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| conceptual understanding in math: Concept-Based Mathematics Jennifer T.H. Wathall, 2016-01-14 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 |
| conceptual understanding in math: Math Games Ted H. Hull, Ruth Harbin Miles, Don S. Balka, 2013-04 Focus on the teaching and learning of mathematics through the use of games. Based on current research and correlated to College and Career Readiness and other state standards, this resource provides both teachers and students with rich opportunities to engage in the Standards for Mathematical Practice. Each concept-building game supports students' learning and understanding concepts. Games are provided in the following categories: Counting and Cardinality; Operations and Algebraic Thinking; Expressions and Equations; Functions; Numbers and Operations in Base Ten; Numbers and Operations--Fractions; The Number System; Ratio and Proportional Relationships; Measurement and Data; Geometry; and Statistics and Probability. |
| conceptual understanding in math: Helping Children Learn Mathematics National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Mathematics Learning Study Committee, 2002-07-31 Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society. |
| conceptual understanding in math: Conceptual Mathematics F. William Lawvere, Stephen H. Schanuel, 2009-07-30 This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists. |
| conceptual understanding in math: How We Understand Mathematics Jacek Woźny, 2018-04-25 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. |
| conceptual understanding in math: Conceptual and Procedural Knowledge James Hiebert, 2013-08-21 First Published in 1986. This book is intended for those people who are interested in how mathematics is learned. It is intended especially for those who are interested in the mental processes involved in becoming mathematically competent and the mental processes that inhibit such competency from developing. The volume opens with an overview of the issue and then traces the relationships between conceptual and procedural knowledge in mathematics from preschool days through the years of formal schooling. Mathematics educators and cognitive psychologists from a variety of perspectives contribute theoretical arguments and empirical data to illuminate the nature of the relationships and, in tum, the nature of mathematics learning. |
| conceptual understanding in math: Oxford Handbook of Numerical Cognition Roi Cohen Kadosh, Ann Dowker, 2015-07-30 How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding? Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. Numerical cognition is a vibrant area that brings together scientists from different and diverse research areas (e.g., neuropsychology, cognitive psychology, developmental psychology, comparative psychology, anthropology, education, and neuroscience) using different methodological approaches (e.g., behavioral studies of healthy children and adults and of patients; electrophysiology and brain imaging studies in humans; single-cell neurophysiology in non-human primates, habituation studies in human infants and animals, and computer modeling). While the study of numerical cognition had been relatively neglected for a long time, during the last decade there has been an explosion of studies and new findings. This has resulted in an enormous advance in our understanding of the neural and cognitive mechanisms of numerical cognition. In addition, there has recently been increasing interest and concern about pupils' mathematical achievement in many countries, resulting in attempts to use research to guide mathematics instruction in schools, and to develop interventions for children with mathematical difficulties. This handbook brings together the different research areas that make up the field of numerical cognition in one comprehensive and authoritative volume. The chapters provide a broad and extensive review that is written in an accessible form for scholars and students, as well as educationalists, clinicians, and policy makers. The book covers the most important aspects of research on numerical cognition from the areas of development psychology, cognitive psychology, neuropsychology and rehabilitation, learning disabilities, human and animal cognition and neuroscience, computational modeling, education and individual differences, and philosophy. Containing more than 60 chapters by leading specialists in their fields, the Oxford Handbook of Numerical Cognition is a state-of-the-art review of the current literature. |
