Many teachers want to help their students develop a growth mindset about their ability to do mathematics. Research has shown, however, that teachers simply do not know how to promote growth mindsets in their classrooms. Existing research suggests that one way teachers can support students' development of a growth mindset is through the written feedback they provide students. This study combines the research done on students' mindsets and written feedback to examine the interaction between student mindset and written feedback by analyzing written feedback provided to students in a College Algebra class and how students used that feedback based on their homework resubmissions and their interviews. This study suggests that students do not use their written feedback relative to their mindset towards learning mathematics, but rather that their definitions of success in a mathematics class drive their interpretation and use of their written feedback. This study also suggests that students' definitions of success in mathematics contribute to their mindsets towards learning mathematics. Findings from this study inform teachers about how students interpret and use written feedback in a mathematics class. Teachers should provide students with opportunities to change their definitions of success in mathematics, which may change their mindset towards learning mathematics.

College Algebra is a gatekeeper course that serves as an obstacle for many students pursuing STEM careers. Lack of success in this course could be a key reason why the United States lags behind other industrialized countries in the number of students graduating with STEM majors and joining the STEM workforce. Of the many topics presented in College Algebra that pose problems, students often have particular difficulty with the application of systems of equations in the form of word problems. The present study aims to identify the factors associated with success and failure on systems of equations word problems. The goal was to identify the factors that remained significant predictors of success in order to build a theory to explain why some students are successful and other have difficulty. Using the Opportunity-Propensity Model of Byrnes and colleagues as the theoretical guide (e.g., Byrnes & Miller-Cotto, 2016), the following questions set the groundwork for the current study: (1) To what extent do antecedent (gender, race/ethnicity, socioeconomic status, and university) and propensity factors (mathematical calculation ability, mathematics anxiety, self-regulation, motivation, and ESL) individually and collectively predict success with systems of equations word problems in College Algebra students, and (2) How do these factors relate to each other? Bivariate correlations and hierarchical multiple regression were used to examine the relationships between the factors and word problem set-up as well as correct completion of the word problems presented. Results indicated after all variables were entered, calculation ability, self-regulation as determined by homework score, and anxiety were the only factors to remain significant predictors of student performance on both levels. All other factors either failed to enter as significant predictors or dropped out when the complete set had been entered. Reasons for this pattern of results are discussed, as are suggestions for future research to confirm and extend these findings. / Math & Science Education

This study investigated the ways in which college algebra students watch mathematics instructional videos with the goal of answering the following research questions: (1) How are student responsibility frames similar or different among students within a particular video? (2) How do the various video design principles support or constrain the uses of particular responsibility frames? This research was guided by the cognitive theory of multimedia design and the theory of didactic situations. The cognitive theory of multimedia design outlined principles for video creation and design that could impact student learning from video watching. The theory of didactic situations defined implicit teacher and student responsibilities within the context of the face-to-face mathematics classroom and was applied in this study to students watching mathematics instructional videos. Participants were recruited from five college algebra classes at a university in the northeastern United States and were asked to attend two semi-structured interviews. During the first interview, participants were pretested to determine their prior knowledge about how to solve quadratic functions and to measure their mathematics-related beliefs. During the second interview, participants watched three different videos about solving quadratic equations by completing the square and were asked questions about the mathematics that they viewed in the videos. Transcriptions of audio recordings of these interviews were coded thematically using categories previously identified by the didactic contract for the face-to-face classroom and expanding the types of student responsibilities identified specifically for video watching as needed. This study found that participants, regardless of overall prior knowledge or mathematics-related beliefs, but who had prior knowledge of completing the square, held a responsibility to use the specific set of steps they were taught by their teacher to solve problems. Additionally, participants at some levels of prior knowledge expressed a responsibility to not watch videos that showed a visual representation of the mathematics. Findings also suggested a student heuristic for the selection and use of mathematics instructional videos that may be useful to both mathematics teachers and video creators. / Math & Science Education

There is a need to understand the relationship between, the traditional 16-week versus an 8-week, and college-level mathematics success rates. This study applied chi-square (χ2) and analysis of variance to compare and contrast which course length of time, 8-weeks or 16-weeks, for college algebra resulted in a higher proportion of students successfully completing the course. In addition, success rates among ethnicities, gender, and age groups were also examined. The population sample for this study was 231 students enrolled in college algebra from fall 2004 through fall 2007. Data was analyzed on four sections of the traditional 16-week courses and four sections of 8-week courses. Success was defined as earning a grade of A, B, or C in the course. The study found that overall there was no significant difference in success rates for the 8-week and 16-week college algebra courses. However, significant differences were found in success rates among Asian, Pacific Islander students enrolled in the 8-week and 16-week courses. No significant differences in success rates were found for White, Non-Hispanic; African-American, and Hispanic, Mexican American students. There was a significant difference in the number of A's, B's, C's, D's and F's among White, Non-Hispanic students, but there was no difference in A's, B's, C's, D's or F's for African-American; Hispanic, Mexican American and Asian, Pacific Islander. When considering success rates among genders, no difference was found in success rates for males or females who were enrolled in the 8-week and 16-week college algebra courses. There were a significant greater number of students in the age group (23-30) who were successful in the 16-week college algebra course than in the 8-week college algebra course. However, no differences in success rates were found in the age groups (18-22) and (31-40).

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