How Students Learn

How Students Learn
Author: National Research Council
Publisher: National Academies Press
Total Pages: 633
Release: 2005-01-23
Genre: Education
ISBN: 0309074339

How do you get a fourth-grader excited about history? How do you even begin to persuade high school students that mathematical functions are relevant to their everyday lives? In this volume, practical questions that confront every classroom teacher are addressed using the latest exciting research on cognition, teaching, and learning. How Students Learn: History, Mathematics, and Science in the Classroom builds on the discoveries detailed in the bestselling How People Learn. Now, these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. Organized for utility, the book explores how the principles of learning can be applied in teaching history, science, and math topics at three levels: elementary, middle, and high school. Leading educators explain in detail how they developed successful curricula and teaching approaches, presenting strategies that serve as models for curriculum development and classroom instruction. Their recounting of personal teaching experiences lends strength and warmth to this volume. The book explores the importance of balancing students' knowledge of historical fact against their understanding of concepts, such as change and cause, and their skills in assessing historical accounts. It discusses how to build straightforward science experiments into true understanding of scientific principles. And it shows how to overcome the difficulties in teaching math to generate real insight and reasoning in math students. It also features illustrated suggestions for classroom activities. How Students Learn offers a highly useful blend of principle and practice. It will be important not only to teachers, administrators, curriculum designers, and teacher educators, but also to parents and the larger community concerned about children's education.

Teaching and Learning of Calculus

Teaching and Learning of Calculus
Author: David Bressoud
Publisher: Springer
Total Pages: 44
Release: 2016-06-14
Genre: Education
ISBN: 3319329758

This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions.

Research in Collegiate Mathematics Education III

Research in Collegiate Mathematics Education III
Author: James J. Kaput
Publisher: American Mathematical Soc.
Total Pages: 330
Release: 1998
Genre: Education
ISBN: 0821808826

Volume 3 of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching and learning mathematics at the post-secondary level. This volume contains information on methodology and research concentrating on these areas of student learning: Problem Solving; Understanding Concepts; and Understanding Proofs.

APOS Theory

APOS Theory
Author: Ilana Arnon
Publisher: Springer Science & Business Media
Total Pages: 259
Release: 2013-08-04
Genre: Education
ISBN: 1461479665

In spite of the fact that APOS Theory has been used extensively in numerous scholarly publications, in the design of textbooks, and in teaching practice, there is no single references that contains all the relevant information about its components, and provides guidance about its application. The goal of this book is to present the main elements of APOS theory. It should be useful for researchers who work with, or would like to learn more about, this theoretical approach, people who are interested in the way which mathematical conceptions are constructed according to this theory, Mathematics Education researchers, graduate students in Mathematics Education, and Mathematics instructors.

Mathematical Analysis I

Mathematical Analysis I
Author: V. A. Zorich
Publisher: Springer
Total Pages: 630
Release: 2016-02-29
Genre: Mathematics
ISBN: 3662487926

This second edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. The first volume constitutes a complete course in one-variable calculus along with the multivariable differential calculus elucidated in an up-to-date, clear manner, with a pleasant geometric and natural sciences flavor.

The Common Core Mathematics Companion: The Standards Decoded, High School

The Common Core Mathematics Companion: The Standards Decoded, High School
Author: Frederick L. Dillon
Publisher: Corwin Press
Total Pages: 505
Release: 2017-09-12
Genre: Education
ISBN: 1506395635

Your User’s Guide to the Mathematics Standards When it comes to mathematics, standards aligned is achievement aligned... In the short time since The Common Core Mathematics Companions for grades K–2, 3–5 and 6–8 burst on the scene, they have been lauded as the best resources for making critical mathematics ideas easy to teach. With this brand-new volume, high school mathematics success is at your fingertips. Page by page, the authors lay out the pieces of an in-depth explanation, including The mathematical progression of each conceptual category, starting with modeling as a unifying theme, and moving through number & quantity, algebra, functions, geometry, and statistics and probability, building from the 8th grade standards The mathematics embedded in each conceptual category for a deeper understanding of the content How standards connect within and across domains, and to previous grade standards, so teachers can better appreciate how they relate How standards connect with the standards for mathematical practice, with a focus on modeling as a unifying theme Example tasks, progressions of tasks, and descriptions of what teachers and students should be doing to foster deep learning The Common Core Mathematics Companion: The Standards Decoded, High School has what every high school teacher needs to provide students with the foundation for the concepts and skills they will be expected to know .

Learning and Understanding

Learning and Understanding
Author: National Research Council
Publisher: National Academies Press
Total Pages: 589
Release: 2002-09-06
Genre: Education
ISBN: 0309074401

This book takes a fresh look at programs for advanced studies for high school students in the United States, with a particular focus on the Advanced Placement and the International Baccalaureate programs, and asks how advanced studies can be significantly improved in general. It also examines two of the core issues surrounding these programs: they can have a profound impact on other components of the education system and participation in the programs has become key to admission at selective institutions of higher education. By looking at what could enhance the quality of high school advanced study programs as well as what precedes and comes after these programs, this report provides teachers, parents, curriculum developers, administrators, college science and mathematics faculty, and the educational research community with a detailed assessment that can be used to guide change within advanced study programs.

Your Mathematics Standards Companion, High School

Your Mathematics Standards Companion, High School
Author: Frederick L. Dillon
Publisher: Corwin Press
Total Pages: 537
Release: 2018-02-06
Genre: Education
ISBN: 1544317433

Transforming the standards into learning outcomes just got a lot easier In this resource, you can see in an instant how teaching to your state standards should look and sound in the classroom. Under the premise that math is math, the authors provide a Cross-Referencing Index for states implementing their own specific mathematics standards, allowing you to see and understand which page number to turn to for standards-based teaching ideas. It’s all here, page by page: The mathematical progression of each conceptual category, starting with modeling as a unifying theme and moving through number and quantity, algebra, functions, geometry, and statistics and probability, building from eighth-grade standards The mathematics embedded in each conceptual category for a deeper understanding of the content How standards connect within and across domains and to previous grade standards, so teachers can better appreciate how they relate How content standards connect with the standards for mathematical practice, with a focus on modeling as a unifying theme Example tasks, progressions of tasks, and descriptions of what teachers and students should be doing to foster deep learning Your Mathematics Standards Companion is your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful high school mathematics curriculum in any state or district.