Our field has generally reached a consensus that active-learning approaches improve student success; however, there is a need to explore the ways that particular instructional approaches affect various student groups. We examined the relationship between gender and student learning outcomes in one context: inquiry-oriented abstract algebra. Using…

This paper offers instructional interventions designed to support undergraduate math students' understanding of two forms of representations of Calculus concepts, mathematical language and graphs. We first discuss issues in students' understanding of mathematical language and graphs related to Calculus concepts. Then, we describe tasks, which are…

Mathematics educators view the equals sign as a bidirectional relation symbol, but the authors have observed that students might not have such flexibility in their understanding of the equals sign. The authors have observed that students have a hard time viewing mathematical properties (for example, log (MN) = log (M) log (N)) with bidirectional…

Supporting student success in introductory mathematics courses is a growing national imperative in order to both diversify and increase the number of well-prepared Science, Technology, Engineering, and Mathematics (STEM) graduates. Efforts to diversify STEM fields have focused on broadening participation, addressing equitable outcomes, and…

This dissertation investigates gender differences in (1) retrospective (i.e., measured after task completion) item-specific confidence judgments, and whether these judgments were warranted. Of particular interest was whether gender interacts with problem difficulty to explain confidence, calibration (speaks to the accuracy of confidence…

What if your students could access "any" resource during a test? How would they react? How would "you" react? This paper presents some results from a trial of allowing students access to notes, calculators, and any device connected to the internet, which occurred during a midterm in a second-year ordinary differential equations…

Ethnomathematics can empirically improve the cognitive abilities of students in elementary and secondary schools. However, in undergraduate study, there are still limited studies on integrating ethnomathematics in learning resources. This study aims to apply interpolation in modelling polynomial functions and integral volume on the shape of…

In this paper, we describe the influence of the implementation of methodology for teaching and learning multiple integrals based on the constructivist approach and the interconnectedness of multiple representations (with an emphasis on dynamic representations) for different mathematical objects using GeoGebra's applications Graphing Calculator and…

In this study, it was aimed to experiment a new method to increase the quality of the history of mathematics course instruction in the primary mathematics education. The method composed by synthesizing project-based and collaborative learning methods was named "Newspaper Preparation Method," and the course was delivered using this…

Governmental and educational organizations have pointed out that students coming into the biological sciences require stronger skills in statistics and data modeling that are not usually addressed in typical engineering-based calculus courses. Our work here documents how faculty in biology and mathematics addressed this issue at a large urban…

Mastery-based testing is an assessment scheme that challenges students to provide complete solutions to problems derived from clear course concepts. Students are allowed multiple attempts to demonstrate mastery, which helps create a classroom environment where students value persistence toward thorough understanding. In this paper, we describe in…

How should our students think about external forcing in differential equations setting, and how can we help them gain intuition? To address this question, we share a variety of problems and projects that explore the dynamics of the undamped forced spring-mass system. We provide a sequence of discovery-based exercises that foster physical and…

Solving systems of linear equations is of central importance in linear algebra and many related applications, yet there is limited literature examining the symbolizing processes students use as they work to solve systems of linear equations. In this paper, we examine this issue by analyzing final exam data from 68 students in an introductory…

This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First,…

The purpose of this mixed-methods study was to explore how undergraduate students in an applied calculus course used the written curriculum (i.e., textbook, online homework system, and previous exams). The study design included three phases: (a) an online survey, (b) individual observations, and (c) student interviews. Students' survey responses…