| conceptual understanding in math: Creating a Language-Rich Math Class Sandra L. Atkins, 2015-09-16 What meanings do your students have for key mathematics concepts? What meanings do you wish them to have? Creating a Language-Rich Math Class offers practical approaches for developing conceptual understandings by connecting concrete, pictorial, verbal, and symbolic representations. The focus is on making mathematics memorable instead of on memorizing. You’ll learn strategies for introducing students to math language that gives meaning to the terms and symbols they use everyday; for building flexibility and precision in students’ use of math language; and for structuring activities to make them more language-rich. Book Features: Detailed directions for sample games and activities for immediate classroom use; Investigations to Try and Questions for Reflection to assist in implementing these ideas into your practice; Graphic organizer for helping students first understand, solve, and defend their solutions to word problems; Blackline masters of game cards and puzzles (also available at http://www.routledge.com/books/details/9781138916296/) |
| conceptual understanding in math: Math Games: Getting to the Core of Conceptual Understanding ebook Ted H. Hull, Ruth Harbin Miles, 2013-04-01 Focus on the teaching and learning of mathematics through the use of games. Based on current research and correlated to College and Career Readiness and other state standards, this resource provides both teachers and students with rich opportunities to engage in the Standards for Mathematical Practice. Each concept-building game supports students' learning and understanding concepts. Games are provided in the following categories: Counting and Cardinality; Operations and Algebraic Thinking; Expressions and Equations; Functions; Numbers and Operations in Base Ten; Numbers and Operations--Fractions; The Number System; Ratio and Proportional Relationships; Measurement and Data; Geometry; and Statistics and Probability. |
| conceptual understanding in math: Mathematical Mindsets Jo Boaler, 2015-10-12 Banish math anxiety and give students of all ages a clear roadmap to success Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students. There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets: Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understanding Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age. |
| conceptual understanding in math: Tools for Teaching Conceptual Understanding, Secondary Julie Stern, Krista Ferraro, Juliet Mohnkern, 2017-02-02 Students become experts and innovators through Concept-Based teaching Innovators don’t invent without a deep understanding of how the world works. With this foundation, they apply conceptual understanding to solve new problems. We want our students to not only retain ideas, but relate them to other things they encounter, using each new situation to add nuance and sophistication to their thinking. To do this, they need conceptual understanding. This book serves as a road map for Concept-Based teaching. Discover how to help students uncover conceptual relationships and transfer them to new situations. Specifically, teachers will learn: Strategies for introducing conceptual learning to students Four lesson frameworks to help students uncover conceptual relationships How to assess conceptual understanding, and How to differentiate concept-based instruction Look no further. For deep learning and innovative thinking, this book is the place to start. The authors tear down the false dichotomies of traditional vs innovative education and provide a practical toolkit for developing creativity and applying knowledge through Concept-Based learning. Every practitioner needs this book to juxtapose what worked well in the 20th Century with what is essential in the 21st Century and beyond. Michael McDowell, Superintendent Ross School District, Ross, CA While most good educators recognise the incredible value of teaching conceptually, it is challenging. The authors have created accessible, practical baby steps for every teacher to use. Dr. Vincent Chan, principal Fairview International School, Kuala Lumpur, Malaysia |
| conceptual understanding in math: Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8 Jennifer M. Bay-Williams, John J. SanGiovanni, 2021-03-02 Because fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: Seven Significant Strategies to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers. |
| conceptual understanding in math: Guided Math: A Framework for Mathematics Instruction Sammons, Laney, 2017-03-01 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. |
| conceptual understanding in math: Principles to Actions National Council of Teachers of Mathematics, 2014-02 This text offers guidance to teachers, mathematics coaches, administrators, parents, and policymakers. This book: provides a research-based description of eight essential mathematics teaching practices ; describes the conditions, structures, and policies that must support the teaching practices ; builds on NCTM's Principles and Standards for School Mathematics and supports implementation of the Common Core State Standards for Mathematics to attain much higher levels of mathematics achievement for all students ; identifies obstacles, unproductive and productive beliefs, and key actions that must be understood, acknowledged, and addressed by all stakeholders ; encourages teachers of mathematics to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning. |
