In Brazil we have identified a predilection of the authors of Mathematical History books for the discussion of the fundamentals of Differential and Integral Calculus. On the other hand, when we consider the teaching of Mathematics in the school context, it is essential to know the teaching of the historical and dynamic evolution of the concepts,…

The purpose of this study was to explore first-generation, low-income, students' of color experiences with math placement and pre-calculus/calculus courses, focusing on their self-belief in being successful in math. As part of the Progress Through Calculus National Science Foundation research project, eight first-generation, low-income, students…

We create a continuous, nowhere monotone function, which would be more suitable for students. (Contains 3 figures.)

In this paper we describe computer-aided assessment methods used in online Calculus courses and the data they produce. The online learning environment collects a lot of time-stamped data about every action a student makes. Assessment data can be harnessed into use as a feedback, predictor, and recommendation facility for students and instructors.…

Mathematicians use example generation to test and verify mathematical ideas; however, the processes through which undergraduates learn to productively generate examples are not well understood. We engaged calculus students in a teaching experiment designed to develop skills in productively generating examples to learn novel concepts. This article…

We delineate some types of structured practice (modeling, requests, feedback, and space-making) that help students learn to pose appropriate questions and to initiate exploration of those questions. Developing skills requires practice, so we suggest ways to embed structured practice into existing class sessions. Including structured practice is…

In nineteenth-century America, students buried their mathematics books. This practice consistently celebrated the milestone of passing through collegiate mathematics, yet it changed due to national events. This article considers the case of Bowdoin College, where students buried their books differently before and after the Civil War. Antebellum,…

Purpose: Calculus is generally offered as a freshman year course and is a prerequisite for some advanced STEM-related courses in some undergraduate programs. However, some students experience difficulties in Calculus courses, leading to lower levels of achievement. Thus, there is a need to examine the factors which may be related to students'…

Undergraduates pursue degrees in disciplines in which they hold an affect or possess an interest. Math and science majors possess a positive affect for mathematics; however, to maximize the number of math majors, it is important to boost the motivation of non-math majors to learn mathematics. This study examines the relationships between…

Homework varies widely in importance among both teachers and students, as well as in subject areas. In mathematics, it is generally expected that it plays a critical role in students' understanding of mathematics and will be assigned daily. However, it is also understood that whether students take homework seriously can be difficult to ascertain.…

This mixed qualitative and quantitative methods study addressed the effect of technology on college algebra and survey of calculus students' understanding. This research study was conducted in fall 2016 on eight college algebra classes with a total of 315 students, and in summer 2017, on two survey of calculus classes with a total of 40 students…

Classroom flipping is the practice of moving new content instruction out of class time, usually packaging it as online videos and reading assignments for students to cover on their own, and devoting in-class time to interactive engagement activities. Flipping has garnered a large amount of hype from the popular education media and has been adopted…

The purpose of this article is to offer teaching ideas in the treatment of the definite integral concept and the Riemann sums in a technology-supported environment. Specifically, the article offers teaching ideas and activities for classroom for the numerical methods of approximating a definite integral via left- and right-hand Riemann sums, along…

Why would anyone think of teaching and learning mathematics directly from primary historical sources? We aim to answer this question while sharing our own experiences, and those of our students across several decades. We will first describe the evolution of our motivation for teaching with primary sources, and our current view of the advantages…

Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM) is surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph of velocity against displacement. In this way, the condition b ? [square root]4mk for the occurrence of the non-oscillating critical damping and…