA] 2017; National Science Board 2016). In mathematics-related fields in particular, the racial/ethnic disparities are striking. Hispanic/Latinx individuals (6%) and African Americans (9%) hold only a small proportion of mathematics jobs, whereas Whites (70%) dominate employment in these positions (Funk and Parker 2018). Moreover, the percentage of bachelor’s degrees awarded in mathematics to African Americans has decreased since the late 1990’s (National Science Foundation [NSF] 2017). Women, on the other hand, make up approximately 40% of mathematics bachelor’s and master’s degree holders, but a smaller percentage earn doctoral degrees in mathematics or pursue careers in computer science and mathematics (NSF 2017). Thus, despite recent efforts, women and under-represented ethnic groups remain under represented in STEM fields, especially mathematics.
Inclusive STEM high schools represent one mechanism created to increase interest and persistence in STEM across students from underrepresented groups (Peters-Burton et al. 2014). Such schools have emerged across the U.S. as an alternative to highly competitive mathematics- and science-focused high schools, which admit students based on academic achievement (e.g., standardized test scores) (Subotnik et al. 2010, 2011). Adoption rates of STEM school models across the United States are documented in the literature (Forman et al. 2015; Lesseig et al. 2019; Lynch et al. 2018). This literature highlights the unprecedented growth rates of these schools and their importance within American educational systems striving to cultivate students’ twenty-first-century skills and to prepare them for STEM careers. For instance, Forman et al. (2015) identified 949 unique STEM high schools across 48 states (exceptions: Montana and West Virginia) and the District of Columbia, and they were able to collect data from administrators and teachers in 291 of those schools across 37 states. Similarly, SRI International identified that more than half of the 315 STEM high schools in their investigation to be inclusive STEM high schools (Peters-Burton et al. 2014; Subotnik et al. 2010). Moreover, several states, specifically Texas and Ohio, have established networks to create, monitor, and support inclusive STEM high schools and the students they serve. More than 50 secondary schools have been established in Texas under the T-STEM network (Bicer et al. 2015), and the Ohio STEM Learning Network (Basham et al. 2010) has opened 10 inclusive STEM schools throughout the state. New York, California, Washington, and North Carolina are all currently replicating the models set forth in Texas and Ohio as well (Education Development Center, Inc. 2018). Together, these findings stress the importance of research investigating instructional strategies being carried out within inclusive STEM high schools as such schools are reaching more and more students every year.
Inclusive STEM schools help broaden the pipeline to STEM careers by providing all students with high-quality and engaging STEM educational experiences, including extensive STEM learning opportunities, access to college prep coursework, and support systems for success both in- and outside the classroom. To do so, inclusive STEM high schools strive to increase student engagement, improve students’ STEM self-identity and efficacy, and increase students’ readiness for post-secondary STEM programs and careers (Bicer et al. 2015; Gnagey and Lavertu 2016; Means et al. 2017). A sizeable body of literature investigating inclusive STEM schools has emerged since the President’s Council of Advisors on Science and Technology issued their 2010 report (PCAST 2010; Peters-Burton et al. 2014). However, at this writing, only limited information is available about how inclusive STEM schools implement specific strategies to improve student outcomes, especially for students from groups traditionally underrepresented in STEM. In one study, LaForce et al. (2019) found that strong implementation of inclusive STEM school strategies was associated with reductions in gender and race/ethnicity gaps in science attitudes and overall academic achievement. However, more studies that systematically examine the implementation of an array of instructional strategies used by inclusive STEM schools to boost students’ STEM-related attitudes are needed. Thus, the present study aims to investigate associations between inclusive STEM school strategies and students’ mathematics-related attitudes, and whether these associations differ based on students’ gender and racial/ethnic identity. This study is an important next step in this line of research as it serves to help educators and researchers gain a better understanding of the mechanisms of specific instructional practices used in inclusive STEM schools, and how these practices contribute to students’ mathematics-related attitudes. It also investigates how such practices may contribute to reductions in STEM attitude gaps between different groups of students. Given the demonstrated necessity of these types of outcomes for students’ persistence in STEM, this knowledge is a timely contribution to the efforts being made to broaden participation.
