In this note, I present an 'easy-to-be-remembered' shortcut for promptly solving the ubiquitous integral [line integral] x[superscript n] e[superscript alpha x] dx for any integer n>0 using only the successive derivatives of x[superscript n]. Some interesting applications are indicated. The shortcut is so simple that it could well be included…

"Representational transformation diagrams" are used to compare and contrast standard textbook presentations of vector line integrals in undergraduate courses in both mathematics and physics. These presentations are taken as the lower anchor in a learning trajectory. Two principal approaches in the lower division are identified, roughly…

In this paper we present two simulations designed with GeoGebra that illustrate dynamically a key concept in Vector Calculus: line integrals of vector fields, along with other associated mathematical properties and applications. Students are not required to know the GeoGebra environment: a user-friendly interface with buttons, functionalities and…

The literature dealing with student understanding of integration in general and the Fundamental Theorem of Calculus in particular suggests that although students can integrate properly, they understand little about the process that leads to the definite integral. The definite integral is naturally connected to the antiderivative, the area under…

Programming with Computer Algebra Systems (CAS) has become an important tool as a support in Computer lectures in Mathematics subjects aimed at Engineering degrees. In this paper, the authors present their teaching experience within the concept "Line Integration" with the help of two specific CAS: DERIVE and MAXIMA. When introducing the…

Electricity and magnetism are closely related phenomena with a well-known symmetry found in Maxwell equations. An essential part of any electricity and magnetism course includes the analysis of different field source distributions through Gauss's and Ampere's laws to compute and interpret different physical quantities, such as electric flux,…

Ampère's law is presented in introductory physics as a relation between the line integral of the magnetic field around a closed loop and the net current crossing any open surface spanning that loop. By allowing the surface to pass between the plates of a charging parallel-plate capacitor, Maxwell realized that this law is incomplete and introduced…

We engaged five mathematicians who conduct research in the domain of complex analysis or use significant tools from complex analysis in their research in interviews about basic concepts of differentiation and integration of complex functions. We placed a variety of constructivist, social-constructivist, and embodied theories in mathematics…

In introductory texts Ampere's law is generally introduced in the steady-current form ?B · dl = µ[subscript 0]I, and it is later extended to a more general form involving the so-called displacement current I[subscript d], ?B · dl = µ[subscript 0](I + I[subscript d]) · (1). Here the line integral is to be taken along a closed…

This article focuses on mother tongue teaching in Arabic, Dari, Pashto and Somali as it is practised in a linguistically diverse primary school in Denmark. The article draws on a linguistic ethnography of language teaching across the curriculum, and the analysis focuses on three mother tongue teachers. Drawing on classroom observations and…

Methods of teaching the Calculus are presented in honour of Sir Isaac Newton, by discussing an extension of his original proofs and discoveries. The methods, requested by Newton to be used that reflect the historical sequence of the discovered Fundamental Theorems, allow first-time students to grasp quickly the basics of the Calculus from its…

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…

This work comprises an investigation about basic Quantum Mechanics (QM) teaching in the high school. The organization of the concepts does not follow a historical line. The Path Integrals method of Feynman has been adopted as a Reference Conceptual Structure that is an alternative to the canonical formalism. We have designed a didactic sequence…

Research into didactics of calculus has maintained a long-standing interest in students' grasp of the relations between definite integrals and areas. This study comes to contribute to this line of research by unpacking how students use the concept of area to find definite integrals. Specifically, we focus on mathematical situations where the…

This paper is based on ethnographic research of Australian and South Korean primary school students' experiences of on-line synchronous intercultural exchanges as part of a school partnership. Starting with an embodied understanding of learning, I discuss the applicability of body pedagogies to the on-line context in a classroom setting by…