What Is Mathematics School Guide To Conceptual Understanding Of Mathematics
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What Is Mathematics School Guide To Conceptual Understanding Of Mathematics
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Author : Catalin Barboianu
language : en
Publisher: PhilScience Press
Release Date : 2021-01-18
What Is Mathematics School Guide To Conceptual Understanding Of Mathematics written by Catalin Barboianu and has been published by PhilScience Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-18 with Education categories.
This is not a mathematics book, but a book about mathematics, which addresses both student and teacher, with a goal as practical as possible, namely to initiate and smooth the way toward the student's full understanding of the mathematics taught in school. The customary procedural-formal approach to teaching mathematics has resulted in students' distorted vision of mathematics as a merely formal, instrumental, and calculatory discipline. Without the conceptual base of mathematics, students develop over time a "mathematical anxiety" and abandon any effort to understand mathematics, which becomes their "traditional enemy" in school. This work materializes the results of the inter- and trans-disciplinary research aimed toward the understanding of mathematics, which concluded that the fields with the potential to contribute to mathematics education in this respect, by unifying the procedural and conceptual approaches, are epistemology and philosophy of mathematics and science, as well as fundamentals and history of mathematics. These results argue that students' fear of mathematics can be annulled through a conceptual approach, and a student with a good conceptual understanding will be a better problem solver. The author has identified those zones and concepts from the above disciplines that can be adapted and processed for familiarizing the student with this type of knowledge, which should accompany the traditional content of school mathematics. The work was organized so as to create for the reader a unificatory image of the complex nature of mathematics, as well as a conceptual perspective ultimately necessary to the holistic understanding of school mathematics. The author talks about mathematics to convince readers that to understand mathematics means first to understand it as a whole, but also as part of a whole. The nature of mathematics, its primary concepts (like numbers and sets), its structures, language, methods, roles, and applicability, are all presented in their essential content, and the explanation of non-mathematical concepts is done in an accessible language and with many relevant examples.
Concept Based Mathematics
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Author : Jennifer T.H. Wathall
language : en
Publisher: Corwin Press
Release Date : 2016-01-14
Concept Based Mathematics written by Jennifer T.H. Wathall and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-14 with Education categories.
Give math students the connections between what they learn and how they do math—and suddenly math makes sense If your secondary-school students are fearful of or frustrated by math, it’s time for a new approach. When you teach concepts rather than rote processes, you show students math’s essential elegance, as well as its practicality—and help them discover their own natural mathematical abilities. This book is a road map to retooling how you teach math in a deep, clear, and meaningful way —through a conceptual lens—helping students achieve higher-order thinking skills. Jennifer Wathall shows you how to plan units, engage students, assess understanding, incorporate technology, and even guides you through an ideal concept-based classroom. Practical tools include: Examples from arithmetic to calculus Inquiry tasks, unit planners, templates, and activities Sample assessments with examples of student work Vignettes from international educators A dedicated companion website with additional resources, including a study guide, templates, exemplars, discussion questions, and other professional development activities. Everyone has the power to understand math. By extending Erickson and Lanning’s work on Concept-Based Curriculum and Instruction specifically to math, this book helps students achieve the deep understanding and skills called for by global standards and be prepared for the 21st century workplace. "Jennifer Wathall’s book is one of the most forward thinking mathematics resources on the market. While highlighting the essential tenets of Concept-Based Curriculum design, her accessible explanations and clear examples show how to move students to deeper conceptual understandings. This book ignites the mathematical mind!" — Lois A. Lanning, Author of Designing Concept-based Curriculum for English-Language Arts, K-12 "Wathall is a master at covering all the bases here; this book is bursting with engaging assessment examples, discussion questions, research, and resources that apply specifically to mathematical topics. Any math teacher or coach would be hard-pressed to read it and not come away with scores of ideas, assessments, and lessons that she could use instantly in the classroom. As an IB Workshop Leader and instructional coach, I want this book handy on a nearby shelf for regular referral – it′s a boon to any educator who wants to bring math to life for students." — Alexis Wiggins, Instructional Coach, IB Workshop Leader and Consultant
Concept Rich Mathematics Instruction
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Author : Meir Ben-Hur
language : en
Publisher: ASCD
Release Date : 2006
Concept Rich Mathematics Instruction written by Meir Ben-Hur and has been published by ASCD this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Education categories.
Presents an instructional approach that helps students in every grade level understand math concepts so they can apply them on assessments, across the curriculum, and outside of school. Provides teaching practices and lesson ideas that give students a stronger foundation for reasoning and problem solving.