The Importance of Mathematics Attitudes
Many education theories report the importance of attitudes (specifically, self-beliefs and “liking,” or motivational attitudes) in academic achievement and postgraduate career plans (e.g., Theory of Planned Behavior; Ajzen 1991; Social Cognitive Career Theory; Lent et al. 1994; Expectancy-value Theory; Wigfield and Eccles 2000; Attribution Theory; Weiner 1985). However, the current study was grounded in a social constructivist theoretical frame (Pritchard and Woollard 2013). According to social constructivists, learning is a social process, which takes place when an individual (e.g., student) is actively engaged within their learning context (e.g., classroom). Both constructivist learning theory (Hein 1991) and social learning theory (Bandura and Walters 1977) emphasize the social aspects of learning, and how social interaction is critical to the development of cognition, which in turn, allows individuals to construct their own understanding of the world around them during the learning process. A social constructivist approach was appropriate for this study because it allowed us to better understand how contextual variables within the learning environment (i.e., instructional strategies) contribute to the development of students’ socio-cognitive processes, specifically mathematics intrinsic motivation and ability beliefs. As a result, we applied this theoretical framework to our research investigating associations between instructional strategies and students’ mathematics attitudinal outcomes.
Nevertheless, while a social constructivist theoretical framework certainly underscores our approach in this research investigation as well as our assumptions, it is also important to highlight that the primary focus of this research is to test a theory of action^{1} derived from the inclusive STEM school leaders and founders themselves (LaForce et al. 2016). This theory of action was derived through a component approach adept at measuring the fidelity of innovations (Century and Cassata 2014; Century et al. 2010), and use of this approach identified the critical components, or elements, of inclusive STEM school models. Results of interviews with STEM school creators, leaders, and key teachers and review of written materials about each school (e.g., mission statements; student handbooks) supported the development of this theory of action, which highlights associations between engagement in STEM instructional strategies and students’ attitudes and knowledge about STEM disciplines, including mathematics-related attitudes. In this theory of action model, attitudes are an intermediate student outcome that ultimately contributes to academic achievement outcomes (e.g., GPA) and student interest in STEM careers (LaForce et al. 2017). The “bottom up” approach (i.e., using interview data to construct the theory of action) employed here is one additional step for deepening this research compared to studies that have used a “top down,” literature-based approach to defining inclusive STEM schools. Moreover, this approach grounded within a social constructivist paradigm provided us with the ideal conditions in which to further disentangle associations between instructional strategies and students’ math intrinsic motivation and ability.
However, more work is needed to create equity across desired student STEM outcomes. National reports indicate that academic achievement gaps in mathematics remain, with White and Asian students continuing to outperform both African American and Hispanic/Latinx students (Lee 2002; National Assessment Educational Progress [NAEP] 2015; Tate 1997). While much attention is paid to achievement gaps as a critical factor in STEM workforce pipeline diversity, less research has focused on the role of attitudes in reducing these gaps. Research suggests that students’ mathematics attitudes are not only indicative of educational attainment in mathematics, but also indicators of their interest in pursuing future STEM careers (Wang 2012; Riegle-Crumb et al. 2011). For instance, students’ beliefs about their ability to successfully complete mathematics problems were found to be a stronger predictor of mathematics performance outcomes regardless of students’ mathematics ability levels or prior mathematics-related academic achievement (Stevens et al. 2004). Moreover, compared to mathematics achievement, students’ mathematics self-concept (i.e., attitudes) was found to be a stronger predictor of STEM major choice (Sax et al. 2015) and interest in future careers using mathematics (Goldman and Penner 2016). Assessing students’ attitudes may be critical for closing achievement gaps between White students and those students in under-represented groups. Specifically, mathematics intrinsic motivation is closely related to mathematics achievement (Gottfried et al. 2007), and some research has suggested the importance of enhancing African American students’ mathematics beliefs (e.g., self-efficacy beliefs) as one way to help reduce gaps in mathematics achievement between African American and White students (Kitsantas et al. 2011).
Previous research provides evidence in support of associations between students’ mathematics attitudes, mathematics achievement, and future STEM-related career choices (Else-Quest et al. 2013); however, explorations of differences in mathematics attitudes based on gender identity and racial/ethnic identity group status have yielded mixed results. For instance, Stevens et al.’ (2006) research indicated that although Hispanic students reported higher mathematics interest and intrinsic motivation, their feelings of mathematics self-efficacy and actual mathematics performance were significantly lower than White students. Similarly, African American students were more likely to report lower mathematics beliefs compared to White students (Pajares and Kranzler 1995). On the other hand, Else-Quest et al. (2013) found that African American adolescents had significantly higher mathematics value attitudes compared to their White counterparts.
Research examining gender differences in mathematics attitudes has yielded more consistent, though disappointing, findings. More specifically, female students are less likely to report positive mathematics attitudes, and are more likely to possess lower mathematics motivation and interest compared to their male peers (Leedy et al. 2003; Pajares 2005; Pajares and Miller 1994; Rech 1994; Sax et al. 2015; Tocci and Engelhard 1991). Together these findings emphasize the complexity of mathematics attitudes and achievement for students from underrepresented groups, and highlight the importance of research focusing on the interrelated nature of these outcomes as a means to promote improvements in inclusive STEM school education more broadly.
