Author: Danilo R. Diedrichs
Publisher: CRC Press
ISBN: 1000581667
Category : Mathematics
Languages : en
Pages : 552

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Book Description
This unique and contemporary text not only offers an introduction to proofs with a view towards algebra and analysis, a standard fare for a transition course, but also presents practical skills for upper-level mathematics coursework and exposes undergraduate students to the context and culture of contemporary mathematics. The authors implement the practice recommended by the Committee on the Undergraduate Program in Mathematics (CUPM) curriculum guide, that a modern mathematics program should include cognitive goals and offer a broad perspective of the discipline. Part I offers: An introduction to logic and set theory. Proof methods as a vehicle leading to topics useful for analysis, topology, algebra, and probability. Many illustrated examples, often drawing on what students already know, that minimize conversation about "doing proofs." An appendix that provides an annotated rubric with feedback codes for assessing proof writing. Part II presents the context and culture aspects of the transition experience, including: 21st century mathematics, including the current mathematical culture, vocations, and careers. History and philosophical issues in mathematics. Approaching, reading, and learning from journal articles and other primary sources. Mathematical writing and typesetting in LaTeX. Together, these Parts provide a complete introduction to modern mathematics, both in content and practice. Table of Contents Part I - Introduction to Proofs Logic and Sets Arguments and Proofs Functions Properties of the Integers Counting and Combinatorial Arguments Relations Part II - Culture, History, Reading, and Writing Mathematical Culture, Vocation, and Careers History and Philosophy of Mathematics Reading and Researching Mathematics Writing and Presenting Mathematics Appendix A. Rubric for Assessing Proofs Appendix B. Index of Theorems and Definitions from Calculus and Linear Algebra Bibliography Index Biographies Danilo R. Diedrichs is an Associate Professor of Mathematics at Wheaton College in Illinois. Raised and educated in Switzerland, he holds a PhD in applied mathematical and computational sciences from the University of Iowa, as well as a master’s degree in civil engineering from the Ecole Polytechnique Fédérale in Lausanne, Switzerland. His research interests are in dynamical systems modeling applied to biology, ecology, and epidemiology. Stephen Lovett is a Professor of Mathematics at Wheaton College in Illinois. He holds a PhD in representation theory from Northeastern University. His other books include Abstract Algebra: Structures and Applications (2015), Differential Geometry of Curves and Surfaces, with Tom Banchoff (2016), and Differential Geometry of Manifolds (2019).

Author: Lyn D. English
Publisher: Routledge
ISBN: 1135192766
Category : Education
Languages : en
Pages : 942

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Book Description
This book brings together mathematics education research that makes a difference in both theory and practice - research that anticipates problems and needed knowledge before they become impediments to progress.

Author: Celia Hoyles
Publisher: Psychology Press
ISBN: 9780750709392
Category : Education
Languages : en
Pages : 274

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Book Description
Rethinking the Mathematics Curriculum explores maths curricula around the world, and the differences in expectation, culture and politics that form them.

Author: Dhir, Harpreet Kaur
Publisher: IGI Global
ISBN: 1799869695
Category : Education
Languages : en
Pages : 468

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Book Description
The need to develop 21st-century competencies has received global recognition, but instructional methods have not been reformed to include the teaching of these skills. Multiple frameworks include creativity, critical thinking, communication, and collaboration as the foundational competencies. Complexities of planning curriculum and delivering instruction to develop the foundational competencies requires professional training. However, despite training, instructional practice can be impacted by barriers caused by personal views of teachers, economic constraints, access to resources, social challenges, pandemic, overwhelming pace of global shifts, and other influences. With digitalization entering the field of education, it is unclear if technology has helped in removing or eliminating the barriers or has, itself, become another obstruction in integrating the competencies. Gaining an educator's perspective is essential to understanding the barriers as well as solutions to mitigate the impediments through innovative instructional methods being practiced across the globe via digital or non-digital platforms. The need for original contributions from educators exists in this area of barriers to 21st-century education and the role of digitalization. The Handbook of Research on Barriers for Teaching 21st-Century Competencies and the Impact of Digitalization discusses teaching the 21st-century competencies, namely critical thinking, creativity, collaboration, and communication. This book presents both the problems or gaps causing barriers and brings forth practical solutions, digital and non-digital, to meet the educational shifts. The chapters will determine the specific barriers that exist, whether political, social, economic, or technological, to integrating competencies and the methods or strategies that can eliminate these barriers through compatible instructional approaches. Additionally, the chapters provide knowledge on the impacts of digitalization in general on teaching and learning and how digital innovations are either beneficial to removing impediments for students or rather causing obstructions in integrating the four competencies. This book is ideally intended for educators and administrators working directly with students, educational researchers, educational software developers, policymakers, teachers, practitioners, and students interested in how 21st-century competencies can be taught while facing the impacts of digitalization on education.

Author: Ştefan Vladutescu
Publisher: Infinite Study
ISBN: 606114346X
Category :
Languages : en
Pages : 200

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Book Description
There are people for whom are too few things they do not know how to do, to approach them, to understand them. There are people who is enough to look at them because they understood the significance in your eyes, are people for whom you have not finished the uttered sentence and they are given the solution, there are ...people!

