Mine the Gap for Mathematical Understanding, Grades 6-8
Mine the Gap for Mathematical Understanding, Grades 6-8

Author: John SanGiovanni

Publisher: Corwin Press

Published: 2017-09-12

Total Pages: 409

ISBN-13: 1506379834

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Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni and Jennifer Rose Novak help us value our students’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. The authors lay out 180 high-quality tasks aligned to the standards and big ideas of Grades 6–8 mathematics, including number systems, integers, ratio and proportion, equations and expressions, geometry, and statistics and probability. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality task what you might anticipate before students work with the task four student examples of the completed task showcasing a distinct "gap" commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning, better at discerning the quality and clarity of students’ understanding, and better at planning teaching based on the gaps you see.

Building Thinking Classrooms in Mathematics, Grades K-12
Building Thinking Classrooms in Mathematics, Grades K-12

Author: Peter Liljedahl

Publisher: Corwin Press

Published: 2020-09-28

Total Pages: 454

ISBN-13: 1544374844

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A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling "non-thinking" student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.

Daily Routines to Jump-Start Problem Solving, Grades K-8
Daily Routines to Jump-Start Problem Solving, Grades K-8

Author: John J. SanGiovanni

Publisher: Corwin Press

Published: 2023-04-03

Total Pages: 233

ISBN-13: 1071910671

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Finally! A book that helps solve the problem of teaching problem-solving! Learning to be a problem solver is hard. Teaching students how to be problem solvers themselves can be even harder. Some students may learn to mimic procedures to come up with correct answers, but are they really learning to solve problems? To become independent problem solvers, students need to practice exploring, tinkering, and most importantly thinking!! The bite-size routines in this guide are perfect for teachers looking for the interesting, engaging, and doable practice students need to become problem-solving masters. These flexible, modifiable bursts of quality practice are designed to get students to look at problems in different ways, spark discussion, make connections, and boost mathematics achievement. This collection addresses the common challenges students and teachers face when learning to problem solve by Developing students’ mathematical reasoning and conceptual understanding Building students’ skills with various problem-solving strategies Nurturing mathematical confidence and improving identity and agency Fortified with standards for math practices and processes, the ideas in this guide develop the reasoning and critical-thinking skills for students to become independent problem-solvers for life!

Intensifying Mathematics Interventions for Struggling Students
Intensifying Mathematics Interventions for Struggling Students

Author: Diane Pedrotty Bryant

Publisher: Guilford Publications

Published: 2021-07-05

Total Pages: 226

ISBN-13: 1462546196

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"This book, Intensive Mathematics Interventions, provides a thorough background knowledge about mathematics difficulties across the grade span. Even more valuable to educators-this book provides user friendly guidance on how to address all of the elements of mathematics difficulties from preschool to secondary grades. Each topic provides clear guidance to support decision making about intensive instruction including examples, ideas, practices, and suggestions. You will learn about the characteristics of students with math difficulties, how to use date to progress monitor them, how to intensify interventions, specific evidence-based practices for addressing early numeracy, time and money, whole numbers, rational numbers, word problem solving strategies, algebra and even technology"--

Teaching Elementary Mathematics to Struggling Learners
Teaching Elementary Mathematics to Struggling Learners

Author: Bradley S. Witzel

Publisher: Guilford Publications

Published: 2016-01-24

Total Pages: 193

ISBN-13: 1462523129

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Packed with effective instructional strategies, this book explores why certain K-5 students struggle with math and provides a framework for helping these learners succeed. The authors present empirically validated practices for supporting students with disabilities and others experiencing difficulties in specific areas of math, including problem solving, early numeracy, whole-number operations, fractions, geometry, and algebra. Concrete examples, easy-to-implement lesson-planning ideas, and connections to state standards, in particular the Common Core standards, enhance the book's utility. Also provided is invaluable guidance on planning and delivering multi-tiered instruction and intervention.

Teaching Math to Multilingual Students, Grades K-8
Teaching Math to Multilingual Students, Grades K-8

Author: Kathryn B. Chval

Publisher: Corwin Press

Published: 2021-01-07

Total Pages: 317

ISBN-13: 1071810839

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Using strengths-based approaches to support development in mathematics It’s time to re-imagine what’s possible and celebrate the brilliance multilingual learners bring to today’s classrooms. Innovative teaching strategies can position these learners as leaders in mathematics. Yet, as the number of multilingual learners in North American schools grows, many teachers have not had opportunities to gain the competencies required to teach these learners effectively, especially in disciplines such as mathematics. Multilingual learners—historically called English Language Learners—are expected to interpret the meaning of problems, analyze, make conjectures, evaluate their progress, and discuss and understand their own approaches and the approaches of their peers in mathematics classrooms. Thus, language plays a vital role in mathematics learning, and demonstrating these competencies in a second (or third) language is a challenging endeavor. Based on best practices and the authors’ years of research, this guide offers practical approaches that equip grades K-8 teachers to draw on the strengths of multilingual learners, partner with their families, and position these learners for success. Readers will find: • A focus on multilingual students as leaders • A strength-based approach that draws on students’ life experiences and cultural backgrounds • An emphasis on maintaining high expectations for learners’ capacity for mastering rigorous content • Strategies for representing concepts in different formats • Stop and Think questions throughout and reflection questions at the end of each chapter • Try It! Implementation activities, student work examples, and classroom transcripts With case studies and activities that provide a solid foundation for teachers’ growth and exploration, this groundbreaking book will help teachers and teacher educators engage in meaningful, humanized mathematics instruction.

Mine the Gap for Mathematical Understanding, Grades K-2
Mine the Gap for Mathematical Understanding, Grades K-2

Author: John SanGiovanni

Publisher: Corwin Press

Published: 2016-10-31

Total Pages: 385

ISBN-13: 1506382290

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Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our young learners’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. SanGiovanni lays out 160 high-quality tasks aligned to the standards and big ideas of grades K-2 mathematics, including counting and representing numbers, number relationships and comparison, addition and subtraction within 100 and 1000, money and time, and multiplication and division. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality taskwhat you might anticipate before students work with the task 4 student examples of the completed task showcasing a distinct "gap" commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks. It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see.

Mathematical Problem Solving
Mathematical Problem Solving

Author: ALAN H. SCHOENFELD

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 426

ISBN-13: 1483295486

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This book is addressed to people with research interests in the nature of mathematical thinking at any level, topeople with an interest in "higher-order thinking skills" in any domain, and to all mathematics teachers. The focal point of the book is a framework for the analysis of complex problem-solving behavior. That framework is presented in Part One, which consists of Chapters 1 through 5. It describes four qualitatively different aspects of complex intellectual activity: cognitive resources, the body of facts and procedures at one's disposal; heuristics, "rules of thumb" for making progress in difficult situations; control, having to do with the efficiency with which individuals utilize the knowledge at their disposal; and belief systems, one's perspectives regarding the nature of a discipline and how one goes about working in it. Part Two of the book, consisting of Chapters 6 through 10, presents a series of empirical studies that flesh out the analytical framework. These studies document the ways that competent problem solvers make the most of the knowledge at their disposal. They include observations of students, indicating some typical roadblocks to success. Data taken from students before and after a series of intensive problem-solving courses document the kinds of learning that can result from carefully designed instruction. Finally, observations made in typical high school classrooms serve to indicate some of the sources of students' (often counterproductive) mathematical behavior.

Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8
Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8

Author: Jennifer M. Bay-Williams

Publisher: Corwin

Published: 2021-03-02

Total Pages: 265

ISBN-13: 1071818430

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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.