Inclusive STEM School Overview
Inclusive STEM high schools intend to increase access to high-quality STEM education for students from all backgrounds, regardless of prior academic achievement (White House Office of Science and Technology Policy 2015). These schools differ from selective enrollment STEM high schools, which admit students based on academic achievement (Subotnik et al. 2011). Instead, inclusive STEM high schools use open enrollment procedures to attract a more-diverse student body (Peters-Burton et al. 2014). Additionally, these schools are dedicated, more broadly, to enhancing students’ acquisition of twenty-first century skills, including problem solving, critical thinking, technology use, and cooperative learning (LaForce et al. 2016), which are strategies often linked to college completion and workplace success (Burrus et al. 2013).
Previous research (LaForce et al. 2016, 2019) highlights variability across STEM school models, and the importance of examining the complex impact of strategies used by inclusive STEM schools on student success. Studies investigating associations between attending a STEM school and students’ mathematics achievement have mixed findings. One study found a positive effect of STEM school attendance on students’ standardized mathematics exam scores (Hansen 2014), whereas other research findings indicate no significant effects of STEM school participation on mathematics outcomes (Young et al. 2011). To our knowledge, there are no studies investigating the contribution of different instructional strategies used in inclusive STEM school settings on the development of students’ mathematics attitudes. Overall, inclusive STEM high schools, by design, have the potential to reduce inequalities in STEM-related outcomes. However, further examination of these schools, with a specific focus on teaching and learning experiences taking place within them, is needed in order to gain a clear understanding of whether inclusive STEM schools actual do reduce persistent inequalities.
Strategies of Inclusive STEM Schools
Inclusive STEM high schools are not uniform entities employing “one-size fits all” approaches, and as a result, scholars have begun to examine common instructional strategies present across inclusive STEM schools (LaForce et al. 2016). One framework (LaForce et al. 2016), referred to as the 8 Elements^{2} of STEM Schools, identifies eight over-arching educational goals shared by inclusive STEM high schools, and 76 components (e.g., student autonomy) that describe the concrete ways STEM schools operate to achieve those goals (organized under the Elements) (see LaForce et al. 2016).
Elements under investigation and the percentage of school leaders emphasizing the strategy
Element | Strategies | Percent of school leaders who emphasized strategy |
---|---|---|
PBL | Student cooperation and teamwork | 60% |
Student autonomy | 55% | |
Rigorous learning | Cognitively demanding work | 30% |
Personalization of learning | Student autonomy | 55% |
Career, technology, and life skills | Student cooperation and teamwork | 60% |
Technology use | 45% |
These five strategies have been identified in prior studies with non-STEM schools as contributing to mathematics attitudes and self-concept as well. Cognitively-demanding mathematics curricula contributed positively to students’ learning gains in the subject (Blair et al. 2005), whereas meaningful technology use in the classroom has been linked to improved mathematics achievement and self-efficacy attitudes (Barkatsas et al. 2009; Li and Ma 2010; Nugent et al. 2010; Pierce et al. 2007). Cooperative learning has been shown to promote students’ problem-solving, active learning, and mathematics achievement (Leikin and Zaslavsky 1997; Zakaria et al. 2010). At the same time, researchers have noted the importance of structuring classrooms to facilitate student risk-taking during mathematics lessons so that students are not afraid to make mistakes (Sharma 2015). Although these findings have demonstrated valuable data, most of these studies were not conducted in an inclusive STEM school context. That is, at this writing, how these instructional strategies boost students’ mathematics attitudes in an inclusive STEM school context as well as how these strategies interact with each other in such settings remain largely unexamined.
- 1.
How are instructional strategies (i.e., student autonomy, cooperation and teamwork, technology use, risk taking, and cognitively-demanding work) associated with students’ mathematics attitudes?
- 2.
How do these associations vary for students of different gender and racial/ethnic identities?
Method
Participants
Participants in the current study were 504 ninth to twelfth grade students (9th: 39%, 10th: 23%, 11th: 22%, and 12th: 16%) from 16 inclusive STEM high schools that were part of a larger project investigating the effectiveness of inclusive STEM school models (LaForce et al. 2016, 2019). This larger project was a five-year study that included 20 inclusive STEM high schools across seven states (i.e., Ohio, Texas, Washington, California, North Carolina, Tennessee, and New York). Students as well as educators from these schools participated in a wide array of quantitative (i.e., questionnaires) and qualitative (i.e., interviews, focus groups, and classroom observations) data collection activities. This study focused on data collected from students who reported about learning experiences and instructional strategies in a mathematics class on a questionnaire administered in Spring 2015. The analytic sample included slightly more female students (55%) than male students (45%), and was racially/ethnically diverse (12% African American; 31% Hispanic; 46% White; and 11% Asian).
