In this paper, the Singapore school calculus curriculum at the upper secondary and the pre-university levels is examined in the light of the Singapore mathematics curriculum framework. Three key features of the calculus content are discerned: (1) an intuitive approach to calculus supported by the use of technology; (2) an emphasis on techniques;…

Studying the effectiveness of remedial courses in higher education has attracted a lot of interest from educational researchers and practitioners. Remediation is associated with significant economic and social costs while the results are usually dubious. In this paper, we apply a widely used method called Regression Discontinuity Design (RDD) to…

Faced with students failing to complete Calculus 1 at rates of almost 50%, the Department of Mathematics at Western Michigan University addressed the lack of progression of STEM majors through this gateway course and, thus, through their intended majors. In this case study, we describe the four-year process of redesigning our single variable…

Research has shown the majority of students who have completed a university calculus course reason about the definite integral primarily in terms of prototypical imagery or in purely algorithmic and non-quantitative ways. This dissertation draws on the framework of Emergent Quantitative Models to identify how calculus students might develop a…

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying…

Translation by a vector in the coordinate plane is first introduced in precalculus and connects to the basic theory of vector spaces in linear algebra. In this article, the authors explore the topic of collision detection in which the idea of a translation vector plays a significant role. Because collision detection has various applications in…

Using administrative data from nearly 270,000 transfer-intending students who began at 70 community colleges across three state systems, this paper seeks to identify a set of metrics that will be useful to community college leaders as they formatively assess their colleges' efforts to improve STEM transfer outcomes. We find that a relatively…

Logarithms, pivotal in advanced mathematics and real-world applications, often present challenges to students who resort to rote memorization without grasping their essence. While the emotional dimensions of learning mathematics are increasingly recognized, research in this area remains limited. This dissertation addresses this gap by examining a…

Students often struggle in the transition from high school to college. One component of this struggle is adjusting study habits to navigate new academic expectations. Another is establishing new relationships in college that can support their emotional well-being and academic success. We administered surveys consisting primarily of open-ended…

The contents of calculus, known for their complexity, present significant challenges for students, particularly in mastering multiple integrals and effectively visualizing related concepts. The transition to distance learning prompted by the COVID-19 pandemic has further complicated the learning process in multiple integrals. In line with this and…

For institutions offering multiple sections of Calculus 1, course coordination allows for consistency among the sections through the reduction of variation of material and/or instructional approaches. Studies on course coordination have shown that a coordinated system can bring benefits to instructors and promote equality for students across…

We developed the Physics Inventory of Quantitative Literacy (PIQL) to assess students' quantitative reasoning in introductory physics contexts. The PIQL includes several "multiple-choice-multipleresponse" (MCMR) items (i.e., multiple-choice questions for which more than one response may be selected) as well as traditional single-response…

In Thai mathematics classrooms, there is a lack of attention to support students' mathematical problem-solving skills by working from real-world contexts that make sense to students. This study aimed to investigate how preservice mathematics teachers' problem-solving can be explored in their content course, intervening with technology and…

In this study, we investigated female and male students' sense of belonging and their academic performance measured by the Force Concept Inventory (FCI) and course grades in a calculus-based introductory physics course at a large public university in the United States. We find that compared to male students, female students' sense of belonging was…