This study investigated two undergraduate mathematics students' meanings for derivatives of univariable and multivariable functions when creating linear approximations. Both participants completed multivariable calculus at least two semesters prior to participating in a sequence of four to five exploratory teaching interviews. One purpose of the…

Linear algebra is gaining increased attention due to its applications in many modern high-tech industries, such as artificial intelligence, machine learning, and robotics. Coordinate systems underlie many concepts in linear algebra and promote students' spatial thinking of key concepts by imposing a visual aspect to courses that may otherwise be…

The enduring debate surrounding college algebra, traditionally a gateway for STEM pathways, underscores the necessity for curricular evolution in response to the rising popularity of non-STEM majors. This dissertation explores the success of an applied college algebra course designed for non-STEM students. The study aimed to determine whether this…

Calculus has long been known as a "gateway course" to STEM fields in postsecondary education. To moderate this gatekeeping effect, Montclair State University researchers developed a peer-led, inquiry-based instructional support (IBIS) to run parallel to Calculus classes. The design of the IBIS model was informed by an instructional…

Undergraduate students' understanding of function continuity has not been explored broadly in previous research. The relevant findings in the literature are predominantly concerned with calculus students' understanding and misconceptions of continuity. Many of these misunderstandings are tied to the relationships which continuity has with limits…

The purpose of this comparative study was to determine if and to what extent there was a statistically significance difference in college students' motivation--amotivation, external regulation, introjection, identification, intrinsic motivation--to learn Algebra I between in-person instruction and online instruction in Central Arizona. The theory…

Student success is an integral part of systemic change research. However, students' lived experiences and voices are often subdued in this programme, leaving the change that occurs to be evaluated upon measures that do not capture a holistic view of the experiences students and their shifting identities during the roll-out of those changes. These…

The COVID-19 pandemic led to a global lockdown and compelled institutions to shift to emergency remote teaching. This transition and the lack of knowledge of using technology affected teaching practices, including assessment. Confronted with new contexts for assessment and threats to validity caused by ineffective proctoring, many instructors had…

Play has been discussed by mathematicians and mathematics educators as essential to mathematical progress and has been widely acknowledged to have a role in learning. Yet, play is rarely acknowledged, leveraged, or studied for mathematics learners beyond early childhood. Moreover, there are theoretical and empirical challenges with designing for…

This qualitative research study explores how students negotiate their identities as mathematics learners in a college algebra quadratics unit that implements asset-based frameworks that reframe mathematics curriculum to support student awareness of their capacities. This study adds to existing research discourse on teaching and learning…

Reversing the trend of US STEM graduation rates lagging other industrialized nations requires that we look at the entire pipeline of potential STEM students, including the vast number that start their journeys in remedial math classrooms in two-year colleges. Most research to date has focused on either Learning Support (LS) success or STEM…

The topic of this research study is mastery learning, an educational theory that began with the work of John Carrol in 1963. The core principle of this theory is that all students can achieve uniform learning outcomes, but it will take some students longer than others to reach the same performance goals. The problem that this research study…

The issue of college readiness persists in higher education, with many students entering college unprepared for the demands of college-level coursework. This challenge is particularly pronounced in math-intensive fields, where students frequently encounter struggles in corequisite math courses. The problem statement asserts that underprepared…

Counting is an intellectual activity that is usually identified with the assignment of positive whole numbers ("1, 2, 3, 4, ...") in one-to-one correspondence with a collection of items in one's attentional field. Taking into account a broader, "combinatorial" meaning of the term, counting extends far beyond this description.…

This mixed-methods study investigated the impact of the Foundations of Mathematical Reasoning course within the Quantitative Reasoning Pathway developed by the Dana Center for Mathematics Pathways at the University of Texas at Austin on student motivation in mathematics. Quantitative research was conducted to determine the effects of the…