Author: Linfan Mao
Publisher: Infinite Study
ISBN: 1599730197
Category : Mathematics
Languages : en
Pages : 215

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Book Description
800x600 Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";} Smarandache Geometries as generalizations of Finsler, Riemannian, Weyl, and Kahler Geometries. A Smarandache geometry (SG) is a geometry which has at least one smarandachely denied axiom (1969). An axiom is said smarandachely denied (S-denied) if in the same space the axiom behaves differently (i.e., validated and invalided; or only invalidated but in at least two distinct ways). Thus, as a particular case, Euclidean, Lobachevsky-Bolyai-Gauss, and Riemannian geometries may be united altogether, in the same space, by some SGs. These last geometries can be partially Euclidean and partially non-Euclidean. The novelty of the SG is the fact that they introduce for the first time the degree of negation in geometry, similarly to the degree of falsehood in fuzzy or neutrosophic logic. For example an axiom can be denied in percentage of 30 Also SG are defined on multispaces, i.e. unions of Euclidean and non-Euclidean subspaces, or unions of distinct non-Euclidean spaces. As an example of S-denying, a proposition , which is the conjunction of a set i of propositions, can be invalidated in many ways if it is minimally unsatisfiable, that is, such that the conjunction of any proper subset of the i is satisfied in a structure, but itself is not. Here it is an example of what it means for an axiom to be invalidated in multiple ways [2] : As a particular axiom let's take Euclid's Fifth Postulate. In Euclidean or parabolic geometry a line has one parallel only through a given point. In Lobacevskian or hyperbolic geometry a line has at least two parallels through a given point. In Riemannian or elliptic geometry a line has no parallel through a given point. Whereas in Smarandache geometries there are lines which have no parallels through a given point and other lines which have one or more parallels through a given point (the fifth postulate is invalidated in many ways). Therefore, the Euclid's Fifth Postulate (which asserts that there is only one parallel passing through an exterior point to a given line) can be invalidated in many ways, i.e. Smarandachely denied, as follows: - first invalidation: there is no parallel passing through an exterior point to a given line; - second invalidation: there is a finite number of parallels passing through an exterior point to a given line; - third invalidation: there are infinitely many parallels passing through an exterior point to a given line.

Author: Jon Schiller
Publisher: CreateSpace
ISBN: 1453633626
Category :
Languages : en
Pages : 250

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Book Description
Your author, Dr. Jon Schiller, decided to write this book about Education in the 21st Century after observing what changes are taking place in the Public Schools from Kindergarten thru the 12th grade in high school. His co-author Emilie Manns Smyth had a unique experience teaching 18 years in the California elementary school system in Fullerton and in Huntington Beach, California. Then 25 years after retirement and after living in Spain for 17 years, she returned to California and began substitute teaching in a school district in the County of Santa Barbara all grades from Kindergarten through High School Seniors. She taught all classes offered to her, from high school honors English, special education classes at all levels, English as a Second Language classes, Physical Education at all levels, Automobile Mechanics, Drivers Education and Shop classes. This allowed her to contribute observations she had seen in the California school system and what was taught to the students over this wide range of years.

Author: Njurai, Evelyn
Publisher: IGI Global
ISBN:
Category : Education
Languages : en
Pages : 352

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Book Description
In the face of emerging challenges in the field of mathematics education, educators and researchers find themselves navigating the complexities of globalization and innovations. As classrooms become more diverse and educational landscapes evolve, there is a need for an understanding of the multifaceted impacts of these forces. The very essence of mathematics education is shifting, influenced by global trends, cultural dynamics, and technological advancements. It is within this context that Impacts of Globalization and Innovation in Mathematics Education offers a profound exploration of the challenges and opportunities that arise in this era. One of the central predicaments faced by educators and scholars is the dynamic nature of globalization and innovation, which introduces unprecedented complexities in mathematics education. While cultural diversity in classrooms brings valuable perspectives, it also poses challenges in developing inclusive and effective teaching strategies. The integration of innovative practices faces resistance due to cultural conflicts and identity issues. Additionally, the fast-paced changes in global trends and the dissemination of information through media influence how mathematics education is perceived and practiced. This creates a demand for a thorough examination of the relationship between globalization, innovation, and the field of mathematics education.

Author: Paramita Cahyaningrum Kuswandi
Publisher: Springer Nature
ISBN: 2384762451
Category : Electronic books
Languages : en
Pages : 467

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Book Description

Author: OECD
Publisher: OECD Publishing
ISBN: 9264932399
Category :
Languages : en
Pages : 295

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Book Description
The OECD's Programme for International Student Assessment (PISA) does more than assess what students know. PISA examines how they use their knowledge and skills to meet real-life challenges, offering invaluable insights into both the quality and equity of education worldwide. In this final volume of the PISA 2022 initial report, Volume V: Learning Strategies and Attitudes for Life takes a deep dive into one of the most critical aspects of modern education: students' readiness for lifelong learning. This volume explores how education systems prepare students to navigate and thrive in an unpredictable future, focusing on their learning strategies, motivation and self-beliefs. It also delves into the role of socio-economic background, gender and the support students receive from parents and teachers in shaping their readiness for sustained lifelong learning. As education evolves to meet the challenges of tomorrow, this volume provides crucial insights for educators and policy makers who want to foster resilient, self-directed learners who are ready to succeed in a rapidly changing world.