Examining the Impact of Mathematics Identity on the Choice of ...

Session F2H

Examining the Impact of Mathematics Identity on the Choice of Engineering Careers for Male and Female Students Cheryl A.P. Cass, Zahra Hazari, Jennifer Cribbs, Philip M. Sadler, and Gerhard Sonnert [email protected], [email protected],[email protected], [email protected], [email protected] Abstract - Previous research suggests strong connections between mathematics background and persistence in engineering career aspirations. This study expands on this research by examining how mathematics identity impacts the choice of engineering careers for male and female students. Our framework encompasses interest, recognition, performance, and competence as central factors that contribute to the development of mathematics identity. The data used in this study were drawn from the Factors Influencing College Success in Mathematics (FICS-Math) project; the survey included questions on students’ demographics, mathematics background/experiences, interest in mathematics, and career aspirations. Results indicate that factors of mathematics interest, mathematics competence and performance, and mathematics recognition are significant predictors of the choice of an engineering career, even after controlling for SAT/ACT math scores and demographics such as parental education. Moreover, the interaction between mathematics recognition and gender is also significant with the estimate indicating that females who are recognized in mathematics are more likely to choose engineering careers. This work reaffirms the importance of mathematics to engineering career choices and furthers the discussion by looking beyond mathematics grades to ascertaining the importance of mathematics identity. Index Terms–Engineering career choice, Gender, Mathematics identity, Quantitative assessment INTRODUCTION I. Mathematics Preparation and Engineering Career Aspirations The mathematics preparation that students bring with them into engineering programs has been found to be central to their success in these programs [1, 2]. Bowen and associates discussed the lack of prior mathematics preparation as a major barrier affecting undergraduate engineering enrollment and described a Bridging Technology with Mathematics program that was designed to help combat this problem [3]. Much of the research thus far has focused on prior mathematics course grades as

predictors for subsequent academic performance and persistence in STEM. For example, after observing higher academic performance by college students who enroll in Applied Honors Calculus II (AHC-II) when compared to students enrolling in Regular Calculus II, Mesa and colleagues inquired whether enrollment in AHC-II had a positive impact on performance in later courses in the engineering curriculum. They found that the impact of AHC-II on engineering student performance in subsequent courses was not significant and that Advanced Placement scores were responsible for the observed differences in AHC-II [4]. Thus, in this case, the mathematics preparation at the high school level was deemed an important factor to include in future models predicting academic performance in engineering. Furthermore, Parsons and colleagues’ regression model showed that, for first-year engineering students, increased mathematics preparation (i.e. higher grades in prior math courses) predicted a 12% increase in college mathematics grades while increased confidence levels predicted a 5% increase in grades [2]. Previous research has also shown that increased out-of-class mathematics instruction (e.g. enrollment in Project Lead the Way (PLTW) courses) does not always serve as a solution for mathematics deficiency; Tran and Nathan concluded that students enrolled in PLTW showed significantly smaller math assessment gains when compared with students who did not enroll [5]. Furthermore, research results indicate strong connections between mathematics background and persistence in engineering career aspirations. However, most of the work examining engineering persistence occurs at the undergraduate level, with a lack of focus on critical pre-college experiences. For example, Winkelman explored how concepts of mathematics affect perceptions of engineering design by novice engineering students. His data exposed a variety of contrasting viewpoints associated with mathematics concepts; mathematics was described as both a gateway and gatekeeper to engineering and as favoring closed solutions, which implies both reliability and suppression of creativity [1]. In a further example, Li and colleagues reviewed two decades of research with the aim of developing a classification system for engineering student characteristics (external, internal, and demographic) to understand their effects on engineering educational outcomes, including persistence. Key characteristics cited as

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Session F2H predictive of persistence in the review included mathematics preparation, self-ratings of mathematical ability, and enjoyment in studying mathematics [6]. The role of gender has also been considered when evaluating the effect of mathematics on STEM trajectories. Camp and colleagues found that women in physical, mathematical, and computer sciences and engineering performed better in high school mathematics courses and on SAT exams when compared with women in social, psychological, and life sciences [7]. In support, other research found that a greater percentage of freshmen female engineering students were certain of their choice of majors, had higher GPAs and ACT scores, and took more advanced mathematics courses[6]. Furthermore, in a qualitative study of females who ranked at or above the 95th percentile on the quantitative section of the SAT exam, O’Shea and associates found that educators can promote STEM careers for mathematically gifted females using an “attribution style that enables them to clearly acknowledge their talents in math” [8].

study, Solomon and colleagues reported on the role of a mathematics support center in the development of an undergraduate mathematics community of practice; the authors describe a collaborative atmosphere where mathematics students cultivate relationships with tutors and peers, and where students can see themselves as active participants in a mathematics community [12].

