Teaching Algebra Conceptually

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Concept-Based Mathematics

Author : Jennifer T.H. Wathall
Publisher : Corwin Press
ISBN 13 : 150633265X
Total Pages : 307 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis Concept-Based Mathematics by : Jennifer T.H. Wathall

Download or read book Concept-Based Mathematics written by Jennifer T.H. Wathall and published by Corwin Press. This book was released on 2016-01-14 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Tasks and Competencies in the Teaching and Learning of Algebra

Author : Alex Friedlander
Publisher : National Council of Teachers of English
ISBN 13 : 9780873537599
Total Pages : 260 pages
Book Rating : 4.5/5 (375 download)

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Book Synopsis Tasks and Competencies in the Teaching and Learning of Algebra by : Alex Friedlander

Download or read book Tasks and Competencies in the Teaching and Learning of Algebra written by Alex Friedlander and published by National Council of Teachers of English. This book was released on 2018-02-28 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tasks and Competencies in the Teaching and Learning of Algebra provides a conceptual approach that will encourage students learning algebra to employ a variety of thinking processes and strategies and, most importantly, will enable them to truly understand the concepts that underlie the problems they are solving. The authors' framework develops those skills and competencies, aligned with the goals of the Common Core State Standards, that are necessary for an integrated, conceptual learning of algebra. The book's four chapters include tasks focusing on algebraic expressions, equations, and functions, followed by tasks that integrate several mathematical concepts. Each of the 48 tasks in this book contains: a classroom-ready task, with items arranged by increasing order of complexity a discussion of the task's main ideas and objectives solutions for each item in the task, with suggestions of various methods that students might use; and a listing of the essential competencies that students can develop by working on the task. All 48 tasks are also available at NCTM's More4U website as downloadable and printable worksheets to hand out to students. With its strong conceptual framework, Tasks and Competencies in the Teaching and Learning of Algebra is designed to enable teachers, teacher educators, and curriculum designers to help students at all levels master the ideas and practices found in algebra and to develop skills they can use throughout their mathematics education.

Helping Children Learn Mathematics

Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309131987
Total Pages : 53 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Helping Children Learn Mathematics by : National Research Council

Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Activating Math Talk

Author : Paola Sztajn
Publisher : Corwin Press
ISBN 13 : 1071821571
Total Pages : 225 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis Activating Math Talk by : Paola Sztajn

Download or read book Activating Math Talk written by Paola Sztajn and published by Corwin Press. This book was released on 2020-09-24 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Course in Linear Algebra

Author : David B. Damiano
Publisher : Courier Corporation
ISBN 13 : 0486469085
Total Pages : 466 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis A Course in Linear Algebra by : David B. Damiano

Download or read book A Course in Linear Algebra written by David B. Damiano and published by Courier Corporation. This book was released on 2011-01-01 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Suitable for advanced undergraduates and graduate students, this text introduces basic concepts of linear algebra. Each chapter contains an introduction, definitions, and propositions, in addition to multiple examples, lemmas, theorems, corollaries, andproofs. Each chapter features numerous supplemental exercises, and solutions to selected problems appear at the end. 1988 edition"--

Lessons for Algebraic Thinking

Author : Maryann Wickett
Publisher : Math Solutions
ISBN 13 : 0941355489
Total Pages : 331 pages
Book Rating : 4.9/5 (413 download)

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Book Synopsis Lessons for Algebraic Thinking by : Maryann Wickett

Download or read book Lessons for Algebraic Thinking written by Maryann Wickett and published by Math Solutions. This book was released on 2002 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lessons for K-8 teachers on making algebra an integral part of their mathematics instruction.

Challenges and Strategies in Teaching Linear Algebra

Author : Sepideh Stewart
Publisher : Springer
ISBN 13 : 3319668110
Total Pages : 381 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Challenges and Strategies in Teaching Linear Algebra by : Sepideh Stewart

Download or read book Challenges and Strategies in Teaching Linear Algebra written by Sepideh Stewart and published by Springer. This book was released on 2018-02-01 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book originated from a Discussion Group (Teaching Linear Algebra) that was held at the 13th International Conference on Mathematics Education (ICME-13). The aim was to consider and highlight current efforts regarding research and instruction on teaching and learning linear algebra from around the world, and to spark new collaborations. As the outcome of the two-day discussion at ICME-13, this book focuses on the pedagogy of linear algebra with a particular emphasis on tasks that are productive for learning. The main themes addressed include: theoretical perspectives on the teaching and learning of linear algebra; empirical analyses related to learning particular content in linear algebra; the use of technology and dynamic geometry software; and pedagogical discussions of challenging linear algebra tasks. Drawing on the expertise of mathematics education researchers and research mathematicians with experience in teaching linear algebra, this book gathers work from nine countries: Austria, Germany, Israel, Ireland, Mexico, Slovenia, Turkey, the USA and Zimbabwe.

Linear Algebra

Author : Jim Hefferon
Publisher : Orthogonal Publishing L3c
ISBN 13 : 9780989897563
Total Pages : pages
Book Rating : 4.8/5 (975 download)

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Book Synopsis Linear Algebra by : Jim Hefferon

Download or read book Linear Algebra written by Jim Hefferon and published by Orthogonal Publishing L3c. This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "This text covers a standard first course : Gauss's method, vector spaces, linear maps and matrices, determinants, and eigenvalues and eigenvectors. In addition, each chapter ends with some topics such as brief applications. What sets it apart is careful motivation, many examples, and extensive exercise sets. Together these help each student master the material of this course, and also help an instructor develop that student's level of mathematical maturity. This book has been available online for many years and is widely used, both in classrooms and for self-study. It is supported by worked answers for all exercises, beamer slides for classroom use, and a lab manual of computer work"--Page 4 of cover.

Conceptual Model-Based Problem Solving

Author : Yan Ping Xin
Publisher : Springer Science & Business Media
ISBN 13 : 9462091048
Total Pages : 267 pages
Book Rating : 4.4/5 (62 download)

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Book Synopsis Conceptual Model-Based Problem Solving by : Yan Ping Xin

Download or read book Conceptual Model-Based Problem Solving written by Yan Ping Xin and published by Springer Science & Business Media. This book was released on 2013-02-11 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Rough Draft Math

Author : Amanda Jansen
Publisher : Taylor & Francis
ISBN 13 : 1003839126
Total Pages : 224 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Rough Draft Math by : Amanda Jansen

Download or read book Rough Draft Math written by Amanda Jansen and published by Taylor & Francis. This book was released on 2023-10-10 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Talking and writing about unfinished ideas is vital to learning mathematics, but most students only speak up when they think they have the right answer - especially middle school and high school students. Amanda Jansen and her collaborating teachers have developed a breakthrough approach to address this challenge. In Rough Draft Math: Revising to Learn, Jansen shares the power of infusing math class with the spirit of revision so that students feel comfortable thinking aloud as they problem-solve rather than talking only to perform right answers. Creating a Community of Learners: As part of the rough draft framework, a class of students becomes an equitable and inclusive community of thinkers, one where students feel safe to engage in discourse while developing mathematical competency and confidence Practical Application of Innovative Ideas: This book includes specific teaching techniques and a range of classroom vignettes showing rough draft math in action within a student-centered teaching approach. Children can develop solutions at their own pace and share thought processes behind their conclusions Classroom Tested: Jansen has developed the concept of rough draft math in collaboration with a diverse group of dynamic and reflective teachers. Rough Draft Math provides a blueprint for educators to allow free-thinking discussion while maintaining the mathematical learning goalsRough Draft Math, Jansen shows how to create an energetic classroom culture where students readily participate and share their evolving understanding while engaging in math talk, collaborative problem solving, and ongoing revision of ideas. '

Beyond Formulas in Mathematics and Teaching

Author : Daniel Chazan
Publisher : Teachers College Press
ISBN 13 : 9780807739181
Total Pages : 222 pages
Book Rating : 4.7/5 (391 download)

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Book Synopsis Beyond Formulas in Mathematics and Teaching by : Daniel Chazan

Download or read book Beyond Formulas in Mathematics and Teaching written by Daniel Chazan and published by Teachers College Press. This book was released on 2000-01-01 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the author’s experience as a researcher and teacher of lower-track students, Beyond Formulas in Mathematics and Teaching illuminates the complex dynamics of the algebra classroom. From within this setting, Daniel Chazan thoughtfully explores topics that concern all dedicated educators, how to really know one’s students, how to find engaging material, and how to inspire meaningful classroom conversations. Throughout, he addresses the predicaments that are central to the lives of teachers who work in standard educational settings. By highlighting teaching dilemmas, Chazan prompts readers to consider what their own responses would be in similar situations. With an eye to ways of restructuring roles and relationships, Beyond Formulas in Mathematics and Teaching is essential reading for educators seeking to enhance their teaching practices and understanding of students who may be estranged from school.

Approaches to Algebra

Author : N. Bednarz
Publisher : Springer Science & Business Media
ISBN 13 : 9400917325
Total Pages : 342 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Approaches to Algebra by : N. Bednarz

Download or read book Approaches to Algebra written by N. Bednarz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.

Learning and Instruction

Author : National Research Council
Publisher :
ISBN 13 : 9780309385152
Total Pages : 206 pages
Book Rating : 4.3/5 (851 download)

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Book Synopsis Learning and Instruction by : National Research Council

Download or read book Learning and Instruction written by National Research Council and published by . This book was released on 2003-12-04 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Strategic Education Research Partnership (SERP) is a bold, ambitious plan that proposes a revolutionary program of education research and development. Its purpose is to construct a powerful knowledge base, derived from both research and practice, that will support the efforts of teachers, school administrators, colleges of education, and policy officialsâ "with the ultimate goal of significantly improving student learning. The proposals in this book have the potential to substantially improve the knowledge base that supports teaching and learning by pursuing answers to questions at the core of teaching practices. It calls for the linking of research and development, including instructional programs, assessment tools, teacher education programs, and materials. Best of all, the book provides a solid framework for a program of research and development that will be genuinely useful to classroom teachers.

Mathematical Mindsets

Author : Jo Boaler
Publisher : John Wiley & Sons
ISBN 13 : 1118415531
Total Pages : 320 pages
Book Rating : 4.1/5 (184 download)

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Book Synopsis Mathematical Mindsets by : Jo Boaler

Download or read book Mathematical Mindsets written by Jo Boaler and published by John Wiley & Sons. This book was released on 2015-10-12 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Open Middle Math

Author : Robert Kaplinsky
Publisher : Taylor & Francis
ISBN 13 : 1003839886
Total Pages : 193 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Open Middle Math by : Robert Kaplinsky

Download or read book Open Middle Math written by Robert Kaplinsky and published by Taylor & Francis. This book was released on 2023-10-10 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Math Recess

Author : Sunil Singh
Publisher : Impress, LP
ISBN 13 : 9781948334105
Total Pages : 290 pages
Book Rating : 4.3/5 (341 download)

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Book Synopsis Math Recess by : Sunil Singh

Download or read book Math Recess written by Sunil Singh and published by Impress, LP. This book was released on 2019-03-26 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the theme of recess, this book holds a deep and imaginative collection of fun mathematical ideas, puzzles, and problems. Written for anyone interested in or actively engaged in schools-parents, teachers, administrators, school board members-this book shows math as a playful, fun, and wonderfully human activity that everyone can enjoy.

The Problem with Math Is English

Author : Concepcion Molina
Publisher : John Wiley & Sons
ISBN 13 : 1118237021
Total Pages : 310 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis The Problem with Math Is English by : Concepcion Molina

Download or read book The Problem with Math Is English written by Concepcion Molina and published by John Wiley & Sons. This book was released on 2012-09-06 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.