Author: John SanGiovanni
Publisher: Corwin Press
ISBN: 1506379834
Category : Education
Languages : en
Pages : 409
Book Description
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.
Mine the Gap for Mathematical Understanding, Grades 6-8
Author: John SanGiovanni
Publisher: Corwin Press
ISBN: 1506379834
Category : Education
Languages : en
Pages : 409
Book Description
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.
Publisher: Corwin Press
ISBN: 1506379834
Category : Education
Languages : en
Pages : 409
Book Description
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.
Mine the Gap for Mathematical Understanding, Grades K-2
Author: John SanGiovanni
Publisher: Corwin Press
ISBN: 1506382290
Category : Education
Languages : en
Pages : 385
Book Description
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.
Publisher: Corwin Press
ISBN: 1506382290
Category : Education
Languages : en
Pages : 385
Book Description
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.
Mine the Gap for Mathematical Understanding, Grades 3-5
Author: John SanGiovanni
Publisher: Corwin Press
ISBN: 1506375502
Category : Education
Languages : en
Pages : 385
Book Description
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 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. SanGiovanni lays out 180 high-quality tasks aligned to the standards and big ideas of Grades 3-5 mathematics, including addition and subtraction of multi-digit whole numbers, multiplication and division of single and multi-digit whole numbers, foundational fraction concepts, foundational decimal concepts, and operations with fractions and decimals. 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 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.
Publisher: Corwin Press
ISBN: 1506375502
Category : Education
Languages : en
Pages : 385
Book Description
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 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. SanGiovanni lays out 180 high-quality tasks aligned to the standards and big ideas of Grades 3-5 mathematics, including addition and subtraction of multi-digit whole numbers, multiplication and division of single and multi-digit whole numbers, foundational fraction concepts, foundational decimal concepts, and operations with fractions and decimals. 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 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.
Uncovering Student Thinking in Mathematics, Grades K-5
Author: Cheryl Rose Tobey
Publisher: Corwin Press
ISBN: 1452223866
Category : Education
Languages : en
Pages : 233
Book Description
This book provides 25 easily administered assessments of learners' math knowledge that help teachers monitor learning in real time and improve all students' math skills.
Publisher: Corwin Press
ISBN: 1452223866
Category : Education
Languages : en
Pages : 233
Book Description
This book provides 25 easily administered assessments of learners' math knowledge that help teachers monitor learning in real time and improve all students' math skills.
Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8
Author: Jennifer M. Bay-Williams
Publisher: Corwin
ISBN: 1071818430
Category : Education
Languages : en
Pages : 265
Book Description
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.
Publisher: Corwin
ISBN: 1071818430
Category : Education
Languages : en
Pages : 265
Book Description
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.
Qualitative Research and the Modern Library
Author: Valeda Dent Goodman
Publisher: Elsevier
ISBN: 1780632681
Category : Language Arts & Disciplines
Languages : en
Pages : 209
Book Description
Qualitative Research and the Modern Library examines the present-day role and provides suggestions for areas that might be suited to this type of research for the purposes of evaluation. The author discusses how the results from such research might be applied, and the overall impact of using this type of research to inform development of a more user-centred organisation. The book provides a thoughtful look at the implications of using qualitative research to inform decision-making processes within libraries and is written by an author and library researcher with international experience in various types of libraries, implementing/improving programs and services, and supporting user needs. - Fills a gap in the current literature that hasn't been found in journal articles written on this topic - Contains practical applications of qualitative research principles, with practical examples of select projects - Written by an author and library researcher with international experience in various types of libraries, including work with large-scale qualitative studies, research design and evaluation of library services
Publisher: Elsevier
ISBN: 1780632681
Category : Language Arts & Disciplines
Languages : en
Pages : 209
Book Description
Qualitative Research and the Modern Library examines the present-day role and provides suggestions for areas that might be suited to this type of research for the purposes of evaluation. The author discusses how the results from such research might be applied, and the overall impact of using this type of research to inform development of a more user-centred organisation. The book provides a thoughtful look at the implications of using qualitative research to inform decision-making processes within libraries and is written by an author and library researcher with international experience in various types of libraries, implementing/improving programs and services, and supporting user needs. - Fills a gap in the current literature that hasn't been found in journal articles written on this topic - Contains practical applications of qualitative research principles, with practical examples of select projects - Written by an author and library researcher with international experience in various types of libraries, including work with large-scale qualitative studies, research design and evaluation of library services
The Common Core Mathematics Companion: The Standards Decoded, High School
Author: Frederick L. Dillon
Publisher: Corwin Press
ISBN: 1506395635
Category : Education
Languages : en
Pages : 505
Book Description
Your User’s Guide to the Mathematics Standards When it comes to mathematics, standards aligned is achievement aligned... In the short time since The Common Core Mathematics Companions for grades K–2, 3–5 and 6–8 burst on the scene, they have been lauded as the best resources for making critical mathematics ideas easy to teach. With this brand-new volume, high school mathematics success is at your fingertips. Page by page, the authors lay out the pieces of an in-depth explanation, including The mathematical progression of each conceptual category, starting with modeling as a unifying theme, and moving through number & quantity, algebra, functions, geometry, and statistics and probability, building from the 8th grade standards The mathematics embedded in each conceptual category for a deeper understanding of the content How standards connect within and across domains, and to previous grade standards, so teachers can better appreciate how they relate How standards connect with the standards for mathematical practice, with a focus on modeling as a unifying theme Example tasks, progressions of tasks, and descriptions of what teachers and students should be doing to foster deep learning The Common Core Mathematics Companion: The Standards Decoded, High School has what every high school teacher needs to provide students with the foundation for the concepts and skills they will be expected to know .
