College Level Students' Understanding of Functions in the Context of Modelling Dynamic Situations

College Level Students' Understanding of Functions in the Context of Modelling Dynamic Situations
Author: Devrim Turan
Publisher:
Total Pages: 0
Release: 2021
Genre:
ISBN:

One of the critical tasks in early mathematical education is teaching the concept of function and its different representations through diverse examples and dynamic tasks. This task is meant to enable students to develop meaningful and powerful constructions between functional concepts and procedures, to conceptualize a function as a generalized process that accepts input and produces output and, therefore, to build essential conceptual and analytical thinking of functions that are necessary to form a covariational conception of function. This is particularly useful for College level students enrolled in Calculus courses who need a strong covariational conception of function to further succeed in mathematics courses. My thesis reveals that, from a sample group of college level students enrolled in Calculus courses at Concordia University, many participants do not have a strong conceptual or/and analytical thinking of functions that is essential in meaningfully modeling dynamic situations. Majority of students, who have obstacle(s) or/and pseudo-thought(s) or/and misconception(s) due to them having weak analytical/conceptual understanding of functions, do not move flexibly between different representations of functions and fail to view a function as a process that maps values of one variable to values of another variable. Consequently, these students generally do not reason dynamic functional situations covariationally at a higher level. This outcome questions the readiness of Calculus students for subsequent mathematics courses, as well as the effectiveness of prior school curriculum in mathematics education.

Modelling and Simulation

Modelling and Simulation
Author: Louis G. Birta
Publisher: Springer Nature
Total Pages: 558
Release: 2020-01-01
Genre: Computers
ISBN: 3030188698

This hands-on textbook/reference presents an introduction to the fundamental aspects of modelling and simulation, both for those wishing to learn about this methodology and also for those who have a need to apply it in their work. The text is supported by illustrative examples, drawn from projects formulated within the domains of discrete-event dynamic systems (DEDS) and continuous-time dynamic systems (CTDS). This updated new edition has been enhanced with new illustrative case studies, and additional examples demonstrating some new features and the effectiveness of the ABCmod conceptual modelling framework. Changes that facilitate the development of simulation models with ABSmod/J are illustrated. New material includes a presentation of the experimentation strategy called “design of experiments” and three new chapters that explore the optimization-simulation interface. Topics and features: presents a goal-based and project-oriented perspective of modelling and simulation; describes the ABCmod framework, an activity-based conceptual modelling framework for DEDS; examines the simulation-optimization interface in both the CTDS and DEDS domains; provides numerous illustrative examples, case studies and useful algorithms, as well as exercises and projects at the end of most chapters; includes appendices on probability and statistics, the GPSS programming environment, and relevant MATLAB features; provides supplementary software and teaching support material at an associated website, including lecture slides and a methodology for organizing student projects. Serving as an essential guide to the foundations of modelling and simulation, this practical primer is ideal for senior undergraduate and junior graduate-level students. Also suitable for self-study, the book will be of great benefit to professionals seeking insight into the vast potential of this rapidly evolving problem-solving paradigm.

Dynamic Modeling of Environmental Systems

Dynamic Modeling of Environmental Systems
Author: Michael L. Deaton
Publisher: Springer Science & Business Media
Total Pages: 210
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461213002

A primer on modeling concepts and applications that is specifically geared toward the environmental field. Sections on modeling terminology, the uses of models, the model-building process, and the interpretation of output provide the foundation for detailed applications. After an introduction to the basics of dynamic modeling, the book leads students through an analysis of several environmental problems, including surface-water pollution, matter-cycling disruptions, and global warming. The scientific and technical context is provided for each problem, and the methods for analyzing and designing appropriate modeling approaches is provided. While the mathematical content does not exceed the level of a first-semester calculus course, the book gives students all of the background, examples, and practice exercises needed both to use and understand environmental modeling. It is suitable for upper-level undergraduate and beginning-graduate level environmental professionals seeking an introduction to modeling in their field.

