participants' beliefs about the factors that contribute to mathematical success. For this study, we focused on three questions that targeted their beliefs about why some students do well in mathematics and the attributes of students who succeed in mathematics. After the interviews were completed, we listened to the recording and identified the location of the participants' responses to the three questions. We wrote detailed notes that described each participant's beliefs about the factors that contributed to mathematical success and transcribed specific statements that captured these beliefs. All authors read and re-read these descriptions and wrote statements or phrases that reflected the meaning underlying the teachers' statements. Then we met to collectively discuss our observations and identified statements/phrases that cohered. We summarized these statements into themes which are described next. Findings Teachers' responses converged around five themes in relation to the reasons for students' success in mathematics. In what follows, we describe teachers' responses under each theme.

Innate abilities and dispositions. Participants indicated that there was some inborn traits responsible for students' mathematical success. Some alluded to innate cognitive abilities while others described more dispositional traits. Participants stated that some students were born with high mathematical aptitude, or their brains were designed to be proficient at math. Connie and Abby's statements reflected these perspectives, stating respectively "Some people are just born with a high skill in math…[they] think mathematically" and "…that's just how their brain is made up". Others described traits of students who are successful at math in ways that would suggest they were inborn and not developed through experience. Some of these traits included "well-behaved" (Eva), "creative (Elizabeth)", "takes initiative (Kimber)", "has a growth mindset (Pablo)", "resilient" (Joanna). These traits were described as the students' natural inclinations in how to act or behave.

Parental influence. The majority of teachers attributed mathematical expertise to parental influences to some degree in both positive and negative ways. However, the nature of the influence that teachers described varied. Influences that were regarded as positive included parental support and encouragement to do well, providing opportunities to support brain development, and creating access to resources that support mathematical thinking. One of the three factors supporting mathematical expertise that Connie stated was the student's homelife. In particular, "whether there are clear expectations and encouragement at home". Negative influences included parents projecting their own experiences with math onto their children, and lack of encouragement to do well mathematically. Karen recalled parents making statements like "math was hard for me so it will be hard for them".

Nature of the subject. Teachers also remarked that developing expertise in math is difficult because understanding concepts in the discipline is generally challenging. Elizabeth stated that developing knowledge of math requires initial interaction with concrete objects and learning how to talk about and describe what you are making sense of. She stated that "students generally struggle with explaining" and that does not bode well for developing expertise. Similarly, Joanna mentioned "Students don't have an opportunity to concretely understand what numbers are, what is happening if you're adding, subtracting something and have that concrete hands-on experience". While Joanna and Elizabeth referred to difficulties in developing a strong conceptual foundation, Eva described the role of practice, stating "math is a matter of practice so if you are more active then you will succeed".

Good mathematics teaching. Four teachers identified high-quality teaching as playing an important role in students' mathematical success. Joanna described how the role of the educator and teaching became most salient for her when she taught kindergarten after teaching third grade. She reflected "Teaching kindergarten was really humbling. I didn't realize how much teaching had to happen in kindergarten for my third graders to know what they know". Similarly, Smith foregrounded the role of the educator in unearthing students' abilities to engage meaningfully in mathematics. She stated, "It's the educator's responsibility to ensure that all students feel heard, that create a space where students feel that they can participate and contribute". Smith made it clear that distinctions along race and gender lines tend to be imposed by adults and that when students are placed in classrooms with educators who know their value, they will do well mathematically.

Race but not race. Unlike Smith who consistently explained why mathematical expertise should not be attributed to gender and/or race, some teachers would state the race and/or gender were not factors but in their descriptions of reasons would include proxies for race. For example, Abby talked about language being a barrier to success, "Schools in the US, white students (advantaged) do better, and this is due to students being accustomed to English and learning connected to their real-life contexts". Others ascribed racialized and gendered dispositional traits to students although rejecting this idea in other parts of the interview. Connie described that Black and Latino boys often have a "smart mouth" and that often correlated with success, while girls tended to be more reserved. Further, Abby stated that "lower-level" and Hispanic students do not put forth effort, resulting in negative mathematical outcomes.

With respect to commonalities across teachers' demographics, there were no distinct patterns by race across the responses that fell within the abovementioned themes, except for good mathematics teaching. We noted that both teachers of color and white teachers described innate characteristics (i.e., ability, dispositions) and external factors (i.e., parents, resources) as reasons for students' mathematical success. However, only teachers of color provided reasons for mathematical success that reflected the belief that high-quality teaching played a role in students' mathematics success. It may be that while white teachers recognized the factors external to the student support or hinder students' mathematical outcomes, they may not consider teaching as significant enough to outweigh other factors or they do not position themselves as having a critical role to play in students' success.

The teachers' responses in the study indicate a wide range of beliefs around mathematical success. Although some teachers highlighted and centered teachers as being partially responsible for inspiring students to engage with mathematics (i.e., contextual factors external to the student), there were other teachers who centered students as being solely responsible for how successfully they relate and connect to mathematics. In this regard, teachers referred to innate characteristics and dispositions as the reason for students' success, which aligns with the tenets of genetic determinism (Keller, 2005). Thus, success in mathematics is connected to students' abilities to use their own "creativity", "focused nature", "initiative", and/or "resilience" to deal with challenging mathematics concepts. Teachers also described students' effort (growth mindset), the role of parents, and resources accessible within the home, as responsible for mathematical success. These reflect attributions aligned social determinism and school meritocracy (cf., Jost et al., 2005;Rangal & Keller, 2011). Interestingly, some teachers suggested that the mathematics was itself a challenging discipline, thus lack of success was not person-related.

The variety of responses from in-service teachers suggests the need to further research how attributional beliefs about students' mathematical success are developed and sustained. However, the real danger lies in within-service teachers' beliefs in one sole factor that determines success. This leads to the further perpetuation of beliefs such as social determinism, genetic determinism, and school meritocracy which largely emphasize one factor without considering contextual aspects, social identities (e.g., race), stereotyping, and equal access and opportunity. By considering the social, political, racialized and gendered contexts that impact student success, educators consider factors that influence students' mathematical success beyond personal attributions and characteristics. Teachers that consider many different factors can aid in pushing back against both positive and negative stereotypes about students who succeed in math and those who do not while also being more culturally responsive to the needs of all of their students.