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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

Albalawi, Abdullah S. – International Journal of Research in Education and Science, 2018

This study aimed at investigating the effectiveness of using flipped classrooms in teaching the Math2 course for the preparatory year's students at the University of Tabuk, Saudi Arabia. The Math2 course was organized via an (ADDE) design model, with recorded videos of the topics included in the study; it was implemented by a Moodle platform and…

Descriptors: Foreign Countries, Educational Technology, Technology Uses in Education, Homework

Lynch, Frank H.; Page, Breeanna S. – PRIMUS, 2018

This paper uses the lens of a calculus student to examine different solutions to a weekly puzzler from the radio show "Car Talk," hosted by Tom and Ray Magliozzi. The puzzler describes an automobile that is traveling 75 miles per hour and is 75 miles from its destination. The trip is completed by traveling 1 mile at 75 miles per hour, 1…

Descriptors: Calculus, Problem Solving, Word Problems (Mathematics), Mathematics Instruction

Harwood, R. Corban – PRIMUS, 2018

This article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project implementation is given for both lower- and upper-division mathematics courses with an emphasis on mathematical…

Descriptors: Mathematics Instruction, Mathematical Models, Active Learning, Student Projects

Norton, Paran; Bridges, William; High, Karen – Journal of STEM Education: Innovations and Research, 2018

This paper examines the impact of departmental policy changes on the trend in DFW proportions for introductory calculus at a large research university, where DFW denotes the proportion of students receiving a grade of D, F, or withdrawing from the course. We defined three distinct policy periods: Traditional (2002-2005), Active Learning (SCALE-UP)…

Descriptors: College Students, College Mathematics, Mathematics Education, Calculus

Duzhin, Fedor; Gustafsson, Anders – Education Sciences, 2018

Course instructors need to assess the efficacy of their teaching methods, but experiments in education are seldom politically, administratively, or ethically feasible. Quasi-experimental tools, on the other hand, are often problematic, as they are typically too complicated to be of widespread use to educators and may suffer from selection bias…

Descriptors: Self Evaluation (Individuals), Artificial Intelligence, College Faculty, Instructional Effectiveness

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)

Lu, Owen H. T.; Huang, Anna Y. Q.; Huang, Jeff C. H.; Lin, Albert J. Q.; Ogata, Hiroaki; Yang, Stephen J. H. – Educational Technology & Society, 2018

Blended learning combines online digital resources with traditional classroom activities and enables students to attain higher learning performance through well-defined interactive strategies involving online and traditional learning activities. Learning analytics is a conceptual framework and is a part of our Precision education used to analyze…

Descriptors: Blended Learning, Educational Technology, Technology Uses in Education, Data Collection

Traxler, Adrienne; Henderson, Rachel; Stewart, John; Stewart, Gay; Papak, Alexis; Lindell, Rebecca – Physical Review Physics Education Research, 2018

Research on the test structure of the Force Concept Inventory (FCI) has largely ignored gender, and research on FCI gender effects (often reported as "gender gaps") has seldom interrogated the structure of the test. These rarely crossed streams of research leave open the possibility that the FCI may not be structurally valid across…

Descriptors: Physics, Science Instruction, Sex Fairness, Gender Differences

Mediating Relationship of Differential Products in Understanding Integration in Introductory Physics

Amos, Nathaniel; Heckler, Andrew F. – Physical Review Physics Education Research, 2018

In the context of introductory physics, we study student conceptual understanding of differentials, differential products, and integrals and possible pathways to understanding these quantities. We developed a multiple choice conceptual assessment employing a variety of physical contexts probing physical understanding of these three quantities and…

Descriptors: Physics, Introductory Courses, Science Instruction, Scores

Young, Nicholas T.; Heckler, Andrew F. – Physical Review Physics Education Research, 2018

In the context of a generic harmonic oscillator, we investigated students' accuracy in determining the period, frequency, and angular frequency from mathematical and graphical representations. In a series of studies including interviews, free response tests, and multiple-choice tests developed in an iterative process, we assessed students in both…

Descriptors: Interviews, Accuracy, Multiple Choice Tests, Algebra

Jones, Steven R. – Educational Studies in Mathematics, 2018

Many mathematical concepts may have prototypical images associated with them. While prototypes can be beneficial for efficient thinking or reasoning, they may also have self-attributes that may impact reasoning about the concept. It is essential that mathematics educators understand these prototype images in order to fully recognize their benefits…

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