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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
Moreno-Armella, Luis – ZDM: Mathematics Education, 2021
The aim of this paper is to narrate a significant part of the experience of a professor over several semesters teaching fundamental ideas of the "Theory of Calculus." The narrative explains how his didactic and mathematical mentality evolved as he witnessed students' conceptual difficulties, as they were confronted with situations that…
Descriptors: Mathematics Instruction, Calculus, Mathematical Concepts, Concept Formation
Reed, Zackery; Tallman, Michael A.; Oehrtman, Michael – PRIMUS, 2023
We offer an analysis of calculus assessment items that highlights ways to evaluate students' application of important meanings and support their engagement in generative ways of reasoning. Our central aim is to identify characteristics of items that require students to apply their understanding of key ideas. We coordinate this analysis of…
Descriptors: Mathematics Instruction, Calculus, Mathematical Concepts, Concept Formation
Osborne, Jason M.; Cook, William; Bossé, Michael J. – PRIMUS, 2021
In this paper we introduce the reader to a foundational topic of differential geometry: the curvature of a curve. To make this topic engaging to a wide audience of readers, we develop this intuitive introduction employing only basic geometry without calculus and derivatives. It is hoped that this introduction will encourage many more to both…
Descriptors: Mathematics Instruction, Geometry, Geometric Concepts, High Schools
Davidovic, Milena D.; Markovic-Topalovic, Tatjana; Sliško, Josip; Božic, Mirjana – Physics Teacher, 2020
In the same chapter of his book "Opera Geometrica," Torricelli published two discoveries: 1) initial velocity of a jet from a container increases with the square root of the depth of the hole; 2) he drew the pattern of jets from three openings at the wall of a container filled with water to constant level "H" and determined the…
Descriptors: Science Instruction, Physics, Scientific Concepts, Concept Formation
Hoban, Richard A. – International Journal of Mathematical Education in Science and Technology, 2021
Many students do not have a deep understanding of slope. This paper defines what a deep understanding of slope is in terms of mathematics-education theory. The various factors which help explain why such a deep understanding is difficult to acquire are then discussed. These factors include the following: the different representations for slope;…
Descriptors: Mathematical Concepts, Concept Formation, Mathematics Instruction, College Freshmen
OShaughnessy, J. – PRIMUS, 2019
This paper investigates the advantages of using a two-step homework system. First, technology is used to collect and grade traditional homework. Then, students are expected to present and explain problems from their assignments in class. Several versions of implementation are discussed for different course levels and sizes. Through these methods,…
Descriptors: Mathematics Instruction, College Mathematics, Homework, Educational Technology
Burch, Lori; Tillema, Erik S.; Gatza, Andrew M. – Mathematics Teacher: Learning and Teaching PK-12, 2021
As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a +…
Descriptors: Algebra, Mathematics Instruction, Calculus, Mathematics Teachers
Breen, Sinead; O'Shea, Ann; Pfeiffer, Kirsten – Teaching Mathematics and Its Applications, 2016
We report here on students' views of example generation tasks assigned to them in two first year undergraduate Calculus courses. The design and use of such tasks was undertaken as part of a project which aimed to afford students opportunities to develop their thinking skills and their conceptual understanding. In interviews with 10 students, we…
Descriptors: Undergraduate Students, Student Attitudes, College Mathematics, Calculus
Gratzer, William; Krishnan, Srilal – International Journal of Mathematical Education in Science and Technology, 2008
The revolution of technology in education has heralded a new wave of learning styles and in some cases total dependence on technology. Yet, statistics reveal no significant improvement in student performance in Mathematics and a downward trend in basic algebra skills. The major impediment in the learning process is lack of understanding of the…
Descriptors: Mathematics Instruction, Mathematics Skills, Mathematical Concepts, Comprehension
Bingolbali, Erhan; Monaghan, John – Educational Studies in Mathematics, 2008
Concept image and concept definition is an important construct in mathematics education. Its use, however, has been limited to cognitive studies. This article revisits concept image in the context of research on undergraduate students' understanding of the derivative which regards the context of learning as paramount. The literature, mainly on…
Descriptors: Undergraduate Students, Mathematics Education, Calculus, Transformations (Mathematics)
Gordon, Sheldon P. – PRIMUS, 2008
Most college algebra courses are offered in the spirit of preparing the students to move on toward calculus. In reality, only a vanishingly small fraction of the million students a year who take these courses ever get to calculus. This article builds a strong case for the need to change the focus in college algebra to one that better meets the…
Descriptors: Calculus, Algebra, College Mathematics, Mathematics Instruction
Bukova-Guzel, Esra – Educational Sciences: Theory and Practice, 2007
The purpose of this study is to design a constructivist learning environment that helps learning the limit concept. The study is a pretest-posttest quasi-experimental research. The control and the experimental groups were chosen from the students attending a calculus course. Worksheets were used to assess students' learning of the limit concept.…
Descriptors: Constructivism (Learning), Experimental Groups, Control Groups, Data Analysis

Tall, David; Vinner, Shlomo – Educational Studies in Mathematics, 1981
A number of general ideas intended to be helpful in analyzing differences in concept images among individuals are formulated. These ideas are applied to the specific concepts of continuity and limits, as taught in the secondary school and university. (MP)
Descriptors: Calculus, Cognitive Processes, College Mathematics, Concept Formation
Bingolbali, Erhan; Monaghan, John – International Group for the Psychology of Mathematics Education, 2004
This report explores first year undergraduate mechanical engineering and mathematics students' conceptions of the derivative and the contribution that membership of different departments may have on these conceptions. Quantitative results suggest that mechanical engineering students develop a proclivity for rate of change aspects of the derivative…
Descriptors: Engineering Education, Undergraduate Students, Mathematics Education, Concept Formation