| conceptual understanding in math: Visible Maths Peter Mattock, 2019-02-08 Peter Mattock's Visible Maths: Using representations and structure to enhance mathematics teaching in schools supports teachers in their use of concrete and pictorial representations to illustrate key mathematical ideas and operations. Viewing the maths lesson as an opportunity for pupils to develop a deep understanding of mathematical concepts and relationships, rather than simply to follow fixed processes that lead to 'the answer', is increasingly recognised as the pinnacle of best practice in maths education. In this book, Peter Mattock builds on this approach and explores in colourful detail a variety of visual tools and techniques that can be used in the classroom to deepen pupils' understanding of mathematical operations. Covering vectors, number lines, algebra tiles, ordered-pair graphs and many other representations, Visible Maths equips teachers with the confidence and practical know-how to take their pupils' learning to the next level. The book looks at the strengths, and flaws, of each representation so that both primary and secondary school teachers of maths can make informed judgements about which representations will benefit their pupils. The exploration begins at the very basics of number and operation, and extends all the way through to how the representations apply to algebraic expressions and manipulations. As well as sharing his expert knowledge on the subject, Peter draws on relevant research and his own experience of using the representations in order to support teachers in understanding how these representations can be implemented effectively. Visible Maths also includes a glossary covering the key mathematical terms, as well as a chapter dedicated to answering some of the questions that may arise from the reading of the book. Furthermore, the accompanying diagrams and models are displayed in full colour to illustrate the conceptual takeaways and teaching techniques discussed. Suitable for teachers of maths in primary and secondary school settings. |
| conceptual understanding in math: Daily Math Stretches: Building Conceptual Understanding Levels 6-8 Laney Sammons, 2011-03-18 Jumpstart your students' minds with daily warm-ups that get them thinking mathematically and ready for instruction. Daily Math Stretches offers practice in algebraic thinking, geometry, measurement, and data for grades 6-8 to provide an early foundation for mastering mathematical learning. Written by Guided Math author Laney Sammons and with well-known, research-based approaches, this product provides step-by-step lessons, assessment information, and a snapshot of how to facilitate these math discussions in your classroom. Digital resources are also included for teacher guidance with management tips, classroom set-up tips, and interactive whiteboard files for each stretch. |
| conceptual understanding in math: Understanding and Teaching Primary Mathematics Tony Cotton, 2014-04-29 How would you teach the concept of odd and even numbers to a child? What is the probability of throwing a three on a six-sided die? How could you help a child who is confusing ratio and proportion? By seamlessly combining subject knowledge and pedagogy, the second edition of Understanding and Teaching Primary Mathematics will not only build your own confidence in mathematics, but also equip you with the curriculum understanding and pedagogical know-how to excel at teaching maths to children of any age. Written in a clear and accessible way, the book guides you through the fundamental ideas which are at the heart of teaching and learning maths, with special focus on observation and assessment of primary and early years children. Hallmark features Links to the classroom and research are provided throughout to help you relate educational theory to your own teaching practice. Portfolio and audit tasks allow you to assess your own subject knowledge and build up a portfolio of evidence to gain Qualified Teacher Status. The accompanying extra resources offers topic-specific self-audits for you to monitor your progress, exemplar lesson plans, a range of Portfolio Tasks mapped directly to current teacher standards and web-links to up-to-date online resources. New to this edition Resource Inspiration boxes give inviting examples of different activities to do with your class to provide inspiration for your own teaching. High quality videos with corresponding discussion, have been expertly selected from Teachers TV help to widen your skills and develop your practice, offering tips, lesson ideas and classroom resources. |