Measures
Mathematics Attitudes
- 1)
Mathematics intrinsic motivation: Four items (α = 0.97) were used to assess students’ motivation in mathematics (e.g., I enjoy solving mathematics problems).
- 2)
Mathematics ability beliefs: This measure consisted of four items (α = 0.93) assessing students’ beliefs about their mathematics abilities (e.g., I can figure out how to do the most difficult mathematics problems if I try).
Instructional Strategies
- 1)
Student autonomy: Four items (α = 0.79) assessed student engagement in independent learning (e.g., I worked without a teacher managing my organization or time).
- 2)
Cooperation and teamwork: Four items (α = 0.85) assessed cooperative learning and the degree to which students worked together to achieve learning goals (e.g., Another student helped me with an assignment or problem that I was struggling with).
- 3)
Technology use: Three items (α = 0.84) assessed use of technology in student learning processes (e.g., I had all of the technological resources needed to complete assignments/reach goals).
- 4)
Risk-taking: Four items (α = 0.82) assessed the extent to which students took risks during learning (e.g., I sought out new things to try in class).
- 5)
Cognitively-demanding work: Four items (α = 0.87) assessed how students were challenged in their classes (e.g., I considered alternative explanations or arguments for findings or conclusions).
Response Bias Control
- 1)
General school intrinsic motivation: Four items (α = 0.86) assessed the level of students’ intrinsic motivation toward schoolwork in general (e.g., I enjoy doing my schoolwork).
- 2)
General school ability beliefs: Eight items (α = 0.92) assessed students’ beliefs in their abilities to succeed in their schoolwork (e.g., When faced with difficult tasks, I know that I will accomplish them).
Descriptive statistics for all continuous measures
Measures | Minimum | Maximum | Mean | Std. Deviation |
---|---|---|---|---|
Mathematics intrinsic motivation | 1.00 | 6.00 | 3.74 | 1.61 |
Mathematics ability beliefs | 1.00 | 6.00 | 4.22 | 1.31 |
Student autonomy | 1.00 | 6.00 | 3.90 | 1.07 |
Cooperation/ teamwork | 1.00 | 6.00 | 3.66 | 1.10 |
Technology use | 1.00 | 6.00 | 3.71 | 1.37 |
Risk-taking | 1.00 | 6.00 | 3.25 | 1.17 |
Cognitively-demanding work | 1.00 | 6.00 | 3.55 | 1.18 |
General school intrinsic motivation | 1.00 | 6.00 | 3.59 | 1.37 |
General school ability beliefs | 1.00 | 6.00 | 4.49 | 0.98 |
Analytic Strategy
Hierarchical multiple-regression analyses were used to investigate associations between the five instructional strategies and students’ mathematics attitudes. Two separate eight-step models were used to investigate the mathematics intrinsic motivation and mathematics ability beliefs outcome variables. In both models, demographic variables, including students’ gender identity (dummy coded, male students as the reference group) and race/ethnicity (dummy coded, Caucasian/White as the reference group) were entered at step 1. In step 2, grade level (dummy coded, 9th grade as the reference group) and school type (dummy coded, predominantly Caucasian/White students as the reference group) variables were included. The main effect of each instructional strategy—student autonomy (step 3), cooperation and teamwork (step 4), technology use (step 5), risk taking (step 6), and cognitively-demanding work (step 7)—as well as interaction terms between gender identity (or race/ethnicity) and each STEM school instructional strategy (e.g., step 3: autonomy*gender; autonomy*race/ethnicity) were entered into the model at each subsequent step. The final step (8) included a measure of students’ general intrinsic motivation toward schoolwork or general ability beliefs as a control variable, which corresponded to the mathematics intrinsic motivation and mathematics ability beliefs outcome variables for each model. Each continuous instructional strategy variable was centered around the sample mean. Interaction terms were created by multiplying gender (or race/ethnicity variables) and each mean-centered instructional strategy.
All statistical analyses were performed using the Statistical Package for the Social Sciences © (SPSS) Version 24 software, and the interaction figures were created in Interaction! program for Windows (Soper 2006–2013).
Results
Research Question 1
How are instructional strategies (i.e., student autonomy, cooperation and teamwork, technology use, risk taking, and cognitively-demanding work) associated with students’ mathematics attitudes?