Developing Mathematical Thinking
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Author : Jonathan D. Katz
language : en
Publisher: Rowman & Littlefield
Release Date : 2014-07-07
Developing Mathematical Thinking written by Jonathan D. Katz and has been published by Rowman & Littlefield this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-07 with Education categories.
In this country we have done a poor job of helping students come to see the wonder, beauty and power of mathematics. Standards can be brought into the picture, but unless we think about what it means to truly engage students in mathematics we will continue to be unsuccessful. The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.
A Leader S Guide To Mathematics Curriculum Topic Study
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Author : Page Keeley
language : en
Publisher: Corwin Press
Release Date : 2012-05-30
A Leader S Guide To Mathematics Curriculum Topic Study written by Page Keeley and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-30 with Education categories.
The Curriculum Topic Study (CTS) process, funded by the National Science Foundation, helps teachers improve their practice by linking standards and research on how children learn mathematics to classroom practice. Keyed to the core book Mathematics Curriculum Topic Study, this resource helps maths professional development leaders.
Conceptual Understanding In Mathematics
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Author : Brian R. Evans
language : en
Publisher:
Release Date : 2015-08-06
Conceptual Understanding In Mathematics written by Brian R. Evans and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-06 with categories.
This brief handbook is intended for educators, parents/guardians, students, or anyone simply interested in understanding the reasoning behind selected basic, and not so basic, mathematical topics. Another intention of the handbook is to present the reader with a selected group of counterintuitive results found in mathematics, which would prove interesting for the reader and for students in mathematics. Despite the emphasis on understanding in the educational research literature and teacher education programs, many students continue to learn mathematics procedurally with a lack of real conceptual understanding. Research shows that many new teachers revert to teaching the way they were taught when they were in school, and not the way they were taught to teach in their teacher education programs. Moreover, teachers often claim that they believe in teaching for understanding and through problem solving, but continue to teach their students procedural knowledge only. Perhaps for some teachers it can be a lack of understanding in their own mathematical background that prevents them from teaching from an understanding perspective. When a person learns mathematics procedurally without real understanding, he or she is more likely to later forget what was learned rather than if the mathematics if fully understood initially. This handbook is intended for those interested in knowing the "why" behind selected mathematical concepts. Further, this book presents mathematics in a motivating way to make the subject more interesting. There is a reciprocal relationship between understanding and enjoying mathematics because people generally find mathematics more interesting when they truly understand what they are learning.The contents of this book begin with the basics structure of the number system and then progresses through basic operations, exponents, logarithms, compound interest, fractions, decimals, percentages, area of selected shapes, counting techniques, and calculus. As the book progresses, the mathematics becomes more sophisticated. The author recommends the reader attempt to understand the content of the entire book, but acknowledges that some readers may wish to stop at a certain point or ask someone for more assistance. In some cases, skipping to other sections of the book may prove useful. For example, it might make sense to skip the sections on exponents, logarithms, and compound interest in order to get to the section on fractions after the reader read about basic operations. The book is meant to be an overview of important topics, but some readers may focus on one or more sections only. Mathematics is a fascinating subject and hopefully this brief handbook will be a start for further mathematical explorations. If approached from the right perspective, mathematics can be enjoyable and engaging, and understanding the deep mathematical ideas behind the basic concepts will motivate a person to want to learn more. This is a major shift in the way in which mathematics can be viewed.
Key Concepts In Mathematics
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Author : Timothy J. McNamara
language : en
Publisher: Corwin Press
Release Date : 2007
Key Concepts In Mathematics written by Timothy J. McNamara and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Education categories.
"Includes a large number of user-friendly examples that integrate mathematics content and process standards. The step-by-step guidance and explanations in each chapter are beneficial."-Melissa Miller, TeacherRandall G. Lynch Middle School, Farmington, AR "Great activities that are exploratory in nature. A valuable resource."-Carol Amos, Teacher Leader and Mathematics CoordinatorTwinfield Union School, Plainfield, VT Increase students' mathematics achievement with rich problem-solving lessons and activities that are aligned with NCTM standards! Helping teachers envision how math standards can be integrated into the secondary classroom, Key Concepts in Mathematics, Second Edition presents engaging activities and ready-to-use lessons aligned with NCTM content and process standards. This user-friendly book by mathematics educator Timothy J. McNamara is filled with a generous collection of lessons for each of the ten NCTM standards, with many activities that address multiple standards, and numerous practical suggestions for extending the lessons beyond the curriculum. In addition, this updated resource combines standards-based mathematics and technology by incorporating TI-73 Explorer(tm) and TI-83 Plus graphing calculator applications and programs. Each chapter offers: Ready-to-use lessons, hands-on activities, practical suggestions, and an abundance of "good problems" Suggestions for integrating multiple topics and concepts in each lesson Strategies to strengthen student engagement, understanding, and retention by building connections among mathematics topics This exciting guide delivers exactly what is needed for today's standards-based math classroom!