| conceptual understanding in math: The Problem with Math Is English Concepcion Molina, 2012-09-06 Teaching K-12 math becomes an easier task when everyone understands the language, symbolism, and representation of math concepts Published in partnership with SEDL, The Problem with Math Is English illustrates how students often understand fundamental mathematical concepts at a superficial level. Written to inspire ?aha? moments, this book enables teachers to help students identify and comprehend the nuances and true meaning of math concepts by exploring them through the lenses of language and symbolism, delving into such essential topics as multiplication, division, fractions, place value, proportional reasoning, graphs, slope, order of operations, and the distributive property. Offers a new way to approach teaching math content in a way that will improve how all students, and especially English language learners, understand math Emphasizes major attributes of conceptual understanding in mathematics, including simple yet deep definitions of key terms, connections among key topics, and insightful interpretation This important new book fills a gap in math education by illustrating how a deeper knowledge of math concepts can be developed in all students through a focus on language and symbolism. |
| conceptual understanding in math: Concept-rich Mathematics Instruction Meir Ben-Hur, 2006 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. |
| conceptual understanding in math: Activating Math Talk Paola Sztajn, Daniel Heck, Kristen Malzahn, 2020-09-24 Achieve High-Quality Mathematics Discourse With Purposeful Talk Techniques Many mathematics teachers agree that engaging students in high quality discourse is important for their conceptual learning, but successfully promoting such discourse in elementary classrooms—with attention to the needs of every learner—can be a challenge. Activating Math Talk tackles this challenge by bringing practical, math-specific, productive discourse techniques that are applicable to any lesson or curriculum. Framed around 11 student-centered discourse techniques, this research-based book connects purposeful instructional techniques to specific lesson goals and includes a focus on supporting emergent multilingual learners. You will be guided through each technique with Classroom examples of tasks and techniques spanning grades K–5 Reflection moments to help you consider how key ideas relate to your own instruction Classroom vignettes that illustrate the techniques in action and provide opportunities to analyze and prepare for your own implementation Group discussion questions for engaging with colleagues in your professional community Achieving high-quality mathematics discourse is within your reach using the clear-cut techniques that activates your math talk efforts to promote every student’s conceptual learning. |
| conceptual understanding in math: The Cambridge Handbook of Cognition and Education John Dunlosky, Katherine A. Rawson, 2019-02-07 This Handbook reviews a wealth of research in cognitive and educational psychology that investigates how to enhance learning and instruction to aid students struggling to learn and to advise teachers on how best to support student learning. The Handbook includes features that inform readers about how to improve instruction and student achievement based on scientific evidence across different domains, including science, mathematics, reading and writing. Each chapter supplies a description of the learning goal, a balanced presentation of the current evidence about the efficacy of various approaches to obtaining that learning goal, and a discussion of important future directions for research in this area. It is the ideal resource for researchers continuing their study of this field or for those only now beginning to explore how to improve student achievement. |
| conceptual understanding in math: Open Middle Math Robert Kaplinsky, 2023-10-10 This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking. |
| conceptual understanding in math: What is a Mathematical Concept? Elizabeth de Freitas, Nathalie Sinclair, Alf Coles, 2017-06-22 Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept? |
| conceptual understanding in math: Building Mathematical Comprehension: Using Literacy Strategies to Make Meaning Sammons, Laney, 2017-03-01 Apply familiar reading comprehension strategies and relevant research to mathematics instruction to aid in building students' comprehension in mathematics. This resource demonstrates how to facilitate student learning to build schema and make connections among concepts. In addition, it provides clear strategies to help students ask good questions, visualize mathematics, and synthesize their understanding. This resource is aligned to College and Career Readiness Standards. |
| conceptual understanding in math: Learning to Teach Mathematics Randall J. Souviney, 1994 |
