We investigate aspects of reform enacted in 66 class observations from 18 institutions collected as part of the National Study of University Calculus in the US. We examined four aspects related to how problems were solved in class: the extent of student involvement, the representations and technology used, and specific features of the problems…

Background: Calculus instruction is underexamined as a source of racialized and gendered inequity in higher education, despite research that documents minoritized students' marginalizing experiences in undergraduate mathematics classes. This study fills this research gap by investigating mathematics faculty's perceptions of the significance of…

Many researchers have stressed the embodied nature of mathematical understanding. Here we explore how embodied knowledge may evolve as students learn a basic calculus concept: the rate of change. We examined undergraduate students with different levels of calculus knowledge working in pairs to model the rate of change in an everyday phenomenon.…

For many years, multiple representations have played a major role in the teaching and learning of mathematics (NCTM, 2014). The present study defined and investigated a particular phenomenon called representational conflict, which can arise when students simultaneously use multiple representations on the same mathematical task. Representational…

The purpose of this study is to examine the characteristics of students' thinking about graphs while evaluating statements from Calculus. We conducted clinical interviews in which undergraduate students evaluated mathematical statements using graphs to explain their reasoning. We report our classification of students' thinking about aspects of…

This study focuses on students' understanding of multiple representations of functions. It examines student responses to a task in which calculus students are asked to evaluate the derivative at a point of the cubing function when represented piecewise. Results suggest that attending to the graph of the piecewise function does not improve…

The Mathematical Association of America's "Precalculus to Calculus: Insights and Innovations Conference" brought together representatives of mathematics departments from across the country with members of two national research projects to share and discuss both research findings and on-the-ground concerns of faculty. In this article, we…

Background: Graduation rates in engineering programs continue to be a concern in higher education. Prior research has documented an association between students' experiences in first-year mathematics courses and graduation rates, but the influences of the mathematics courses completed and the grades earned are not fully understood. Purpose: The…

Students' perceptions of cost are important predictors of academic and motivational outcomes. Though cost has been described as the anticipated effort one must put forth on an activity and what an individual sacrifices to complete a task, no known work has examined the extent to which anticipated cost beliefs predict experienced cost or whether…

Recently, a new source of data with great potential for use in the mathematics classroom has become available. The smartphones in our pockets are packed with sensors. Most phones have at a minimum global positioning, accelerometer, magnetometer, and gyroscope sensors. We give an example of the collection and analysis of global positioning sensor…

This article describes a Standards-Based Grading (SBG) implementation used in a variety of lower-level mathematics courses, notably including the use of oral re-assessments. A retrospective study of this implementation was conducted that showed that female students take advantage of optional oral re-assessments at greater rates than male students…

Students' attitudes toward mathematics and the strength of their mathematics preparation typically go hand in hand such that their specific effects are difficult to disentangle. Employing the method of propensity weighting of a continuous variable, we built hierarchical linear models in which mathematics attitudes and preparation are uncorrelated.…

The first day of many mathematics classes is filled with the formalities of the syllabus and a lecture introduction to the course content. Here, an alternative is presented where modeling is placed as the centerpiece to orient students to the work of differential equations; namely, to capture as beautifully and compactly as possible through the…

Our university is one campus of the larger, 23-campus California State University system. In 2017, the Chancellor of the system discontinued the developmental mathematics programs at all 23 campuses. This caught us by surprise and compelled us to act quickly. This article gives an overview of our response, highlighting the change our department…

Modeling projects in differential equations and engineering courses create an authentic activity and an opportunity to attain the holy grail of "deeper" learning. However, what do we mean by "deeper" learning and how do we create an environment that encourages that? This article describes a proposal and case study in using…