Conceptual Maths
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Conceptual Maths
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Author : Peter Mattock
language : en
Publisher: Crown House Publishing Ltd
Release Date : 2023-01-05
Conceptual Maths written by Peter Mattock and has been published by Crown House Publishing Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-05 with Education categories.
Written by Peter Mattock, Conceptual Maths: Teaching 'about' (rather than just 'how to do') mathematics in schoolsaims to empower teachers to support students on a comprehensive and coherent journey through school mathematics. Showcasing the best models, metaphors and representations, it provides excellent examples, explanations and exercises that can be used across the curriculum. Concepts are at the heart of the study of mathematics. They are the ideas that remain constant whenever they are encountered, but which combine and build upon each other to create the mathematical universe. It is the structure of each concept that gives rise to the procedures that are used in calculation and problem-solving - and, by learning about these structures, a learner can make sense of how different processes work and use them flexibly as need demands. In his first book,Visible Maths, Peter Mattock focused on the use of representations and manipulatives as images and tools and how this can provide a window into some of these mathematical structures. His aim in Conceptual Mathsis to go deeper, beyond the procedures, and to shed greater light on the structures of the subject's different concepts. The book explores how a variety of visual tools and techniques can be used in the classroom to deepen pupils' understanding of mathematical structures, concepts and operations, including: number; addition and subtraction; multiplication and multiples; division and factors; proportionality; functionality; measures; accuracy; probability; shape and transformation; and vectors, among many others. In so doing, Peter equips teachers with the confidence and practical know-how to help learners assimilate knowledge of mathematical concepts into their schema and take their learning to the next level. Containing numerous full-colour diagrams and models to illustrate the conceptual takeaways and teaching techniques discussed, Conceptual Mathsalso includes a glossary covering the key mathematical terms. Suitable for teachers of maths in primary, secondary and post-16 settings
Conceptual Mathematics
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Author : F. William Lawvere
language : en
Publisher: Cambridge University Press
Release Date : 1997-10-09
Conceptual Mathematics written by F. William Lawvere and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-09 with Mathematics categories.
In the last fifty years, the use of the notion of 'category' has led to a remarkable unification and simplification of mathematics. Written by two of the best known participants in this development, Conceptual Mathematics is the first book to serve as a skeleton key to mathematics for the general reader or beginning student and as an introduction to categories for computer scientists, logicians, physicists, linguists etc. While the ideas and techniques of basic category theory are useful throughout modern mathematics, this book does not presuppose knowledge of specific fields but rather develops elementary categories such as directed graphs and discrete dynamical systems from the beginning. The fundamental ideas are then illuminated in an engaging way by examples in these categories.
How We Understand Mathematics
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Author : Jacek Woźny
language : en
Publisher: Springer
Release Date : 2018-04-25
How We Understand Mathematics written by Jacek Woźny and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-25 with Mathematics categories.
This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested in the engaging question of how mathematics works and why it works so well.
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.
Daily Math Stretches Building Conceptual Understanding Levels K 2
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Author : Laney Sammons
language : en
Publisher: Teacher Created Materials
Release Date : 2010-05-30
Daily Math Stretches Building Conceptual Understanding Levels K 2 written by Laney Sammons and has been published by Teacher Created Materials this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-30 with Education categories.
Take an in-depth look at math stretches-warm-ups that get students in grades K-2 thinking about math and ready for instruction! Written by Guided Math author, Laney Sammons, this resource features step-by-step lessons, assessment information, and a snapshot of what the warm-ups look like in the classroom. Daily Math Stretches: Building Conceptual Understanding is correlated to the Common Core State Standards. 192pp.
New Foundations In Mathematics
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Author : Garret Sobczyk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-28
New Foundations In Mathematics written by Garret Sobczyk 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 2012-10-28 with Mathematics categories.
The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
A Concept Of Limits
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Author : Donald W. Hight
language : en
Publisher: Courier Corporation
Release Date : 2012-07-17
A Concept Of Limits written by Donald W. Hight and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-17 with Mathematics categories.
An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. Many exercises with solutions. 1966 edition.
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 Maths Lesson Planning And Frameworks Mastery Logic And Reasoning In The Classroom
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Author : Linda (Yuqian) Wang
language : en
Publisher: McGraw-Hill Education (UK)
Release Date : 2023-11-24
Developing Maths Lesson Planning And Frameworks Mastery Logic And Reasoning In The Classroom written by Linda (Yuqian) Wang and has been published by McGraw-Hill Education (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-24 with Education categories.
“This book highlights the essential relationship between lesson planning and key mathematical elements such as mastery and reasoning. The exemplification of ideas through useful classroom strategies gives the book a practical basis, as well as theoretical. I have no doubt that even experienced teachers will find this book enlightening and encourage them to re-evaluate elements of their practice.” Hayley Hands, Secondary PGCE Mathematics Lead, Newcastle University, UK “Developing Maths Lesson Planning and Frameworks provides much food for thought and includes many immediate ‘take aways’ to reflect on or try out. This book will help enhance any maths teacher's lesson planning, from the trainee teacher to the experienced practitioner.” Rose-Marie Rochester, Archimedes NE Maths Hub Lead/BHCET Director of Maths, UK Addressing the maths skills gap, Wang et al. propose a new method for maths lesson planning that harnesses the power of reasoning in mathematics teaching. Using a pedagogical approach called the Causal Connectivity Framework (CCF), this book helps teachers to support students in actively discovering the logical foundations upon which classroom activities are linked together. The authors have diverse expertise and experiences as maths teachers, teacher educators and researchers, and this alternative approach is the result of long-term collaboration aimed at building up successful maths lessons from the very first steps – lesson planning. Developing Maths Lesson Planning and Frameworks: •Offers practical advice within a theoretical framework •Ties in with UK National Curriculum requirements •Contains detailed practical examples and visual aids throughout Reasoning is a critical component of maths learning, making this essential reading for maths teachers and teacher trainees as they help students to achieve maths mastery. Linda Wang is Assistant Professor and PGCE secondary maths Lead at Durham University, UK. She is particularly interested in curriculum design at both secondary and lower primary level mathematics, and developing the educational impact partnership model to deliver Continuing Professional Development (CPD) to future-orientate Mathematics education. Chris Brown is Professor of Education at the University of Southampton, UK. His research interests include using Professional Learning Networks (PLNs) to promote the collaborative learning of teachers, as well as how research evidence can and should, but often doesn’t, aid the development of education policy and practice. Jeremy Dawson is Area Co-ordinator for the Advanced Maths Support Programme at Durham University, UK. He has worked in a variety of diverse school settings around North East England and has extensive experience of teaching mathematics from KS2-KS5, as well as contributing and assisting on gifted and talented programs for prospective university entrants.
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 help students 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 to help students achieve higher-order thinking skills. Jennifer Wathall shows you how to plan units, engage students, assess understanding, incorporate technology, and there’s even a companion website with additional resources.