| conceptual understanding in math: Conceptual Model-Based Problem Solving Yan Ping Xin, 2013-02-11 Are you having trouble in finding Tier II intervention materials for elementary students who are struggling in math? Are you hungry for effective instructional strategies that will address students’ conceptual gap in additive and multiplicative math problem solving? Are you searching for a powerful and generalizable problem solving approach that will help those who are left behind in meeting the Common Core State Standards for Mathematics (CCSSM)? If so, this book is the answer for you. • The conceptual model-based problem solving (COMPS) program emphasizes mathematical modeling and algebraic representation of mathematical relations in equations, which are in line with the new Common Core. • “Through building most fundamental concepts pertinent to additive and multiplicative reasoning and making the connection between concrete and abstract modeling, students were prepared to go above and beyond concrete level of operation and be able to use mathematical models to solve more complex real-world problems. As the connection is made between the concrete model (or students’ existing knowledge scheme) and the symbolic mathematical algorithm, the abstract mathematical models are no longer “alien” to the students.” As Ms. Karen Combs, Director of Elementary Education of Lafayette School Corporation in Indiana, testified: “It really worked with our kids!” • “One hallmark of mathematical understanding is the ability to justify,... why a particular mathematical statement is true or where a mathematical rule comes from” (http://illustrativemathematics.org/standards). Through making connections between mathematical ideas, the COMPS program makes explicit the reasoning behind math, which has the potential to promote a powerful transfer of knowledge by applying the learned conception to solve other problems in new contexts. • Dr. Yan Ping Xin’s book contains essential tools for teachers to help students with learning disabilities or difficulties close the gap in mathematics word problem solving. I have witnessed many struggling students use these strategies to solve word problems and gain confidence as learners of mathematics. This book is a valuable resource for general and special education teachers of mathematics. - Casey Hord, PhD, University of Cincinnati |
| conceptual understanding in math: The Development of Mathematics Throughout the Centuries Brian Evans, 2014-02-24 Throughout the book, readers take a journey throughout time and observe how people around the world have understood these patterns of quantity, structure, and dimension around them. The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Contex provides a brief overview of the history of mathematics in a very straightforward and understandable manner and also addresses major findings that influenced the development of mathematics as a coherent discipline. This book: Highlights the contributions made by various world cultures including African, Egyptian, Babylonian, Chinese, Indian, Islamic, and pre-Columbian American mathematics Features an approach that is not too rigorous and is ideal for a one-semester course of the history of mathematics. Includes a Resources and Recommended Reading section for further exploration and has been extensively classroom-tested |
| conceptual understanding in math: Mastering Math Manipulatives, Grades 4-8 Sara Delano Moore, Kimberly Rimbey, 2021-10-04 Put math manipulatives to work in your classroom and make teaching and learning math both meaningful and productive. Mastering Math Manipulatives includes everything you need to integrate math manipulatives—both concrete and virtual—into math learning. Each chapter of this richly illustrated, easy-to-use guide focuses on a different powerful tool, such as base ten blocks, fraction manipulatives, unit squares and cubes, Cuisenaire Rods, Algebra tiles and two-color counters, geometric strips and solids, geoboards, and others, and includes a set of activities that demonstrate the many ways teachers can leverage manipulatives to model and reinforce math concepts for all learners. It features: · Classroom strategies for introducing math manipulatives, including commercial, virtual, and hand-made manipulatives, into formal math instruction. · Step-by-step instructions for over 70 activities that work with any curriculum, including four-color photos, printable work mats, and demonstration videos. · Handy charts that sort activities by manipulative type, math topic, domains aligned with standards, and grade-level appropriateness. |
| conceptual understanding in math: Knowing and Teaching Elementary Mathematics Liping Ma, 2010-03-26 Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work. |
| conceptual understanding in math: Teaching and Learning Mathematics Online James P. Howard, II, John F. Beyers, 2020-05-10 Online education has become a major component of higher education worldwide. In mathematics and statistics courses, there exists a number of challenges that are unique to the teaching and learning of mathematics and statistics in an online environment. These challenges are deeply connected to already existing difficulties related to math anxiety, conceptual understanding of mathematical ideas, communicating mathematically, and the appropriate use of technology. Teaching and Learning Mathematics Online bridges these issues by presenting meaningful and practical solutions for teaching mathematics and statistics online. It focuses on the problems observed by mathematics instructors currently working in the field who strive to hone their craft and share best practices with our professional community. The book provides a set of standard practices, improving the quality of online teaching and the learning of mathematics. Instructors will benefit from learning new techniques and approaches to delivering content. Features Based on the experiences of working educators in the field Assimilates the latest technology developments for interactive distance education Focuses on mathematical education for developing early mathematics courses |