II. Framing the Study with Mathematics Identity This study expands on this mathematics assessment-based research by examining how mathematics identity impacts the choice of engineering careers for male and female students. Since confidence and skill in mathematics play a central role in engineering pursuits, our research is grounded in a theoretical framework centered around students’ mathematics identities (i.e. how students see themselves with respect to mathematics). As illustrated in Figure 1, the framework positions interest, recognition, performance, and competence as central factors that contribute to the development of mathematics identity. Recognition refers to perceived recognition by others as being a good mathematics student while interest addresses a desire and/or curiosity to think about and understand mathematics. Measures of performance refer to a belief in ability to perform on required mathematics tasks, and competence involves a belief in ability to understand mathematics content. Prior research has focused on the link between selfefficacy and performance in mathematics. For example Berger and Karabenik found that self-efficacy of 9th grade mathematics students predicted reported use of learning strategies including rehearsal, organization, elaboration, metacognition, help seeking, time and study [9]. Additionally, Kitsantas and colleagues discuss the need for mathematics educators to focus on enhancing student selfefficacy and to structure homework assignments such that they can be completed in a timely manner [10]. However, self-efficacy is constructed to examine highly task-specific self-perceptions, usually on the short-term. In contrast, the macro-level framework presented allows assessment of how students view themselves with regard to mathematics over a long period of time, in a more global context. Solomon argues the importance of considering mathematics identity within multiple communities of practice (i.e. not only the immediate classroom environment) [11]. In a subsequent

FIGURE 1. FRAMEWORK FOR STUDENTS’ IDENTIFICATION WITH MATHEMATICS (ADAPTED FROM [13])

While using a mathematics identity framework, the goal of this study was to begin to understand how aspects of mathematics identity predict engineering career choice for male and female students. In future work, we aim to examine mathematics classroom experiences in an effort to make recommendations for adapting mathematics courses with the primary focus of improving mathematics identity development and increasing the potential for students to enter or remain on engineering career paths.


Session F2H III. Research Questions The following research questions were addressed in this study to explore how elements of mathematics identity align with the theoretical framework and how they impact the engineering-related career decisions of male and female students:  How well do items on the FICS-Math survey align to the theorized mathematics identity sub-constructs?  To what extent do the mathematics identity subconstructs predict the choice of an engineering career for female and male students?

non-parametric covariance matrix was created for use in the factor analysis. A promax rotation was employed since the theory allows correlation between the sub-constructs, i.e. the factors were not expected to be orthogonal. Next, the factors were regressed on the choice of engineering as a career, i.e. engineering career choice was set as the dependent variable in a logistic regression model, while controlling for mathematics scores from SAT/ACT standardized tests, highest levels of parental education, and gender. Interactions between gender and the mathematics identity sub-constructs were also included in an effort to find factors that influence females differently than males.

