Like many math educators, I have spent much of my career bound to traditional methods of instruction and assessment. In recent years, motivated by a growing understanding that such approaches may not result in equitable or inclusive classroom environments, my teaching philosophy has shifted radically. In this article, I describe how I transformed…

The flipped classroom model interchanges the roles of in-class and out-of-class time to allow students more time to engage with cognitively demanding tasks when expert help from their instructor is more available. An extensive body of literature supports the effectiveness of this model. In contrast, I present a case study of a less-successful…

GeoGebra mathematical software is the best alternative way of teaching and learning calculus in the 21st century by exploration and visualization. This software opposes the traditional teaching and learning method, or solution only approaches and make the teaching and learning process more active in the classroom which goes with the constructive…

This paper presents a "virtual reality" based lesson for a common Calculus topic, including a description of how the lecture was implemented in both a virtual reality and an augmented reality hardware system. This lesson was delivered to a number of calculus classes and we describe the student response to the lesson via a quiz and a…

Ordinary Differential Equations I, is one of the core courses for science and engineering majors. Practical problem solving in science and engineering programs require proficiency in mathematics. Improving student performance and retention in mathematics classes requires inventive approaches. At the University of Central Florida (UCF) the…

Despite the overwhelming amount of research on students' interpretations of rates of change in real-world physical science contexts, similar studies in real-world economic contexts are sparse. Contributing towards addressing this gap in knowledge, this study reports on how 12 pairs of business calculus students interpreted marginal change…

Active learning techniques, such as peer instruction and group work, have been gaining a lot of traction in universities. Taking a natural next step in re-evaluating current practices, many institutions recently started experimenting student-centred group exams. In order to assess the feasibility and effectiveness of collaborative assessments, we…

My goal in crafting homework in calculus is twofold: to provide scaffolding for students to develop a theoretical understanding of calculus concepts and to incorporate good mathematical exposition, including justification and proof when appropriate. I achieve these goals by creating weekly homework sets that students work on in groups of three or…

Various research studies have established that nearly half of all students who decide to pursuit a math, science, or engineering field change their mind and seek a different major. The National Center for Education Statistics shows a decrease in the number of degrees in engineering and related fields from 36,900 degrees in the 2003-2004 academic…

As calculus instruction moves further from lecture-based instruction toward student-centered pedagogy, support services must align with the changing goals for the course. This paper describes the work of a department as they collectively design and redesign a co-requisite Calculus I course, in an effort to better promote students' academic and…

In this paper, we provide a report of preliminary findings of the Morgan State University (MSU) Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL) project and its focus on culturally responsive teaching (CRT) as an active learning framework for pre-calculus instruction. The paper concludes with a…

Responsive instruction--or instruction that foregrounds and takes up the disciplinary substance of student thinking--is both a hallmark of recent STEM education reforms and challenging to enact. This kind of instruction may be especially challenging in instructional contexts that mandate or rely on curriculum with set, structured learning…

In a flipped classroom, an increasingly popular pedagogical model, students view a video lecture at home and work on exercises with the instructor during class time. Advocates of the flipped classroom claim the practice not only improves student achievement but also ameliorates the achievement gap. We conduct a randomized controlled trial at West…

Effectiveness of mathematical education as non-linear, composite and open system, formation and development of cognitive abilities of the trainee are wholly defined in the solution of complex tasks by means of modern achievements in science to high school practice adaptation. The possibility of complex tasks solution arises at identification of…

In this paper, the knowledge dimension for Revised Bloom's taxonomy (RBT) is unpacked for integral calculus. As part of this work, the 11 subtypes of the knowledge dimension are introduced, and through document analysis of chapter 4 of the RBT handbook, these subtypes are defined. Then, by consulting materials frequently used for teaching integral…