Model fit indices for students’ mathematics intrinsic motivation and ability beliefs
Step | Adjusted R^{2} | R^{2} change | F change | |||
---|---|---|---|---|---|---|
Intrinsic motivation | Ability beliefs | Intrinsic motivation | Ability beliefs | Intrinsic motivation | Ability beliefs | |
1 | 0.02 | 0.03 | 0.03 | 0.04 | 3.75** | 4.63** |
2 | 0.02 | 0.04 | 0.01 | 0.02 | 1.33 | 2.36 |
3 | 0.09 | 0.09 | 0.07 | 0.06 | 7.78** | 6.73** |
4 | 0.10 | 0.11 | 0.03 | 0.02 | 2.92* | 2.64* |
5 | 0.12 | 0.12 | 0.03 | 0.03 | 3.02* | 2.89* |
6 | 0.17 | 0.17 | 0.06 | 0.05 | 6.65** | 5.78** |
7 | 0.18 | 0.17 | 0.01 | 0.01 | 1.65 | 1.35 |
8 | 0.41 | 0.49 | 0.22 | 0.30 | 188.40** | 297.86 |
Results for mathematics intrinsic motivation and ability beliefs final model (Step 8)
Variables | Mathematics intrinsic motivation | Mathematics ability beliefs | ||||
---|---|---|---|---|---|---|
B | SE B | t | B | SE B | t | |
Female students | −0.18 | 0.12 | −1.59 | −0.21 | 0.09 | −2.41* |
African American | 0.26 | 0.19 | 1.4 | 0.35 | 0.14 | 2.48* |
Hispanic | 0.33 | 0.18 | 1.9 | 0.08 | 0.13 | 0.57 |
Asian | 0.67 | 0.22 | 3.09** | 0.14 | 0.16 | 0.83 |
10th grade | −0.36 | 0.15 | −2.37* | −0.25 | 0.11 | −2.17* |
11th grade | −0.08 | 0.16 | −0.52 | −0.21 | 0.12 | −1.8 |
12th grade | −0.31 | 0.17 | −1.79 | −0.27 | 0.13 | −2.03* |
School type | −0.28 | 0.16 | −1.72 | −0.04 | 0.12 | −0.35 |
Autonomy | −0.2 | 0.11 | −1.86 | −0.11 | 0.08 | −1.37 |
Autonomy*Female students | 0.31 | 0.14 | 2.16* | 0.11 | 0.11 | 1 |
Autonomy*African American | 0.51 | 0.24 | 2.14* | 0.03 | 0.18 | 0.19 |
Autonomy*Hispanic | 0 | 0.17 | −0.01 | −0.02 | 0.13 | −0.19 |
Autonomy*Asian | 0.01 | 0.28 | 0.03 | −0.22 | 0.21 | −1.04 |
Cognitively demanding work (CDW) | 0.08 | 0.11 | 0.75 | 0.12 | 0.08 | 1.49 |
CDW*Female students | 0.15 | 0.14 | 1.06 | −0.17 | 0.1 | −1.66 |
CDW*African American/Black | −0.24 | 0.22 | −1.11 | −0.13 | 0.16 | −0.81 |
CDW*Hispanic | −0.27 | 0.16 | −1.72 | 0.01 | 0.12 | 0.1 |
CDW*Asian | −0.07 | 0.29 | −0.24 | 0.14 | 0.22 | 0.63 |
Cooperation and teamwork (CT) | −0.08 | 0.12 | −0.73 | −0.11 | 0.09 | −1.27 |
CT*Female students | 0.07 | 0.14 | 0.49 | 0.08 | 0.11 | 0.75 |
CT*African American | −0.22 | 0.24 | −0.91 | −0.01 | 0.18 | −0.08 |
CT*Hispanic | −0.02 | 0.16 | −0.11 | 0.1 | 0.12 | 0.88 |
CT*Asian | 0.07 | 0.23 | 0.3 | 0.12 | 0.17 | 0.68 |
Risk-taking | 0.27 | 0.12 | 2.35* | 0.23 | 0.09 | 2.61* |
Risk-Taking*Female students | −0.15 | 0.14 | −1.1 | 0.03 | 0.1 | 0.25 |
Risk-Taking*African American | 0.02 | 0.22 | 0.11 | −0.15 | 0.17 | −0.91 |
Risk-Taking*Hispanic | 0.12 | 0.16 | 0.73 | −0.16 | 0.12 | −1.33 |
Risk-Taking*Asian | −0.05 | 0.22 | −0.22 | −0.13 | 0.17 | −0.78 |
Technology use | 0.02 | 0.08 | 0.22 | −0.03 | 0.06 | −0.48 |
Technology Use *Female students | 0.01 | 0.1 | 0.05 | 0.04 | 0.07 | 0.61 |
Technology Use *African American | −0.06 | 0.15 | −0.36 | 0.01 | 0.12 | 0.11 |
Technology Use *Hispanic | 0.15 | 0.11 | 1.31 | 0.13 | 0.09 | 1.49 |
Technology Use *Asian | 0.05 | 0.15 | 0.33 | 0.02 | 0.12 | 0.15 |
General school motivation | 0.62 | 0.05 | 13.73** | N/A | N/A | N/A |
General school ability beliefs | N/A | N/A | N/A | 0.84 | 0.05 | 17.26** |
Research Question 2
How do these associations vary for students of different gender and racial/ethnic identities?
