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James S. Wolper – International Journal of Mathematical Education in Science and Technology, 2024
Adjusting the Calculus I curriculum by putting modelling and differential equations literally at its centre leads to a better-organised and better-motivated course. The biggest change is including a section on "qualitative" and "numerical" solutions to ordinary differential equations between the customary sections on…
Descriptors: Mathematics Instruction, Teaching Methods, Advanced Courses, Calculus
Kalman, Dan – PRIMUS, 2023
In the precalculus curriculum, logistic growth generally appears in either a discrete or continuous setting. These actually feature distinct versions of logistic growth, and textbooks rarely provide exposure to both. In this paper, we show how each approach can be improved by incorporating an aspect of the other, based on a little known synthesis…
Descriptors: Mathematics Education, Calculus, Teaching Methods, Mathematical Models
Jennifer A. Czocher; Elizabeth Roan; Abigail Quansah; Andrew Baas – International Journal of Mathematical Education in Science and Technology, 2024
Students exit calculus with understandings of change that want for conceptual depth and are disconnected from real-world contexts. In this paper, we present a problem that will develop their skills in using "change" concepts for learning differential equations through modelling. The problem comes from a qualitative study of how STEM…
Descriptors: STEM Education, Calculus, Undergraduate Students, Modeling (Psychology)
Christian Farkash; Michael Storm; Thomas Palmeri; Chunhui Yu – Mathematics Teaching Research Journal, 2024
Several studies indicate that exploring mathematical ideas by using more than one approach to prove the same statement is an important matter in mathematics education. In this work, we have collected a few different methods of proving the multinomial theorem. The goal is to help further the understanding of this theorem for those who may not be…
Descriptors: Undergraduate Students, College Mathematics, Mathematics Skills, Mathematical Models
Kerri Spooner – International Journal of Mathematical Education in Science and Technology, 2024
Gaining useful insight into real-world problems through mathematical modelling is a valued activity across several disciplines including mathematics, biology, computer science and engineering. Differential equations are a valuable tool used in modelling. Modelling provides a way for students to engage with differential equations within a…
Descriptors: Mathematical Models, Relevance (Education), Learning Experience, Calculus
Wade, Carol H.; Wilkens, Christian; Sonnert, Gerhard; Sadler, Philip M. – Journal of Mathematics Education at Teachers College, 2023
Although the secondary-tertiary transition has been investigated in mathematics education research with different focuses and theoretical approaches, it remains a major issue for students in the transition. With success in a science, technology, engineering, or mathematics (STEM) major at stake, we investigated a novel approach to support the…
Descriptors: Secondary School Mathematics, College Mathematics, Calculus, Instructional Design
Ely, Robert – ZDM: Mathematics Education, 2021
Several new approaches to calculus in the U.S. have been studied recently that are grounded in infinitesimals or differentials rather than limits. These approaches seek to restore to differential notation the direct referential power it had during the first century after calculus was developed. In these approaches, a differential equation like dy…
Descriptors: Mathematics Instruction, Teaching Methods, Calculus, Mathematical Concepts
Nievergelt, Yves – PRIMUS, 2022
This article provides conceptual ideas, data, and exercises, for integrating original sources of recent, state of the art, world-class life science research in the undergraduate mathematics curriculum and classroom. To this end, this article shows how one of the main goals of calculus in the life sciences, fitting parameters to data and assessing…
Descriptors: Calculus, Mathematics Instruction, Teaching Methods, Undergraduate Students
Hochmuth, Reinhard – International Journal of Mathematical Education in Science and Technology, 2022
The systematic design and analysis of tasks which can be implemented in first-year university courses and point to advanced inner- and extra-mathematically rich issues and their rationales is an open problem in the didactics of mathematics in higher education. Potentials of such tasks can be seen with regard to learning processes in the first year…
Descriptors: Undergraduate Students, Mathematics Instruction, Task Analysis, Teaching Methods
Sandra Barragán; Orlando Aya; Camilo Soto – Mathematics Teaching Research Journal, 2023
Articulated pedagogical and didactic strategies allow improving academic quality and strengthen individual and institutional cognitive processes such as student retention. Mathematical modelling, articulated with complementary actions, contributes to teaching and learning processes within situations that go beyond the classroom since they are…
Descriptors: Mathematical Models, STEM Education, Educational Quality, Algebra
Richard Velasco; Dae S. Hong – North American Chapter of the International Group for the Psychology of Mathematics Education, 2023
In this study, we examined one experienced mathematician's class practices, with particular attention to cognitive model described in genetic decomposition. Our findings indicate that students only had limited opportunities to be familiar with the first three steps in genetic decomposition, which may potentially lead students to answer limit tasks…
Descriptors: Mathematics Education, Mathematical Concepts, Mathematics Skills, Mathematics Instruction
Tola Bekene Bedada; M. F. Machaba – Education Inquiry, 2024
This article presents an instructional technology-based cycle model intended to support and facilitate the teaching and learning of mathematics, particularly calculus. The study used quantitative methods with quasi-experimental research that uses non-randomised assignments of the study group that are categorised into experimental and control…
Descriptors: Models, Mathematics Instruction, Computer Software, Educational Technology
Michelle Cirillo; Dawn Berk; Raymond LaRochelle; Kristen N. Bieda; Fran Arbaugh – International Journal of Research in Undergraduate Mathematics Education, 2024
The recent push toward active learning -- engaging students in the learning process -- is meant to benefit students. Yet there is still much to learn about students' perceptions of this phenomenon. We share results from an interview study of students' perceptions of features of two active learning models institutionalized at a large…
Descriptors: Active Learning, Mathematics Instruction, Undergraduate Students, Student Attitudes
Charity N. Watson; Pablo Duran; Adam Castillo; Edgar Fuller; Geoff Potvin; Laird Kramer – International Journal of Mathematical Education in Science and Technology, 2025
College calculus plays an important role in STEM students' degree and career aspirations. One of the key factors considered in assessing a student's ability to be successful in calculus is their proficiency in topics from prior mathematics courses such as algebra and precalculus. This study set out to examine the impact of students' precalculus…
Descriptors: Active Learning, Calculus, Mathematics Instruction, Teaching Methods
Kilty, Joel M.; McAllister, Alex M. – PRIMUS, 2020
In our modern world, we are inundated and grapple with data daily. As mathematicians, we are often more comfortable discussing the behavior of functions presented analytically, in contrast with the data-driven or tabular presentations of functions ubiquitous in our culture. This paper introduces an entry-level course, Mathematical Modeling and…
Descriptors: Calculus, Teaching Methods, Mathematics Instruction, College Mathematics