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Hausberger, Thomas; Derouet, Charlotte; Hochmuth, Reinhard; Planchon, Gaetan – International Journal of Research in Undergraduate Mathematics Education, 2021

This paper investigates the phenomenon of compartmentalisation of knowledge in the teaching and learning of continuous probability distributions and integral calculus at the secondary-tertiary transition in France. Using the Anthropological Theory of the Didactic (ATD), and in particular the key notion of praxeology, we investigate in which sense…

Descriptors: Mathematics Instruction, Probability, Calculus, Secondary School Mathematics

Kaur, Manmohan; Wangler, Thomas – International Journal for Technology in Mathematics Education, 2014

Although most calculus students are comfortable with the Cartesian equations of curves and surfaces, they struggle with the concept of parameters. A multivariable calculus course is really the time to nail this concept down, once and for all, since it provides an easy way to represent many beautiful and useful surfaces, and graph them using a…

Descriptors: Creativity, Technology Uses in Education, Calculus, Mathematical Concepts

Clark, Thomas J. – PRIMUS, 2019

The first day of many mathematics classes is filled with the formalities of the syllabus and a lecture introduction to the course content. Here, an alternative is presented where modeling is placed as the centerpiece to orient students to the work of differential equations; namely, to capture as beautifully and compactly as possible through the…

Descriptors: Equations (Mathematics), Calculus, Mathematical Models, College Mathematics

Pawlaschyk, Thomas; Wegner, Sven-Ake – International Journal of Mathematical Education in Science and Technology, 2020

In this note, we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task design that gives students the opportunity to conjecture, refute and prove. What is new is that the complexity in our problems is limited and thus the tasks can also be used in homework…

Descriptors: Homework, Mathematics Instruction, Teaching Methods, Calculus

Yoon, Caroline; Dreyfus, Tommy; Thomas, Michael O. J. – Mathematics Education Research Journal, 2010

Two complementary processes involved in mathematical modelling are mathematising a realistic situation and applying a mathematical technique to a given realistic situation. We present and analyse work from two undergraduate students and two secondary school teachers who engaged in both processes during a mathematical modelling task that required…

Descriptors: Undergraduate Students, Mathematical Models, Secondary School Teachers, Calculus

Sofronas, Kimberly S.; DeFranco, Thomas C.; Vinsonhaler, Charles; Gorgievski, Nicholas; Schroeder, Larissa; Hamelin, Chris – Journal of Mathematical Behavior, 2011

This article presents the views of 24 nationally recognized authorities in the field of mathematics, and in particular the calculus, on student understanding of the first-year calculus. A framework emerged that includes four overarching end goals for understanding of the first-year calculus: (a) mastery of the fundamental concepts and-or skills of…

Descriptors: Calculus, Mathematics Instruction, Comprehension, Mathematical Concepts

Rabin, Jeffrey M.; Burgasser, Adam; Bussey, Thomas J.; Eggers, John; Lo, Stanley M.; Seethaler, Sherry; Stevens, Laura; Weizman, Haim – International Journal of STEM Education, 2021

Rate of change concepts from calculus are presented and applied rather differently in college mathematics, physics, biology, and chemistry classes. This is not simply a matter of pedagogical style but reflects real cultural differences between these disciplines. We describe the efforts of our interdisciplinary collaboration to understand and…

Descriptors: STEM Education, Interdisciplinary Approach, College Mathematics, College Science

Mesa, Vilma; Ma, Yue; Quiroz, Carlos; Gerami, Saba; Liakos, Yannis; Judson, Thomas; Chamberlain, Lynn – ZDM: Mathematics Education, 2021

The goal of this study is to identify the multiple ways in which instructors take advantage of a feature designed into university textbooks that seeks to invite students to get acquainted with the content prior to attending the class in which such content will be discussed. We present an analysis of teacher instrumentation of this feature, which…

Descriptors: College Faculty, Questioning Techniques, Textbook Content, Textbooks

Tretter, Thomas – Science Teacher, 2012

Teachers strive to engage students in rich and varied experiences involving exploration. These experiences should be accessible to all types of learners (e.g., visual, kinesthetic, mathematically inclined), offering multiple pathways for engagement at different levels of sophistication and accommodating both conceptual and computational…

Descriptors: Physics, Video Technology, Teaching Methods, Science Instruction

Koshy, Thomas; Gao, Zhenguang – College Mathematics Journal, 2012

This article studies the convergence of the infinite series of the reciprocals of the Catalan numbers. We extract the sum of the series as well as some related ones, illustrating the power of the calculus in the study of the Catalan numbers.

Descriptors: Mathematics, Numbers, Computation, College Mathematics

Roberts, A. Wayne, Ed. – 1996

This book discusses the calculus reform effort. The first essay captures the basic themes that should characterize a calculus course that is modern in its vision as well as its pedagogy and content. The next section contains essays on the vision of calculus reform: "Visions of Calculus" (Sharon Cutler Ross); "Nonalgebraic Approaches…

Descriptors: Calculus, College Mathematics, Curriculum Development, Educational Change

Hong, Ye Yoon; Thomas, Michael O. J. – Mathematics Education Research Journal, 2015

Recent studies of the transition from school to university mathematics have identified a number of epistemological gaps, including the need to change from an emphasis on equality to that of inequality. Another crucial epistemological change during this transition involves the movement from the pointwise and global perspectives of functions usually…

Descriptors: Foreign Countries, Epistemology, Mathematics Instruction, College Mathematics

Dence, Thomas; Dence, Joseph – College Mathematics Journal, 2010

The integral of 1/(1 + x[superscript 2]) is standard in elementary calculus, but the related integral 1/(1 + x[superscript 4]) rarely appears. In this article we examine the latter integral, computing its value by four different methods; several that involve standard elementary calculus techniques, and several involving complex integration.

Descriptors: Calculus, College Mathematics, Mathematics Instruction, Computation

Edwards, Thomas; Özgün-Koca, S. Asli; Chelst, Kenneth – Mathematics Teacher: Learning and Teaching PK-12, 2021

In this article, the authors share activities designed to help students make a connection between the complex roots of X[superscript 2] - 2x + 5 = 0 and the graph of y = X[superscript 2] - 2x + 5. We piloted these activities in three precalculus classes. The activities involved both concrete and technological representations of the mathematical…

Descriptors: Calculus, Mathematics Instruction, Graphs, Computer Software

Hamilton, Jason; Pfaff, Thomas J. – PRIMUS, 2014

In this article we provide a simple way to think about the concept of sustainability and provide a number of examples for incorporating sustainability education into commonly taught mathematics courses. Scientific assessments have concluded that ecosystem services (the benefits that humans derive from the functioning of Earth's natural…

Descriptors: Sustainability, Mathematics Instruction, Environmental Education, Relevance (Education)