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Habre, Samer – Teaching Mathematics and Its Applications: An International Journal of the IMA, 2012

Research on writing in mathematics has shown that students learn more effectively in an environment that promotes this skill and that writing is most beneficial when it is directed at the learning aspect. Writing, however, necessitates proficiency on the part of the students that may not have been developed at earlier learning stages. Research has…

Descriptors: Equations (Mathematics), Writing Skills, Calculus, Comprehension

Camacho-Machín, M.; Guerrero-Ortiz, C. – International Journal of Mathematical Education in Science and Technology, 2015

The aim of this paper is to present and discuss some of the evidence regarding the resources that students use when they establish relationships between a contextual situation and an ordinary differential equation (ODE). We present research results obtained from work by seven students in a graduate level course in mathematics education, where they…

Descriptors: Equations (Mathematics), Mathematics Instruction, Graduate Students, College Science

McCartney, Mark – International Journal of Mathematical Education in Science and Technology, 2013

A well-known mathematical puzzle regarding a worm crawling along an elastic rope is considered. The resulting generalizations provide examples for use in a teaching context including applications of series summation, the use of the integrating factor for the solution of differential equations, and the evaluation of definite integrals. A number of…

Descriptors: Mathematics, Puzzles, Mathematics Instruction, Calculus

Walsh, Jim; McGehee, Richard – College Mathematics Journal, 2013

A dynamical systems approach to energy balance models of climate is presented, focusing on low order, or conceptual, models. Included are global average and latitude-dependent, surface temperature models. The development and analysis of the differential equations and corresponding bifurcation diagrams provides a host of appropriate material for…

Descriptors: College Mathematics, Mathematics Instruction, Energy, Climate

Pennell, S.; Avitabile, P.; White, J. – PRIMUS, 2009

The introductory differential equations course can be made more relevant to engineering students by including more of the engineering viewpoint, in which differential equations are regarded as systems with inputs and outputs. This can be done without sacrificing any of the usual topical coverage. This point of view is conducive to student…

Descriptors: Equations (Mathematics), Calculus, Introductory Courses, Engineering Education

Bruder, Andrea; Kummel, Miro – PRIMUS, 2019

We present our experience with an open-ended lab activity that we designed for students with a Calculus 1 background. With the goal of learning how scientists study transport in streams, the students collected data on how a pulse of leaves travels down a nearby stream. Students who had little to no experience with data with two independent…

Descriptors: Calculus, Pollution, Inquiry, Problem Based Learning

de la Pen~a, Lisandro Herna´ndez – Journal of Chemical Education, 2016

The solution of simple kinetic equations is analyzed without referencing any topic from differential equations or integral calculus. Guided by the physical meaning of the rate equation, a systematic procedure is used to generate an approximate solution that converges uniformly to the exact solution in the case of zero, first, and second order…

Descriptors: Kinetics, Chemistry, Problem Solving, Equations (Mathematics)

Erickson, Amy H. Lin – PRIMUS, 2010

This material has been used twice as an out-of-class project in a mathematical modeling class, the first elective course for mathematics majors. The only prerequisites for this course were differential and integral calculus, but all students had been exposed to differential equations, and the project was assigned during discussions about solving…

Descriptors: Majors (Students), Elective Courses, Equations (Mathematics), Calculus

An Exploration of Metacognition and Its Effect on Mathematical Performance in Differential Equations

Smith, Mary Jarratt – Journal of the Scholarship of Teaching and Learning, 2013

Research suggests that students in certain contexts who are "metacognitively aware learners" demonstrate better academic performance (Shraw & Dennison, 1994; Md. Yunus & Ali, 2008). In this research, the metacognitive levels for two classes of differential equations students were studied. Students completed a survey adapted from…

Descriptors: Metacognition, Equations (Mathematics), Mathematics Instruction, College Students

Winkel, Brian J. – PRIMUS, 2011

We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and two-species competition models. We discuss student-evolved strategies and offer "Mathematica" code for a gradient search approach. We use historical (1930s) data from microbial studies of the Russian biologist,…

Descriptors: Population Growth, Calculus, Mathematics Instruction, College Mathematics

Greer, Meredith L.; Ewing, Holly A.; Cottingham, Kathryn L.; Weathers, Kathleen C. – College Mathematics Journal, 2013

We describe a collaboration between mathematicians and ecologists studying the cyanobacterium "Gloeotrichia echinulata" and its possible role in eutrophication of New England lakes. The mathematics includes compartmental modeling, differential equations, difference equations, and testing models against high-frequency data. The ecology…

Descriptors: College Mathematics, Ecology, Cooperation, Earth Science

Benacka, Jan – EURASIA Journal of Mathematics, Science & Technology Education, 2016

The article gives an account of an experiment in which sixty-eight high school students of age 16 - 19 developed spreadsheet applications that simulated fall and projectile motion in the air. The students applied the Euler method to solve the governing differential equations. The aim was to promote STEM to the students and motivate them to study…

Descriptors: High School Students, STEM Education, Mathematical Models, Spreadsheets

Rasmussen, Chris – North American Chapter of the International Group for the Psychology of Mathematics Education, 2016

A challenge in mathematics education research is to coordinate different analyses to develop a more comprehensive account of teaching and learning. I contribute to these efforts by expanding the constructs in Cobb and Yackel's (1996) interpretive framework that allow for coordinating social and individual perspectives. This expansion involves four…

Descriptors: Mathematics Education, Teaching Methods, Mathematics Instruction, Mathematical Concepts

Hulsizer, Heidi – International Journal of Research in Education and Science, 2016

Videos have been used in classrooms for decades, but student-produced video has recently become a viable, economical option to enhance learning. Students were asked to create videos to be used for their exam review in two different undergraduate mathematics courses: Differential Equation and Complex Analysis. Students were then surveyed about…

Descriptors: Mathematics, Mathematics Instruction, Mathematics Curriculum, Video Technology

Ng, Chiu-king – Physics Education, 2016

Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM) is surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph of velocity against displacement. In this way, the condition b ? [square root]4mk for the occurrence of the non-oscillating critical damping and…

Descriptors: Problem Solving, Calculus, Motion, Qualitative Research