How Math Works
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Author : G. Arnell Williams
language : en
Publisher: Rowman & Littlefield Publishers
Release Date : 2013-04-04
How Math Works written by G. Arnell Williams and has been published by Rowman & Littlefield Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-04 with Education categories.
We hear all the time how American children are falling behind their global peers in various basic subjects, but particularly in math. Is it our fear of math that constrains us? Or our inability to understand math’s place in relation to our everyday lives? How can we help our children better understand the basics of arithmetic if we’re not really sure we understand them ourselves? Here, G. Arnell Williams helps parents and teachers explore the world of math that their elementary school children are learning. Taking readers on a tour of the history of arithmetic, and its growth into the subject we know it to be today, Williams explores the beauty and relevance of mathematics by focusing on the great conceptual depth and genius already inherent in the elementary mathematics familiar to us all, and by connecting it to other well-known areas such as language and the conceptual aspects of everyday life. The result is a book that will help you to better explain mathematics to your children. For those already well versed in these areas, the book offers a tour of the great conceptual and historical facts and assumptions that most simply take for granted. If you are someone who has always struggled with mathematics either because you couldn’t do it or because you never really understood why the rules are the way they are, if you were irritated with the way it was taught to you with the emphasis being only on learning the rules and “recipes” by rote as opposed to obtaining a good conceptual understanding, then How Math Works is for you!
Measuring What Counts
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Author : National Research Council
language : en
Publisher: National Academies Press
Release Date : 1993-02-01
Measuring What Counts written by National Research Council and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-02-01 with Education categories.
To achieve national goals for education, we must measure the things that really count. Measuring What Counts establishes crucial research- based connections between standards and assessment. Arguing for a better balance between educational and measurement concerns in the development and use of mathematics assessment, this book sets forth three principlesâ€"related to content, learning, and equityâ€"that can form the basis for new assessments that support emerging national standards in mathematics education.
Concept Mapping In Mathematics
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Author : Karoline Afamasaga-Fuata'i
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-21
Concept Mapping In Mathematics written by Karoline Afamasaga-Fuata'i and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-21 with Education categories.
Concept Mapping in Mathematics: Research into Practice is the first comprehensive book on concept mapping in mathematics. It provides the reader with an understanding of how the meta-cognitive tool, namely, hierarchical concept maps, and the process of concept mapping can be used innovatively and strategically to improve planning, teaching, learning, and assessment at different educational levels. This collection of research articles examines the usefulness of concept maps in the educational setting, with applications and examples ranging from primary grade classrooms through secondary mathematics to pre-service teacher education, undergraduate mathematics and post-graduate mathematics education. A second meta-cognitive tool, called vee diagrams, is also critically examined by two authors, particularly its value in improving mathematical problem solving. Thematically, the book flows from a historical development overview of concept mapping in the sciences to applications of concept mapping in mathematics by teachers and pre-service teachers as a means of analyzing mathematics topics, planning for instruction and designing assessment tasks including applications by school and university students as learning and review tools. This book provides case studies and resources that have been field tested with school and university students alike. The findings presented have implications for enriching mathematics learning and making problem solving more accessible and meaningful for students. The theoretical underpinnings of concept mapping and of the studies in the book include Ausubel’s cognitive theory of meaningful learning, constructivist and Vygotskian psychology to name a few. There is evidence particularly from international studies such as PISA and TIMSS and mathematics education research, which suggest that students’ mathematical literacy and problem solving skills can be enhanced through students collaborating and interacting as they work, discuss and communicate mathematically. This book proposes the meta-cognitive strategy of concept mapping as one viable means of promoting, communicating and explicating students’ mathematical thinking and reasoning publicly in a social setting (e.g., mathematics classrooms) as they engage in mathematical dialogues and discussions. Concept Mapping in Mathematics: Research into Practice is of interest to researchers, graduate students, teacher educators and professionals in mathematics education.