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Author: Catalin Barboianu Publisher: PhilScience Press ISBN: 9731991980 Category : Education Languages : en Pages : 315
Book Description
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.
Author: Catalin Barboianu Publisher: PhilScience Press ISBN: 9731991980 Category : Education Languages : en Pages : 315
Book Description
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.
Author: Meir Ben-Hur Publisher: ASCD ISBN: 141660359X Category : Education Languages : en Pages : 162
Book Description
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.
Author: Jennifer T.H. Wathall Publisher: Corwin Press ISBN: 150633265X Category : Education Languages : en Pages : 307
Book Description
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
Author: Brian R. Evans Publisher: ISBN: 9781515378020 Category : Languages : en Pages : 188
Book Description
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.
Author: Jonathan D. Katz Publisher: Rowman & Littlefield ISBN: 147581058X Category : Education Languages : en Pages : 145
Book Description
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.
Author: Sandra Goff Publisher: Rain Publishing Incorporated ISBN: 9780991661893 Category : Education Languages : en Pages : 90
Book Description
As we strive to create a seamless and meaningful mathematics experience for our students, it is important for us to have a strong understanding of what conceptual knowledge looks like in the classroom. This understanding is essential to planning engaging lessons, delivering effective classroom instruction and developing valid assessments that are a balanced combination of factual knowledge, procedural fluency and conceptual knowledge. 10 Concepts Every Math Teacher Should Know demonstrates the following: -It is important for teachers to have a clear understanding of how concepts evolve across grade levels. -Understanding how these concepts evolve will help teachers design experiences for students that deepen their understanding of mathematics. -Understanding how these concepts work will build our students' confidence in their ability to be problem solvers. -It is critical for teachers to use the same conceptual language across grade levels to increase our students' chances of success.
Author: Sammons, Laney Publisher: Shell Education ISBN: 1618137956 Category : Education Languages : en Pages : 266
Book Description
Use a practical approach to teaching mathematics that integrates proven literacy strategies for effective instruction. This professional resource will help to maximize the impact of instruction through the use of whole-class instruction, small-group instruction, and Math Workshop. Incorporate ideas for using ongoing assessment to guide your instruction and increase student learning, and use hands-on, problem-solving experiences with small groups to encourage mathematical communication and discussion. Guided Math supports the College and Career Readiness and other state standards.
Author: Albert B. Bennett Publisher: McGraw-Hill Europe ISBN: 9780071310024 Category : Mathematics Languages : en Pages :
Book Description
Overview: Albert B. Bennett, Jr. and L. Ted Nelson have presented hundreds of workshops on how to give future teachers the conceptual understanding and procedural fluency they will need in order to successfully teach elementary-school mathematics. The Eighth Edition of Mathematics for Elementary Teachers: A Conceptual Approach continues their innovative, time-tested approach: an emphasis on learning via specific, realistic examples and the extensive use of visual aids, hands-on activities, problem-solving strategies and active classroom participation. Special features in the text ensure that prospective teachers will gain not only a deeper understanding of the mathematical concepts, but also a better sense of the connections between their college math courses and their future teaching experiences, along with helpful ideas for presenting math to their students in a way that will generate interest and enthusiasm. The text draws heavily on NCTM Standards and contains many pedagogical elements designed to foster reasoning, problem-solving and communication skills. The text also incorporates references to the virtual manipulative kit and other online resources that enhance the authors' explanations and examples.
Author: Matthew R. Larson Publisher: ISBN: 9781936763696 Category : Education Languages : en Pages : 176
Book Description
Copublished with the National Council of Teachers of Mathematics, this book focuses on individuals involved in K 12 mathematics education particularly educators and parents who seek to improve their understanding of mathematics and help students succeed. The authors tackle popular misconceptions and misguided discourse about mathematics education and draw on peer-reviewed research about instruction that can significantly improve student learning."
Author: Mary Fiore Publisher: Pembroke Publishers Limited ISBN: 1551389258 Category : Education Languages : en Pages : 128
Book Description
Focus on “moving” the teaching and learning of mathematics by shifting instruction and assessment practices. This unique book uses critical thinking skills — inferring and interpreting, analyzing, evaluating, making connections, synthesizing, reasoning and proving, and reflecting — to help students make sense of mathematical concepts and support numeracy.
Author: Catalin Barboianu
Author: Catalin Barboianu
Author: Meir Ben-Hur
Author: Jennifer T.H. Wathall
Author: Brian R. Evans
Author: Jonathan D. Katz
Author: Sandra Goff
Author: Sammons, Laney
Author: Albert B. Bennett
Author: Matthew R. Larson
Author: Mary Fiore