[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] Research in physics education has contributed substantively to improvements in the learning and teaching of university physics by informing the development of research-based instructional materials for physics courses. Reports on the design of these…

We describe the development and initial validity assessment of the 20-item BioCalculus Assessment (BCA), with the objective of comparing undergraduate life science students' understanding of calculus concepts in different courses with alternative emphases (with and without focus on biological applications). The development process of the BCA…

The topic of continuity is typically not introduced until calculus and then reexamined in real analysis. Recognizing the connections between secondary school mathematics and the advanced mathematics studied at the college level allows teachers to better identify mathematical concepts in student ideas, motivate students by piquing their curiosity,…

Problem-solving is regarded as a major component of mathematical performance, and well-designed problem-solving-based learning environments have the potential to assist students in developing a meaningful understanding of mathematical concepts and procedures. In this respect, given its various features, dynamic mathematics software has been…

Graphing calculators are hand-held technological tools currently used in mathematics classrooms. Teachers' perspectives on using graphing calculators are important in terms of exploring what teachers think about using such technology in advanced mathematics courses, particularly precalculus courses. A descriptive intrinsic case study was conducted…

This study illustrates how mathematical communication and learning are inherently multimodal and embodied; hence, sight-disabled students are also able to conceptualize visuospatial information and mathematical concepts through tactile and auditory activities. Adapting a perceptuomotor integration approach, the study shows that the lack of access…

Classroom voting can be an effective way to stimulate student discussions. In this pedagogy, the instructor poses a multiple-choice question to the class, and then allows a few minutes for consideration and small-group discussion before students vote, either with clickers, cell phones, or a non-electronic method. After the vote the instructor…

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'…