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Nortvedt, Guri A.; Siqveland, Arvid – International Journal of Mathematical Education in Science and Technology, 2019

Are students transitioning from the secondary level to university studies in mathematics and engineering adequately prepared for education at the tertiary level? In this study, we discuss the prior mathematical knowledge and skills demonstrated by Norwegian engineering ("N" = 1537) and calculus ("N" = 626) university students…

Descriptors: Mathematics Instruction, Calculus, Engineering Education, Foreign Countries

Dolores-Flores, Crisólogo; Rivera-López, Martha Iris; García-García, Javier – International Journal of Mathematical Education in Science and Technology, 2019

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures,…

Descriptors: Mathematics Instruction, Mathematical Concepts, Foreign Countries, Arithmetic

Swidan, Osama; Naftaliev, Elena – International Journal of Mathematical Education in Science and Technology, 2019

This study was designed to micro-analyze the role of the design of interactive diagrams in learning-teaching the concept of the indefinite integral. The presented case study focuses on the engagement of one pair of 17-year-old students with an interactive diagram for graphically learning-teaching the indefinite integral concept. The authors…

Descriptors: Undergraduate Students, Mathematics Education, Visual Aids, Mathematical Concepts

Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2019

Recently, Wilmer III and Costa introduced a method into the mathematics education research literature which they employed to construct solutions to certain classes of ordinary differential equations. In this article, we build on their ideas in the following ways. We establish a link between their approach and the method of successive…

Descriptors: Mathematics Instruction, Problem Solving, Equations (Mathematics), Teaching Methods

Hoban, Richard A. – International Journal of Mathematical Education in Science and Technology, 2019

Many students do not have a deep understanding of the integral concept. This article defines what a deep understanding of the integral is in respect to integration involving one independent variable; briefly discusses factors which may inhibit such an understanding; and then describes the design of a mathematical resource for introducing students…

Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Calculus

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita – International Journal of Mathematical Education in Science and Technology, 2018

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Descriptors: Calculus, Algebra, Geometric Concepts, Mathematics Instruction

García-García, Javier; Dolores-Flores, Crisólogo – International Journal of Mathematical Education in Science and Technology, 2018

In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas,…

Descriptors: Foreign Countries, High School Students, Mathematics Skills, Calculus

Ponce Campuzano, Juan Carlos; Matthews, Kelly E.; Adams, Peter – International Journal of Mathematical Education in Science and Technology, 2018

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year…

Descriptors: Mathematics, History, College Freshmen, College Science

Cunningham, Daniel W. – International Journal of Mathematical Education in Science and Technology, 2018

Modern calculus textbooks carefully illustrate how to perform integration by trigonometric substitution. Unfortunately, most of these books do not adequately justify this powerful technique of integration. In this article, we present an accessible proof that establishes the validity of integration by trigonometric substitution. The proof offers…

Descriptors: Mathematics Education, Trigonometry, Calculus, Mathematical Concepts

de Camargo, André Pierro – International Journal of Mathematical Education in Science and Technology, 2018

In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying…

Descriptors: Mathematics Education, Calculus, Mathematical Logic, Equations (Mathematics)

Burns-Childers, Annie; Vidakovic, Draga – International Journal of Mathematical Education in Science and Technology, 2018

The purpose of this study was to gain insight into 30, first year calculus students' understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up…

Descriptors: Calculus, Mathematics Instruction, Mathematical Concepts, Protocol Analysis

Hyland, Diarmaid; van Kampen, Paul; Nolan, Brien C. – International Journal of Mathematical Education in Science and Technology, 2018

This paper reports on the first part of a multiphase research project that seeks to identify and address the difficulties encountered by physics students when studying differential equations. Differential equations are used extensively by undergraduate physics students, particularly in the advanced modules of their degree. It is, therefore,…

Descriptors: Foreign Countries, Outcomes of Education, Teaching Methods, Equations (Mathematics)

Engelke Infante, Nicole; Murphy, Kristen; Glenn, Celeste; Sealey, Vicki – International Journal of Mathematical Education in Science and Technology, 2018

Knowing when students have the prerequisite knowledge to be able to read and understand a mathematical text is a perennial concern for instructors. Using text describing Newton's method and Vinner's notion of concept image, we exemplify how prerequisite knowledge influences understanding. Through clinical interviews with first-semester calculus…

Descriptors: Calculus, Mathematical Concepts, Imagery, Schemata (Cognition)

Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2018

This paper is based on the presumption that teaching multiple ways to solve the same problem has academic and social value. In particular, we argue that such a multifaceted approach to pedagogy moves towards an environment of more inclusive and personalized learning. From a mathematics education perspective, our discussion is framed around…

Descriptors: Mathematics Instruction, Calculus, Problem Solving, Case Studies

Vandenbussche, J.; Ritter, L.; Scherrer, C. – International Journal of Mathematical Education in Science and Technology, 2018

Strong prerequisite skills are essential to student success in the calculus sequence; however, many students arrive in Calculus I with weaknesses that are difficult for them to overcome. In this paper, we describe an approach to early incentivized remediation of prerequisite material in a Calculus I course. We present data that supports the idea…

Descriptors: Calculus, Mathematics Instruction, Remedial Mathematics, At Risk Students