| conceptual understanding in math: Concept Mapping as an Assessment Tool for Conceptual Understanding in Mathematics Haiyue JIN, 2022-05-05 This book investigates the practicability and effectiveness of the concept map as a tool for assessing students’ conceptual understanding in mathematics. The author first introduces concept mapping and then employs it to investigate students’ conceptual understanding of four different mathematical topics. Alongside traditional scoring methods, she adopts Social Network Analysis, a new technique, to interpret student-constructed concept maps, which reveals fresh insights into the graphic features of the concept map and into how students connect mathematical concepts. By comparing two traditional school tests with the concept map, she examines its concurrent validity and discusses its strengths and drawbacks from the viewpoint of assessing conceptual understanding. With self-designed questionnaires, interviews, and open-ended writing tasks, she also investigates students and teachers’ attitudes toward concept mapping and describes the implications these findings may have for concept mapping’s use in school and for further research on the topic. Scholars and postgraduate students of mathematics education and teachers interested in concept mapping or assessing conceptual understanding in classroom settings will find this book an informative, inspiring, and overall valuable addition to their libraries. |
| conceptual understanding in math: Knowing and Learning Mathematics for Teaching National Research Council, Mathematical Sciences Education Board, Center for Education, Mathematics Teacher Preparation Content Workshop Program Steering Committee, 2001-02-25 There are many questions about the mathematical preparation teachers need. Recent recommendations from a variety of sources state that reforming teacher preparation in postsecondary institutions is central in providing quality mathematics education to all students. The Mathematics Teacher Preparation Content Workshop examined this problem by considering two central questions: What is the mathematical knowledge teachers need to know in order to teach well? How can teachers develop the mathematical knowledge they need to teach well? The Workshop activities focused on using actual acts of teaching such as examining student work, designing tasks, or posing questions, as a medium for teacher learning. The Workshop proceedings, Knowing and Learning Mathematics for Teaching, is a collection of the papers presented, the activities, and plenary sessions that took place. |
| conceptual understanding in math: Pictorial Mathematics Guillermo Mendieta, 2006-02 Pictorial Mathematics is a comprehensive and engaging resource for teaching and learning second through algebra level mathematics. It uses multiple representations and effective visuals to help learners with a wide variety of learning styles to develop a strong conceptual understanding of each concept. Pictorial Mathematics provides the perfect bridge between the abstract and the concrete. Its 400 pages are packed with invaluable tools to help teachers, parents and the learner develop meaning, connections and a deeper conceptual understanding of key mathematical concepts. Inside, you?ll find such resources as:More than 1,000 engaging visual exercises, Powerful and engaging models for the development of conceptual understanding of place value, fractions, ratios, geometry, the four operations and algebra concepts, Energizing tasks -- for small groups, large classrooms, or individuals alike, Master guides to create personalized pictorial problems, Tools to differentiate instruction, A complete set of 38 pictorial templates: from printable manipulatives to graphing paper with suggested activities for these. For previews of the book go to www.pictorialmath.com. |
| conceptual understanding in math: Big Ideas Math Ron Larson, Laurie Boswell, 2019 |
| conceptual understanding in math: Math on the Move Malke Rosenfeld, 2016-10-18 Kids love to move. But how do we harness all that kinetic energy effectively for math learning? In Math on the Move, Malke Rosenfeld shows how pairing math concepts and whole body movement creates opportunities for students to make sense of math in entirely new ways. Malke shares her experience creating dynamic learning environments by: exploring the use of the body as a thinking tool, highlighting mathematical ideas that are usefully explored with a moving body, providing a range of entry points for learning to facilitate a moving math classroom. ...--Publisher description. |
| conceptual understanding in math: International Handbook of Research on Teachers' Beliefs Helenrose Fives, Michele Gregoire Gill, 2014-08-21 Teacher beliefs play a fundamental role in the education landscape. Nevertheless, most educational researchers only allude to teacher beliefs as part of a study on other subjects. This book fills a necessary gap by identifying the importance of research on teacher beliefs and providing a comprehensive overview of the topic. It provides novices and experts alike a single volume with which to understand a complex research landscape. Including a review of the historical foundations of the field, this book identifies current research trends, and summarizes the current knowledge base regarding teachers’ specific beliefs about content, instruction, students, and learning. For its innumerable applications within the field, this handbook is a necessity for anyone interested in educational research. |
| conceptual understanding in math: Concept-Based Curriculum and Instruction for the Thinking Classroom H. Lynn Erickson, 2007 This indispensable guide combines proven curriculum design with teaching methods that encourage students to learn concepts as well as content and skills for deep understanding across all subject areas. |
| conceptual understanding in math: Elementary Mathematics Pedagogical Content Knowledge James E. Schwartz, 2008 Schwartz Powerful Ideas in Elementary Mathematics: Pedagogical Content Knowledge for Teachers, 1/e ISBN: 0205493750 This book would be a great tool for helping [today's future elementary teachers] acquire a 'gut level' understanding of mathematics concepts. - Hester Lewellen, Baldwin-Wallace College, OH The writing in this text is very clear and would easily be understood by the intended audience. The real-world examples put the various math concepts into a context that is easily understood. The vignettes at the beginning of each chapter are interesting and they get the reader to begin thinking about the math concepts that will follow. Each of the chapters seem to build on one another and the author often refers back to activities and concepts from previous chapters which is meaningful to the reader because it lets the reader know that the information they are learning builds their conceptual understanding of other mathematical concepts. - Melany L. Rish, University of South Carolina, Aiken Organized around five key concepts or powerful ideas in mathematics, this text presents elementary mathematics content in a concise and nonthreatening manner for teachers. Designed to sharpen teachers' mathematics pedagogical content knowledge, the friendly writing style and vignettes relate math concepts to real life situations so that they may better present the content to their students. The five powerful ideas (composition, decomposition, relationships, representation, and context) provide an organizing framework and highlight the interconnections between mathematics topics. In addition, the text thoroughly integrates discussion of the five NCTM process strands. Features: Icons highlighting the NCTM process standards appear throughout the book to indicate where the text relates to each of these. Practice exercises and activities and their explanations reinforce math concepts presented in the text and provide an opportunity for reflection and practice. Concise, conversational chapters and opening vignettes present math contents simply enough for even the most math-anxious pre-service teachers. |
| conceptual understanding in math: Daily Math Stretches: Building Conceptual Understanding Levels 3-5 Sammons, Laney, 2017-03-01 Jumpstart your students’ minds with daily warm-ups that get them thinking mathematically and ready for instruction. Daily Math Stretches offers practice in algebraic thinking, geometry, measurement, and data for grades 3-5 to provide an early foundation for mastering mathematical learning. Written by Guided Math author Laney Sammons and with well-known, research-based approaches, this product provides step-by-step lessons, assessment information, and a snapshot of how to facilitate these math discussions in your classroom. Digital resources are also included for teacher guidance with management tips, classroom set-up tips, and interactive whiteboard files for each stretch. |
| conceptual understanding in math: Daily Math Stretches: Building Conceptual Understanding Levels K-2 Sammons, Laney, 2017-03-01 Jumpstart your students’ minds with daily warm-ups that get them thinking mathematically and ready for instruction. Daily Math Stretches offers practice in algebraic thinking, geometry, measurement, and data for grades K-2 to provide an early foundation for mastering mathematical learning. Written by Guided Math’s author Laney Sammons and with well-known, research-based approaches, this product provides step-by-step lessons, assessment information, and a snapshot of how to facilitate these math discussions in your classroom. Digital resources are also included for teacher guidance with management tips, classroom set-up tips, and interactive whiteboard files for each stretch. |
CONCEPTUAL Definition & Meaning - Merriam-Webster
The meaning of CONCEPTUAL is of, relating to, or consisting of concepts. How to use conceptual in a sentence.
CONCEPTUAL | English meaning - Cambridge Dictionary
conceptual The introduction lays out a conceptual framework for the book. notional There is a notional improvement in air quality that cannot be demonstrated. theoretical Vitamin …
CONCEPTUAL Definition & Meaning - Dictionary.com
Conceptual definition: pertaining to concepts or to the forming of concepts.. See examples of CONCEPTUAL used in a sentence.
CONCEPTUAL definition and meaning | Collins English Dictionary
Conceptual means related to ideas and concepts formed in the mind. ...replacing old laws with new within the same conceptual framework. 2 meanings: 1. relating to or concerned with …
conceptual adjective - Definition, pictures, pronunciation and …
Definition of conceptual adjective in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
What does conceptual mean? - Definitions.net
Conceptual refers to something relating to or based on mental concepts and ideas. It pertains to the abstract, theoretical, or intellectual aspects of a topic or field, rather than its practical or …
Conceptual - definition of conceptual by The Free Dictionary
conceptual - being or characterized by concepts or their formation; "conceptual discussions"; "the schizophrenic loses ability to abstract or do conceptual thinking"; "sex is a notional category, …
Conceptual - Definition, Meaning & Synonyms - Vocabulary.com
Something is conceptual when it deals primarily with abstract or original thoughts. A conceptual plan is one in an early stage. To make it work, you'll need to flesh out the details.
Conceptual Definition & Meaning | Britannica Dictionary
The plans have both conceptual and practical difficulties. The software is conceptually similar to an earlier product but is much easier to use.
conceptual - Wiktionary, the free dictionary
Apr 8, 2025 · conceptual (comparative more conceptual, superlative most conceptual) Of, or relating to concepts or mental conception.
CONCEPTUAL Definition & Meaning - Merriam-Webster
The meaning of CONCEPTUAL is of, relating to, or consisting of concepts. How to use conceptual in a sentence.
CONCEPTUAL | English meaning - Cambridge Dictionary
conceptual The introduction lays out a conceptual framework for the book. notional There is a notional improvement in air quality that cannot be demonstrated. theoretical Vitamin …
CONCEPTUAL Definition & Meaning - Dictionary.com
Conceptual definition: pertaining to concepts or to the forming of concepts.. See examples of CONCEPTUAL used in a sentence.
CONCEPTUAL definition and meaning | Collins English Dictionary
Conceptual means related to ideas and concepts formed in the mind. ...replacing old laws with new within the same conceptual framework. 2 meanings: 1. relating to or concerned with concepts; …
conceptual adjective - Definition, pictures, pronunciation and …
Definition of conceptual adjective in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
What does conceptual mean? - Definitions.net
Conceptual refers to something relating to or based on mental concepts and ideas. It pertains to the abstract, theoretical, or intellectual aspects of a topic or field, rather than its practical or tangible …
Conceptual - definition of conceptual by The Free Dictionary
conceptual - being or characterized by concepts or their formation; "conceptual discussions"; "the schizophrenic loses ability to abstract or do conceptual thinking"; "sex is a notional category, …
Conceptual - Definition, Meaning & Synonyms - Vocabulary.com
Something is conceptual when it deals primarily with abstract or original thoughts. A conceptual plan is one in an early stage. To make it work, you'll need to flesh out the details.
Conceptual Definition & Meaning | Britannica Dictionary
The plans have both conceptual and practical difficulties. The software is conceptually similar to an earlier product but is much easier to use.
conceptual - Wiktionary, the free dictionary
Apr 8, 2025 · conceptual (comparative more conceptual, superlative most conceptual) Of, or relating to concepts or mental conception.