Asian students reported significantly higher mathematics intrinsic motivation compared to White students (B = 0.67, p < 0.01). That is, holding other variables constant, Asian students scored 0.67 units higher on mathematics intrinsic motivation than White students. Tenth grade students reported significantly lower mathematics intrinsic motivation compared to ninth grade students (B = −0.36, p < 0.05); 10th graders scored 0.36 units lower than 9th graders when holding other variables constant. Significant autonomy by gender (B = 0.31, p < 0.05) and autonomy by race/ethnicity (B = 0.51, p < 0.05) interactions resulted for mathematics intrinsic motivation. Simple slopes analysis of these interactions was conducted for female and male students, and also for African American and White students. Coefficients for the simple slopes were generated through “Interaction!” program, and they were reported in text to illustrate the direction and magnitude of the interaction effect.^{4} More specifically, when engaging in greater autonomy, both female students (B = 0.50, p < 0.01) and African American (B = 0.51, p < 0.05) students reported higher mathematics intrinsic motivation than male students (B = 0.25, p < 0.05) and White students (B = 0.37, p < 0.01), respectively.
Female students reported significantly lower mathematics ability beliefs compared to male students (B = −0.21, p < 0.05). African American students reported significantly higher mathematics ability beliefs compared to White students (B = 0.35, p < 0.05). That is, holding other variables constant, female students scored 0.21 units lower than male students, and African American students scored 0.35 unites higher than White students on ability beliefs, respectively. Tenth (B = −0.25, p < 0.05) and 12th (B = −0.27, p < 0.05) grade students reported significantly lower mathematics ability beliefs compared to ninth graders; 10th and 12th graders scored 0.25 and 0.27 units lower than 9th graders, respectively (see Table 3 for model fit indices and Table 4 for all statistics).
Discussion
In recent years, research has examined the role STEM-focused (including inclusive STEM) high schools play in addressing the comparatively low achievement of U.S. students in STEM, particularly for girls and students from under-represented ethnic groups (e.g., Academic Competitiveness Council 2007; Carnegie Corporation of New York 2009). However, the specific instructional strategies that inclusive STEM high schools use, and the mechanisms through which these strategies facilitate students’ learning in STEM, remain largely unexamined. Understanding the potential values of these strategies is pivotal when it comes to unpacking the “black box” of these schools—that is, how exactly they may contribute to improved outcomes for students, and specifically those students currently underrepresented in STEM. As such, this study investigated associations between instructional strategies used in inclusive STEM high schools and students’ attitudes toward mathematics, and how those associations may differ for diverse groups of students.
Our findings indicate that encouraging engagement in risk-taking behaviors when studying mathematics may benefit students’ mathematics intrinsic motivation and mathematics ability beliefs. Risk-taking behaviors (i.e., “taking risks” during learning), help to promote general academic attainments. More specifically, risk-takers have been found to be more likely to perform difficult tasks, tolerate failure, and seek novel ways to solve problems (Clifford 1988, 1991; Meyer et al. 1997; Sharma 2015). This finding also highlights the importance of encouraging educators to help strengthen students’ risk-taking behaviors during mathematics lessons as a means to promote students’ mathematical thinking and abilities to solve challenging problems. Furthermore, we did not find any amplification or inhibitory effects of gender on associations between engaging in risk-taking behaviors and mathematics attitudes, which was surprising given that previous research has identified that male students are more likely to take risks (Byrnes et al. 1999). As a result, future studies are needed to disentangle how engaging in risk-taking behaviors may affect boys’ and girls’ mathematics attitudes.
Meanwhile, we found that when girls and African American students experienced higher levels of autonomy in their mathematics classes, their self-reported intrinsic motivation toward mathematics was higher than boys and White students. This finding suggests that when girls and students from under-represented ethnic groups are given more independence in and ownership of their learning, more freedom to set and manage their learning goals, and more trust in making choices, their mathematics-related attitudes may increase, thus reducing gender and race/ethnicity gender gaps.
These findings may have resulted for several reasons. One possible explanation for these results may be related to stereotype threat, which occurs when an individual or group’s performance (in this case, girls or under-represented ethnic group students) is negatively affected by concern about conforming to a stereotype about their group (Steele 1997). Stereotype threat has been associated with girls’ and under-represented ethnic group students’ underperformance in STEM (Beasley and Fischer 2012; Cheryan et al. 2011; Harper 2010; Smeding 2012; Walton and Spencer 2009) and may provide possible support for why girls and students from under-represented ethnic groups are underrepresented in STEM majors and careers (Spencer et al. 2016). It is plausible that increased trust, ownership, and control (i.e., autonomy) in mathematics classes, particularly in an inclusive STEM high school environment intended to increase underrepresented students’ participation in STEM, may help to reduce stereotype threat for girls and students from under-represented ethnic groups.