Publisher: Corwin Press
ISBN: 1506395635
Category : Education
Languages : en
Pages : 505
Book Description
Your User’s Guide to the Mathematics Standards When it comes to mathematics, standards aligned is achievement aligned... In the short time since The Common Core Mathematics Companions for grades K–2, 3–5 and 6–8 burst on the scene, they have been lauded as the best resources for making critical mathematics ideas easy to teach. With this brand-new volume, high school mathematics success is at your fingertips. Page by page, the authors lay out the pieces of an in-depth explanation, including The mathematical progression of each conceptual category, starting with modeling as a unifying theme, and moving through number & quantity, algebra, functions, geometry, and statistics and probability, building from the 8th grade standards The mathematics embedded in each conceptual category for a deeper understanding of the content How standards connect within and across domains, and to previous grade standards, so teachers can better appreciate how they relate How standards connect with the standards for mathematical practice, with a focus on modeling as a unifying theme Example tasks, progressions of tasks, and descriptions of what teachers and students should be doing to foster deep learning The Common Core Mathematics Companion: The Standards Decoded, High School has what every high school teacher needs to provide students with the foundation for the concepts and skills they will be expected to know .
Daily Routines to Jump-Start Problem Solving, Grades K-8
Author: John J. SanGiovanni
Publisher: Corwin Press
ISBN: 1071910671
Category : Education
Languages : en
Pages : 233
Book Description
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!
Publisher: Corwin Press
ISBN: 1071910671
Category : Education
Languages : en
Pages : 233
Book Description
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!
Productive Math Struggle
Author: John J. SanGiovanni
Publisher: Corwin
ISBN: 1544369433
Category : Education
Languages : en
Pages : 217
Book Description
All students face struggle, and they should—it is how they learn and grow. The teacher’s job is not to remove struggle, but rather to value and harness it, helping students develop good habits of productive struggle. But what’s missing for many educators is an action plan for how to achieve this, especially when it comes to math. This book guides teachers through six specific actions—including valuing, fostering, building, planning, supporting, and reflecting on struggle—to create a game plan for overcoming obstacles by sharing · Actionable steps, activities, and tools for implementation · Instructional tasks representative of each grade level · Real-world examples showcasing classroom photos and student work
Publisher: Corwin
ISBN: 1544369433
Category : Education
Languages : en
Pages : 217
Book Description
All students face struggle, and they should—it is how they learn and grow. The teacher’s job is not to remove struggle, but rather to value and harness it, helping students develop good habits of productive struggle. But what’s missing for many educators is an action plan for how to achieve this, especially when it comes to math. This book guides teachers through six specific actions—including valuing, fostering, building, planning, supporting, and reflecting on struggle—to create a game plan for overcoming obstacles by sharing · Actionable steps, activities, and tools for implementation · Instructional tasks representative of each grade level · Real-world examples showcasing classroom photos and student work
Children's Errors in Mathematics
Author: Alice Hansen
Publisher: Learning Matters
ISBN: 1473905532
Category : Education
Languages : en
Pages : 305
Book Description
This practical guide to children’s common errors and misconceptions in mathematics is a popular planning tool for primary trainees. It supports a deeper understanding of the difficulties encountered in mathematical development. This third edition has been updated to link to the new National Curriculum. New for this edition is a chapter on addressing errors misconceptions which explores how errors can best be identified and countered. The text examines misconceptions individually and in each case provides a description of the error alongside an explanation of why the error happens. The text also considers the role of the teacher in understanding and addressing children’s common mathematical misconceptions.
Publisher: Learning Matters
ISBN: 1473905532
Category : Education
Languages : en
Pages : 305
Book Description
This practical guide to children’s common errors and misconceptions in mathematics is a popular planning tool for primary trainees. It supports a deeper understanding of the difficulties encountered in mathematical development. This third edition has been updated to link to the new National Curriculum. New for this edition is a chapter on addressing errors misconceptions which explores how errors can best be identified and countered. The text examines misconceptions individually and in each case provides a description of the error alongside an explanation of why the error happens. The text also considers the role of the teacher in understanding and addressing children’s common mathematical misconceptions.