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Segla Kossivi – Journal of Computers in Mathematics and Science Teaching, 2025
First-year college students experience difficulties in understanding the concepts of derivatives and integrals. At the postsecondary level, the use of static visualization and other traditional instruction delivery methods often are unable to meet students' needs in calculus. This problem is current and essential in the field of education and…
Descriptors: Calculus, Mathematics Instruction, Concept Formation, Mathematical Concepts
Manuel Santos-Trigo; Matías Camacho-Machín; Fernando Barrera-Mora – ZDM: Mathematics Education, 2024
The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look…
Descriptors: Mathematics Instruction, Calculus, Barriers, Problem Solving
T. Clark – PRIMUS, 2024
A standard element of the undergraduate ordinary differential equations course is the topic of separable equations. For instructors of those courses, we present here a series of novel modeling scenarios that prove to be a compelling motivation for the utility of differential equations. Furthermore, the growing complexity of the models leads to the…
Descriptors: Mathematics Instruction, Undergraduate Study, College Mathematics, Equations (Mathematics)
Yu, F. – PRIMUS, 2023
A productive understanding of rate of change concept is essential for constructing a robust understanding of derivatives. There is substantial evidence in the research that students enter and leave their Calculus courses with naive understandings of rate of change. Implementing a short unit on "what is rate of change" can address these…
Descriptors: Mathematics Instruction, College Mathematics, Calculus, Mathematical Concepts
George Ashline; Bret Findley; Mitchell Andrea; Dylan Wawruck – PRIMUS, 2024
We describe the components and implementation of an activity for multivariable calculus featuring applications to the field of chemistry. This activity focuses on the isobaric thermal expansion coefficient found using partial differentiation of the volume of an ideal gas with respect to temperature as pressure is held constant. Broader goals of…
Descriptors: Learning Activities, Mathematics Instruction, Calculus, Chemistry
The Structure of Students' Mathematical Errors in Solving Calculus Problems Based on Cognitive Style
In Hi. Abdullah; Hery Suharna; Mustafa AH. Ruhama – International Education Studies, 2024
The understanding mathematical concept is an error that often occurs in classroom learning among students when solving mathematical problems. The most difficult part for students is solving problems, because it requires numeracy skills, high concept mastery, as well as the ability to use good language, and so on so that students don't make any…
Descriptors: Error Patterns, Problem Solving, Cognitive Style, Calculus
Anass El Guenyari; Mohamed Chergui; Bouazza El Wahbi – Mathematics Teaching Research Journal, 2024
The present study falls into the efforts to improve practices for addressing errors produced by learners in various situations involving the calculation of integrals. We attempt to clarify as precisely as possible the types of errors that secondary school students produce when using integrals in algebraic and graphical frames. Based on the…
Descriptors: Calculus, Error Patterns, Factor Analysis, Mathematics Instruction
Thabiso Khemane; Padayachee Pragashni; Shaw Corrinne – IEEE Transactions on Education, 2024
This study investigates the challenges faced by second-year undergraduate engineering students in understanding Stokes' theorem in vector calculus, focusing on the misconceptions found in interconnected concepts that form its foundation. Stokes' theorem involves the application of line integrals, surface integrals, the curl of a vector field, and…
Descriptors: Calculus, Misconceptions, Mathematical Concepts, Concept Formation
Dogan, Hamide; Shear, Edith; Contreras, Angel F. Garcia; Hoffman, Lion – International Journal of Mathematical Education in Science and Technology, 2022
We investigated understanding of the linear independence concept based on the type and nature of connections displayed in seven non-mathematics majors' interview responses to a set of open-ended questions. Through a qualitative analysis, we identified six categories of frequently displayed connections. There were also recognizable differences in…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Undergraduate Students
Rabiei, Nima; Saleeby, Elias G. – International Journal of Mathematical Education in Science and Technology, 2022
In the multivariable calculus course, a standard application of triple integration is to find volumes of bounded regions in R[superscript 3]. In this article, we consider the problem of computing volumes, by way of examples, of regions bounded by planes and quadric surfaces. For illustration, we present the solution to two basic but non-standard…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Calculus
Harel, Guershon – ZDM: Mathematics Education, 2021
The paper presents analyses of multivariable calculus learning-teaching phenomena through the lenses of DNR-based instruction, focusing on several foundational calculus concepts, including "cross product," "linearization," "total derivative," "Chain Rule," and "implicit differentiation." The…
Descriptors: Calculus, Mathematics Instruction, Teaching Methods, Mathematical Concepts
Nilsen, Hans Kristian; Knutsen, Kristoffer Heggelund – International Journal of Research in Undergraduate Mathematics Education, 2023
In this paper we focus on Norwegian first-year engineering students' interpretations of differentials and definite integrals. Through interviews with 15 engineering students, we investigated how the students interpreted the different symbols involved in the Fundamental Theorem of Calculus (FTC), as displayed in the textbook used in their calculus…
Descriptors: Engineering Education, Teaching Methods, Mathematics Instruction, Student Attitudes
Hong, Dae S. – AERA Online Paper Repository, 2023
This study explores calculus students' opportunities to learn the concepts of integral by examining one mathematician's videotaped lessons and the textbook. The results show that both lessons and textbook introduced important cognitive resources very briefly and focused on procedures and techniques of integration. Implications to these results…
Descriptors: Calculus, Teaching Methods, Mathematics Instruction, Video Technology
Franklin Yu – ProQuest LLC, 2022
This dissertation reports on three studies about students' conceptions and learning of the idea of instantaneous rate of change. The first study investigated 25 students' conceptions of the idea of instantaneous rate of change. The second study proposes a hypothetical learning trajectory, based on the literature and results from the first study,…
Descriptors: Student Attitudes, Mathematical Concepts, Learning Trajectories, Calculus
Gencev, Marian; Šalounová, Dana – International Journal of Mathematical Education in Science and Technology, 2023
The aim of this paper is to present a teaching proposal for the theoretical part relating to the first- and second-order linear difference equations with constant coefficients suitable for the first-year students at various types of universities. In contradistinction to the methods often applied (memorization of algorithms without a proper…
Descriptors: Teaching Methods, Mathematics Instruction, Problem Solving, Geometric Concepts