Although no significant interactions were observed between instructional strategies and gender and racial/ethnic identity on mathematics ability beliefs, we did find that female students reported lower mathematics ability beliefs than male students. This finding echoed what was observed in previous studies in that female students are more likely to underestimate their mathematics abilities and report lower mathematics attitudes (e.g., Leedy et al. 2003; Pajares 2005; Tocci and Engelhard 1991). On the other hand, we also found that African American students reported higher mathematics ability beliefs than their White counterparts. This finding aligns with Else-Quest et al. (2013) who found that African American students had higher mathematics value attitudes than White students; however, it conflicts with Pajares and Kranzler’s (1995) work. Together, this collection of findings suggests that gender and racial/ethnic identity differences in mathematics attitudes are complex and warrant further exploration.
Results also indicated that as students get older, their mathematics attitudes tend to become less positive, which is consistent with research that found students’ science intrinsic motivation and ability beliefs decrease as they progress through high school (LaForce et al. 2019). Students’ attitudes toward mathematics may become more negative with age for several reasons. On the one hand, entering a new school (in the 9th grade), especially one dedicated to STEM, has the potential to peak students’ STEM-related interests and excitement. However, students’ enthusiasm may wane as they become accustomed to the instructional strategies and environment in their STEM school. However, more longitudinal research is needed to gain insight into the factors that influence changes in students’ STEM attitudes over time.
Limitations
The results of the current study must be interpreted in light of several limitations. First, this study only examined students enrolled in inclusive STEM high schools; students attending non-STEM schools were not assessed, which limits our ability to compare how these instructional strategies impact students in different educational contexts. Future research should examine students attending a variety of school types to promote generalizability of the findings and, as well to further disentangle the role inclusive STEM school environments play in students’ development of mathematics attitudes.
In addition, this study collected data from students across high school grade levels (9th–12th); however, no longitudinal data were collected. As such, specific changes in students’ STEM attitudes over time, particularly for girls and students from under-represented ethnic groups, cannot be understood through this study. Examining changes in students’ STEM attitudes longitudinally, such as with growth curve modeling, could provide further insight about the potential value these instructional strategies may contribute to student outcomes.
Despite collecting data from teachers in the larger project, teacher-level data could not be linked to student-level data in the current study due to matching issues. Although student-level data can be linked to schools, only 17 schools participated, and this low number of clusters (i.e., schools) limited the capability to apply Hierarchical Linear Modeling (HLM) to generate accurate estimates. Moreover, to determine if HLM was appropriate for the current study, we also conducted unconditional HLM first, and then, calculated the intra-class coefficients (ICCs). The ICCs were much lower than the desired cut-off point (0.10) required to support examination of conditional HLM (Kreft and de Leeuw 1998). In the future, given the availability of high-quality nested data, HLM approaches may be considered to account for variance across different levels of data as a means to estimate more accurate parameters.
Only mathematics attitudinal outcomes were examined in this study. This study did not collect any mathematics-specific or STEM-focused achievement data although participating schools provided students’ cumulative GPA. Cumulative GPA, as a summary of GPA values over multiple academic years, does not necessarily reflect the potential benefits of STEM strategies students experienced during one academic year, and through, one particular math course. In addition, our previous study examined associations between STEM strategies and students’ attitudes toward science and academic achievement (i.e., cumulative GPA), yet few associations emerged between STEM strategies and cumulative GPA (LaForce et al. 2019). Nevertheless, students’ attitudes represent important predictors in the pursuit of STEM majors (Britner and Pajares 2001); therefore, future research needs to examine academic achievement to disentangle the multifaceted associations between students’ attitudes, academic achievement, and exposure to STEM instructional strategies. Establishing research-practice partnerships (RPP) represents an effective way to collect the different types of data needed to better understand how these variables are linked.
Finally, we also encourage future researchers to employ intersectional conceptual and analytical approaches (Else-Quest and Hyde 2016a, b) when examining gender and race/ethnicity gaps in inclusive STEM school students’ mathematics attitudes. We recognize that carrying out an additive analytic approach, similar to the one implemented in the current study, limits the conclusions that can be drawn regarding students’ dual identities (e.g., being Asian and female students; being African American and a male student). Future research must investigate the effect of gender and race/ethnicity simultaneously using intersectional conceptual and analytic approaches in order to inform the creation of strategies aimed at reducing educational inequities in STEM.