METHODS

RESULTS

I. Data The data used in this study was drawn from the Factors Influencing College Success in Mathematics (FICS-Math) project which focuses on finding evidence for the most effective strategies that prepare students for college calculus success. Funded by the National Science Foundation, FICSMath is a large-scale study which surveyed a nationally representative sample of college students enrolled in introductory calculus courses in the fall semester of 2009. Drawing from a stratified random sample of colleges and universities across the US, the national survey study obtained data from 10,492 students attending 336 college calculus courses at 134 institutions. The respondents were 60% male and 34% female, with 6% not reporting their gender. In terms of race and ethnicity, respondents were 66.7% White, 4.6% African-American, 10.7% Asian, 8.9% Hispanic, and 0.4% American Indian/Alaskan Native. The FICS-Math survey included questions on students’ demographics, academics, mathematics interests, and high school mathematics experiences. The development of the FICS-Math survey was led by three components: 1) a literature review to identify factors that may influence success in mathematics, 2) an extraction of items from previous national studies (Factors Influencing College Science Success-FICSS and Persistence Research in Science & Engineering-PRiSE) and, 3) open-ended responses from 185 mathematicians and 84 mathematics teachers across the nation via a survey administered online. II. Analysis The R statistical software package (version 2.1.2) was employed to pursue examination of both research questions. First, an exploratory factor analysis was conducted to examine how well the items on the FICS-Math survey related to mathematics identity load on the theorized subconstructs. If the resulting factors align with the framework, then the data also supports the construct validity of the subconstructs discussed in the framework (interest, recognition, performance, and competence). From the FICS-Math survey, 11 items related to the sub-constructs were included in the factor analysis. Since several of these items were binary, a

I. Factor Analysis for Mathematics Identity Sub-Constructs The 11 items aligned on the theorized sub-constructs with competence and performance items loading under the same factor. Thus, performance and competence were combined under factor 3. Factor loadings ranged from 0.45 to 0.85 indicating that, to a great extent, items accurately captured the same construct. TABLE I FACTOR ANALYSIS FOR MATHEMATICS IDENTITY SUB-CONSTRUCTS

Factor 1: Interest (% of cumulative variance explained = 18) Survey Item Statement Loading Q44dislike I wish I did not have to take math -0.56 Q44enjoy I enjoy learning math 0.84 Q44interest Math is interesting 0.78 Q44lookforw I look forward to taking math 0.59 Factor 2: Recognition (% of cumulative variance explained = 32) Survey Item Q45mathpersonp

Statement Loading Degree to which 0.74 parents/relatives/friends see you as a math person Q45mathpersons Degree to which you see yourself as a 0.81 math person Q45mathpersont Degree to which math teachers see you 0.55 as a math person Factor 3: Competence and Performance (% of cumulative variance explained = 44) Survey Item Q44exam Q44understand Q44nervous Q44persist

Statement I can do well on the exams I understand the math I have studied Math makes me nervous Setbacks do not discourage me

Loading 0.67 0.55 -0.46 0.45

The factor “interest” encompasses original survey items including “I wish I did not have to take math,” “I enjoy learning math,” “Math is interesting,” and “I look forward to taking math,” which explains 18 percent of the cumulative variance. When constructing the subsequent “interest” composite, the first item (“I wish I did not have to take math”) was reverse coded. The factor “recognition” comprises survey items “Degree to which parents/relatives/friends see you as a math person,” “Degree to which you see yourself as a math person,” and “Degree to which math teacher sees you as a math person” and explains 32% of the cumulative variance. The combined


Session F2H performance/competence factor includes survey items “I can do well on the exams,” “I understand the math I have studied,” “Math makes me nervous,” and “Setbacks do not discourage me.” The third item (“Math makes me nervous”) was reverse coded before creating the “performance/competence” composite. Together with the first two factors, the third factor explains 44% of the cumulative variance. A scree plot revealed that very little additional variance is explained by including more factors. The details of this analysis including survey items, factor loadings, and percent of variance explained are summarized in Table 1.

factor. This likely indicates that a person’s beliefs regarding their ability to perform in mathematics and their ability to understand are closely related – more closely related than the other sub-constructs. In the theory, then, the performance and competence circles overlap to a greater degree. Using a semi-structured interview approach, Burton aimed to understand the difference between teacher and student perspectives of confidence in mathematics. Students confirmed that “confidence and success are closely intertwined” and their discourse often indicated the strength of the relationship between perceived competence and ability to perform [14].

II. Logistic Regression Predicting Choice of Engineering Career with Mathematics Identity Sub-Constructs

Research Question 2: To what extent do the mathematics identity sub-constructs predict the choice of an engineering career for female and male students?

Results from the regression model predicting choice of engineering as a career, with a focus on mathematics identity factors and gender interactions, appear in Table 2. Although both parents’ education levels were initially included in the model as controls, only mother’s education was significant. Subsequently, father’s education was removed from the model. When looking at the mathematics identity subconstructs, math interest (p