Mathematical Modelling

Mathematical Modelling
Author: C Haines
Publisher: Elsevier
Total Pages: 511
Release: 2007-08-01
Genre: Mathematics
ISBN: 0857099418

This book continues the ICTMA tradition of influencing teaching and learning in the application of mathematical modelling. Each chapter shows how real life problems can be discussed during university lectures, in school classrooms and industrial research. International experts contribute their knowledge and experience by providing analysis, insight and comment whilst tackling large and complex problems by applying mathematical modelling. This book covers the proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications. Covers the proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications Continues the ICTMA tradition of influencing teaching and learning in the application of mathematical modelling Shows how real life problems can be discussed during university lectures, in school classrooms and industrial research

Modeling Life

Modeling Life
Author: Alan Garfinkel
Publisher: Springer
Total Pages: 456
Release: 2017-09-06
Genre: Mathematics
ISBN: 3319597310

This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?

Learning from Dynamic Visualization

Learning from Dynamic Visualization
Author: Richard Lowe
Publisher: Springer
Total Pages: 392
Release: 2017-05-18
Genre: Education
ISBN: 3319562045

This volume tackles issues arising from today’s high reliance on learning from visualizations in general and dynamic visualizations in particular at all levels of education. It reflects recent changes in educational practice through which text no longer occupies its traditionally dominant role as the prime means of presenting to-be-learned information to learners. Specifically, the book targets the dynamic visual components of multimedia educational resources and singles out how they can influence learning in their own right. It aims to help bridge the increasing gap between pervasive adoption of dynamic visualizations in educational practice and our limited understanding of the role that these representations can play in learning. The volume has recruited international leaders in the field to provide diverse perspectives on the dynamic visualizations and learning. It is the first comprehensive book on the topic that brings together contributions from both renowned researchers and expert practitioners. Rather than aiming to present a broad general overview of the field, it focuses on innovative work that is at the cutting edge. As well as further developing and complementing existing approaches, the contributions emphasize fresh ideas that may challenge existing orthodoxies and point towards future directions for the field. They seek to stimulate further new developments in the design and use of dynamic visualizations for learning as well as the rigorous, systematic investigation of their educational effectiveness.the volume="" sheds="" light="" on="" the="" complex="" and="" highly="" demanding="" processes="" of="" conceptualizing,="" developing="" implementing="" dynamic="" visualizations="" in="" practice="" as="" well="" challenges="" relating="" research="" application="" perspectives.

Model-Based Approaches to Learning

Model-Based Approaches to Learning
Author:
Publisher: BRILL
Total Pages: 357
Release: 2019-02-11
Genre: Education
ISBN: 9087907117

Model-Based Approaches to Learning provides a new perspective called learning by system modeling. This book explores the learning impact of students when constructing models of complex systems.

A Framework for K-12 Science Education

A Framework for K-12 Science Education
Author: National Research Council
Publisher: National Academies Press
Total Pages: 400
Release: 2012-02-28
Genre: Education
ISBN: 0309214459

Science, engineering, and technology permeate nearly every facet of modern life and hold the key to solving many of humanity's most pressing current and future challenges. The United States' position in the global economy is declining, in part because U.S. workers lack fundamental knowledge in these fields. To address the critical issues of U.S. competitiveness and to better prepare the workforce, A Framework for K-12 Science Education proposes a new approach to K-12 science education that will capture students' interest and provide them with the necessary foundational knowledge in the field. A Framework for K-12 Science Education outlines a broad set of expectations for students in science and engineering in grades K-12. These expectations will inform the development of new standards for K-12 science education and, subsequently, revisions to curriculum, instruction, assessment, and professional development for educators. This book identifies three dimensions that convey the core ideas and practices around which science and engineering education in these grades should be built. These three dimensions are: crosscutting concepts that unify the study of science through their common application across science and engineering; scientific and engineering practices; and disciplinary core ideas in the physical sciences, life sciences, and earth and space sciences and for engineering, technology, and the applications of science. The overarching goal is for all high school graduates to have sufficient knowledge of science and engineering to engage in public discussions on science-related issues, be careful consumers of scientific and technical information, and enter the careers of their choice. A Framework for K-12 Science Education is the first step in a process that can inform state-level decisions and achieve a research-grounded basis for improving science instruction and learning across the country. The book will guide standards developers, teachers, curriculum designers, assessment developers, state and district science administrators, and educators who teach science in informal environments.

Author:
Publisher: IOS Press
Total Pages: 4947
Release:
Genre:
ISBN: