Student understanding of integration has become a topic of recent interest in calculus research. Studies have shown that certain interpretations of the definite integral, such as the area under a curve or the values of an anti-derivative, are less productive in making sense of contextualized integrals, while on the other hand understanding the…

In this paper, we compare and contrast our experiences in using standards-based grading in different courses and across two separate institutions to explore the related tradeoffs and subtleties in designing and implementing such grading systems, guided by innovation diffusion theory. We summarize our individual courses, use Linda Nilson's criteria…

WestEd is undertaking a multiyear series of implementation studies intended to inform the California State University (CSU) system about the implementation of Executive Order 1110 (EO 1110). A major policy adopted by the CSU Chancellor's Office in 2017, EO 1110 requires CSU campuses to eliminate non-credit developmental courses in Written…

Until recently, the vast majority of California's community college students--hundreds of thousands of students each year--started in remedial courses that slowed down or halted their academic progress. Attrition was high, particularly for Latino and African American students. Few students went on to complete the gateway courses necessary to…

California's AB 705 required community colleges to implement changes that would maximize students' likelihood of starting and completing transfer-level (or degree-appropriate) coursework in English and math/quantitative reasoning within one year. Under the law, colleges must use high school information (e.g., GPA, coursework, and/or grades in…

The purpose of this institutional ethnography was to better understand the experiences of undergraduate women in math and physics in order to identify and explore the institutional practices that coordinated their daily work. Through the framework of feminist standpoint theory, I collected student and faculty interviews, observations, and textual…

The use of web based software for learning opportunities abound, but what impact do they have on students' mathematics learning beyond the initial experience? This 2-phase, 17-month case study of 50 freshmen investigates the use of web-based learning and face-to-face lecture on students' future academic achievement in mathematics. First, the study…

Large foundational courses delivered in lecture halls are disadvantaged in eliciting participation from all students and maintaining engagement throughout the class session. We introduced a question-driven method facilitated by an audience response system, namely TopHat™, that allows the instructor to engage students in solving Calculus problems…

This paper examines the students' experiences with instructional delivery (ID) of distance and online learning of undergraduate mathematics in two major Nigerian universities. Purposive sampling was used in the study to select mathematics students from University of Lagos Distance Learning Institute (DLI) and the National Open University of…

Peer-led team learning (PLTL), specifically the model known as 'Workshops', has been shown to contribute positively and significantly to student success in STEM courses across subjects (Gosser et al., 2001). Our research adds to the SOTL literature describing the effectiveness of Workshops by reporting on the changes in student leaders. We examine…

In this thesis, I study some aspects of how students learn to use math to make sense of physical phenomena. Solving physics problems usually requires dealing with algebraic expressions. That can take the form of reading equations you're given, manipulating them, or creating them. It's possible to use equations simply according to formal rules of…

The mathematics behind Inge Lehmann's discovery that the inner core of the Earth is solid is explained using data collected around the Earth on seismic waves and their travel time through the Earth.

Rene Descartes' method for finding tangents (equivalently, subnormals) depends on geometric and algebraic properties of a family of circles intersecting a given curve. It can be generalized to establish a calculus of subnormals, an alternative to the calculus of Newton and Leibniz. Here we prove subnormal counterparts of the well-known…

Given a function defined on a subset of the plane whose partial derivatives never change sign, the signs of the partial derivatives form a two-dimensional pattern. We explore what patterns are possible for various planar domains.

A stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.