The article examines how a high school teacher designed an honors precalculus blended-learning class in North Carolina. By making videos of precalculus lectures where she had students watch during their days off from the class, the teacher was able to have her students work on problem solving and inquiry-based activities in groups when in-class.…

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…

This paper investigates how three widely used calculus textbooks in the U.S. realize the derivative as a point-specific object and as a function using Sfard's communicational approach. For this purpose, the study analyzed word-use and visual mediators for the "limit process" through which the derivative at a point was objectified, and…

This study examines the mathematical questioning of undergraduate Calculus I instructors for the purpose of detailing the ways in which instructors are using their questions. The emphasis is on verbal questions because of their in-the-moment value and ability to get students engaged in discourse. Calculus I is of particular interest because of its…

Taking notes is a popular activity for students attending instructional lectures and has been linked to achievement. Research on note-taking has shown that the contents and usefulness of student notes depends on several factors, including the pace of the lecture and the presence of organizational and selection cues. However, this research has…

Textbooks in applied mathematics often use graphs to explain the meaning of formulae, even though their benefit is still not fully explored. To test processes underlying this assumed multimedia effect we collected performance scores, eye movements, and think-aloud protocols from students solving problems in vector calculus with and without graphs.…

This study explored student agency in an active-learning business calculus course. The lecture-style instructional practices typically used in this course at this institution allow few opportunities for students to interact with their peers, interface with the instructor one-on-one, or do mathematics during class time. Additionally, this course…

Students who attend two-year institutions are not always academically prepared for the level of work that is required to be successful. Two-year institutions determine students' readiness for college-level mathematics courses using one of three placement methods. However, few empirical studies have investigated which placement methods are most…

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,…

[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…

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…