Though women earn nearly half of the mathematics baccalaureate degrees in the United States, they make up a much smaller percentage of those pursuing advanced degrees in mathematics and those entering mathematics-related careers. Through semi-structured interviews, this study took a qualitative look at the beliefs held by five undergraduate women mathematics students about themselves and about mathematicians. The findings of this study suggest that these women held stereotypical beliefs about mathematicians, describing them to be exceptionally intelligent, obsessed with mathematics, and socially inept. Furthermore, each of these women held the firm belief that they do not exhibit at least one of these traits, the first one being unattainable and the latter two being undesirable. The results of this study suggest that although many women are earning undergraduate degrees in mathematics, their beliefs about mathematicians may be preventing them from identifying as one and choosing to pursue mathematical careers.

Mathematical statements involving both universal and existential quantifiers occur frequently in advanced mathematics. Despite their prevalence, mathematics students often have difficulties interpreting and proving quantified statements. Through task-based interviews, this study took a qualitative look at undergraduate mathematics students' interpretations and proof-attempts for mathematical statements involving multiple quantifiers. The findings of this study suggest that statements of the form "There exists . . . for all . . ." (which can be referred to as EA statements) evoked a larger variety of interpretations than statements of the form "For all . . . there exists . . ." (AE statements). Furthermore, students' proof techniques for such statements, at times, unintentionally altered the students' interpretations of these statements. The results of this study suggest that being confronted with both the EA and AE versions of a statement may help some students determine the correct mathematical meanings of such statements. Moreover, knowledge of the structure of the mathematical language and the use of formal logic may be useful tools for students in proving such mathematical statements.Quantification is an important component of the mathematical language. Two commonly used quantifiers in mathematics are the universal quantifier ( ) and the existential quantifier ( ). Common phrases used to express the universal quantifier are "for all", "for every", and "for each", such as in the example, "For all x in the real numbers, x 2 > 0". Phrases frequently used to represent the existential quantifier are "there exists", "there is", and "there is at least one", such as in the example, "There exists a real number x, such that x 2 = 5".Mathematical statements involving both universal and existential quantifiers occur frequently in advanced mathematics. Calculus students often face mathematical statements involving multiple quantifiers when studying limits and continuity. Students continuing to study mathematics beyond calculus will see such statements again in nearly all their further mathematics classes, for example the division algorithm in number theory, the definition of a group in abstract algebra, the definition of open and closed sets in topology, and convergence of functions in analysis, just to name a few. Although some textbook authors write such definitions and theorems in ways that avoid using multiple quantifiers explicitly, the underlying structure remains the same. Despite the prevalence of quantified

The purpose of this study was to investigate what motivates women to choose mathematics as an undergraduate major and to further explore what shapes their future career goals, paying particular attention to their undergraduate experiences and their perceptions of the role of gender in these decisions. A series of semi-structured, individual interviews were conducted with twelve undergraduate women mathematics majors who were attending either a large public university or a small liberal arts college. This study found that strong mathematical identities and enjoyment of mathematics heavily influenced their decisions to major in mathematics. At the career selection stage, these women desired careers that are service-oriented, social in nature, and involved mathematical applications. For those planning to become teachers, the desire to help others predominantly influenced their career decision. Many of the non-teaching majors were unaware of mathematical careers other than teaching that satisfied these career qualities. Implications of these results with respect to women's participation in mathematics are discussed.

Several key factors have emerged from the literature contributing to the explanation of STEM participation (or lack of), including mathematics mindset, mathematics anxiety, mathematics identity, and mathematics self-efficacy. Despite the research on the relations of these variables to career interest, few studies have integrated them and examined their intertwined relations in one model. The purpose of this study was to use a structural equation modeling approach to answer the central question: To what extent are the factors of mathematics mindset, mathematics anxiety, mathematics identity, and mathematics self-efficacy related to each other and a STEM career choice? The results highlight a key finding that mathematics identity serves as a full mediator between mathematics mindset and STEM career interest as well as between mathematics anxiety and STEM career interest. K E Y W O R D S mathematics anxiety, mathematics identity, mathematics mindset, mathematics self-efficacy, STEM career choice | 285 CRIBBS et al.

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