Future Directions
This exploratory research study is an early step toward understanding associations between STEM strategies and students’ attitudes toward mathematics in the context of inclusive STEM schools. Although they share common goals related to broadening participation in STEM education and building a healthy pipeline to future STEM careers, each inclusive STEM school has its own framework, structure, and specific strategies employed to grow students’ STEM interests and increase their STEM achievement. However, the current body of research related to inclusive STEM schools primarily examines inclusive STEM schools as one uniform entity and attempts to pinpoint effective solutions for all schools homogenously without digging into the “black box” of each individual STEM school to learn more about specific strategies and practices taking place (LaForce et al. 2019). Our research found promising results related to improving mathematics attitudes through the examined STEM school strategies; however, these strategies, alone, are not sufficient to increase underrepresented students’ attitudes toward mathematics. Inclusive STEM high schools are a complex innovation employing many different types of strategies, and some are more effective at shaping students’ attitudinal and academic achievement outcomes than others. As a result, future research should continue to focus on examining the unique characteristics of these schools, particularly characteristics that differentiate them not only from traditional high schools, but also from other inclusive STEM schools. In addition, we selected five specific STEM school strategies (e.g., cognitively-demanding work; technology use) to explore in this study; other strategies exist, including guided independent research studies (Bruce-Davis et al. 2014). Further exploration of these additional strategies will help provide more-targeted suggestions for academic improvements within these schools, and may also provide explanations for the mixed findings present here, and in the literature.
Furthermore, this study used student-focused items (i.e. “I did this…”) because they align more closely with inclusive STEM school models exemplified in the 8 Elements framework (LaForce et al. 2016). In the original data collection, our study included questionnaire measures differentiating teacher-facilitated strategies (e.g., “My teacher asked me to support my conclusions with evidence”) and student experiences (e.g. “I supported my conclusions with evidence”). During analysis, it was discovered that the two were highly correlated, and essentially the same construct. We learned that there was gray area between “teacher facilitated” and “student driven” items, and that in these schools, it was not possible to statistically separate the two constructs with our measures. We see all student learning activities (in inclusive STEM high schools we studied) as facilitated by someone at some point. Students, particularly at the stage in which this data was collected, may do independent strategies to support themselves and their learning without the direct request of a teacher in any given moment. However, students may also engage in these behaviors because the teachers and staff in the school have effectively facilitated them through their norms and culture. Thus, we excluded “my teacher asked me to…” types of questions and allowed the student experiential questions to stand as the more appropriate measures for understanding inclusive STEM classroom strategies. As time goes on and more and more students experience self-directed learning strategies at younger ages, it may be appropriate for future research to distinguish between students’ own intrinsically-motivated learning strategies and teacher-facilitated strategies. With future research distinguishing the two strategies, more attention should be given to teacher attitudes and the specific facilitating role that they can play in implementing different strategies. For example, how their readiness for change and their willingness to implement new strategies in the context of inclusive STEM schools may exemplify or inhibit differences in STEM-related outcomes for different groups of students.
In addition, since students’ attitudes are malleable, and cannot be changed by one-time efforts in a single setting, future research should capture the change in students’ STEM attitudes and their longitudinal exposure to STEM school strategies through more-rigorous research designs. Longitudinally examining students’ STEM attitudes through multiple data points can depict the changing patterns of students’ STEM attitudes and provide in-depth understanding of the implementation of STEM strategies over time in relation to how students’ attitudes may have fluctuated. As a result, targeted strategies can be applied to certain time periods or to certain age groups (e.g., grade levels) for more targeted improvement. Longitudinal research also helps to explain variations of the implementation (i.e., STEM school models) over time.
Footnotes
- 1.
Please refer to the website: http://outlier.uchicago.edu/s3/findings/roadmap/ for more information regarding the theory of action.
- 2.
The Elements include (1) problem-based learning (PBL); (2) rigorous learning; (3) personalization of learning; (4) career, technology, and life skills; (5) school community and belonging; (6) external community; (7) staff foundations; and (8) essential factors (LaForce et al. 2016).
- 3.
For both mathematics intrinsic motivation and mathematics ability beliefs, we reported unstandardized coefficients (B) in the original units of the scales corresponding to each variable, in the text. Standardized coefficients (β) were not reported, yet available from the authors upon request. Moreover, only significant findings were reported in text (please see tables for other non-significant findings).
- 4.
Coefficients for simple slopes generated by “Interaction!” program were only reported in text, not in tables.
- 5.
The current study emphasized the use of instructional strategies within the context of inclusive STEM schools in relation to gender and race/ethnicity gaps on students’ mathematics attitudes. Thus, we did not focus on discussing intersectionality theories or provide a thorough discussion of individual and social contexts related to intersectionality. However, we provided additional intersectional analysis for those who are interested.
Notes
Acknowledgements
This research was supported by a grant from the National Science Foundation (1238552).
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